A Chord Progression that doesn't start... ??
-:j:-
For example like: II - V - I
How does your brain know that the 'home' chord is the 'I' if you have not
introduced it ??
.j.
Joey Goldstein
It's only an implication until you actually arrive at I in an emphatic manner.
> .j.
--
Joey Goldstein
http://www.joeygoldstein.com
joegold AT sympatico DOT ca
Matthew Fields
Joey Goldstein <joegoldATsympaticoDOTca> wrote:
>
>
>-:j:- wrote:
>>
>> What does it mean when a chord progression does NOT start from the 'I' ??
>>
>> For example like: II - V - I
>>
>> How does your brain know that the 'home' chord is the 'I' if you have not
>> introduced it ??
>
>It's only an implication until you actually arrive at I in an emphatic manner.
>
>> .j.
>
And in classical music, it's only an implication until you've arrived
at it through a perfect authentic cadence--which contains three
chords and lands on a downbeat.
This is part of what's exciting about the opening of Beethoven's first--
it sounds like it starts on the dominant, V-I -- but in retrospect that
turns out to have been I-IV, and hadn't had enough chords to be a
perfect authentic cadence after all.
So, as a listener, you may be trying to figure out the structure of
the music as you hear it, and the set of expectations you bring can be
strung along, confirmed, or dashed.
When a piece starts on ii, the very fact that it makes you ask
"what does it mean" suggests that this musical strategy captures your
attention and makes you listen more attentively to what follows, in
the hopes that it will somehow "explain" the confusion you felt at
the opening.
It's great sporting fun.
--
Matthew H. Fields http://personal.www.umich.edu/~fields
Music: Splendor in Sound
To be great, do things better and better. Don't wait for talent: no such thing.
Brights have a naturalistic world-view. http://www.the-brights.net/
Jon Slaughter
"-:j:-" <jyr...@hotmale.com> wrote in message
news:cv2a5j$e7h$1...@phys-news1.kolumbus.fi...
Heh, I've always wondered too...
My guess, is that your brain doesn't know, but when it hears the II-V, it
treats it as a V- I in the dominant key, then it hears the V - I, which is
I - IV in the dominant...
but depending on how the I - IV is presented, if strong enough your ear
might hear it has a V - I... and hence you knew that the II was acting as a
secondary dominant...
i.e., you really have V - I - IV, which is perfectly valid... so your ear
just doens't know by the chord symbols itself.... gotta be something more...
i.e. V - I - IV doesnt' sound complete, while
II - V - I does...
in C,
D - G - C
in G
D - G - C
I suppose you could say that since D is not in C, you start in G, but
depending on the melody and voicing, you could modulate to C(or even change
keys?)... or you could just be in G(would then depend on what comes after C)
What I'm trying to say is, is that you probably can't tell just by the roman
numeral notation... you have to look/hear the music to know and probably
your "ear" will "assume" lots of things.
I suppose you could even say the II - V could be heard as a I - IV?
so you would have I - IV - bVII ...
I would imagine that when the ear hears the bVII(C in key of D), it "knows
something is up"... not sure how it handles this, but like I said, my guess
is that it depends on the actually music/rhythm/harmony(voicing).... and
maybe even texture? also what follows would be very important too...if you
have I - IV - bVII - I (i.e. D G C D), then you have some sort of aug. 6
chord(or something?)?... obivously the C isn't acting as a I.... if you have
I - IV - bVII - bVII, then probably its really II - V - I - I?
Anyways, thats my guess ;/ makes sense to me ;)
Jon
Steve Latham
Joey and Matt both replied that you're not really sure until you get to a I,
or have a cadence.
Additionally, there are some progressions that have stronger implications
(or maybe safer assumptions) than others.
If you hear something like FM to GM. The only place where there are two
major chords right next to each other is if they are IV and V in a Major key
(VI to VII is a possibility in minor). So if FM is IV, and GM is V, then it
means that I must be CM.
Likewise, ii and V (or more especially, iio V in minor) lay in a
relationship that implies the I. This is how you can have pieces that go
ii - V - ii - V for a long time - you know what key they're in (or at least
you can make a pretty good assumption, there's always exceptions in
music) -if you have two minor chords a fourth apart - am and D, that means
the am must be ii, and the D must be V therefore making G I. This is the
only way those two chords (minor and major( will line up with chords in the
key.
Some chords are not so easy to tell - if you get C to F, you can't be sure
if the C is I or the F is I because it could be: C I - F IV, or F I - C IV -
in that case you can only be sure if there's something beyond the chords
(like how they're placed rhythmically) to help you make a guess (and then it
can still be sketchy). A cadence will of course help confirm your
suspicions.
Also, some chords by themselves help to identify a key: G7 must be V in C
because it's the only naturally occurring Mm7 (Dominant 7) chord diatonic to
the key. Obviously, the more information you have (without a cadence or
Tonic chord) the stronger an assumption you can make.
Note that this only works when all of the chords belong to the same key
(although there's some sets than can still imply a key even if some of the
chords are borrowed or are secondary chords etc. because of the pattern, or
frequency of use in that way). It becomes a lot tougher when you have C Maj7
followed by D Maj7!
So, without a confirmation of the key (such as a cadence or other absolute
indicator) the key is only implied - but, there are some progressions,
patterns, and chords that can more strongly point to a tonic than others.
Cheers,
Steve
Andre Schnoor
It's like a movie or novel, where obviously unrelated narrative threads
start separately and meet somewhere in the middle of the story, unfolding
the big picture.
Andre
paramucho
wrote:
Home is the same whether you come out of the front door or go in the
back door.
-:j:-
lot better.
.j.
Albert Silverman
complicated, and those who are indoctrinated with Ancient Theory have *no*
idea how to explain this!
They also cannot explain what is meant by a "home" chord, a "tonic," a
"key," a "tonal center," a "secondary dominant," and on and on and on and
on into the night.
In other words, you have come to the *wrong* place for a RELEVANT answer
to your question. What you will receive here is a lot of Ancient Gibberish
and incredibly incoherent and irrational "explanations."
This is the way that it is in Wonderland!
By the way, I have answered your question many times in the past, but have
found that it is hopeless to attempt it in this Wonderful community.
If I were you, I would stop trying to get your answer *here*.
Albert Silverman
(Al is in Wonderland!)
where relevance is irrelevant
>
>
> .j.
>
>
>
Albert Silverman
> In article <4214B3DA...@nowhere.net>,
> Joey Goldstein <joegoldATsympaticoDOTca> wrote:
>
> So, as a listener, you may be trying to figure out the structure of
> the music as you hear it, and the set of expectations you bring can be
> strung along, confirmed, or dashed.
See what I mean?
>
> When a piece starts on ii, the very fact that it makes you ask
> "what does it mean" suggests that this musical strategy captures your
> attention and makes you listen more attentively to what follows, in
> the hopes that it will somehow "explain" the confusion you felt at
> the opening.
Are you now thoroughly enlightened?
Has the "doctor" cured what ails you?
>
> It's great sporting fun.
Who is the prey and who is the hunter, "doctor"?
Albert Silverman
(Al is in Wonderland!)
where relevance is irrelevant
and confusion rains.....
>
Joey Goldstein
Albert Silverman wrote:
>
> On 2005-02-17, -:j:- <jyr...@hotmale.com> wrote:
> In other words, you have come to the *wrong* place for a RELEVANT answer
> to your question.
Albert, if you are the only person in the Universe who can answer his
question then this is the *right* place for him to have come, because
this is the *only* place in the Universe where *anyone* pays any
attention at all to your "ideas" about music.
Does the fact that you can't see this make you an idiot?
paramucho
<slv...@panix.com> wrote:
>On 2005-02-17, -:j:- <jyr...@hotmale.com> wrote:
>> What does it mean when a chord progression does NOT start from the 'I' ??
>>
>> For example like: II - V - I
>>
>> How does your brain know that the 'home' chord is the 'I' if you have not
>> introduced it ??
>>
>I could answer this question for you, but the answer is long and
>complicated, and those who are indoctrinated with Ancient Theory have *no*
>idea how to explain this!
We're still waiting for you to get beyond an introduction to your
theory. Given that, it seems that you're saying that there is no way
the poster can find an answer to his question anywhere.
-:j:-
"Albert Silverman" wrote:
> -:j:- wrote:
> > What does it mean when a chord progression does NOT start from the 'I'
??
> >
> > For example like: II - V - I
> >
> > How does your brain know that the 'home' chord is the 'I' if you have
not
> > introduced it ??
> >
> I could answer this question for you, but the answer is long and
> complicated, and those who are indoctrinated with Ancient Theory have *no*
> idea how to explain this!
I'd like to hear an answer from your perspective. It's good to look things
from meny different angels... you get more clearer picture...
> If I were you, I would stop trying to get your answer *here*.
Well can you then recommend some better place for this kind of questions?
.j.
Matthew Fields
In twelve years, you still haven't shown us your music like you promised, Al.
Matthew Fields
In twelve years, you still haven't shown us your music like you promised, Al.
Steve Latham
"-:j:-" <jyr...@hotmale.com> wrote in message
news:cv792j$6f7$1...@phys-news1.kolumbus.fi...
>
> I'd like to hear an answer from your perspective.
No, you really don't.
It's good to look things
> from meny different angels...
Yes, those that were outcast.
you get more clearer picture...
>
Oh, it will give you a clear picture.
>
>> If I were you, I would stop trying to get your answer *here*.
>
>
> Well can you then recommend some better place for this kind of questions?
-:j:-, you'll see.
-:j:-
"Steve Latham" wrote:
>
> "-:j:-" wrote:
>
> >
>
> No, you really don't.
Why not? It might be interesting.
.j.
Joey Goldstein
You'll understand soon enough.
In the meantime try a GoogleGroups search on Albert Silverman.
Albert Silverman
>
> "Albert Silverman" wrote:
>> -:j:- wrote:
>> > What does it mean when a chord progression does NOT start from the 'I'
> ??
>> >
>> > For example like: II - V - I
>> >
>> > How does your brain know that the 'home' chord is the 'I' if you have
> not
>> > introduced it ??
>> >
>> I could answer this question for you, but the answer is long and
>> complicated, and those who are indoctrinated with Ancient Theory have *no*
>> idea how to explain this!
>
>
> I'd like to hear an answer from your perspective. It's good to look things
> from meny different angels... you get more clearer picture...
I am indeed a different angel!
However, those here who have been indoctrinated with Ancient Theory
consider me to be The Devil--not an angel.
But to make a long story short, the answer to this dilemma lies in the
*phrasing*, as I have repeatedly emphasized. Furthermore, one *must* start
with the basic concept of departure-and-return, which is evident in very
simple pieces, and then work up to more complicated situations in which
the departure and return or not evident, if it even exists at all.
Additionally, in all but the simplest of pieces, there will be a change in
the "tonal center," which is what you refer to in your post as the "home"
chord, and which is mistakenly referred to in Ancient Theory as the
"tonic," thus hopelessy confusing the idea of a tonal center, which is
free from an association with any particular scale, and the "tonic" degree
of a diatonic scale. These two things are *separate and independent from
each another*, and it is nothing less than a disgrace to hopelessly mix
them up together, as is done in Ancient Theory.
And of course, it makes no sense at all to identify various chords in
terms of diatonic scale degrees, such as I, II, V, etc. So you see, some
very well entrenched absurdities must be tossed into the garbage can, as a
basic prerequisite for untangling the mess that you have centered upon in
your post.
In other words, those who are "in bed" with Ancient Theory will NEVER be
able to sort out these things in a manner which you can
understand--because they do not understand these things themselves.
But this of course will not keep them from answering your question. Just
don't believe these irrelevant "answers"!
> > >>
If I were you, I would stop trying to get your answer *here*. >
>
> Well can you then recommend some better place for this kind of questions?
I wish that I could but I cannot. I believe that, to get a straight and
sensible answer to your question, you would have to be studying
composition (seriously) in an appropriate academic environment. So-called
"music theory" for The Masses is worse than useless, since it is simply
for the purpose of preserving Ancient Musical History, which has very
little to do with explaining musical principles.
Garth Wallace
In the sense that timecube.com is interesting.
Marco R
>>
>> Well can you then recommend some better place for this kind of questions?
>
>I wish that I could but I cannot. I believe that, to get a straight and
>sensible answer to your question, you would have to be studying
>composition (seriously) in an appropriate academic environment. So-called
>"music theory" for The Masses is worse than useless, since it is simply
>for the purpose of preserving Ancient Musical History, which has very
>little to do with explaining musical principles.
>
>
>Albert Silverman
>(Al is in Wonderland!)
>where relevance is irrelevant
??????????????????????????????????????????????????????????????????????????????????????????????
Oh, great Socrates of music theory, let us all proclaim our ignorance
so that we may begin to tread upon the true path of musical
enlightenment that your usenet ramblings have only begun to
illuminate.
- Marco
don groves
at m...@rco.rosano hath writ:
I tried this already -- it doesn't work. Sarcasm and/or irony
are lost on Albert, he will just keep posting the same stuff he
always has. It is said that a fool who persists in his folly
will become wise -- Al may be the counterexample.
--
dg (domain=ccwebster)
Tom Korth
"Albert Silverman" <slv...@panix.com> wrote in message
news:slrnd1g0ge...@panix1.panix.com...
>
> I wish that I could but I cannot. I believe that, to get a straight and
> sensible answer to your question, you would have to be studying
> composition (seriously) in an appropriate academic environment.
Where you will also be required to study 4 years of "ancient" theory, ear
training, music history, counterpoint, etc. as the core of your Mus. B. in
Composition!
Tom
Albert Silverman
There is of course nothing "wrong" with studying Ancient Theory, ear
training, music history, counterpoint, etc. I have never said that there
*is* anything wrong with this.
What *is* very wrong, however, is failing to disclose Ancient Theory for
exactly what it is--Ancient Musical History. Let me repeat: Ancient Theory
does *not* provide any reasonably accurate explanation of musical
principles. As an example, it *cannot* provide an answer to the question
which started this thread here in Wonderland. The reason? Because it has
no answer that is based upon musical principles.
As I have stated, these *real* answers are buried deep within a study of
musical composition, well hidden from The Masses who have no "need to
know". Rather, what they do need to know is how to pass an exam, so that
they can proudly trumpet that, having passed the prerequisite exams, they
now understand music theory.
ROTFL
Albert Silverman
(Al is in Wonderland!)
where relevance is irrelevant
>
> Tom
>
>
don groves
Silverman at slv...@panix.com hath writ:
There is a grain of truth in what you say about education here
Al, but then you go and ruin it by saying things that are
patently false. Ancient Theory, as you call it, is *precisely*
"an accurate explanation of musical principles", as practiced by
Bach, Mozart, Beethoven, and countless others, whom most of us
consider to be great composers.
Ancient Theory is *exactly* the compilation of "real answers
buried deep within a study of musical composition". That's what
it is! Your theory, as far as I can understand it from the
fragments you've posted here from time to time, contradicts a lot
of what was actually done, not in theory, but in practice, by the
great composers of the last 300 years.
So, who are we to emulate, them or you?
--
dg (domain=ccwebster)
Matthew Fields
Al, you've never shown any knowledge of any of the topics or curricula
that you criticize. Where's your music, Al?
Albert Silverman
No it is not. It is an explanation of musical *style*. Period. Your
problem (and the problem of those who do not understand Ancient Theory) is
that you *do not know the difference between principle and style*. And
that is the trouble with music education--in a nutshell.
>
> Ancient Theory is *exactly* the compilation of "real answers
> buried deep within a study of musical composition". That's what
> it is!
NO. That is *not* what it is.
> Your theory, as far as I can understand it from the
> fragments you've posted here from time to time, contradicts a lot
> of what was actually done, not in theory, but in practice, by the
> great composers of the last 300 years.
Again, you are confusing principle with style.
Furthermore, Ancient Theory does *not* correlate with musical practice, in
many, many, many ways. It is an utter and total disaster.
>
> So, who are we to emulate, them or you?
You are to "emulate" *no one*. What you *should* be doing is attempting to
understand the musical principles involved. These principles can then be
used in a study of musical styles.
This process has *nothing to do at all* with "emulating" anybody.
don groves
OK, at last we are getting somewhere, maybe. Please give me an
example of what you mean by "style" vs. what you mean by
"principle". Then I might be able to see where my "confusion"
lies. It won't do any good to just repeat what has already been
said in general terms, I need a concrete example.
--
dg (domain=ccwebster)
Albert Silverman
Just one grain?
>>
>> No it is not. It is an explanation of musical *style*. Period. Your
>> problem (and the problem of those who do not understand Ancient Theory) is
>> that you *do not know the difference between principle and style*. And
>> that is the trouble with music education--in a nutshell.
>>
>> >
>> > Ancient Theory is *exactly* the compilation of "real answers
>> > buried deep within a study of musical composition". That's what
>> > it is!
>>
>> NO. That is *not* what it is.
>>
>> > Your theory, as far as I can understand it from the
>> > fragments you've posted here from time to time, contradicts a lot
>> > of what was actually done, not in theory, but in practice, by the
>> > great composers of the last 300 years.
>>
>> Again, you are confusing principle with style.
>>
>> Furthermore, Ancient Theory does *not* correlate with musical practice, in
>> many, many, many ways. It is an utter and total disaster.
>
> OK, at last we are getting somewhere, maybe. Please give me an
> example of what you mean by "style" vs. what you mean by
> "principle". Then I might be able to see where my "confusion"
> lies. It won't do any good to just repeat what has already been
> said in general terms, I need a concrete example.
Well, if you insist, but do not expect to find anything basically
different from what I have been saying all along. Here is a statement of
musical principle:
In triad-based music, there are nine chord forms (containing either three
or four tones) which may exist at twelve different structural locations
(functional roots).
Here is a statement about compositional style, as it relates to the above
principle:
The *choice* of which chord form to use at which structural location is a
stylistic matter. In any composition, not every chord form is used at
every location. What is referred to as "key" is, in fact, a
stylistic "template" that is used to select which chords are used at which
locations. A "mode" is another template, used to select a different group
of chords at particular structural locations.
For example, a "major key" template selects a major triad (three tones) or
a major tetrad (four tones, commonly referred to as a "dominant 7th") at
location {2}, which is referred to in Ancient Theory as V.
As another example, a "minor key" template selects a minor triad (three
tones) at location (12), which is referred to in Ancient Theory as IV. It
also selects a major triad at location (2).
Chords which lie "outside" the particular key are readily identified in
terms of their structural locations. For example, an Ancient Neapolitan
Sixth is a major triad at location {8}, etc.
Really very simple in concept (principle).
I have been through this same exercise a great many times, but Ancient
Indoctrinees will *never* be able to understand the significance of
principle versus style. NEVER.
Albert Silverman
(Al is in Wonderland!)
where relevance is irrelevant
and residents have no principles
don groves
I'm trying here, Al, inspite of your negativity. Humor me.
First -- how does your "functional root" differ from "tonic" as
used by we ATs (Ancient Theorists)?
It would help if I had a map of your "locations". You say above
that what I would call a V chord corresponds to location 2 and
what I would call a IV chord corresponds to location 12. Does
this mean there is a simple one-to-one correspondence between
locations and the 12 chromatic notes of a scale? Is it a
constant relationship or does it depend on which note is the
"functional root"? Will you please post this map so I can better
visualize your terms?
--
dg (domain=ccwebster)
don groves
groves at dgr...@domain.net hath writ:
>
> It would help if I had a map of your "locations". You say above
> that what I would call a V chord corresponds to location 2 and
> what I would call a IV chord corresponds to location 12. Does
> this mean there is a simple one-to-one correspondence between
> locations and the 12 chromatic notes of a scale? Is it a
> constant relationship or does it depend on which note is the
> "functional root"? Will you please post this map so I can better
> visualize your terms?
Sorry, I mistyped there -- that should be "12 chromatic tones of
an octave", not scale.
--
dg (domain=ccwebster)
Bob Pease
Plonk!
RJ Pease
Albert Silverman
>
> I'm trying here, Al, inspite of your negativity. Humor me.
>
> First -- how does your "functional root" differ from "tonic" as
> used by we ATs (Ancient Theorists)?
The Ancient "tonic" is functional root {01}. This is the stable resting
point for the harmony.
>
> It would help if I had a map of your "locations".
I posted this map several times quite a while ago here--long before you
stumbled across this Wonderful newsgroup.
I will dig it up. At the moment, I do not remember the exact title of the
posts which contained it. I *do* remember, however, that I got **NO**
response to, even though this map clearly indicates the one-to-one
correspondence between the Ancient Roman Numerals (which refer to
diatonic scale degrees) and the numbers which I use to indicate
functional roots. I enclose these numbers in curly brackets, even though
I forgot to do this in my recent hurried response to your post.
> You say above
> that what I would call a V chord corresponds to location 2 and
> what I would call a IV chord corresponds to location 12. Does
> this mean there is a simple one-to-one correspondence between
> locations and the 12 chromatic notes of a scale?
As you have corrected: the 12 tones of the equally-tempered scale.
> Is it a
> constant relationship or does it depend on which note is the
> "functional root"?
I don't understand what you mean by this.
> Will you please post this map so I can better
> visualize your terms?
As soon as I can dig it up from my voluminous archive of my past postings,
going back a long time.
Matthew Fields
Try something new. Demonstrate your principles with music--your own music.
don groves
>
> >
> > I'm trying here, Al, inspite of your negativity. Humor me.
> >
> > First -- how does your "functional root" differ from "tonic" as
> > used by we ATs (Ancient Theorists)?
>
> The Ancient "tonic" is functional root {01}. This is the stable resting
> point for the harmony.
> >
> > It would help if I had a map of your "locations".
>
> I posted this map several times quite a while ago here--long before you
> stumbled across this Wonderful newsgroup.
>
> I will dig it up. At the moment, I do not remember the exact title of the
> posts which contained it. I *do* remember, however, that I got **NO**
> response to, even though this map clearly indicates the one-to-one
> correspondence between the Ancient Roman Numerals (which refer to
> diatonic scale degrees) and the numbers which I use to indicate
> functional roots. I enclose these numbers in curly brackets, even though
> I forgot to do this in my recent hurried response to your post.
I promise to read it and comment. I won't dismiss it out-of-hand
and will try my best to understand it. Can't ask for much more
than that.
--
dg (domain=ccwebster)
drahcir
<slv...@panix.com> wrote:
>
>However, those here who have been indoctrinated with Ancient Theory
>consider me to be The Devil--not an angel.
That's a good one! The only one who fancies you a devil is YOU. You
think you keep people up at night with your drivel. In fact, you are a
nothing -- a pathetic nothing who has no connection to music outside
of this newsgroup If there were one iota of worth in your "theory"
you would be able to respond to the following, posted here numerous
times and ignored by you. Why? Because it shows you to be the nothing
that you are.
You claim to have devised a set of principles which describes common
practice music better than traditional theory, yet you refuse to do
the one thing that would demonstrate your theory to be superior: post
an analysis of a seriouis piece of music using your theory and
traditional theory, and show why yours is better. When prodded to do
so in the past, the best you could come up with was a hopelessly
convoluted analysis of "Beautiful Dreamer" using ONLY your "theory",
clearly demonstrating that you have no knowledge of the "ancient"
theory you so confidently condemn. This should make it clear to any
reader that you in fact have no clue what music is about and are
simply a lonely, old man starving for attention.
Albert Silverman
Here is the simple one-to-one mapping between the twelve functional roots
and those Ancient Roman Numerals that are used routinely in a
"traditional" analysis but whose theoretical significance is almost
universally not understood. Performance by rote......
========================================================================
(1) {1} {2} {3} {4} {5} {6} {7} {8} {9} (10} {11} {12}
(2) I V II VI III VII IV# I# V# II# VI# IV
(2a) or Vb IIb VIb IIIb VIIb
(3) C G D A E B F# C# G# D# A# F
(3a) or Gb Db Ab Eb Bb
------------------------
Line (1) : functional root
Line (2) : Ancient Roman Numeral designation (scale degree)
Line (3) : Corresponding root-tones if root-tone at {1} is C
Lines (2a) and (3a) show enharmonic equivalent notations for so-called
"chromatic" roots.
FUNCTIONAL ROOT and ROMAN NUMERAL EQUIVALENTS
========================================================================
Feel free to ask questions. Perhaps you will be the very first one to do
so, after my posting this chart so many times in the past, along with a
very detailed explanation of its meaning. And I do mean *detailed*,
although I have not included this here. I long ago discarded that idea as
futile.
Of course, this chart is only a very small portion of the entire
(chord-based) theory (*not* style!)
Albert Silverman
> On Sun, 20 Feb 2005 03:20:46 +0000 (UTC), Albert Silverman
><slv...@panix.com> wrote:
>
>>
>>However, those here who have been indoctrinated with Ancient Theory
>>consider me to be The Devil--not an angel.
>
> That's a good one! The only one who fancies you a devil is YOU. You
> think you keep people up at night with your drivel.
Why of course they don't. But I wonder why our resident kook "doctor"
feels compelled to answer every one of my posts. He of course does not
read them and is not interested in them. Of course.
> In fact, you are a
> nothing -- a pathetic nothing who has no connection to music outside
> of this newsgroup. If there were one iota of worth in your "theory"
> you would be able to respond to the following, posted here numerous
> times and ignored by you. Why? Because it shows you to be the nothing
> that you are.
But *you* do seem to be enchanted with nothing, don't you?
>
> You claim to have devised a set of principles which describes common
> practice music better than traditional theory, yet you refuse to do
> the one thing that would demonstrate your theory to be superior: post
> an analysis of a seriouis piece of music using your theory and
> traditional theory, and show why yours is better. When prodded to do
> so in the past, the best you could come up with was a hopelessly
> convoluted analysis of "Beautiful Dreamer" using ONLY your "theory",
> clearly demonstrating that you have no knowledge of the "ancient"
> theory you so confidently condemn.
Then that makes two of us, doesn't it?
But only *one* who is willing to sign his name to his posts.
Now then, which one is the phantom?
Albert Silverman
(Al is in Wonderland!)
where relevance is irrelevant
and phantoms don't have the guts to identify themselves
This should make it clear to any
> reader that you in fact have no clue what music is about and are
> simply a lonely, old man starving for attention.
Gee whiz, I sure got it here, didn't I?
Thank you.
don groves
Ok, thanks. What I see here is the traditional circle-of-fifths
laid out linearly and you have renamed the Roman numerals used in
Ancient Theory(tm) analysis according to their positions in the
circle-of-fifths. Right so far?
Two Questions:
How is this info used in analysis (or composition) differently
from AT?
How does the rest of your theory depend on what you've shown me
so far?
--
dg (domain=ccwebster)
Matthew Fields
Albert Silverman <slv...@panix.com> wrote:
>On 2005-02-23, drahcir <as...@asdf.com> wrote:
>> On Sun, 20 Feb 2005 03:20:46 +0000 (UTC), Albert Silverman
>><slv...@panix.com> wrote:
>>
>>>
>>>However, those here who have been indoctrinated with Ancient Theory
>>>consider me to be The Devil--not an angel.
>>
>> That's a good one! The only one who fancies you a devil is YOU. You
>> think you keep people up at night with your drivel.
>
>Why of course they don't. But I wonder why our resident kook "doctor"
>feels compelled to answer every one of my posts. He of course does not
>read them and is not interested in them. Of course.
I'm a thorn in your side, Albert, because you don't make music.
You sure did.
>Thank you.
You're welcome, poser.
Richard Ratner
<slv...@panix.com> wrote:
>On 2005-02-23, drahcir <as...@asdf.com> wrote:
>> On Sun, 20 Feb 2005 03:20:46 +0000 (UTC), Albert Silverman
>><slv...@panix.com> wrote:
>>
>>>
>>>However, those here who have been indoctrinated with Ancient Theory
>>>consider me to be The Devil--not an angel.
>>
>> That's a good one! The only one who fancies you a devil is YOU. You
>> think you keep people up at night with your drivel.
>
>Why of course they don't. But I wonder why our resident kook "doctor"
>feels compelled to answer every one of my posts. He of course does not
>read them and is not interested in them. Of course.
I think you have an unhealthy obsession with Matt. Do you see his name
anywhere in the post to which you are supposedly replying? The reason
for this obsession -- in your poor "brain" you have constructed a
scenario where Ancient Theory, for some reason represented by Matt,
conflicts with Modern Theory, represented by <giggle> you. This is the
extent of your musical life, you buffoon.
>
>> In fact, you are a
>> nothing -- a pathetic nothing who has no connection to music outside
>> of this newsgroup. If there were one iota of worth in your "theory"
>> you would be able to respond to the following, posted here numerous
>> times and ignored by you. Why? Because it shows you to be the nothing
>> that you are.
>
>But *you* do seem to be enchanted with nothing, don't you?
Enchanted? Not at all. Just enjoying throwing a bit of reality your
way.
>>
>> You claim to have devised a set of principles which describes common
>> practice music better than traditional theory, yet you refuse to do
>> the one thing that would demonstrate your theory to be superior: post
>> an analysis of a seriouis piece of music using your theory and
>> traditional theory, and show why yours is better. When prodded to do
>> so in the past, the best you could come up with was a hopelessly
>> convoluted analysis of "Beautiful Dreamer" using ONLY your "theory",
>> clearly demonstrating that you have no knowledge of the "ancient"
>> theory you so confidently condemn.
>
>Then that makes two of us, doesn't it?
A non-reply posing as a reply. This has nothing to do with me. This is
a question posed to YOU. I am not the one claiming not only to
comprehend traditional theory, but to have devised a system that
explains music better. Just post the analyses, oaf, or keep quiet.
>
>But only *one* who is willing to sign his name to his posts.
The use of my first name reversed seems to have drawn a reply, doesn't
it? Usually you simply ignore me in the hope that I will give up.
>
>Now then, which one is the phantom?
>
You are not a phantom, you are a nothing. No, check that, you are a
pathetic joke.
>Albert Silverman
>(Al is in Wonderland!)
>where relevance is irrelevant
>and phantoms don't have the guts to identify themselves
>
> This should make it clear to any
>> reader that you in fact have no clue what music is about and are
>> simply a lonely, old man starving for attention.
>
>Gee whiz, I sure got it here, didn't I?
>
>Thank you.
Anytime!
Albert Silverman
Yes. I have pointed this out many times in past posts.
>
> Two Questions:
> How is this info used in analysis (or composition) differently
> from AT?
The Circle of Fifths is not employed as an *integral* part of Ancient
Theory. Rather, it is used as a "convenient" adjunct, to be used
peripherally in explanation when the formal "theory" breaks down or fails
to correlate with practice or is incoherent or irrational or ludicrous
or.........
One *HUGE* difference, to which I have referred many times in my posts but
cannot be understood by Ancient Indoctrinees (it is a fundamental break
with Ancient Concepts) is the *break in the "circle"* between {01} and
{12) (Ancient I and IV). That is, in my theory, the linear representation
is *FUNDAMENTAL*; root {12} is the outer limit of the structural universe,
as it were. This has very important implications, and all of the many
details which follow in my theoretical formulation depend upon this
*non-circular* representation of the twelve functional roots.
>
How does the rest of your theory depend on what you've shown me > so far?
That is a very long story, which I have broached in my recent articles
here entitled "The Harmonic Structure." I assume that you have them. If
so, have you tried to read them?
Additionally, it is very important that *chord construction* be
understood. This has been touched upon very briefly in my article on chord
construction, posted in the not too distant past. A much more detailed
description has been provided quite some time ago--more than once. But
again, since it conflicts with the Ancient "tertiary" chord construction
process (and for very good reason), this Wonderful community has totally
failed to appreciate the significance or utility of it. As expected.
Yet another aspect, very fundamental and of course *not understood* by
Ancient Indoctrinees, is the underlying *dynamic* process by which
functional root {01} is determined *from the musical context*. It cannot
(repeat: cannot) be determined from the tones in any of the chords, as it
is, by definition, in Ancient Theory.
And then, as a whole separate portion of this theory, is the complex
subject of tone "tendencies," where they come from, how they relate to
chord "tensions," and most important, how they contribute to VOICE-LEADING
during chord progression. In order to understand this extremely important
concept, one *must* learn how different chord tones have *implied*
tendencies or the lack of them, by virtue of their construction. It is
these implied tendencies which are basic in voice-leading. Under certain
conditions of *phrasing*, these implied tendencies become
aurally-perceptible, such as with the common progression from a so-called
"dominant 7th" to a tonic triad (in Ancient-Speak).
Etc., etc., etc. It is a long and complex story, which has little
resemblance to Ancient Nonsense.
USM
> In article <4214B3DA...@nowhere.net>,
> Joey Goldstein <joegoldATsympaticoDOTca> wrote:
>>
>>
>> -:j:- wrote:
>>>
>>> What does it mean when a chord progression does NOT start from the
>>> 'I' ??
>>>
>>> For example like: II - V - I
>>>
>>> How does your brain know that the 'home' chord is the 'I' if you
>>> have not introduced it ??
>>
>> emphatic manner.
>>
>>> .j.
>>
>
> And in classical music, it's only an implication until you've arrived
> at it through a perfect authentic cadence--which contains three
> chords and lands on a downbeat.
>
> This is part of what's exciting about the opening of Beethoven's
> first-- it sounds like it starts on the dominant, V-I -- but in
> retrospect that turns out to have been I-IV, and hadn't had enough
> chords to be a perfect authentic cadence after all.
>
> So, as a listener, you may be trying to figure out the structure of
> the music as you hear it, and the set of expectations you bring can be
> strung along, confirmed, or dashed.
>
> When a piece starts on ii, the very fact that it makes you ask
> "what does it mean" suggests that this musical strategy captures your
> attention and makes you listen more attentively to what follows, in
> the hopes that it will somehow "explain" the confusion you felt at
> the opening.
>
> It's great sporting fun.
It`s a common explanation, but is unsatisfactory because it causes another
paradox:
Inference, suspension, resolution and denial can only offer a partial,
first-instance answer as to why we track music`s centres. In practice,
these concepts get fuzzier as a peice becomes more familiar - and the
reverse affect can be observed, that is, a tune can continue to grow on you
even when you know it by heart. How would we appreciate, in the way you
desribe, repetition of familiar music - when *all* our expectations are met?
An answer must describe music`s emotive potential in terms of both cognition
and recognition. One possibility is to change the word "expectation" to
"anticipation", though this still leaves the term "suspension" somewhere in
the limbo of cognitive semantics. I hate the word, but a more "holistic"
veiw is required. And that means bottom-up, rather than top-down.
If we accept that for any stimulus there is an associated neuronal response,
then we`re really discussing inference, suspension, resolution and denial of
a directly coresponding biological equillibrium. It`s a combination of
cellular geometry, complexity & thermodynamics. So to answer -:j:- the
brain "knows" the home chord because it is the most neurodynamically
efficient resolution of the stimulus activity. This is why foreknowledge of
a peice of music doesn`t make it overfamiliar immediately after learning.
Recurret expectation isn`t paradoxical if we discard the notion that
"attention" to music is necessarilly wilfull - they`re just subsiduary to
the fact that we follow music`s tonal and rhythmic centres in exactly the
same way a train follows the tracks, whether we like it or not. This is why
we can`t just "switch off" to shite music or that of noisy neighbors, and
indeed why Plato felt music should be legally regulated.
Here`s a cool analogy i once read: Imagine a machine that is "concious" -
it`s energy comes from a dynamo attached to wheels on a trolley, and the
whole thing is set on tracks, and travelling downhill under gravity`s pull.
Such a being would have the same kind of difficulty understanding time,
motion, it`s existence and sentience that we have in understanding the flow
of music. But it`s really just a matter of getting the bigger picture. All
nervous activity is a thermodynamic phase-transition. We are but
temporarily balancing on the edge of chaos. Conciousness is illusory, and
the way music hooks into our nervous responses and manipulates our physical
being is proof that we are determined entirely by forces beyond our sphere
of influence.
As Joey says, that sucks...... but at least it makes sense.
USM
>
> Additionally, in all but the simplest of pieces, there will be a
> change in the "tonal center," which is what you refer to in your post
> as the "home" chord, and which is mistakenly referred to in Ancient
> Theory as the "tonic," thus hopelessy confusing the idea of a tonal
> center, which is free from an association with any particular scale,
> and the "tonic" degree of a diatonic scale. These two things are
> *separate and independent from each another*, and it is nothing less
> than a disgrace to hopelessly mix them up together, as is done in
> Ancient Theory.
On this "change in tonal centre" - do you mean tonal modualtion? This
doesn`t seem particulary common in most "popular" music - i`d consider it a
trick usually found in more complicated stuff than what most people listen
to... dunno. Also, you mention a "tonic degree of the diatonoc scale" - is
this the octave? I`m not sure i understand your distinction between terms.
Do you mean "tonal centre" as the symmetrical centre of the melodic contour,
as opposed to the "fundamental tonic" of the key signature?
> And of course, it makes no sense at all to identify various chords in
> terms of diatonic scale degrees, such as I, II, V, etc. So you see,
> some very well entrenched absurdities must be tossed into the garbage
> can, as a basic prerequisite for untangling the mess that you have
> centered upon in your post.
To be honest, i don`t see much point in this either. I geuss if it helps
people play then it has some value, but i don`t really see why it`s worth
the hassle - unless you needed to tranmit chord sequences across the cosmos
using morse code or something... hey we`ve all been there...
> In other words, those who are "in bed" with Ancient Theory will NEVER
> be able to sort out these things in a manner which you can
> understand--because they do not understand these things themselves.
But still, they make great databases. A database doesn`t need to understand
jack....
> But this of course will not keep them from answering your question.
> Just don't believe these irrelevant "answers"!
>
>>>>>
> If I were you, I would stop trying to get your answer *here*. >
>>
>> Well can you then recommend some better place for this kind of
>> questions?
> I wish that I could but I cannot. I believe that, to get a straight
> and sensible answer to your question, you would have to be studying
> composition (seriously) in an appropriate academic environment.
> So-called "music theory" for The Masses is worse than useless, since
> it is simply for the purpose of preserving Ancient Musical History,
> which has very little to do with explaining musical principles.
As Tom suggests - given your points on stagnation in musical academia, i
wouldn`t want to study an entire course just for the benefit of say a 2-week
module halfway thru term 3 - in any event the relevant module may be too
constrained or just more entrenched irrelevence. Personally i wouldn`t mind
doing a phd thesis on music`s various paradoxes (and getting paid to do
it) - but wouldn`t be able to hack the qualifying dergee course as my
interests are too narrow. Oh and i`m a nut.
I can`t find the reference, but the phenomenon -:j:- describes has been
studied. IIRC, all people, even those untrained in music, "feel" notes
absent from a triad as inferred, even with pure tones. This is sometimes
taken to imply a physical template for the triad, though i think that`s
unlikely. Whole, or rational numbers would seem to be the underlying
function. Although recursive division by 2 also works (but of course i
would say that).....
The best solution to this question i`ve found is biological equillibrium
systems - temperature, metabolism, electrostatic potentials and geometry in
self-organising cell assemblies, resonating Hebbian networks etc. etc. blah
blah blah as the Dr. would say.
Here`s some work by a Prof. Joseph Goguen i found last week:
http://www.cs.ucsd.edu/~goguen/projs/arts.html
http://www.cs.ucsd.edu/~goguen/pps/mq.pdf
This guy publishes papers in Science and Nature. Dynamical systems has a
reputation for Grand Unifying Theories, and yet seems to fit music cognition
better than anything else i`ve read. This is where i`m hedging my bets. I`d
like to say i had an open mind on the subject, but i don`t see how any
theory could supercede this - it provides accurate explanations,
descriptions, and predictions in all aspects of music perception, and solves
the apparent paradoxes and dichotemies.
USM
I agree fully with these points, so far.
USM
>
> There is a grain of truth in what you say about education here
> Al, but then you go and ruin it by saying things that are
> patently false. Ancient Theory, as you call it, is *precisely*
> "an accurate explanation of musical principles", as practiced by
> Bach, Mozart, Beethoven, and countless others, whom most of us
> consider to be great composers.
>
> Ancient Theory is *exactly* the compilation of "real answers
> buried deep within a study of musical composition". That's what
> it is! Your theory, as far as I can understand it from the
> fragments you've posted here from time to time, contradicts a lot
> of what was actually done, not in theory, but in practice, by the
> great composers of the last 300 years.
>
> So, who are we to emulate, them or you?
I don`t wish to demean you with examples, but they`re obvious and multiple.
We`ve got where we are through a series of inspired mistakes, not a perfect
set of laws inhereted from say, Pythagoras. We stand on the shoulders of
giants who were actually quite wrong in their details, even as applied to
themselves.... The ancients are to be comended where they were right, the
atomic nature of matter, the genetic nature of qualia and reproduction,
heliocentricity etc. etc. But for the greater part of our history all art,
science, religion and philosophy were considered as parts of the same theme,
the Great Chain of Being. And on many important points integral to the
understanding of music it was completely wrong. That`s not to say that the
music of Bach, Mozart and Beethoven was "wrong" - it was and remains
beautiful, some such works are in themselves perfect expositions of the
Great Theme. But the Theme itself was still mostly wrong.....
USM
Sorry but he`s right - the percieved principals of any period define that
style, or at least the likely acceptable parameters. Confusing the two is
to confuse cause and effect....
USM
This statement fully desribes the available pallette of rational chords in
the 12tet chromatic scale. It is axiomatic.
>
> Here is a statement about compositional style, as it relates to the
> above principle:
>
> The *choice* of which chord form to use at which structural location
> is a stylistic matter. In any composition, not every chord form is
> used at every location. What is referred to as "key" is, in fact, a
> stylistic "template" that is used to select which chords are used at
> which locations. A "mode" is another template, used to select a
> different group of chords at particular structural locations.
>
> For example, a "major key" template selects a major triad (three
> tones) or a major tetrad (four tones, commonly referred to as a
> "dominant 7th") at location {2}, which is referred to in Ancient
> Theory as V.
>
> As another example, a "minor key" template selects a minor triad
> (three tones) at location (12), which is referred to in Ancient
> Theory as IV. It also selects a major triad at location (2).
>
> Chords which lie "outside" the particular key are readily identified
> in terms of their structural locations. For example, an Ancient
> Neapolitan Sixth is a major triad at location {8}, etc.
>
> Really very simple in concept (principle).
I`m a bit slow, so i had to read it three times, but this seems correct
also. It is simple. In combination with modal chomatisism (which you
include anyway), this seems to me a thorough description of Western harmonic
conventions. Simple and thorough is Good. Reduction is the most powerful
tool we have in science and philosophy. This model neatly supercedes the
contorted terminology of ancient theory, you should get someone with gfx
skills to help out with diagrams, do a web page or something. It`s worth
sharing with students imo.....
> I have been through this same exercise a great many times, but Ancient
> Indoctrinees will *never* be able to understand the significance of
> principle versus style. NEVER.
>
> Albert Silverman
> (Al is in Wonderland!)
> where relevance is irrelevant
> and residents have no principles
Heh. Us nutters should take over this asylum, eh.
USM
> Try something new. Demonstrate your principles with music--your own
> music.
dead horse. flogging. kettle. black.
USM
You`re right, this is difficult to grasp. Could you further articulate this
non-circularity? What are the irrational consequences of circularity, if
that`s the implication...?
I need to read more to fully understand - i`ll need to reread this a few
times too. I can certainly appreciate that a simple core of an idea can
have complex outcomes, but i`m too tired and no doubt indoctrinated to see
the big picture just yet. If a new idea makes more sense than the recieved
wisdom, then it`s worth plugging. I`d geuss knowledge is as good as
acceptance, so maybe it`s just a matter of us lot catching up with you....
>
> Albert Silverman
> (Al is in Wonderland!)
> where relevance is irrelevant
Outlook Express users select Veiw/text size/fixed to veiw the table in
perspective.
Incidently, if all OE users installed OE-Quotefix Usenet would be a lot
easier in the eyes. It correctly displays plain text formatting, unlike
Microsoft`s best:
http://home.in.tum.de/~jain/software/outlook-quotefix/
USM
> Al, you've never shown any knowledge of any of the topics or curricula
> that you criticize. Where's your music, Al?
Who says a theorist or analyst has to be an instrumentalist or composer?
Does a singer have to be a conductor? Are a drummers musical skills
invalidated by his inability to play the saxaphone he`s accompanying? Or
vice versa? Does making music for a living somehow elevate you above us
mere theorist peasants? Do you have potentially ground-breaking theories to
back up your compositions? Why is there any such converse prerequisite for
theorists?
Why not save us all the hassle of having to read your infuriatingly
unimaginitive retorts, and just killfile people who make you feel inferior?
USM
Maybe i`ve missed too much but this seems unfair - has he claimed this is a
useful tool for such analysis? Or is it a compositional approach - if so,
have any qualified composers tried adopting the proposals in a non-biased
experiment? Who, when, what were their results? What do you think "ancient
theory" refers to, and how is it superior or more meaningful or relevant?
Sorry, your rebuttal seems too dismissive and lacks sufficient detail to
justify your assumed higher ground.
USM
> I'm a thorn in your side, Albert, because you don't make music.
>
If someone doesn`t produce to your personal taste they "don`t make music".
Isn`t that a bit Fascist?
Matthew Fields
Matthew Fields
It's a lie you just made up, and no, it isn't the slightest bit Fascist.
Thank you for playing. Have a nice day.
Matthew Fields
USM <TheUl...@SexMagnet.com> wrote:
>Matthew Fields wrote:
>
>> Al, you've never shown any knowledge of any of the topics or curricula
>> that you criticize. Where's your music, Al?
>
>
>Who says a theorist or analyst has to be an instrumentalist or composer?
Everybody--except for Al--at least *hums* a little bit.
>Does a singer have to be a conductor? Are a drummers musical skills
>invalidated by his inability to play the saxaphone he`s accompanying? Or
>vice versa? Does making music for a living somehow elevate you above us
>mere theorist peasants? Do you have potentially ground-breaking theories to
>back up your compositions? Why is there any such converse prerequisite for
>theorists?
Singers have to sing, drummers have to drum, and music theoreticians
have to have some direct contact with music itself lest their theories
be purely speculative and inapplicable to music.
>Why not save us all the hassle of having to read your infuriatingly
>unimaginitive retorts, and just killfile people who make you feel inferior?
The valid part of this question has been answered before, and the invalid
leading-question part will never get answered. I leave it as an exercise
for you to figure out which is which.
Perhaps you're still smarting from the fact that you have tried to
present your own grand unified theory of music based on the "universal
octave", and we've pointed you in the direction of the need to collect
actual evidence in the field rather than simply assume such a universal.
Matthew Fields
USM <TheUl...@SexMagnet.com> wrote:
>>
>> OK, at last we are getting somewhere, maybe. Please give me an
>> example of what you mean by "style" vs. what you mean by
>> "principle". Then I might be able to see where my "confusion"
>> lies. It won't do any good to just repeat what has already been
>> said in general terms, I need a concrete example.
>
>Sorry but he`s right - the percieved principals of any period define that
>style, or at least the likely acceptable parameters. Confusing the two is
>to confuse cause and effect....
You can't have music without music. There's no abstract principle music
that is free of style, though Al has represented Stephen Foster as such.
USM
> In article <421ede47$1...@mk-nntp-2.news.uk.tiscali.com>,
> USM <TheUl...@SexMagnet.com> wrote:
>> Matthew Fields wrote:
>>
>>> Try something new. Demonstrate your principles with music--your own
>>> music.
>>
>> dead horse. flogging. kettle. black.
>>
>
> My music's widely available, nu!
So`s Marilyn Manson`s. Shame about your reasoning though...
USM
> In article <421ed37b$1...@mk-nntp-2.news.uk.tiscali.com>,
> USM <TheUl...@SexMagnet.com> wrote:
>>>
>>> OK, at last we are getting somewhere, maybe. Please give me an
>>> example of what you mean by "style" vs. what you mean by
>>> "principle". Then I might be able to see where my "confusion"
>>> lies. It won't do any good to just repeat what has already been
>>> said in general terms, I need a concrete example.
>>
>> Sorry but he`s right - the percieved principals of any period define
>> that style, or at least the likely acceptable parameters. Confusing
>> the two is to confuse cause and effect....
>
> You can't have music without music. There's no abstract principle
> music that is free of style, though Al has represented Stephen Foster
> as such.
I was trying to avoid being so candid, but if it`s really necessary.... The
"acceptable parameters" of composition through recent centuries have evolved
to reflect the given trends and beliefs in the relationship of music and
culture that formed the basis of the Western tradition (not just music - the
whole shebang). The most obvious example is the supposition of the seven
known planets being embedded in succesive layers of crystal spheres in a
geocentric universe that extended as far as fixed outermost sphere of the
stars (which to be fair is still a bloody long way away) - hence the octave,
refering to the eighth and final tonal degree. Or something like that -
correct me where necessary.
However irrational and clearly wrong this idea might seem to us today, at
the time it made perfect sense - not only that, but it was entirely
consistent with all the observable data, right up to all the latest
theories - Newton`s inverse square law of gravitation, Keppler`s laws of
planetary motion, most religious beliefs and both then-modern and (selected)
historical philosophies of the natural order. Even as recently as Shoenberg
or Holtz, the Great Theme has done more to shape the language and landscape
of today`s music than any other factor - as we all know. Including you.
But err, yes, you can`t have music without music. Very good point there....
Looney
"USM" <TheUl...@SexMagnet.com> wrote in message
news:421ede47$1...@mk-nntp-2.news.uk.tiscali.com...
Why is it so unreasonable to ask a person to provide a demonstration of
their theory in practice?
--
Looney
-------------------------------------------------------------
Rant of the Loon
http://looneytoohey.blogspot.com/
Bob Pease
"Matthew Fields" <sp...@uce.gov> wrote in message
news:bdFTd.104$Ql3...@news.itd.umich.edu...
I have to plonk him.
Like his buddy AL, he seems to live in a world where his FIAT determines
TROOTH.
Al's writings, which I sometimes read piggybacked seem to include
increasing amount of raves about Acnient Theory Indoctrinees.
One of the clear ways to establish lapse into paranoia is when one defines
opposition to even a subset of their ideology as pathology.
Bob Pease
Bob Pease
"Looney" <ant...@thetooheyshatespam.com> wrote in message
news:b1ITd.712$C47...@newssvr14.news.prodigy.com...
usually those guys describe their systems as Purely "Mathematical"
Often the quality of their Math is the same as the amount of Music they
produce.
Bob Pease
USM
> "USM" <TheUl...@SexMagnet.com> wrote in message
> news:421ede47$1...@mk-nntp-2.news.uk.tiscali.com...
>> Matthew Fields wrote:
>>
>>> Try something new. Demonstrate your principles with music--your own
>>> music.
>>
>> dead horse. flogging. kettle. black.
>
> Why is it so unreasonable to ask a person to provide a demonstration
> of their theory in practice?
It is entirely reasonable. But as i understand it, he`s just trying to
simplify something with which we are already very familiar. I`d say that in
this respect he has been succesful - the core proposal is a concise
desription of Western triadic tonality that fits into a single sentence, and
crucially so, using PLAIN ENGLISH. This alone is a noteworthy acheivement -
anything else it does is a bonus. Axioms can be superficial. But useful,
meaningful axioms are information dense - the statement of musical principle
he proposes is a single sentence from which we can derive reams of tonal
relationships - and you`re asking him to write a tune? Surely this sentence
is so broad in it`s scope that it would be virtually impossible to write any
music that didn`t hinge on it in a pivotal sense? Asking him to write a
doodle is irrelevant. Unless he also does a dance, and videos it to share
with us....
Matthew Fields
Al's account of subdominant functions as 11 steps removed from tonic
is *much more complex* and indirect than the usual account.
paramucho
wrote:
It's like the old joke about answering the stranger's question that
"the township is a mile up the road, or 24900 miles in the direction
you're going."
Bob Pease
"paramucho" <i...@beathoven.com> wrote in message
news:421f6a24...@news.ozemail.com.au...
Only if the township is straight North or South of the city-slicker.
or East or West as well if he happens to be on the equator ,
Snicker !!
RJ P
Matthew Fields
The ovalness of the earth isn't the most important factor here, though.
USM
> Perhaps you're still smarting from the fact that you have tried to
> present your own grand unified theory of music based on the "universal
> octave", and we've pointed you in the direction of the need to collect
> actual evidence in the field rather than simply assume such a
> universal.
And i`d geuss if Al presented you with a personalised diamond-encrusted
hand-scribed collection of original Russian operas, you`d be like "Oh thanks
Al. Got music?". ;)
Perhaps you`d care to explain how the program Scala can reproduce all known
tuning systems from octaves? To quote Jourdain "No ethnomusicologist has
ever found any instance of any human not subject to equivalence". You still
haven`t explained who you think is the exception to this rule? So here`s
some more examples for you to ignore - you`ll notice some researchers seem
amazed that their subjects also posess equivalence, while other don`t seem
to appreciate the significance:
-Humans-
There`s so many references in humans, it`d be silly to list them all. Here`s
a few, there`s more on Google.
http://66.102.9.104/search?q=cache:djn7D2HazVUJ:www.worldmusiccentral.org/article.php/2005022017084972+octave+equivalence+in+animals&hl=en
An essay by David Canright:
http://www.redshift.com/~dcanright/harmser/
An excellent paper on reduction, emergence of qualia & music resolution
http://www.elec.qmul.ac.uk/research/thesis/Abdallah2002-thesis.pdf
It has also been shown in infants (Demany and Armand 1984)
-Other animals-
Rhesus monkeys:
http://web.telia.com/~u57011259/Wright.htm
Greater spear-nosed bats - this focuses mainly on communication calls. The
first harmonic is shown as integral in juvenile communication - the
researchers don`t realise the potential implications in adult audiology.
http://www.life.umd.edu/faculty/wilkinson/Bohnetal04.pdf
Recent discovery of independent evolution of near-identical inner ear in
another mammal, with whom the common ancestor we share did not posess such
an adaptation - suggesting a common, bottom-up, rather than top-down
selector for the design of the auditory aparatus:
and more anti-Gould commentary from Simon Conway Morris:
http://www.newscientist.com/article.ns?id=mg18524874.900
Equivalence and non-linearity in cat audiology (again, equivalence basically
unappreciated by researchers)
http://www.vimm.it/cochlea/cochleapages/theory/sndproc/paradox.htm
Perhaps one of the oldest - white rats (Blackwell and Schlossberg 1943)
Here`s a typical attempt at resolving the paradox - i`ve mentioned such
theories that are essentially conditioning arguments - this one apears to be
another version of "subharmonic mistakes in the inferior colliculus" - it`s
the second instance of this theory i`ve found ( i`m calling these up off
Google on the fly - i haven`t actually read them properly myself yet). On
closer inspection this solution is also a conditioning argument, suggesting
we percieve equivalence because of repeated exposure etc.
http://www.people.fas.harvard.edu/~pitkow/octaves/octaves.pdf
The examples i`ve previously mentioned like echolocating bats and dolphins
were from recent, independent articles published in New Scientist - you`ll
need to subscribe to get full access to the online back-cat.
Echolocation may prove to be another strong selector for equivalence - so
far, i`ve read acknowledgments that higher bandwidth screeches have an
accordingly higher resolution, significantly affecting sonar efficacy. It
has been shown in at least two species as a pronounced response - and while
i`ve not yet read any such direct claim, it would seem likely that a broader
bandwidth call will contain and reflect more harmonics than a narrower
bandwidth call, such that lower instances of the first harmonic will return
slightly later, while upper first harmonics will return marginally sooner -
a fundamental, a lower octave and an upper octave might concievably encode 3
dimensional stereospatial information in the minute discrepancies in the
relative reflection speeds of these 3 equivalent frequencies - if there`s
anything in this hypothesis, this may be relevant to improvements in our own
sonar systems - nautical, geological, medical.....
And i`m also saying equivalence can solve rhythm resolution. Before
proceeding, please read up on rhythm resolution, and try to appreciate the
fact that only the first 2 numbers of the prime series seem to have much to
do with most rhythms - 2 and 3. Next, read Boulez 1971 - in music there are
two different "types" of time - "striated" and "smooth".
I don`t wish to contradict Boulez, just further refine his terminology to
match that of cognitive science and information theory - what he`s actually
trying to articulate in striated and smooth time is really just serial and
parallel flow - these are also considered the comparitive temporal
resolution functions of the left and right hemispheres respectively. Where
parallel frequencies in a power of 2 relationship exhibit harmonic
equivalence, serial frequencies in the same relationships form the simplest
possible rythmic structures. The gap between both types of temporal
resolution is around five to ten octaves, with an intervening "dark spot"
that would seem to correlate to the corpus callosum connecting both
hemispheres.
So if bat`s screach calls may be considered an instance of echolocation
using smooth, or parallel time, a dolphin`s similar "click" sequences may be
considered echolocation using striated, or serial time - but both types of
equivalence - serial and parallel - are used by two very different animals
living in two very different environments, and play crucial roles in these
animal`s cognition and survival.
In information theory a pure tone contains no relative information. Neither
does a perfect 2:1 - serial or parallel. In music, language, and
echolocation, this "empty" relative temporal measure is used to encode
information that has a meaningful outcome to the organism. It is nature`s
standard unit of time for information processing, because it also describes
the ambient ground potential for all nodes in a self-organising neural
network.
It`s a simple idea, it just draws on fairly diverse matters. If you can see
any leaps of faith, please point them out.
Bob Pease
Assume sphericity and 25000 mile cirumference.
hint
Great circle or polar spiral?
Extra credit .
Convergence?
RJ P
don groves
TheUl...@SexMagnet.com hath writ:
I don't recall saying he's wrong, so why are you acting like I
did. I merely asked for conrete examples to clear up my
confusion about his meaning(s). Do you have any?
--
dg (domain=ccwebster)
don groves
TheUl...@SexMagnet.com hath writ:
What in the world has this got to do with my post? I was
pointing out to Al that music theory (what he refers to as
Ancient Theory) is nothing more or less than a distillation of
musical practice, what was actually produced by real composers,
during what we call the Common Practice Period, extended today by
the practices of some 20th century composers and jazz.
Right or wrong, the history of art, philosophy, the Great Chain
of Being, etc., have absolutely nothing to do with this
statement.
--
dg (domain=ccwebster)
USM
>
> Al's account of subdominant functions as 11 steps removed from tonic
> is *much more complex* and indirect than the usual account.
Maybe so. I`m certainly no expert, and when i do make music i don`t use
theory (i don`t write or score as i expect you do, i just sequence numbers).
My only point that was that a single sentance axiom has a certain mnemonic
conveniance. If you already understand the point he`s making in your own
terms, then no doubt your established veiw will persist. You could though,
offer an alternative sentance that does the same job in the significantly
less complex way you suggest....?
Albert Silverman
Authority, which cannot tolerate challenge to its discredited "theory".
Indeed, it is Authoritarian control over musical theoretical "education"
which is responsible for the utter disaster in *understanding* musical
principles. This theoretical ignorance is a worldwide cancer, despite the
general high standard of excellence in the instrumental *performance* of
so-called "serious" music.
Albert Silverman
(Al is in Wonderland!)
where relevance is irrelevant
and Ancient Authority is lurking around every corner
USM
> usually those guys describe their systems as Purely "Mathematical"
> Often the quality of their Math is the same as the amount of Music
> they produce.
>
> Bob Pease
Hi Bob. I have made no claim as to having a "system". Musics systems are
mathematical whether we like it or not. We all know i have no maths skills
because i`ve clearly stated so repeatedly from the outset - i came to
discuss this idea in the hope that somebody WITH maths skills AND a
knowledge of music and it`s history AND a good general knowledge besides
might be able to contribute some ideas - and there`s been one or two. The
idea i`ve proposed is that the two fundamental substrates of music - rhythm
and harmony, can both be reduced to serial and parallel resolution of a
power of two scale function - this relationship is the foundation of all
audiology, whether or not i can count to two, so must therefore be telling
us something interesting about our perceptions of sound and the passage of
time, and furthermore, that perhaps it may be taken to define a process of
perception common to other forms of life - i`ve given plenty of examples,
though i believe that many others may be found. Some people here ARE
mathmatically and musically qualified, so i feel this enquiry is both valid
and relevant, and might yet turn up some interesting ideas. Unfortunately
i`ve been dogged down by posters like you, who seem to have plenty of
critisisms, provided they don`t concern the issue at hand....?
Again, for clarity - i`m completely uneducated. About ten years ago i
realised that harmony and rhythm share this minimum relationship, but
couldn`t find any prior reference. I`ve now read a fair bit, and still cant
find any prior reference, beyond many, many analogies between this idea and
those suggested by just about every key theorist back through the Renaisance
to the Ancients. So i`ve continued, and read beyond the Ancients - i don`t
know if there`s such a field as "Paeleomusicology", but if not i`d suggest
that there should be, since the basic elements of our music can be
demonstrated to originate long before the earliest known music theories -
recent analysis of archeological findings from prehistoric graves in Jiahu
in central China suggest that we had a polyphonic tonal system 9,000 years
ago, and that something very close to the traditional "Western" scale
existed as long ago as the 6th millenium BC. Octave equivalence has been
demonstrated in other species form other primates right down to rodents.
I`m not "inventing" any connections, maths, or new words or terms - Like
Matt, your apparent critisism of my enquiry is dishonest, insulting and
unreasonable - quite what i`ve come to expect from those who consider
themselves musically "qualified".......
As previously noted, i find all this knee-jerk denial and misdirection quite
encouraging - if there were rational objections, people would be making
them...?
Matthew Fields
Sure. Subdominants are one fifth below the tonic, not 11 fifths above it.
USM
>
> I don't recall saying he's wrong, so why are you acting like I
> did. I merely asked for conrete examples to clear up my
> confusion about his meaning(s). Do you have any?
No i`m sorry i was getting a bit extra there, and my interference wasn`t
needed anyway - i only meant that Al was "right" to object that your
innitial response somewhat confused the terms "principle" and "style". I
didn`t mean to express the opinion that Al`s theory was "right", only that
his distinction between terms was valid. Appologies..
Matthew Fields
Albert Silverman <slv...@panix.com> wrote:
>On 2005-03-01, USM <TheUl...@SexMagnet.com> wrote:
>> Matthew Fields wrote:
>>
>>>
>>> Al's account of subdominant functions as 11 steps removed from tonic
>>> is *much more complex* and indirect than the usual account.
>>
>> Maybe so. I`m certainly no expert, and when i do make music i don`t use
>> theory (i don`t write or score as i expect you do, i just sequence numbers).
>> My only point that was that a single sentance axiom has a certain mnemonic
>> conveniance. If you already understand the point he`s making in your own
>> terms, then no doubt your established veiw will persist. You could though,
>> offer an alternative sentance that does the same job in the significantly
>> less complex way you suggest....?
>>
>No he cannot,
Too late, I already did.
> because his purpose here is to support Ancient Academic
>Authority,
An imaginary foe of yours.
> which cannot tolerate challenge to its discredited "theory".
Whatever you suppose, Al. The proof of a music theory is in the
applying it. I apply music theory daily to the making of music.
>Indeed, it is Authoritarian control over musical theoretical "education"
>which is responsible for the utter disaster in *understanding* musical
>principles. This theoretical ignorance is a worldwide cancer, despite the
>general high standard of excellence in the instrumental *performance* of
>so-called "serious" music.
>
>
>
>
>Albert Silverman
>(Al is in Wonderland!)
>where relevance is irrelevant
>and Ancient Authority is lurking around every corner
>
Sorry, Al, that's just conspiracy theory you're spouting. The truth is
that classical performers use an acute, broad and deep understanding
of music theory all the time to make split-second decisions regarding
phrasing and balance.
You really ought to give musicmaking a try.
USM
>
> What in the world has this got to do with my post? I was
> pointing out to Al that music theory (what he refers to as
> Ancient Theory) is nothing more or less than a distillation of
> musical practice, what was actually produced by real composers,
> during what we call the Common Practice Period, extended today by
> the practices of some 20th century composers and jazz.
>
> Right or wrong, the history of art, philosophy, the Great Chain
> of Being, etc., have absolutely nothing to do with this
> statement.
Again, apologies - I mistook Al`s term "Ancient Theory" literally, and went
off on one. I like a good excuse to rant on ancient theory, thought this
probably wasn`t one. ;(
Matthew Fields
But actually Al is wrong about this, as are you. Music theory is theory
of actual music, which always has a style. Styles may be more or less
closely related to each other, but there simply are no principles of
music which are true of all styles.
USM
> In article <421ef1e1$1...@mk-nntp-2.news.uk.tiscali.com>,
> USM <TheUl...@SexMagnet.com> wrote:
>> Matthew Fields wrote:
>>
>>> I'm a thorn in your side, Albert, because you don't make music.
>>>
>>
>>
>> If someone doesn`t produce to your personal taste they "don`t make
>> music". Isn`t that a bit Fascist?
>>
>
> It's a lie you just made up, and no, it isn't the slightest bit
> Fascist. Thank you for playing. Have a nice day.
A lie? You asked him to write a tune, he did, but he still "doesn`t make
music"? All i know for sure is that you two must have one of the
longest-running disputes in Usenet history, and it kind of clouds the
atmosphere here to put it mildy. I`ve no idea what started it off, but
everything else here is in the middle of it - and right now one side is
attempting to use rational argument, while the other is using obstreperous
dogma.....
Matthew Fields
USM <TheUl...@SexMagnet.com> wrote:
>Matthew Fields wrote:
>> In article <421ef1e1$1...@mk-nntp-2.news.uk.tiscali.com>,
>> USM <TheUl...@SexMagnet.com> wrote:
>>> Matthew Fields wrote:
>>>
>>>> I'm a thorn in your side, Albert, because you don't make music.
>>>>
>>>
>>>
>>> If someone doesn`t produce to your personal taste they "don`t make
>>> music". Isn`t that a bit Fascist?
>>>
>>
>> It's a lie you just made up, and no, it isn't the slightest bit
>> Fascist. Thank you for playing. Have a nice day.
>
>A lie? You asked him to write a tune, he did, but he still "doesn`t make
>music"?
I asked him to show some demonstration of having actually made music
in any capacity whatsoever. Where is there any evidence that he has?
Even children hum--but there's no evidence Al ever did.
> All i know for sure is that you two must have one of the
>longest-running disputes in Usenet history, and it kind of clouds the
>atmosphere here to put it mildy. I`ve no idea what started it off,
>but everything else here is in the middle of it - and right now one
>side is attempting to use rational argument, while the other is using
>obstreperous dogma.....
In December 1994 Al showed up swinging with both fists declaring all
musicians to be dupes of "The Ancient Theorist" and attacking
everybody he interacted with. He claimed to be the only person on the
internet who really understands music. He has been issuing variations
of that attack ever since. I let him attack me because when I ignore
him he attacks musical beginners, and I prefer for people to join
in the joy of music rather than being driven away by folks like Al.
As for dogma, the notion that octaves are universal something or
others is a dogmatic claim of yours undercut by e.g. Javanese music,
the music of Sethares, the music of Xenakis, etc. Before searching for
an explanation of the phenomenon, you really ought to make sure there
is a phenomenon to be explained. Making that observation doesn't mark
me as dogmatic in any way.
Looney
>
> The proof of a music theory is in...applying it.
Ah, truth.
For reasonable people, this is all that would need to be said.
Joey Goldstein
HARMONIC ORGANIZATION
by Albert Silverman
February 15, 1998
------------------------------------------
WHAT IS MEANT BY "CHORD RELATIONSHIPS"?
Chord-based composition is, in many aspects, analogous to tone-based
melody. Just as there are twelve melodic elements (tones) in the Western
scale, with these tones being organized in a particular manner to create
a
"melodic structure," there are twelve harmonic elements which are
organized
in a particular manner to create a "harmonic structure."
----------
DEFINITION:
The theory of "chord relationships" is concerned with
_the ORGANIZATION of the twelve harmonic elements._
----------
Whereas a melodic element (the tone) has a direct correspondence with
the
musical score, a harmonic element does not. Rather, a harmonic element
is
an abstract (i.e., not related to tones in the score) entity for
organizing
chord relationships. In this capacity, it acts as a base for chord
construction, thus providing the necessary link between the harmonic
element and the musical score.
Gradus Ad Deconfuse-us (steps to deconfusion)
It is of course to be expected that, to one to whom the concept of
structural organization (either melodic or harmonic) is alien (and this
is
particularly true for those who claim to understand what is loosely
called
"jazz theory"), the subject of chord relationships will be confusing and
difficult (if not impossible) to understand. whether or not there is any
hope for rescue from the doctrinaire clutches of Ancient Theory (or from
the strangely-evolved jazz theory) depends primarily upon one's degree
of
prior contact with Ancient Theory. There seems to be a line (call it
"indoctrination," if you will) that, once crossed, rings down a curtain
of
blindness and makes it virtually impossible to understand the nature of
chord relationships.
It stands to reason that, in order to understand what represents a
conflicts with Ancient Theory, one must understand what this theory
*IS*.
Indeed, this is the heart of the problem. For the most part, those who
receive instruction, if any, in this most important theoretical area,
are
taught _procedures (translation: "how-to-do-it"), intertwined with a
host
of irrelevant trivia_ and quaint nomenclature which, while providing an
endless source for interesting discussion, has nothing to do with the
relevant musical principles involved. In other words, the vast majority
of
individuals who study so-called music "theory" are NOT taught the
theoretical concepts (principles), which remain buried far out of sight.
This, then, is my goal; to bring these principles up from the catacombs,
into the light of day.
In a nutshell:
The deconfusion process consists of (1) decomposing what is commonly
referred to (within Musical Academia) as "harmonic theory,"
(2) sifting out that small portion which is RELEVANT to chord
relationships, and (3) putting Humpty Dumpty back together in a
credible (translation: rational and coherent) manner, which conforms
with ALL chord-based musical composition; i.e., without regard to the
particular style or period of composition.
Although there are many steps to deconfusion, which will be revealed as
the
discussion progresses through subsequent articles, there are three steps
which need to be taken early on, in the initiation of this deconfusion
process.
Step #1
Although it is well-known that chords were originally created by
multiple
voices coming together, this is the **WRONG** viewpoint to adopt, if the
purpose is to understand the nature of chord relationships. The RIGHT
viewpoint to take is that of a chord as a basic _unit of composition_; a
harmonic structural building block, as it were.
Perhaps more than anything else, it is this failure to recognize the
chord
as a compositional unit which is responsible for so much of the Ancient
Confusion that I have witnessed in the theoretically-oriented musical
newsgroups on the internet. There are constant references to the
"stability" or instability of INTERVALS, stability-related questions
about
what constitutes a "triad," discussion of Medieval polyphony, references
to
Modern polyphony, references to composition by coincident melodies
composed
from this scale or that scale, etc., etc. None of these things is
relevant
to the chord as a _unit of composition_.
In the face of such constant references to things which are IRRELEVANT
to
chord relationships, it is hardly surprising that so many individuals in
these theory-oriented newsgroups are terribly confused about the nature
of
chord relationships. In fact, they do not even understand the
significance
of chords being related to one another.
Putting first things first:
If you are unsure about the concept of a chord as a _compositional
unit_, you need to do some catching-up before you even begin to
attempt to understand how chords are related to one another
Also, be sure that you understand the distinction between the words
"unit"
and "indivisible." Although chord relationships make no sense unless the
chord is conceived as a compositional unit, this does not mean that a
chord
is indivisible. It can be decomposed into its component tones. Indeed,
this
is necessary in order to construct and use a chord practically; i.e.,
with
reference to a musical score.
Step #2
What is commonly referred to as "harmony" consists of two separate and
distinct components:
(1) acoustics (science) and related matters such as tuning, scale
temperament, overtones, "key character," etc., etc. and
(2) chord relationships.
In other words, _the relationship of one chord to another has NOTHING to
do
with acoustics_, despite never-ending attempts (by "scientifically-
oriented" theorists) to link them together. Rather, chord relationships
are
a MAN-MADE creation, peculiar to Western music.
Step #3
In order to comprehend (as opposed to having a fuzzy conception of)
chord
relationships, it will be necessary to _think in abstract terms_. In
particular, abstract thought (analogy is one example of this process) is
a
powerful tool to use in comparing Ancient Theory with the ideas that I
will
present here.
Unfortunately, individuals who have little, if any, scientific training
(even though the principles of chord relationships have no scientific
basis) generally seem to have extreme difficulty thinking in abstract
terms. Further aggravating this deficiency in those lacking scientific
training, and so destructive to progressive thinking, is that _abstract
thought is the bane of Musical Authority_.
Since academic musical instruction is geared specifically to avoiding
any
"revision" of musical history (thank you for this valuable insight,
Perfesser!), abstract comparisons with other viewpoints, etc., etc.
etc.,
have conveniently been banished from visible (translation: "for the
masses") musical instruction in our Academic Institutions of Learning
(abbr. AIL). The Academic Community needs their money but sees no need
for
them to have an understanding of the musical principles involved in
musical
composition
In a nutshell:
Unless you are anointed into membership in the composer's "inner
circle" of Musical Academia, you have virtually NO chance of learning
the principles of chord relationships on a formal (rigorous) basis.
These principles conflict with the Academic Musical Credo which
proclaims that musical Ancient Art/History will be taught under the
guise of "theory." For those who are not members of this charmed inner
circle, let the REAL theory be damned!
Hopefully you should now know WHY you are so terribly confused!
THE HARMONIC SCALE
Having abandoned nature (i.e., parted company with the science of
acoustics
and related matters), we can now greatly narrow the scope of the
discussion
and get on with the task of describing what Western MAN hath wrought.
----------
DEFINITION:
The "harmonic structure" of Western, chord-based composition consists
of twelve harmonic elements in an ordered (organized) relationship.
----------
These elements are ordered in a "harmonic scale," which is crudely
analogous to the twelve-tone "chromatic scale." This scale is shown in
Table 1.1 below.
========================================================================
(1) {1} {2} {3} {4} {5} {6} {7} {8} {9} (10} {11} {12}
(2) I V II VI III VII IV# I# V# II# VI# IV
(2a) or Vb IIb VIb IIIb VIIb
(3) C G D A E B F# C# G# D# A# F
(3a) or Gb Db Ab Eb Bb
TABLE 1.1 THE HARMONIC SCALE
========================================================================
Either Arabic Numerals enclosed in curly brackets as in Line (1), or
"labels" as in Line (2), can be used to denote the various degrees of
this
scale. Be SURE that you understand that these twelve scale degrees
remain
fixed in place, regardless of which of the two methods is used to
identify
them.
Both of these methods for denoting scale degrees are RELATIVE methods
for
denoting the position of the element in the harmonic order, which is
alternatively referred to as the "STRUCTURAL LOCATION". That is, once
the
first degree of the scale has been identified and the nature of the
"interval" between adjacent elements has been defined, every element
within
the scale is determined.
----------
DEFINITION:
The RELATIVE POSITION of a harmonic element in this scale (i.e., the
scale degree) is referred to as a harmonic "root."
----------
For example, the fourth harmonic scale degree is referred to as "root
{4}"
(Modern) or "root VI" (Ancient), etc.
The root designation is used primarily for analytical purposes,
associated
with root progression, etc.. For practical purposes (such as chord
construction and decomposition), it is necessary to have an ABSOLUTE
method
for identifying harmonic elements. That is, a method is needed for
relating
an element to the musical score.
In a melodic scale, relating an element to a tone in the score is a very
simple process. The _pitch level_ associated with each scale degree can
be
computed if the pitch level of one specific scale degree is known. For
example, in an equally-tempered (the discussion here assumes such scale
temperament) chromatic scale, the MELODIC interval between any two scale
degrees is one semi-tone. Hence, if we know the pitch level of any scale
degree, we need only count up the number of semi-tones to find the pitch
level of some other scale degree.
But since we are talking here about harmony, what is needed is a
definition
of what is meant by a HARMONIC "interval" between adjacent harmonic
scale
degrees. For reasons which will eventually become apparent, this
interval
is that of a perfect fifth (seven semi-tones) between the two TONES
which
are associated with adjacent roots.
----------
DEFINITION:
The unique tone which is associated with a harmonic element is
referred to as the "root-tone."
----------
Be SURE not to confuse "root" with "root-tone." They are different types
of
identification for a harmonic element and serve different purposes.
Therefore, _they cannot be used interchangeably_.
In a nutshell:
The term "root" refers to the _location of the harmonic element within
the harmonic scale_. The term "root-tone" refers to the unique tone
that is associated with the root.
Ordinal numerals versus labels
------------------------------
Modern root identification
The ordinal numeral method of root identification, which I shall
henceforth
refer to as the "Modern" method, uses Arabic Numerals enclosed in curly
brackets, as shown in line (1) of Table 1.1.
Since the harmonic interval between adjacent elements is a perfect
fifth,
the harmonic scale degree (minus one) denotes the number of 5th-degree
steps away from {1}, which I refer to as the "root of central
significance"
(abbr. RCS). The root-tones of the various scale degrees, with tone C
being
the root-tone of root {1}, are shown in line (3) of Table 1.1. For
example,
root {2} (tone G) is one step away from the RCS, root {7} (tone F# or
Gb)
is six steps away from the RCS, etc.
It should be evident that the harmonic scale is simply the Circle of
Fifths, cut between the twelfth and first locations and laid out in a
straight line. The first degree of the harmonic scale is the location at
the top of the circle.
----------
In a nutshell:
The ordinal numeral method of root identification uses a number which,
when one is subtracted from it, denotes the number of 5th-degree steps
away from the root of central significance.
----------
Ancient labels for root identification
Line (2) of Table 1.1 illustrates the use of Ancient labels for root
identification. Although seven of these labels are indeed (Roman)
numerals,
they are NOT ordinal numerals, since _they convey no HARMONICALLY-
significant ordering information_. Specifically, they have no
correlation
with the number of 5th-degree steps away from the RCS, which is the ONLY
harmonically-significant factor in the ordering of the various roots.
For
example, root V is only one step away from the RCS, while root IV is
eleven
steps away from the RCS, etc.
To further confuse an already confusing labeling scheme, the remaining
five
roots are identified by a label consisting of a Roman Numeral with an
appended sharp or flat, as shown in line (2) or (2a). For example, the
root
which is seven steps away from the RCS is identified by the label IIb,
rather than by the ordinal numeral {8).
----------
In an **EXTREMELY** important nutshell:
Because these Ancient labels have no correlation with the number of
5th-degree steps away from the RCS, the fact that they correspond with
the degrees of a diatonic scale is _harmonically irrelevant_.
----------
Believe it or not! Sorry for once again bringing up this trifling
matter,
AT, but you have had plenty of time to sort out the difference between
harmony and melody. Yet, in these hundreds of years, you have not
managed
to do so! Therefore, I will be happy to do this FOR you.
Insofar as explaining the _principles of chord-based composition_ is
concerned, instead of identifying the various roots by the the labels I,
II, III, IV, etc., they might just as well be identified by the labels
apple, banana, grape, peach, etc. At least we would then have a nice
fruit
salad, instead of our table being set with an Ancient witch's brew!
Into the Ancient Abyss
----------------------
Note:
Don't blame ME for this! Blame our friendly Ancient Theorist.
-----
In this Ancient root-identification labeling scheme, the twelve roots
are
divided into two subsets. The primary subset contains SEVEN elements and
is
referred to as the "diatonic" subset, since these elements are ordered
in a
one-to-one correspondence with the seven degrees of a diatonic scale.
Within the diatonic subset, the location of a harmonic element is
generally
identified by the use of a Roman Numeral. For example, the fourth
harmonic
element in the diatonic subset is identified as IV.
The secondary subset contains the remaining five elements, which are
ordered _in relationship to the elements of the primary subset_. This
subset is referred to as the "chromatic" subset, since its elements do
not
correspond with diatonic scale degrees.
Within the chromatic (an Ancient word for "colorful psychedelic"!)
subset,
however, roots are NOT identified by the use of numerals. Rather, labels
within the chromatic subset are clever combinations of Roman Numerals
with
appended sharps or flats, for the scale degrees {7}-{11}. For example,
the
label IIb identifies the eighth element in the harmonic scale, the label
IV# identifies the seventh element, etc.
To top it all off, as you are undoubtedly aware, our Ancient Theorist
has
also created some quaint names for the various elements of the diatonic
subset, and these are often used as a label, instead of a Roman Numeral.
For example, there is "tonic" (for I), "dominant" (for V), "subdominant"
(for IV), etc.
SUMMARY
In Western chord-based composition, there are twelve harmonic elements,
which can be ordered to form a harmonic scale, crudely analogous to the
twelve-tone chromatic scale.
The location of an element within this scale (i.e., the scale degree) is
referred to as a harmonic "root." The most important root is the first
degree, which I refer to as the "root of central significance."
Alternatively, an element may be identified by a unique associated tone,
which is known as the "root-tone" and is used as a base for chord
construction.
A root may be identified either (in the Modern manner) by an ordinal
numeral denoting the harmonic scale degree or by a highly misleading
label
(in the Ancient manner) which refers to an irrelevant scale degree.
CONCLUSION
The information provided in this article is basic and crucial for one
who
wishes to UNDERSTAND the nature of the harmonic process. It will
hopefully
enable you to begin the climb out of that Ancient Abyss into which you
have
fallen. Unless, of course, you like living in a Black Hole, and are
content
to further the Academic Fraud which is being perpetrated at your expense.
----------------
Albert Silverman
Joey Goldstein
BASICS OF CHORD RELATIONSHIPS (INTRODUCTION)
by Albert Silverman
February 5, 1999
--------------------------------------------
Everyone who studies music in one of our academic institutions or music
conservatories gets a dose of what is commonly referred to as "theory."
Therefore, the first order of business is to understand both the generally
accepted meaning of "theory" and the special interpretation which Musical
Academia attaches to this word.
Webster's dictionary defines "theory" as:
"A more or less plausible or scientifically acceptable general
principle offered to explain phenomena."
It can be concluded that, in accordance with this definition,
THEORY IS SYNONYMOUS WITH *UNDERSTANDING*
For example, in the field of science, the phenomena which are explained by
different theories are such things as (in physics) the motion of bodies,
the nature of vibrations, the nature of chemical reactions, etc., etc. In
other words, the explanation which is provided by the theory helps one to
understand the nature of some particular phenomena.
For reasons which will be explained shortly, Musical Academia takes the
position that the phenomenon which is being explained (in accordance with
Webster's definition) by musical "theory" is _musical Art and History_
(which will henceforth be referred to as "Ancient Art"). This
interpretation as to what is meant by "theory" has profound and far-
reaching implications.
CHORD RELATIONSHIPS (HARMONY)
Those who have had any significant contact with music know that what is
commonly referred to as "harmony" (the major body of music theory) deals
with "chords." Considering the preoccupation with chords in teaching the
music of the common-practice period (during which harmony reached the peak
of its development), one would certainly expect that the purpose of
teaching harmonic theory is to provide the student with an UNDERSTANDING of
chord relationships.
Unfortunately, however, this is not the case. At the heart of the problem
is the dismal failure of Ancient Art to come to grips with the nature of
CHORD RELATIONSHIPS
Although the Modern view of chord relationships diverges significantly from
the view in the common-practice period, Ancient Art must necessarily
reflect the prevalent view in that period of time. Indeed, it is the
specific purpose of Musical Academia to avoid "revisionism" of musical
history, with the express purpose of preserving Ancient Art into eternity.
In a cruel joke perpetrated at the expense of theoretical comprehension,
the course in Ancient Art which is dished up to the hapless and unwary
student
UNDER THE GUISE OF "THEORY"
fails miserably to provide him/her with the understanding of basic
theoretical principles.
Compounding the problem, the unwary student is unable to make the crucial
distinction between Ancient Art and the principles of chord relationships.
Needless to say, those who are perpetuating this _theoretical fraud_ upon
students are hardly chomping at the bit to point out this fact. If the
student knew what is deliberately being hidden, he/she might have some
vigorous objections to this trickery.
Were Musical Academia to *REASONABLY* explain the principles of chord
relationships, the objection to referring to Ancient Art as "theory" would
be less strenuous. In that event, the theory would at least be devoted to
an explanation of harmonic PRINCIPLES, rather than simply being an
explanation of musical PRACTICE (how-to-do-it). However, the Ancient
"theoretical explanation" of harmony in the common-practice period is
NOT a reasonable explanation of harmonic principles. On the contrary,
Ancient Art (at least the harmonic portion of it) is a horribly complex
and virtually incomprehensible maze of irrelevance, irrationality,
inconsistency, and incoherence ("i" is a wonderful letter for beginning
a word!) This hardly serves to promote the needed understanding of chord
relationships.
In a nutshell:
Rather than to explain the principles of chord relationships, the
purpose of teaching Ancient Art (the harmonic portion of it) within
Musical Academia is to _explain how music was written_ during the
common-practice period.
What's wrong with this approach to teaching harmony? It all depends upon
one's objective in studying the subject. There is nothing wrong with this
basic philosophy IF one's purpose in studying "theory" is to learn about
the compositional STYLE of this period (ranging roughly from 1650 to 1900).
However, if one's purpose is to learn the principles of chord
relationships, then _studying Ancient Art in the hope of obtaining an
UNDERSTANDING OF THESE IMPORTANT RELATIONSHIPS is futile_. It will not
get the job done. Period.
Who NEEDS to understand chord relationships?
In the ultimate analysis, what it all boils down to in the musical wash is
whether or not Musical Academia should serve those who have a NEED to
understand the principles of chord relationships. In this regard, anyone
who
(1) composes "serious" music based upon the triad,
(2) arranges or transcribes music in the popular style,
(3) improvises in the popular style, or
(4) teaches music in the popular style
needs to understand these principles. And it should be a foregone
conclusion (but apparently it is not) that composers who do not compose
triad-based music and have no intention of doing so nevertheless NEED this
knowledge, _and need it desperately, since it is the backbone of
compositional literacy_.
On the other hand, although it will probably be denied by those who resent
their status as "second-class citizens" in the academic Musical Caste
System, there is very little evidence that the instrumental performer (of
so-called "serious" music) need know much of anything about chord
relationships. All that he (or she) need do is read the notes which are set
in front of him (or her); the principles which were employed to compose the
music are of no practical importance in its performance. In other words, the
instrumental performer _who is not improvising_ can, without any
significant knowledge of chord relationships, safely navigate his/her way
through the printed score, set there as a roadmap. This fact of musical
life is proved thousands of times, day in and day out.
Following an innate law of the universe, that which is not of practical
necessity is guaranteed to fall through the cracks. Not unexpectedly,
therefore, the vast majority of music students are grist for Musical
Academia's mill. Of primary importance in Musical Academia is that the
"purity" of Art Music must not, under any conditions, be diluted by
catering to what it considers to be "heathen" popular interests. Thus it is
quite understandable that, when push comes to shove, Musical Academia will
adhere to its self-appointed charter, which is to teach Ancient Art, and
let those be damned who need something else! Musical Academia will, of
course, be glad to take their money and give them a certificate of
attendance.
Ancient Art versus Chord Relationships
Given the hypothesis that Ancient Art (1) must be preserved, and (2) does
not reasonably explain the principles of chord relationships, how can these
principles be successfully taught, assuming that there is a real desire
to teach them to everyone who "needs" them?
In principle, it is a simple matter to keep Ancient Art and chord
relationships firmly separated. Imagine, if you will, this classroom
scenario:
In this corner, folks, we have that jester, "Ancient Bunko." While he
is an aesthetic fellow who is artistically useful and is not
interested in revising musical history, he is nevertheless a ludicrous
and enigmatic clown, who will entertain us with his ridiculous
patch-and-piece efforts to conform with compositional practice.
Take a bow, AB.
Over here in this other corner, folks, we have "Chord Relationships."
While he has _excellent aural correlation_, is logical and well-
organized, and conforms with triadic compositional practice in ANY
time period, he cannot abide that insufferable prankster/conjurer,
Ancient Bunko. Lighten up, CR.
Be very sure that you keep your fighters straight, or YOU will wind up
on the floor!
What is the problem with this dual approach to teaching harmony? Contrary
to the old saying, honesty is NOT the best policy in the halls of musical
academe. On the contrary, honesty is an unpardonable sin here, wherein
three arguments can be raised against "honesty-in-chord-relationships."
(1) It casts incomprehensible Ancient Art in an unfavorable light.
(2) Eliminating the mystique and incredible confusion that are part and
parcel of musical "art" poses a grave danger to the Academic Musical
Caste System. How can the musical caste be delineated and the riff-raff
kept out of The Club, if the playing field is leveled by destroying the
"understanding barrier" that is part and parcel of Ancient Theory?
(3) Any theory which provides an UNDERSTANDING of chord relationships is
(paraphrasing the words of one typical academic representative who
teaches music theory and composition in a large Midwestern university)
"artistically useless." In other words, boys and girls, eliminate the
mystique, confusion, and absurdity from music "theory" and it is no
longer "art"!
So what is a poor academician to do, without giving away the show? The
generally accepted "solution" to this dilemma is brilliant. Simply teach
Ancient Art to all music students and claim that it is "theory," the
purpose of which is to _explain how music was written in the
STYLE of the common-practice period_.
Reflecting Musical Academia's perceived necessity to camouflage Ancient Art
as "theory," it is unconcerned about providing an understanding of chord
relationships to those whose musical interests lie in the academically-
invisible "popular" sector. The reason, of course, is that, not being
classified as "art music," this lowbrow stuff has no legitimate place
within the halls of academe.
Not only does Musical Academia generally ignore the needs of those whose
primary musical interest is not "art music," but it also sees no need to
provide an understanding of chord relationships _to non-compositional
majors_. Surely, goes the script, the non-compositional major, who has no
need for such understanding, in the eyes of Musical Academia, will be none
the worse for wear if he (or she) emerges from his course in "theory"
_believing that he understands chord relationships_, when what he (or
she) has REALLY been taught is Ancient Art/History.
On the other hand, most students who major in "serious-music" composition
will, if they persevere despite carrying the heavy baggage of Ancient
Art/History, eventually learn the principles of chord relationships; if
not directly from instruction, then by the process of osmosis.
Yet it is essential that, no matter what the circumstances, ALL (even those
who recognize its absurdity) within Musical Academia pay lip service to
Ancient Art. To prove this, after (and if) you learn the principles of
chord relationships, study the books on "theory" by very famous and well-
regarded composers/teachers. With rare exception, the lip service which
they are forced to pay to Ancient Authority will be reflected in incredibly
convoluted, tortuous, and all-but-incomprehensible
(translation: ludicrous) "explanations" of the underlying principles of
their musical craft.
Decrypting Ancient "Theory"!
Although Ancient Art purports to explain the development of "chords" during
the common-practice period, the theoretical principles of chord
relationships, several of which are lurking around somewhere in a typical
course in harmonic "theory" (or in the currently popular "whole music"
approach to teaching music), are virtually buried under a huge pile of
irrelevant and highly confusing detail. This effectively precludes their
recognition. Needless to say, if they can't be recognized, they can't be
understood. But who cares? Certainly not Musical Academia, with its own
self-serving agenda.
Hence if the object is to understand these basic principles, it is
essential that they be extracted from this Ancient Garbage Dump and exposed
to the light of day. To this end (the "decryption" of harmonic Ancient
Theory), I have written a series of articles entitled "The Basics of
Chord Relationships", which is currently in eight parts, plus this
introduction.
Departing from the accepted Ancient academic view that harmonic theory
is a
description of how music was written in the common-practice period, what
will be found in this series of articles is a TRUE theoretical
exposition. As such, its purpose is to explain the principles of chord
relationships in _abstract form_; i.e., divorced from any particular
stylistic framework. Such a "scientific" type of presentation is
extremely powerful in the across-the-board insight (_independent of the
time period in which the music is composed_) which it provides.
Dynamic Function
-----------------
Although virtually obscured in the typical course in harmony (due to the
ridiculous failure of Ancient Theory to recognize the TIME-DEPENDENCY of
the harmonic process at every step of the way, "dynamic function," which is
concerned with the nature of chord relationships within a time-dependent
harmonic organization ("structure"), _is the very heart of the subject_.
In contrast with the inability of Ancient Theory to deal with (translation:
to teach) this most crucial and fundamental area of the subject of
"harmony," my series of articles on chord relationships cuts right to
the chase--and let the chips (and the chumps) fall where they may. It
provides a detailed explanation of both Ancient and Modern (mine)
harmonic structures, and provides an illuminating comparison (if
there is even anyone out there who understands the Ancient structural
role of the diatonic scale).
In a nutshell:
It cannot be over-emphasized that an understanding of dynamic
function is the essential starting point for UNDERSTANDING the role
played by chords in harmonic theory. Sorry about that.
My "Basics of Chord Relationships" discusses Modern (as opposed to Ancient)
chord construction, which is routinely carried out _without regard to
the dynamic function of the chord in a musical context_.
A basic set of four chords is derived with reference to the two
semi-tone intervals of the diatonic major scale. This chord set
provides the basis for all _dynamic chord relationships_ within the
harmonic structure.
This structurally-complete basic chord set is then expanded to include
(1) chords with a chromatically-altered fifth degree, and (2) chords with
"added" (non-essential) tones. A sensible notational system (which
conforms, for the most part, with modern "popular" notation) is also
developed and discussed in detail in part (4).
Joey Goldstein
THE NATURE OF A HARMONIC ROOT
by Albert Silverman
March 2, 1999
------------------------------------------
INTRODUCTION
Part (1) discussed the organization of the twelve harmonic roots,
portraying the ordering of these roots within a "harmonic scale,"
analogous
to the ordering of tones within a melodic scale. The purpose here in
Part
(2) is to illustrate (but without going into the details of chord
construction, which is discussed in later articles) how the harmonic
root
is used in a musical context; i.e., to explain the theoretical principle
of
"root progression."
THE ROOT AS AN ELEMENT IN A DYNAMIC STRUCTURE
A crude analogy can be drawn between a harmonic structure and our solar
system. In this analogy, the RCS is analogous to the sun, while the
remaining eleven roots are analogous to orbiting planets. The harmonic
scale degree is a measure of the "distance" between a musical planet and
the musical sun. Thus root {2} is the root nearest the RCS, while root
{12}
is the most remote root.
========================================================================
***ANCIENT ARTY-FACT***
It is well to point out early on (in the teensy-weensy hope of avoiding
compounding the confusion), that Ancient Theory has no precise
equivalent
for the "root of central significance." Insofar as the RCS is the focus
of
harmonic activity (translation: "stable resting point"), it appears to
be
what our Ancient Theorist refers to as the "tonic".
Unfortunately, however, appearances are deceptive, particularly when it
comes to Ancient Things. The fundamental theoretical concept of a stable
resting point in a dynamic structure is hopelessly confused by our
Ancient
Theorist's dual use of the word "tonic" to mean BOTH (1) a stable
resting
point in the harmonic structure, and (2) the first degree of a major or
minor diatonic scale.
The implication of (2) is that the stable resting point (the RCS) in a
chord-based composition _owes its very existence to the fact that it is
the
first degree of a major or minor diatonic scale_. This is a ***FALSE***
Ancient Assumption. In theoretical point of fact, the existence of a
stable
resting point is quite INDEPENDENT of its association with any
particular
type of melodic scale. Thus, for example, the RCS is a perfectly valid
concept in a compositional style based upon an Ancient "mode" (or some
scale other than a major or minor diatonic scale).
In a nutshell:
The RCS is a stable resting point in the harmonic structure, divorced
from an association with the first degree (or any degree, for that
matter) of any type of melodic scale.
Sorry about that, AT. Really very sorry.
========================================================================
The analogy between this musical solar system and our own solar system
is
imperfect, with regard to the nature of the "gravitational attraction."
In
our solar system, there is a gravitational attraction between each
planet
and the sun. The strength of this attraction is an inverse function of
the
distance between these two bodies. In the musical solar system, however,
the influence of the RCS upon any root is reflected as an _attraction to
the adjacent root nearer the RCS_. Once again, the strength of this
attraction varies as an inverse function of the distance between the
root
in question and the RCS.
For example, {12} is the most remote root in the harmonic structure.
Consequently, there is only a very weak attraction of root {12} toward
root
{11}. The attraction of this most remote root is just strong enough to
keep
it within the "gravitational" field of the RCS. Again, there is an
attraction of root {11} toward root {10}. This attraction is stronger
than
the attraction of root {12} toward root {11}, since root {11} is nearer
the
RCS than root {12}, etc.
The theoretical model for root progression
------------------------------------------
A convenient way in which to view "root progression" is to envision a
"musical astronaut" who, wearing an asbestos suit, makes his home (a
stable
resting point) on the musical sun. To begin his journey through musical
space, he departs from his home at {1} and jumps directly to some
arbitrary
musical planet (a remote root in the harmonic universe). After reaching
this remote planet, he is forced by the gravitational field of the RCS
to
return home. His return path is prescribed by the dynamic attraction
which
propels him to the adjacent root nearer the RCS.
Accordingly, he must visit each intermediate harmonic planet in turn,
before coming to rest at his home on the sun. For example, if his
initial
jump-off is to root {4}, his complete journey through harmonic space
will
be the root progression {1}-->{4}-->{3}-->{2}-->{1}. Such a root
progression is referred to as a cycle of "departure-and-return." It is a
"regular" cycle, since it follows the dynamic prescription of the solar
system model. Referring to Table 1.1, it can be seen that our Ancient
Theorist labels this root progression as I-->VI-->II-->V-->I.
As another example, the simple root progression {1}-->{2}-->{1} is a
regular cycle of departure-and-return. The initial jump-off is to root
{2},
one step away, and the return home is the single step {2}-->{1}. Our
Ancient Theorist labels this root progression as I-->V-->I.
As a third example, the root progression {1}-->{12}-->{2}-->{1}, which
our
Ancient Theorist labels as I-->IV-->V-->I, is NOT a regular cycle of
departure-and-return, since a return from {12}, conducted in accordance
with the dynamic attraction between adjacent roots, would take place as
a
numerically-decreasing succession of roots, beginning at {12} and ending
at {1}.
Analysis of the root progressions of a great many musical scores reveals
that most of them are not regular cycles of departure-and-return. On the
other hand, many root progressions DO occur as regular (or partial,
"chained" root progressions) cycles of departure-and-return, which
suggests
the validity of this dynamic model. Additionally, particularly in simple
pieces, a chord may possess an _aurally-perceptible dynamic tension_,
directed toward a chord built upon the adjacent root nearer the RCS,
which
strongly suggests that the origin of this tension is the theoretical
attraction between adjacent roots in the dynamic model.
These various root progressions can all be explained with the concept of
a
_threshold of aural perceptibility_. In theory, every remote root
possesses
a theoretical attraction toward the adjacent root nearer the RCS. In
practice, however (i.e., in a musical context), the strength of this
attraction may be so small that it cannot be aurally perceived as a
"dynamic tension." That is, the practical manifestation (in a chord) of
this theoretical attraction lies below the aural threshold of
perceptibility.
There are two reasons for this small degree of attraction. First, the
root
upon which the chord is built may be so remote that its attraction
toward
the adjacent root nearer the RCS is too weak to be perceived. And
second,
the attraction of a chord toward a chord built upon the adjacent root
nearer the RCS is a function of the chord form.
As will be shown in Part (6) of this series, there is an _essential set
of
four chord forms, possessing four associated degrees of dynamic
tension_,
which range from zero in a minor triad to a maximum value in a chord
having
the pitch interval pattern of a dominant 7th chord.
In other words, the dynamic tension in a chord is a two-dimensional
function of
(1) the distance of its root from the RCS, and
(2) the chord form.
For example, a minor triad built upon root {2} (just one harmonic step
removed from the RCS) cannot have any dynamic tension in context, even
though the identity of the RCS is firmly retained in the memory. For
precisely this reason, our Ancient Theorist, who just adores the release
of
dynamic tension during the progression V-->I, and who seems to believe
that
chord-based composition is the exclusive province of the common-practice
period, does not "permit" the use of a minor triad at {2} (Ancient V).
Dynamic tension which is too weak to be aurally perceived is referred to
as "implied" dynamic tension. Progression from a chord without aurally
perceptible dynamic tension "free"; i.e., progression to any specific
chord
is not dynamically constrained. In other words, there will be no aural
objection if progression is not to a chord which is built upon the
adjacent
root nearer the RCS.
The classic example of a dynamically-free progression is the progression
from {12}, in {1}-->{12}-->{2}-->{1} (Ancient I-->IV-->V-->I). The
dynamic
tension in {12} lies well below the threshold of aural perceptibility,
due
to its remoteness from {1}, without regard to chord form. In other
words,
lacking an aurally-perceptible dynamic tension, there is nothing to
FORCE
the progression {12}-->{11}, which is theoretically indicated in the
dynamic model. Thus the progression {12}-->{2} is always without dynamic
consequence. This progression is so common because it is a part of the
"stylistic prescription" for composition in the common-practice period.
In the absence of an established harmonic structure
The above discussion of implied dynamic tension versus
aurally-perceptible
dynamic tension assumes that a harmonic structure has been established;
i.e., that the RCS has been identified and is retained in the memory.
The
fundamental rule of harmony (you can frame this and put it on your
wall!)
is:
NO CHORD SOUNDED IN THE ABSENCE OF AN ESTABLISHED
HARMONIC STRUCTURE CAN POSSESS A DYNAMIC TENSION.
Thus a chord _sounded in isolation from a musical context_ cannot
possess
any dynamic tension, whether or not it contains one, or one hundred, or
one
thousand "dissonant intervals." Sorry about that, AT. Really sorry.
The reason for this, of course, is that, in the absence of an
established
harmonic structure, a chord has no "root" association and hence no
"location" within a harmonic structure. Although every chord possesses a
constructional reference tone, this tone is *NOT* a "root-tone" until
the
context associates it with a particular root.
What is the source of the dynamic solar system model?
The dynamic solar system model does NOT owe its existence to any
acoustic
phenomenon. Rather, it reflects _the expectation that chord progression
will occur in a particular manner_. This expectation comes from
continuing,
intensive listening to chord-based composition, which reached its peak
of
development during the common-practice period.
Such tensions are peculiar to Western music, whose "harmony" in the common-
practice period is based upon the diatonic major scale, with its
characteristic semi-tone interval configuration. The crucial importance
of
this semi-tone interval configuration will be discussed in detail in
Part
(5) of this series.
THE HIERARCHIC HARMONIC STRUCTURE
The above discussion has been based upon the assumption that only one
RCS
exists throughout an entire piece. This is seldom the case, however,
except
in the simplest pieces. A more complex piece may contain several changes
in
the RCS throughout the course of the piece. Just as there may be a
progression in context from a chord built upon one root to a chord built
upon another root (this is referred to as a "root progression"), there
may
also be an analogous progression _from one RCS to another RCS_ during
the
course of a piece.
The existence of both root progression and RCS progression within the
same
piece creates a harmonic "hierarchic structure." At the lowest (bottom)
level of this structure, roots are related "dynamically." Under a very
specific set of circumstances which will be discussed shortly, the
dynamic
tension in a chord, heard in context, will become _aurally perceptible_.
The classic example of an aurally perceptible relationship dynamic
tension
is that in the "dominant 7th," assuming that a harmonic structure has
been
established and is retained in memory. This tension is then released
during
the progression to the (Ancient) "tonic" triad.
At the second structural level, there is no dynamic tension in an RCS
(comparable to that in a chord); hence there is no comparable release of
tension in the progression from one RCS to another RCS. Thus, harmonic
progression at these two structural levels differs fundamentally, in
that
there is no _dynamic analogy_ between a root and an RCS.
Modulation
Our Ancient Theorist provides a generalized technique for progressing
"smoothly" from one RCS to another RCS, in chord-based composition of
the
common-practice period. He refers to this smooth change of RCS as a
"modulation." There is, however, no reason at all that a change of RCS
need
be effected "smoothly." In other words, a change of RCS, no matter
whether
it is accomplished smoothly or in brute-force fashion, is a _theoretical
principle_, which is not dependent upon the stylistic practice of any
particular compositional period.
-----
Note:
Unless otherwise noted, the material in this series of articles on the
Basics of Chord Relationships will be concerned only with element
relationships at the lowest structural level. That is, for the most
part,
the discussion in this series of articles will be confined to the
relationship among roots, rather than to the higher-level relationship
among RCSs.
THE ROOT AS AN ANCIENT "FUNCTION"
In principle, a (single-level) harmonic structure is established by
departure-from and return-to a common root, synchronized with the
melodic
phrasing. Once established, it is continuously maintained by repetitive
cycles of departure-and-return. In order that the identity of the RCS
remain fresh in the memory, it is essential that the elapsed time
between
the departure and the return be sufficiently short. Otherwise, the
identity
of the RCS will fade from the memory, which is equivalent to a
disintegration of the harmonic structure.
Although a harmonic structure can readily be established by departure-and-
return, synchronized with the melodic phrasing, our Ancient Theorist
feels
that it is additionally desirable to use specific roots (IV and V) at
certain important phrase endings, which he refers to as "cadences." This
is
a crucial part of his prescription for composing in the "harmonic style"
of
the common-practice period.
Taken together with I, he refers to these three roots as "tonal
functions."
Here is a quote (describing the use of these tonal functions) by Walter
Piston who, in his teaching, is perhaps the most enthusiastic supporter
of
Ancient Theory.
"Dominant and Subdominant seem to give an impression of balanced
support of the tonic, like two equidistant weights on either side
of a
fulcrum."
Other roots also have Ancient "functions." Here is another quote from
the
same source, but in a strange language, which appears to be "Ancient
Gibberish."
"Mediant and Submediant have very little effect on the tonality but
suggest the mode, since they are different in major and minor."
Yes indeed, Walter. Now say it in English!
And finally, root VII and the five chromatic roots have no defined
Ancient
"functions." This does NOT mean, however, that they are excluded from
participation in the harmonic process. It only points up the
single-minded
purpose of Ancient "function," in a harmonic scenario in which roots
other
than the Big Three (I, IV, V) are considered to be of peripheral
importance.
SUMMARY
Assuming that a harmonic structure has been established and that the
identity of the RCS is maintained in the memory (using the technique of
repetitive departure-and-return, synchronized with the phrasing), every
root other than the RCS possesses a dynamic attraction which is directed
toward the adjacent root nearer the RCS. The strength of this attraction
is
an inverse function of the distance of the root from the RCS.
_In theory_, a return to the RCS from any remote structural location
will
be conducted as a "chained" root progression ending at the RCS. The root-
tones of successive roots in the chain are in a 5th-degree relationship.
_In practice_, however, root progression (an abstract concept) is
necessarily implemented as a progression from a chord built upon one
root
to a chord built upon a different root. Such a CHORD progression (the
associated root progression of which can always be identified) only
rarely
follows the theoretical model for ROOT progression presented above, for
the
following reasons.
First, the root upon which the chord is built may be so remote that the
attraction to the adjacent root nearer the RCS may be too weak to be
aurally-perceptible. Under these circumstances, progression from a chord
built upon this root is free from any dynamic constraint. And second,
the
dynamic tension in a chord is also a function of the chord form. In
other
words, dynamic tension is a two-dimensional function of (1) the
remoteness
of the root, and (2) the form of the chord built upon the root. The
dynamic
tension associated with chord form ranges from zero in a minor triad to
some maximum tension in a chord having the pitch interval pattern of an
Ancient "dominant 7th" chord.
CONCLUSION
It should be evident that the dynamic solar system model of a harmonic
structure, while satisfactorily "explaining" the nature of the harmonic
process (i.e., root progression), is not intended to be (and indeed, it
cannot be) used as a model for _composing in some particular harmonic
style_. Rather, the purpose of this model is to illustrate the nature of
root progression in an "idealized" harmonic structure and to explain the
dynamic relationship between two chords _built upon adjacent roots_ in
the
structure. Such relationships are discussed at length in Part (5) of
this
series.
What is missing from the picture is a "stylistic blueprint," as
it were, _which links chord form with structural location_. The most
common
such blueprint is Ancient "key," which will be discussed in Part (3).
Other
such blueprints are the various Ancient "modes." Or there may
conceivably
be no blueprint at all, a compositional anarchy (no plan) aptly
described
as "freestyle." Yet, even in the face of such stylistic anarchy, there
is
still a harmonic structure, provided that an RCS is established and
maintained in the memory.
Unfortunately, despite all of the hoopla which surrounds it, as it
continues to be hyped throughout the musical world by its Proud Papa,
Ancient key, while purporting to provide a blueprint for composing in
the
style of the common-practice period, was virtually ignored by composers
in
the period whose music Ancient Theory is designed to "explain." That is,
the analysis of countless compositions in this period reveals that there
is
NO general conformance with our Ancient Theorist's "key" blueprint.
About
all that can be said for this blueprint is that there is usually
conformity
between Ancient Theory and compositional practice only in the very
simplest
pieces.
The lack of a harmonic structure
In the ultimate "degenerate" form of chord-based composition (typified
by
many works of Richard Wagner), there is no identifiable RCS retained in
the
memory. The lack of an established harmonic structure differs
fundamentally
from "freestyle," in which there exists a harmonic structure, but
without
any stylistic link between chord form and structural location.
----------------
Albert Silverman
Joey Goldstein
CHORD CONSTRUCTION IN ISOLATION
by Albert Silverman
July 9, 1998
------------------------------------------
INTRODUCTION
In Part (3), I explained the Ancient tertiary chord construction
process,
which is characterized by an _interdependence between chord form (pitch
interval pattern) and structural location_. This interdependence, which
is
peculiar to the compositional "style" of the common-practice period, is
referred to by our Ancient Theorist as "key."
In this article, I will explain a different construction method for
creating the _same chord forms_ that result from using the Ancient
tertiary
construction process. This revolutionary and heretofore-secret method of
chord construction (which I refer to cryptically as being applied "in
isolation from a musical context") does not rely upon harmonic
organization.
A chord that is constructed in isolation is fit into the harmonic
structure
by relating its constructional reference tone to the the root-tone of
central significance. This is done by an iterative process for
generating
the twelve root-tones, in 5th-degree steps, as discussed briefly in Part
(1). For example, if the constructional reference tone of a chord is Ab,
and if the root-tone of central significance is tone C, this chord is
located at root {9}, as shown in Table 1.1
Why construct a chord in isolation?
The obvious answer to this question is simply that, in many
circumstances,
there are things that one wishes to know about a chord which do not
involve
the use of the chord in a particular musical context. One obvious thing
is
the analysis of a chord's acoustical properties (sound quality). As I
have
stated previously, these properties have nothing to do with a chord's
relationship with other chords; i.e., with its membership in a harmonic
organization.
But the most important reason, which is not obvious because it has no
parallel in Ancient Theory, involves the analysis of a chord as a
participant in a "dynamic pair-bond relationship." In this analysis, a
specific chord form is decomposed into its component tones. These tones
are
then analyzed to determine their "tendency" and "persistence."
The purpose of such an analysis (which is the subject of the next
article
in this series) is to determine how a chord built upon one root-tone
relates (dynamically) to a chord built upon a root-tone in a 5th-degree
relationship. In other words, it is to explore the "dominant-tonic"
relationship (the Ancient term for a "pair-bond" relationship), without
reference to the particular location of the chord pair within a harmonic
organization.
CHORD CONSTRUCTION
While Ancient tertiary chord construction creates a chord having a
_SCALE
interval pattern_ of three degrees between every two adjacent tones,
independent of the location of the element within the key-array, this
same
chord form is created "in isolation" by employing its _PITCH interval
pattern_ to select the component tones.
Example #1
For example (refer to Table 3.2(a)), the chord C(V:3) contains tones
GBD.
This is a major triad, whose pitch interval pattern is G<43> (this
notation
was explained in Part (3)). To construct this chord in isolation (i.e.,
free from any association with a key-array) requires two steps, since
there
are two pitch intervals, of four and three semi-tones. As the first
step,
we start with tone G as the constructional reference tone and add a
tone,
higher in pitch than tone G, to form a PITCH interval of four semi-tones
with tone G.
The twelve-tone, equally-tempered chromatic scale (starting arbitrarily
with tone C, which is not the "first" tone of the scale, since the
interval
between successive tones is one semi-tone and thus no tone is a
preferential "starting" tone) is shown in Table 4.1.
--------------------------------------------------------------------------
C C# D D# E F F# G G# A A# B
or Db Eb Gb Ab Bb
Table 4.1 THE CHROMATIC SCALE
--------------------------------------------------------------------------
Counting up four semi-tone intervals from tone G, we arrive at tone B,
which is the second tone of our major triad. To get the third tone, we
count up three semi-tones from tone B (taking us into the next octave)
and
arrive at tone D.
Note that we cannot, until such time that this chord may be organized
harmonically, properly refer to the constructional reference tone G as a
"root-tone." All that can be said about this chord _in isolation_ is
that
it is a major triad constructed upon tone G.
Although, in principle, a chord can be constructed in isolation by
selecting its component tones _from the chromatic scale_, as was
illustrated in the above example, there are compelling reasons for
selecting the component tones from the _diatonic major scale based upon
the
chord's constructional reference tone_, along with appropriate chromatic
alterations to obtain tones that are not component tones of this
particular
diatonic scale.
These reasons are to avoid spelling problems, make for easy and rapid
construction and above all else, to _allow for the convenient analysis
of
dynamic chord relationships_. Therefore, in all future discussion, chord
tones will be selected in this manner, rather than selecting them from
the
chromatic scale, as is done in this example.
It should be recognized that this process creates a chord which has the
pitch interval pattern of a chord that was originally created using the
Ancient tertiary construction process. Because this tone selection
requires
chromatic alterations of diatonic scale degrees, it is not "based upon a
diatonic scale," in the same sense as is the tertiary construction process.
Example #2
The chord C(V:4) contains tones GBDF. Its pitch interval pattern is
G<433>,
which can be created, independently of the diatonic C-major scale, by
selecting the first, third, fifth, and lowered seventh degrees of the
diatonic G-major scale;
G A B C D E F#
1 2 3 4 5 6 7
construction: {1,3,5,-7}
DOMINANT SEVENTH: GBDF
Note that the tone F (which is required to form an interval of three semi-
tones with tone D) is not a component tone of the diatonic G-major
scale.
Hence F#, the seventh degree of this scale, is "chromatically lowered"
by
one semi-tone to obtain tone F. The construction of this chord, in
isolation, is noted as G{1,3,5,-7}, where G is the constructional
reference
tone and the numerals refer to the degrees of the diatonic G-major
scale.
The notation -7 refers to a lowered seventh scale degree.
Example #3
The chord C[IV:3] contains tones FAbC. This is the well-known "minor
triad." Its pitch interval pattern is F<34>, which can be created by
selecting the first, lowered third, and fifth degrees of the diatonic
F-major scale.
F G A Bb C D E
1 2 3 4 5 6 7
construction: {1,-3,5}
MINOR TRIAD: FAbC
Example #4
The chord C[II:4] contains tones DFAbB. It is referred to by our Ancient
Theorist as a "diminished seventh" chord. Its pitch interval pattern is
a
"symmetrical" D<333>, which can be created by selecting the first,
lowered
third, lowered fifth, and sixth degrees of the diatonic D-major scale.
D E F# G A B C#
1 2 3 4 5 6 7
construction: {1,-3,-5,6}
DIMINISHED SEVENTH: DFAbB
Example #5
The chord C[III:3] contains tones EbGB. It is referred to by our Ancient
Theorist as an "augmented triad." Its pitch interval pattern is a
"symmetrical" Eb<44>, which can be created by selecting the first,
third,
and raised fifth degrees of the diatonic Eb-major scale.
Eb F G Ab Bb C D
1 2 3 4 5 6 7
construction: {1,3,+5}
AUGMENTED TRIAD: EbGB
NOTATION/NOMENCLATURE
There are at least three different notational schemes to identify chord
FORM; i.e., to identify a chord constructed in isolation. These are:
(1) pitch interval pattern
(2) construction formula
(3) popular-style notation
In addition, a chord form may be identified by its "common name," of
Ancient derivation. As might be expected, anything dreamed up by our
Ancient Theorist should be highly suspect, regarding its rationality and
consistency. And you will not be disappointed here! Rather than trying
to
make any sense of it (which for many names is virtually impossible), the
recommended way to think of the common name for a chord is simply as a
"label" which does not necessarily convey rational information about the
chord form that it identifies. This approach to the common name will
allow
at least allow you to sleep nights!
This being said, it should nevertheless be noted that some common names
actually DO make sense; so consider this a bonus if you happen to run
onto
one of them. For example, the name "triad" refers to a 3-tone chord.
Before
you count your chickens, however, you should be informed that many
3-tone
combinations are NOT triads!
Why? Because the common name "triad" refers ONLY to a three-tone chord
which has been constructed using the Ancient tertiary construction
process.
If no rearrangement of the component tones results in a pitch interval
pattern that matches the pitch interval pattern of a 3-tone combination
constructed by the tertiary process, this chord is NOT a triad, but
rather
a "tone cluster." That's why.
It is not my purpose here to attempt to explain the Ancient reasoning
(if
this word is even applicable) which underlies these names. Just chalk it
up
to "art." Two brief comments are in order, however. Suffice it to say
that
the three-tone combinations _created by the Ancient tertiary
construction
process_ are all referred to as "triads" and the four-tone combinations
created by the Ancient tertiary construction process are all referred to
as
"seventh" chords. Let's see now; "triad" stands for three tones and
"seventh" stands for four tones. Got it, AT!
Note also the perverse common name "dominant seventh," used to identify
a
_pitch interval pattern_. If we were to insist upon rationality in
common
names (heaven forbid!), we would recognize that the term "dominant"
refers
to V, the Ancient label for LOCATION {2} in the harmonic structure.
Therefore, it can do nothing but confuse to use the word "dominant" to
denote a specific pitch interval pattern!
----------
Table 4.2 illustrates these three notational schemes for nine chord
forms
selected from the two key-arrays of Table 3.2 (refer to Part (3)).
=========================================================================
tertiary common pitch construction popular-
notation name interval formula style
pattern notation
-------------------------------------------------------------------------
C(I:3) major triad C<43> C{1,3,5} C
C[IV:3] minor triad F<34> F{1,-3,5} Fm
C[II:3] diminished triad D<33> D{1,-3,-5} Dm-
C[III:3] augmented triad Eb<44> Eb{1,3,+5} Eb+
C(V:4) dominant seventh G<433> G{1,3,5,-7} G7
C(III:4) minor seventh E<343> E{1,-3,5,-7} Em7
C[VII:4] diminished seventh B<333> B{1,-3,-5,6} Bm6-
C[II:4] half-diminished D<334> D{1,-3,-5,-7} Dm7-
C[VI:4] major seventh Ab<434> Ab{1,3,5,7} Ab:7
Table 4.2 SOME COMMON CHORDS: NOTATION/NOMENCLATURE
=========================================================================
Column one is the notation which I used in connection with Table 3.2 (in
Part (3)). It is MY (not our Ancient Theorist's) simplified "tone-
dispersion-free" method for identifying an element within a key-array,
created by the Ancient tertiary construction process. As I explained in
that article, the tone preceding the parentheses or square brackets is
the
reference tone (the first degree) of the diatonic scale used in the
tertiary construction process. Parentheses denote a major diatonic scale
and square brackets denote a (harmonic) minor scale. The Roman Numeral
denotes the scale degree, and the number following the colon separator
denotes the number of tones in the tone combination built upon that
scale
degree.
Pitch interval pattern
----------------------
Column three denotes the construction in terms of the various pitch
intervals, in semi-tones, between adjacent pairs of tones, beginning
with
the constructional reference tone (shown preceding the < bracket) as the
tone of lowest pitch. This sequence of pitch intervals is referred to as
the _pitch interval pattern_. Note that the ONLY pitch intervals which
appear in any pitch interval pattern in this Table contain three or four
semi-tones. This is due to the fact that all of the tone combinations
(or
chords) in this table were generated using the Ancient tertiary
construction process.
Construction formula
--------------------
Column four provides the same pitch interval information that is
provided
in column three, although the information is presented in a different
manner. The pitch intervals of column three are converted to tones that
are
selected from the _diatonic major scale based upon the constructional
reference tone_ (shown preceding the { bracket). The numerals refer to
degrees of this particular diatonic scale. Chromatic alteration of a
tone
is shown by a minus or plus sign preceding the number. A minus sign
indicates that this particular degree is to be chromatically lowered by
one
semi-tone, while a plus sign indicates that this particular degree is to
be
chromatically raised by one semi-tone.
Popular-style notation
----------------------
The fifth column presents my customized "popular-style" notation for the
various chords in the Table. My use of the word "style" here implies
that
not EVERY one of these notations agrees with what is commonly referred
to
as the "popular" notation that is used in fake books, chord charts,
sheet
music, etc. There is NO standard notation to cover all possible
varieties
of chords. Furthermore, what is in current use generally suffers, to one
degree or another, from irrationality and inconsistency. For these
reasons,
I have developed my own popular-style notation, which is
self-consistent,
sensible, efficient, easy to read and to build chords quickly, etc.,
etc.
It is in substantial agreement with notation that is widely used.
Popular-style notation begins with the constructional reference tone,
which
is also given in columns three and four. If the first number in the
pitch
interval pattern is 4, the chord is what *I* refer to (but which gives
our
Ancient Theorist apoplexy) as being in the "major mode." In this case,
no
"mode designator" follows the constructional reference tone. Examples
are
the major triad, augmented triad, dominant seventh, and major seventh.
However, if the first number in the pitch interval pattern is 3, the
chord
is what *I* refer to (again giving our Ancient Theorist apoplexy) as
being
in the "minor mode." In this case, an m follows the constructional
reference tone. Examples are the minor triad, diminished triad, minor
seventh, and diminished seventh.
If the construction formula contains the numeral 7 preceded by a minus
sign, then the notation has a numeral 7 following the mode designator,
if
one is required. However, if the construction formula contains the
numeral
7 without being preceded by a minus sign, then the notation has a :7
following the mode designator, if one is required. An example is the
major
seventh.
If the construction formula contains the numeral +5, then the notation
ends
with a plus sign. An example is the augmented triad.
If the construction formula contains the numeral -5, then the notation
ends
with a minus sign. Examples are the diminished triad, diminished
seventh,
and half-diminished.
If the construction formula contains a numeral 2 or 4 or 6, the manner
in
which these numerals are reflected in the notation depends upon whether
there is also a -7 present. If there is also a -7, then the combination
of
-7 along with 2 or 4 or 6 is denoted by the sum of 7 with 2 or 4 or 6.
But
if there is a 2 or 4 or 6 in the absence of a -7, the numeral 2 or 4 or
6
will appear in the notation. An example is the diminished seventh.
Chords (or tone combinations) in which the construction formula contains
both a 2 or 4 or 6 plus either a 7 or a -7 contain at least five tones
and
will not be discussed at the present time, since this only increases the
complexity without adding anything of conceptual significance.
SUMMARY
A tone combination (or "chord," as the case may be) may be expressed as
a
sequence of pitch intervals (the number of semi-tones spanned), formed
between pairs of tones which are adjacent in pitch. This sequence of
pitch
intervals is referred to as the "pitch interval pattern."
A tone combination (or "chord," as the case may be) may be constructed
from
its pitch interval pattern, starting with an arbitrary constructional
reference tone and adding a tone to form the required pitch interval
with
the tone of lower pitch. This process is iterated, until all of the
pitch
intervals are created. It is known as "constructing a chord in isolation
from a musical context."
Although the tones may be selected from the twelve-tone chromatic scale,
there are excellent reasons for selecting them from the diatonic major
scale based upon the constructional reference tone, with chromatic
alterations as required for a tone which is not a component of this
particular scale. Selecting them in this manner avoids spelling
problems,
is fast and easy to use, and allows for the analysis of dynamic chord
relationships (to be discussed in the next article).
This selection of tones, expressed as numerals standing for the degrees
of
this diatonic scale and enclosed in curly brackets (a plus or minus
prefix
for any tone refers to chromatically raising or lowering the scale
degree,
respectively), is appropriately referred to as the chord's "construction
formula." Optionally, the constructional reference tone precedes the
left
curly bracket in the construction-formula notation.
In general, the pitch interval pattern of a tone combination constructed
in
isolation may be expressed in four different ways:
(1) by its common name
(2) by an ordered sequence of pitch intervals
(3) by its construction formula
(4) by its popular-style notation, which specifies:
(a) the constructional reference tone
(b) a mode designator to denote a pitch interval of three semi-tones
formed between the constructional reference tone and the tone of
next higher pitch
(c) numerals to indicate the presence of scale degrees other than the
first, third, or fifth
(d) a concluding plus or minus to indicate a chromatically raised or
lowered fifth degree, respectively.
CONCLUSION
It is of utmost importance that you not confuse chord construction _in
isolation_ (i.e., free from any association with a musical
context/harmonic
organization) with Ancient tertiary construction, which is an entirely
different process (associated with a particular compositional STYLE)
that
creates a restrictive link between chord form and structural location.
Most important for conceptual clarity, the diatonic scale that is used
in
the creation of a chord from its pitch interval pattern _may be any one
of
twelve different scales_, whereas only a single diatonic scale is
involved
in the generation of numerous chord forms in the Ancient tertiary
construction process.
----------------
Albert Silverman
Joey Goldstein
THE ESSENTIAL CHORD SET
by Albert Silverman
July 15, 1998
-------------------------------------
BRIEF REVIEW
Part (5) illustrated the dynamic (time-dependent) nature of the
progression
from a chord with the same pitch interval pattern as a dominant 7th
chord
(noted henceforth as a [dominant 7th] chord) to another chord built upon
the adjacent root nearer the root of central significance. It was shown
that, if the RCS has been established and is retained in the memory, two
tones in the [dominant 7th] will possess aurally-perceptible
"tendencies,"
which urge progression to two other tones in a semi-tone relationship
with
the tendency tones.
Taken together with the root-tone persistence, these two tendency tones
cause the [dominant 7th] chord to possess a strong "dynamic tension"
which
is directed toward a resolution in a major triad built upon a different
root. Following the indicated tendencies results in a release of the
dynamic tension. Borrowing from Ancient terminology, the root TO which
progression takes place is referred to as the "tonic" root, while the
root
FROM which progression takes place is referred to as the "dominant"
root.
Hence this generalized progression _between ANY two adjacent roots in
the
harmonic structure_ is referred to as a "dominant-tonic" progression.
It was also shown that
the semi-tone melodic interval defined by the progression of a
tendency tone to the tone which it seeks in the tonic chord of
resolution is an interval which exists in the tonic diatonic major
scale. The melodic progression of each of these two tendency tones is
associated with a different semi-tone interval in the tonic diatonic
scale.
Hence, insofar as _this tension would not exist if these semi-tone
intervals were not present in these specific scale locations_, it can be
said that these two semi-tone intervals (in the tonic diatonic major
scale)
are "responsible" for the strong dynamic tension in the [dominant 7th]
chord. The actual source of these dynamic tensions is the listener's
expectation that chord progression will take place in a certain manner.
This comes from long and continued listening to chord-based composition,
which was developed to a peak of perfection during the common-practice
period.
THE FOUR ESSENTIAL CHORDS
In this article, the concept of a dynamic tension which can be linked
with
the semi-tone intervals of the tonic diatonic major scale (in a dominant-
tonic progression) will be extended to three other chord forms.
Since there are two semi-tone intervals in the diatonic major scale,
these
two intervals can be combined in four possible ways:
(1) both intervals
(2) only the interval between the third and fourth degrees
(3) only the interval between the seventh and first degrees
(4) neither interval
By using a dynamic analysis similar to that used to explain how the
dynamic
tension in a [dominant 7th] chord is reflected in practice (using both
semi-tone intervals), it can be shown that there are three chord forms
which utilize combinations (2), (3), and (4) above. These are:
(2) minor-mode seventh (interval between third and fourth degrees)
(3) major triad (interval between seventh and first degrees)
(4) minor triad (no interval)
For example, the minor-mode 7th chord possesses a single tendency tone
(in
its lowered 7th degree). In progression from this chord, the melodic
interval which is formed when this tone progresses to a tone in the
tonic
chord of resolution is found between the third and fourth degrees of the
tonic diatonic major scale.
Similarly, the major triad possesses a single tendency tone (in its
third
degree). in progression from this chord, the melodic interval which is
formed when this tone progresses to a tone in the tonic chord of
resolution
is found between the seventh and first degrees of the tonic diatonic
major
scale.
And finally, in the "degenerate" case, a minor triad has NO tendency
tones.
Hence progression from a minor triad does not depend upon either
semi-tone
interval of the tonic diatonic major scale.
========================================================================
MAJOR-MODE 7TH ([dominant 7th])
construction formula: [1,3,5,-7]
popular-style notation: 7
pitch interval pattern: <433>
This is the top-ranking chord form in the dynamic hierarchy of four
essential chord forms.
For example, the [dominant 7th] chord based upon the root-tone G
contains
the four tones GBDF, and is constructed from the first, third, fifth,
and
lowered 7th degrees of the diatonic G-major scale. (You may wish to
refer
Part (4), which is devoted to chord construction in isolation).
In the dominant-tonic progression GBDF-->GCE (G7-->C), the dominant root-
tone G persists, tone B moves upward by one semi-tone, in accordance
with
its tendency, to tone C, and tone F moves downward by one semi-tone, in
accordance with its tendency, to tone E. The fifth degree D is
dynamically
neutral (as always) and is discarded during the progression. In the
tonic
diatonic major C-scale, the semi-tone interval (B-C) is the interval
between the seventh and first degrees, and the semi-tone interval (F-E)
is
the interval between the fourth and third degrees.
Hence the [dominant 7th] chord uses both intervals of the tonic diatonic
major scale to create a very strong dynamic tension.
MINOR-MODE 7TH
construction formula: 1,-3,5,-7
popular-style notation: m7
pitch interval pattern: <343>
This is the second-ranking chord form in the dynamic hierarchy of four
essential chord forms.
For example, the minor-mode 7th chord based upon the root-tone D
contains
the four tones DFAC, and is constructed from the first, lowered third,
fifth, and lowered seventh degrees of the diatonic D-major scale. (If
you
haven't yet referred to Part (4) to refresh your memory about the use of
a
MAJOR scale to construct this MINOR-mode chord, you may wish to do so
now,
before continuing).
In the dominant-tonic progression DFAC-->DFGB (Dm7-->G7), the dominant
root-tone D persists (as is always the case), the lowered third degree F
persists, the fifth degree A is dynamically neutral, and the lowered
seventh degree C, in accordance with its tendency, moves downward by one
semi-tone.
Note that there are only THREE tones of the G7 chord which are
dynamically
directed by the dynamic tension in the Dm7 chord. These are tones D and
F,
due to persistence, and tone B, due to the downward tendency in tone C.
The
root-tone G in the tonic chord GBDF is _added without dynamic
direction_,
to produce the complete chord, which is recognized as the [dominant 7th]
chord built upon the root-tone G.
This, then, is an example of a "partial definition" of the tonic chord
by
the dynamic tension in the dominant chord. The [dominant 7th] chord is
the
only chord of the set of four essential chords which is capable of
perfectly defining the tonic chord of resolution. The minor-mode 7th,
with
only a single tendency tone, is a dynamically "weaker" chord than is the
[dominant 7th].
In the progression DFAC-->DFGB, the melodic semi-tone interval (C-B) is
found in the tonic G-scale, between the fourth and third degrees. The
tendency in tone C is strong, but since it is not combined with any
other
tendency, the dynamic tension in the minor-mode 7th chord is relatively
moderate, compared with the dynamic tension in the [dominant 7th] chord.
MAJOR TRIAD
construction formula: 1,3,5
popular-style notation: (none)
pitch interval pattern: <43>
This is the third-ranking chord form in the dynamic hierarchy of four
essential chord forms.
For example, the major triad based upon the root-tone G contains the
three
tones GBD, and is constructed from the first, third, and fifth degrees
of
the diatonic G-major scale.
In the dominant-tonic progression GBD-->GCE (G-->C), the dominant
root-tone
G persists, the fifth degree D is dynamically neutral and is discarded
during the progression, and the third degree B, in accordance with its
tendency, moves upward by one semi-tone to tone C.
Therefore, there are only TWO tones of the C-major triad of resolution
which are dynamically defined. These are tones G and C. Once again,
there
is only a partial dynamic definition of the tonic chord. Since the third
degree of the tonic chord _is not dynamically defined_, it may be filled
in
as either tone E or tone Eb, to provide a complete chord of resolution.
In the progression GBD-->GCE, the melodic semi-tone interval (B-C) is
found
the tonic C-scale, between the seventh and first degrees. The upward
tendency in tone B is moderate. However, since there is no other
tendency
tone, the dynamic tension in the major triad is relatively weak,
compared
with the dynamic tension in the [dominant 7th] chord.
MINOR TRIAD
construction formula: 1,-3,5
popular-style notation: m
pitch interval pattern: <34>
This is the bottom-ranking chord form in the dynamic hierarchy of four
essential chord forms.
For example, the minor triad based upon the root-tone G contains the
three
tones GBbD, and is constructed from the first, lowered third, and fifth
degrees of the diatonic G-major scale. (Have you reviewed Part (4) yet?)
In the dominant-tonic progression GBbD-->GCE (Gm-->C), there is no semi-
tone melodic motion. _No tone of the chord GBbD has any tendency_.
Therefore, the minor triad Gm has no dynamic tension and it does not use
either of the two semi-tone intervals of the tonic diatonic major scale.
The most difficult concept to grasp, in connection with the minor triad,
is
that, while the root upon which it is built has a theoretical dynamic
attraction toward the adjacent root nearer the RCS, this theoretical
attraction is not reflected in the practical implementation, when the
chord
form is a minor triad.
Thus it is that a minor triad at {2} (Ancient V), only one harmonic step
distant from the RCS, cannot have any dynamic tension, even though the
identity of the RCS is very strong. Composers in the common-practice
period
felt that it was very important for a chord built upon the root {2}
(Ancient V) to possess a dynamic tension (and preferably the strong
tension
associated with a [dominant 7th] chord) when used at the end of a
phrase.
Therefore, they studiously avoided the use of a minor triad at this
structural location. This avoidance is reflected in the "key" blueprint
(for both major and minor keys), which shows a _major triad_ at this
location (refer to Table 3.5).
========================================================================
SUMMARY
The dynamic tension (usually implied, rather than aurally-perceptible)
in a
chord built upon any root (except {1}) exists in four different degrees,
from zero to some maximum amount, depending upon the particular _chord
form_ employed.
There are four chord forms which comprise the essential basis of the
harmonic process. They are (in decreasing order of dynamic tension):
(1) major-mode 7th (Ancient [dominant 7th])
(2) minor-mode 7th (Ancient minor 7th)
(3) major triad
(4) minor triad
The melodic progression of a "tendency" tone in chord forms (1), (2),
and
(3) is to a tone in the chord of resolution that is one semi-tone
distant
from the tone possessing the tendency. This semi-tone interval can be
found
in the diatonic major scale of the chord of resolution (the "tonic"
diatonic major scale).
Hence the dynamic tension in any of these four chord forms (other than
the
minor triad) can be attributed to one or both semi-tone intervals of the
tonic diatonic major scale.
Albert Silverman
Joey Goldstein
THE PAIR-BOND
by Albert Silverman
July 9, 1998
------------------------------------------
INTRODUCTION
In Part (2), I discussed the nature of the harmonic root, and
illustrated
the concept of root progression in a dynamic harmonic organization,
partially analogous to our solar system. In this partial analogy, there
is
a dynamic attraction from any root, directed toward the adjacent root
nearer the root of central significance. I refer to this attraction
between
adjacent roots as a "pair-bond."
The purpose of this article is to show how this abstract theoretical
attraction between adjacent roots is implemented in practice; i.e., as a
progression from a chord built upon one of these roots to a chord built
upon the other root.
THE ANCIENT DOMINANT-TONIC RELATIONSHIP
Such a progression between two chords built upon adjacent roots will be
illustrated with a "classic" example of the attraction between roots V
and
I. The two chords in this example are (arrived at by using the Ancient
tertiary construction process along with Ancient labels) the 4-tone
chord
built upon root V and the 3-tone chord built upon root I. Referring to
Table 3.2 (which shows the key of C-major), these two chords are C(V:4)
containing tones GBDF and C(I:3) containing tones CEG. Using ordinal
numerals to identify the roots, this is the root progression {2}-->{1}.
_In theory_, this dynamic attraction between two roots in a pair-bond
relationship will result in what is commonly called a "root progression"
which, in the current example refers to the progression from a chord
built
upon root V to a chord built upon root I.
Assuming that the chord GBDF is heard in the context of an established
root
of central significance retained in the memory, this chord, which is
_located only one step away from the RCS_, will possess an aurally-
perceptible "dynamic tension" that seeks a resolution in the chord GCE
(this chord is shown inverted, in order to maintain continuity in three
voices).
In order to disclose the source of this mysterious dynamic tension, it
is
necessary to examine the progressions of the component tones in the
chord
progression GBDF-->GCE. It can be seen that tone B moves upward by one
semi-tone to tone C, tone F moves downward by one semi-tone to tone E,
tone
G remains at the same pitch level, and tone D is discarded from the
chord
of resolution. This tone progression (or stagnation, in the case of tone
G)
is due to both "tendency" and "persistence" in the component tones of
the
chord GBDF.
Although these dynamic effects are aurally detectable, this still tells
us
nothing about their source. But playing Sherlock Holmes, we make an
important discovery! A clue to this mystery lies in the _two semi-tone
progressions_, (B-->C) and (F-->E). Note that the diatonic C-major
scale,
which is used in the Ancient tertiary construction process in this
example,
also contains the two semi-tone intervals (B-C) and (E-F). Thus there
appears to be a connection between the semi-tone PROGRESSIONS (B-->C)
and
(F-->E) and the same INTERVALS (B-C) and (E-F) in the diatonic C-major
scale.
And indeed there is. As it turns out, these two semi-tone intervals,
while
not CAUSING the dynamic tension in the chord GBDF, are nevertheless
"responsible" for it. Were these two semi-tone intervals not to be in
these
precise locations in the scale (between the third and fourth scale
degrees
and between the seventh and first scale degrees), there would be no
dynamic
impetus for this chord progression. Since such dynamic chord
relationships
are the very ESSENCE of "harmony" (even though most folks seem to be
oblivious to this fact!!), there would no harmony as we know it.
Is there dynamic tension in OTHER chord forms?
Most of you recognize the chord GBDF used in this example as a "dominant
7th," which is the common "label" for a chord having the pitch interval
pattern G<433>. In the future discussion, I will use the notation
[dominant
7th] to refer to this label. Those relative few of you who understand
the
Ancient concept of "key" (shown in Table 3.2) know that, using the
Ancient
tertiary construction, this is a 4-tone chord that is built upon the
fifth
degree of a diatonic C-scale; i.e., it is the dominant 7th in the key of C.
In general, a root serves as a base for chord construction; i.e., it has
a
root-tone which is used as the constructional reference. There are a
great
many different chord forms which may be constructed upon a given
root-tone.
In the present example, the chord GBDF, constructed upon root-tone G of
root V, possesses a dynamic tension which urges progression to a chord
constructed upon root-tone C of root I.
The purpose of this example is to illustrate the nature of dynamic
tension,
reflected in tendencies and persistencies in component chord tones. Only
one of the four _essential chord forms_ is illustrated here: the
[dominant
7th], which is built upon a specific root (V). This leads to two
interrelated questions:
(1) Are there OTHER chord forms which possess dynamic tension, and if so,
what are they?
(2) Is it *NECESSARY* to provide a restrictive link between chord form and
structural location, in the Ancient key model blueprint?
The short answer to (1) is that there are just TWO other chord forms in
this essential set which possess dynamic tension. These are the major
triad
and what I call the "minor-mode 7th" chord (our Ancient Theorist calls
it a
"minor 7th"). The remaining chord form, the minor triad, does not
possess
any dynamic tension. The long answer to (1) will be given in Part (6) of
this series.
The answer to question (2) is a resounding NO. However, the discussion
of
this very important issue is beyond the scope of this article, which is
devoted to the pair-bond.
What is the source of dynamic tension?
--------------------------------------
The two semi-tone intervals of the diatonic major scale are
"responsible"
for dynamic tension in a chord, in that they make it possible for such
tension to exist. However, they are not the source of this tension.
But one thing is certain; if you want the answer to this question, don't
ask our Ancient Theorist, since he doesn't know! But not knowing the
answer
has never yet stopped him from offering an ingenious (if wrong)
"explanation" for a mysterious phenomenon. Despite the fact that (as I
pointed out in Part (1)) _chord RELATIONSHIPS are separate and distinct
from acoustics_, he has nevertheless waved his magic wand and come up
with
an acoustically-based "answer" to this very important question.
Are you ready? Here it is, folks! His ingenious explanation for the
dynamic
tension in the chord GBDF in this example is that this "unstable" chord
quality (i.e., dynamic tension) is due to the presence of one or more
"dissonant intervals" contained within the chord. In the current
example,
as his Ancient script goes, the interval (B-F) is the
devilishly-dissonant
interval of the "tritone" (shudder!). This Ancient Debbil just shouts at
you and pounds on your eardrums to get away from its unpleasant
"dissonance" into a more "comfortable" interval, which our Ancient
Theorist
refers to as a "consonant" interval.
Thus the dissonant tritone interval (B-F) in the chord GBDF contracts to
the consonant interval (C-E), after which the chord CEG is soothing and
restful and you just don't have an urge to go anywhere else. Voila! This
is
"harmonic motion" (chord progression) from a dissonant interval to a
consonant interval. THAT explains it. Yes indeed, AT.
Hold it a second, AT. There is just one little problem here. This
dissonance/consonance malarkey DOESN'T explain it. In point of FACT,
tones
B and F in the chord GBDF progress, in contrary semi-tone motion, in
accordance with their tendencies, and this *MELODIC PROGRESSION* in
context
has nothing whatsoever to do with the
INTERVALS CONTAINED WITHIN THE CHORD GBDF.
Sorry about that, AT. And oh yes, one other little thing.
----------
In a dissonant nutshell:
If you folks out there believe that this Ancient dissonant-interval
nonsense is in any way pertinent to chord relationships, you will
NEVER, EVER be able to understand "harmony." Guaranteed.
----------
But we have yet to answer the question: "WHY do tones B and F possess
these
tendencies?" The answer is that these tendencies arise from the
listener's
_expectation that progression from the chord GBDF will take place in a
certain manner_; namely, to the chord GCE. This expectation comes from
continued and intensive listening to chord-based composition, which
reached
its peak of development during the common-practice period. It is
peculiar
to Western music, whose "harmony" in the common-practice period is based
upon the diatonic major scale, with its characteristic semi-tone
interval
configuration.
Most of you are aware that the chord GBDF is referred to as the
"dominant
7th" in the key of C. It is a "7th" chord because, in an "uninverted"
form,
the interval between the tones of lowest and highest pitch is that of
seven
scale degrees, and it is a dominant chord because it is constructed upon
the fifth scale degree. You also know that the chord CEG is referred to
as
the "tonic triad," because it contains three tones and is constructed
upon
the first scale degree. Therefore, our Ancient Theorist refers to this
specific progression, V-->I, as a "dominant-tonic" progression.
The point of exceptional importance is that _the root-tones of V
and I
are separated by an interval of a perfect fifth (seven semi-tones)_.
This root-tone relationship between the participating chords is the
defining characteristic of the pair-bond.
The current example uses a specific chord progression (from a chord
built
upon root V to a chord built upon root I) to illustrate the nature of
the
dynamic pair-bond relationship. In point of fact, as shown in lines (1)
and
(2) of Table 1.1 (which is repeated below for convenience), _there is a
pair-bond relationship between every root and the two adjacent roots (on
either side) in the harmonic organization_. There are two exceptions
here;
root {1}, which has only a pair-bond relationship with root {2}, and
root
{12}, which has only a pair-bond relationship with root {11}.
========================================================================
(1) {1} {2} {3} {4} {5} {6} {7} {8} {9} (10} {11} {12}
(2) I V II VI III VII IV# I# V# II# VI# IV
(2a) or Vb IIb VIb IIIb VIIb
(3) C G D A E B F# C# G# D# A# F
(3a) or Gb Db Ab Eb Bb
TABLE 1.1 THE HARMONIC SCALE
========================================================================
A useful way to view the harmonic organization shown in line (3) is as a
chain of building blocks, where a "building block" is two roots in a pair-
bond relationship. With the exception of roots {1} and {12}, every root
exists as a common root in two adjacent pair-bonds. However, this common
root functions differently in the two adjacent pair-bonds. By
"functioning
differently," it is meant that, in one pair-bond, the common root will
be
the root FROM which progression takes place, while in the other
pair-bond,
this root will be the root TO which progression takes place.
For example, root {3} exists in a pair-bond relationship with both roots
{2} and {4}. In the pair-bond with root {4}, root {3} is the root TO
which
progression takes place. But in the pair-bond with root {2}, root {3} is
the root FROM which progression takes place.
It is necessary to distinguish between these two different pair-bond
functions; i.e., progression TO and progression FROM a chord built upon
one
of the two roots. Borrowing from Ancient terminology, I will refer to
the
root FROM which progression takes place as the "dominant" root, and the
root TO which progression takes place as the "tonic" root.
DEFINITION:
A chord progression within ANY of the eleven pair-bonds in the
harmonic structure is referred to as a "dominant-tonic" progression.
For example, as illustrated in line (2), progression from root II to
root V
is a dominant-tonic progression, progression from root VI to root II is
a
dominant-tonic progression, progression from root IV# (or Vb) to root
VII
is a dominant-tonic progression, progression from root VIb to root IIIb
is
a dominant-tonic progression, etc.
The pair-bond relationship is clearly revealed by identifying the roots
by
ordinal numerals, rather than by Ancient labels. In this method of root
identification, any two roots whose identifiers differ by one are in a
pair-bond relationship. For example, roots {3} and {4} exist in a
pair-bond
relationship, roots {8} and {9} exist in a pair-bond relationship, roots
{11} and {12} exist in a pair-bond relationship, etc.
Note, however, that roots {12} and {1} do NOT exist in a pair-bond
relationship, in contrast with roots {11} and {12}. Although the
root-tones
of adjacent roots correspond with adjacent locations along the circle of
fifths, and the generation of the sequence of root-tones repeats after
root
{12} is reached, there is a "dynamic break" between roots {12} and {1}.
In
other words, _the "circle" of fifths is, in reality, a harmonic fiction,
since it is not dynamically "closed"_.
Gradus Ad Deconfuse-us (steps to deconfusion)
---------------------------------------------
As I explained in Part (3) of this series, the purpose of the Ancient
"key"
model is to provide a link between chord form and seven structural
locations. That is, this link specifies which chord forms can be used at
a
specific location within the diatonic subset of harmonic elements.
In a purported "explanation" of the compositional STYLE (which HE and
his
pupils erroneously refer to as "theory") in the common-practice period,
our
Ancient Theorist claims that chord form and structural location are
linked
in the manner shown in Table 3.2. Yet, a casual observation of all but
the
simplest pieces reveals that this beloved and universally-hyped Ancient
link does not generally conform with compositional practice in ANY time
period.
The correlation between this key model and compositional practice in
that
period became poorer and poorer through the period as composers, with ever-
increasing frequency, used chords built upon the more remote roots in
the
harmonic structure. Therefore, how can it "explain" anything?
Apart from the special exception of root IV (the most remote root in the
structure), these "more remote roots" are roots in the chromatic subset,
the locations of which are not even included in his key model! Hence
chords
built upon these chromatic roots contain tones which are not found
within
the diatonic scale that is the basis for the Ancient tertiary chord
construction. In other words, _the use of chords built upon so-called
"chromatic" roots_ is one reason for the existence of "accidentals";
i.e.,
tones which are foreign to the key signature.
Despite the dismal failure of the key model to explain chord usage in
the
common-practice period, composers generally observed the restrictions as
they relate to the chord forms built upon the very important tonal
functions (I, IV, and V). For example (refer to Table 3.5), in the key
of
C-major, it can be reasonably expected that 3-tone chords built upon
roots
I, IV, and V ({1}, {12}, and {2}) will be major triads, and that a
4-tone
chord built upon root V will be a [dominant 7th]. Or that, in the key of C-
minor, 3-tone chords built upon roots I and IV will be minor triads, and
a
3-tone chord built upon root V will be a major triad.
Our Ancient Theorist is well aware that his key model correlates very
poorly with all but the very simplest musical composition in the common-
practice period. But did this glaring defect force him to abandon it, in
favor of a credible explanation?
IT DID NOT.
What he did instead, in response to this embarrassing dilemma, was to
wave
his little magic wand and create a "designer" terminology _which
effectively negates_ his key model, but which allows him to have his
cake
and eat it too; i.e., he can go about his "explaining" business without
having to admit his chicanery.
Let's see how this scheme works. His designer terminology retains the
words
dominant and tonic, which SUPPOSEDLY refer to two specific degrees of
the
diatonic scale upon which his key model is based. However, in designer
terminology, the meaning of these two words is expanded to include
something different than their meaning in his key model.
In his key model, a "dominant" chord is one that is constructed upon the
fifth scale degree, and *ONLY* upon the fifth degree. But in designer
terminology, the term "dominant" (perhaps with the prefix "secondary" or
"temporary") refers to the chord within a pair-bond FROM which
progression
takes place. That is, a "revised-meaning" dominant chord may refer to a
chord built upon root other than {1}.
Similarly, a "tonic" chord is one that is constructed upon the first
scale
degree, and *ONLY* upon the first degree. But in designer terminology,
the
term "tonic" (perhaps with the prefix "secondary" or "temporary") refers
to
the chord within a pair-bond TO which progression takes place.
Completing
the confusing Ancient cover-up, "THE tonic" means the same thing in
designer terminology as it does in pre-designer terminology: the root of
central significance.
SUMMARY
With the exception of the RCS, there is a "dynamic attraction" from ANY
root in the harmonic structure, which is directed toward the adjacent
root
nearer the RCS. Since the root-tones of any two adjacent roots differ by
a
perfect fifth, this dynamic attraction is between two roots in a
5th-degree
relationship.
I refer to this attraction between two adjacent roots in the harmonic
structure as a "pair-bond." It is due to the influence of the root of
central significance, which is analogous to the sun in our solar system.
The strength of this attraction varies in an inverse function of the
root
from the RCS.
In theory, this attraction will result in a "root progression," which is
a
progression from a chord built upon the root possessing the attraction
to a
chord built upon the adjacent root nearer the RCS. However, for reasons
discussed in Part (2), this attraction usually remains implied; i.e., it
is
seldom strong enough to be aurally perceptible.
Within a pair-bond, the chord FROM which progression takes place is
referred to as a "dominant" chord, and the chord TO which progression
takes
place is referred to as a "tonic" chord, without regard to the
structural
location of the tonic root. Hence a chord progression within ANY of the
eleven pair-bonds in the harmonic structure is referred to as a "dominant-
tonic" progression.
The dynamic tension in a chord built upon any remote root can be traced
to
a tone which has a "tendency" (an aural urge) to move by _one
semi-tone_,
during the chord progression. Note that
THE INTERVAL FORMED BY THE SEMI-TONE MOTION IN THE RESULTING
PROGRESSION IS ONE OF THE SEMI-TONE INTERVALS IN THE TONIC DIATONIC
MAJOR SCALE.
Hence the two semi-tone intervals in the tonic diatonic scale can be
said
to be "responsible" for the dynamic tension in the dominant chord,
insofar
as this tension cannot exist without them. The real source of this
tension,
however, is the listener's expectation that progression will take place
in
a certain manner. And this expectation gets implemented in a form which
depends upon the semi-tone intervals of the diatonic scale.
In the ultimate analysis, there would be no dynamic tension without the
specific placement of the two semi-tone intervals in the tonic diatonic
scale, between the third and fourth and between the seventh and first
scale
degrees. Without such dynamic tension, there would be no pair-bond and
hence no "harmony," as it is known in the Western world.
CONCLUSION
What's wrong with a little innocent Ancient sleight-of-hand, in which
the
key model has been sneakily negated, while still keeping it around for
purposes of inestimably confusing the nomenclature/notation, among a
host
of other obfuscations? A far better question is: "What excuse is there
for
continuing to teach the key model as an _explanation of musical
composition
in the common-practice period_, which it does not 'explain' at all but
instead erects a severe barrier to comprehension?"
The blunt answer is: "There *IS* no excuse, if the purpose is to teach
an
UNDERSTANDING of the principles (theory) of chord-based composition.
However, the stated goal of Musical Academia is NOT to teach
understanding,
but rather to preserve musical Ancient Art/History into eternity. This
is
neatly (and again, sneakily) accomplished by disguising musical Ancient
Art/History as "theory."
No one can doubt that this Academic Ploy has succeeded fabulously. The
result is a comprehensional catastrophe, with theoretical illiterates
continuing to be cranked out of our higher musical institutions of
"learning."
And THIS is supposed to be "education"?
----------------
Albert Silverman
Joey Goldstein
ANCIENT CHORD CONSTRUCTION
by Albert Silverman
July 6, 1998
------------------------------------------
INTRODUCTION
There are (at least) two chord construction procedures, which bear
little
resemblance to each other. In this article, I will discuss what is
commonly
referred to as "tertiary" chord construction. In Part (4), I will
discuss a
different type of construction procedure for creating the _same set of
practically-useful chord forms_. Because the chord forms which are
created
using these two different construction procedures are identical, this
process might well be referred to as "Modern tertiary chord
construction."
Unfortunately, however, the word "tertiary" is linked (by Musical
Academia)
with "Ancient," which presents a nomenclatural dilemma.
ANCIENT TERTIARY CHORD CONSTRUCTION
Ancient tertiary chord construction is what I refer to as a "shotgun"
process. That is, shoot enough pellets and you are bound to hit
something.
However, we'll go along and humor our gun-shy Ancient Theorist, who
chooses
to refer to it as "tertiary" chord construction. For convenient
reference,
Table 1.1 is repeated below:
========================================================================
(1) {1} {2} {3} {4} {5} {6} {7} {8} {9} (10} {11} {12}
(2) I V II VI III VII IV# I# V# II# VI# IV
(2a) or Vb IIb VIb IIIb VIIb
(3) C G D A E B F# C# G# D# A# F
(3a) or Gb Db Ab Eb Bb
TABLE 1.1 THE HARMONIC SCALE
========================================================================
In this well-known construction process (which is discussed to one
degree
or another in countless books on "harmony"), tones are stacked up at
intervals of three scale degrees, _on the seven root-tones of the
Ancient
diatonic subset_. These are the roots which are labeled as I, II, III,
IV,
V, VI, and VII in line (2) of Table 1.1.
Gradus Ad Deconfuse-us (steps to deconfusion)
---------------------------------------------
As I have previously pointed out, the labels that are used in line (2)
correspond with the degrees of an IRRELEVANT diatonic scale. That is,
insofar as the harmonic process (ROOT PROGRESSION) is concerned, we
might
just as well label roots {1}, {2}, and {3} as a peanut, pecan, and
walnut,
etc. This would be less nutty than the labeling scheme used by our
Ancient
Theorist! All that we need to do to use this scale for the analysis of
root
progression is to associate root {1} with some particular tone; that is,
it is *NOT* necessary (our Ancient Theorist to the contrary
notwithstanding) that this tone be associated with the first
degree of a diatonic scale. We can (indeed, SHOULD) do this
by using departure-and-return, in conjunction with the musical
phrasing.
On the other hand, a diatonic scale IS the foundation of the Ancient
tertiary construction process, which is used to link particular chord
forms
with structural locations; i.e., to provide a _stylistic blueprint for
composition_. In other words, the use of a diatonic scale is ESSENTIAL
in
creating this stylistic link between chord form and structural location.
It
is NOT ESSENTIAL in the identification of roots in Table 1.1.
----------
A challenge to non-readers:
Now then, does anyone out there wish to claim that I have said that
"The diatonic scale is irrelevant"? If you do, then be sure to include
a direct quote from my writing in your post!
----------
After this link is created, it can be used as a stylistic "key"
blueprint,
if so desired, _WITHOUT REFERENCE TO ANY DIATONIC SCALE_. For example,
in
the key of C-major, the 3-tone chord built upon the third scale degree
is a
minor triad. Referring to Table 1.1, we see that Ancient III is root
{5}.
Continuing in this manner, we generate Table 3.5, which presents such
blueprints for 3-tone and 4-tone chords in the keys of C-major and
C-minor.
You may wish to pass over Table 3.5 at the present time but study it
later
in the discussion. It is not essential at this point, although it
provides
clarification of the above *VERY* important concept.
-----
The Ancient tertiary construction process uses the diatonic scale to
which
the labels refer. There are two such diatonic scales, which are referred
to
as the "major" and "harmonic minor" scales. They are shown below in
Table 3.1:
========================================================================
scale degree I II III IV V VI VII
major C D E F G A B
harmonic minor C D Eb F G Ab B
Table 3.1 MAJOR AND HARMONIC MINOR SCALES BASED UPON TONE C
========================================================================
On any given root-tone, it is possible to construct a maximum of FIVE
tone
combinations (beginning with the minimum permissible combination of
three
tones), before the tones repeat themselves in the third octave. Thus the
set of five tone combinations constructed upon any root-tone consists of
combinations which contain 3, 4, 5, 6, and 7 tones.
For example, the five possible tone combinations constructed in this
manner
upon the first degree (tone C) of the diatonic C-major scale are as
follows:
three tones: CEG
four tones : CEGB
five tones : CEGBD
six tones : CEGBDF
seven tones: CEGBDFA
Similarly, the five possible tone combinations constructed in this
manner
upon the first degree (tone C) of the diatonic harmonic C-minor scale
are
as follows:
three tones: CEbG
four tones : CEbGB
five tones : CEbGBD
six tones : CEbGBDF
seven tones: CEbGBDFAb
Using the same tertiary construction process to construct tone
combinations
upon all of the seven tones of the diatonic C-major and C-minor scales
creates two different two-dimensional arrays, which are shown below in
Tables 3.2(a) and 3.2(b), respectively.
------------------------------------------------------------------------
I II III IV V VI VII
C D E F G A B
3) CEG DFA EGB FAC GBD ACE BDF
4) CEGB DFAC EGBD FACE GBDF ACEG BDFA
5) CEGBD DFACE EGBDF FACEG GBDFA ACEGB BDFAC
6) CEGBDF DFACEG EGBDFA FACEGB GBDFAC ACEGBD BDFACE
7) CEGBDFA DFACEGB EGBDFAC FACEGBD GBDFACE ACEGBDF BDFACEG
(a) C-Major
I II III IV V VI VII
C D Eb F G Ab B
3) CEbG DFAb EbGB FAbC GBD AbCEb BDF
4) CEbGB DFAbC EbGBD FAbCEb GBDF AbCEbG BDFAb
5) CEbGBD DFAbCEb EbGBDF FAbCEbG GBDFAb AbCEbGB BDFAbC
6) CEbGBDF DFAbCEbG EbGBDFAb FAbCEbGB GBDFAbC AbCEbGBD BDFAbCEb
7) CEbGBDFAb DFAbCEbGB EbGBDFAbC FAbCEbGBD GBDFAbCEb AbCEbGBDF BDFAbCEbG
(b) C-Minor
Table 3.2 THE KEYS OF C-MAJOR AND C-MINOR
------------------------------------------------------------------------
In case you are not aware of it, our Ancient Theorist refers to this 5x7
array (35 elements) as a "key."
Referencing elements in the array
---------------------------------
The simplest way in which to reference an element in the array is by its
coordinates (root and number of tones). The vertical coordinate denotes
the
number of tones in the combination and the horizontal coordinate denotes
the root upon which the combination is constructed.
Since the root identifies a scale degree but not the associated tone,
the
coordinates alone are insufficient to identify particular tones. For
example, the coordinates II:4 tell us only that it is a 4-tone
combination
constructed upon the second degree of some diatonic scale. If we want to
know the identity of the tones in this tone combination, we need to know
the type of scale, along with the reference root-tone (the first scale
degree).
The referencing system which I will use in this discussion (it should be
noted that it is NOT the system that is used by our Ancient Theorist for
identifying tone combinations; his system additionally identifies the
manner in which the tones are dispersed along the musical staff) is as
follows. A set of coordinates enclosed in parentheses denotes an element
in
a major scale array, while a set of coordinates enclosed in square
brackets
denotes an element in a minor scale array. The number of tones in the
combination is indicated by a colon which follows the Roman Numeral. If
it
is needed, I will indicate the first degree of the scale, preceding the
parentheses or brackets.
For example, the notation C(IV:5) refers to the tone combination FACEG,
which is the 5-tone combination constructed upon the fourth degree of
the
diatonic C-major scale. As another example, the notation C[II:4] refers
to
the tone combination DFAbC, which is the 4-tone combination constructed
upon the second degree of the diatonic (harmonic) C-minor scale.
Tone combination versus "chord"
-------------------------------
Webster's dictionary defines a chord as "A combination of tones which
blend harmoniously when sounded together."
What constitutes "harmonious" is subjective, varying with individual
perception, the dispersal of the various tones along the musical staff,
and
the time period in which the assessment is made. However, there is
general
agreement that virtually ALL of the 3-tone combinations qualify as
"chords"
in accordance with this definition, without respect to the dispersal of
the
tones along the musical staff, and independent of the time period.
Similarly all 4-tone combinations in both arrays, with the possible
exception of [III:4], qualify as "chords," subject to certain
restrictions
upon the manner in which the tones are dispersed along the musical
staff.
On the other hand, none of the 6-tone and 7-tone combinations qualifies
as
a chord, within Webster's definition, while the "harmonious" status of
the
5-tone combinations is open to debate.
What good is this information? Not much, except that if we want to
listen
to "pleasant-sounding" music, we can probably do it by restricting the
music to the use of 3-tone and 4-tone combinations from the two
35-element
arrays, paying particular attention to the tone dispersal of any 4-tone
combinations that we might wish to use.
Chord form versus structural location
-------------------------------------
If we compare the 3-tone chords in Table 3.2(a), we see that (I:3),
(IV:3),
and (V:3) have the same PITCH interval pattern, in addition to having
the
same scale interval pattern. Assuming that the three tones are dispersed
along the musical staff in the same order as they appear in the array,
the
pitch interval between the tone of lowest pitch (the constructional root-
tone) and the middle tone of the chord is four semi-tones, where a semi-
tone is the interval between any two adjacent tones in the twelve-tone
chromatic scale. However, the pitch interval between the middle tone and
the tone of highest pitch is only three semi-tones.
Hence, the pitch interval pattern of this chord is <43>, where the <>
brackets denote a pitch interval pattern and the numbers denote
successive
pitch intervals (expressed in semi-tones) between adjacent tones in the
chord. For example, in the chord (I:3), containing tones CEG, the pitch
interval between tones C and E is four semi-tones, and the pitch
interval
between tones E and G is three semi-tones.
As most of you are aware, a chord having the pitch interval pattern <43>
(assuming that the tones are arranged in the same manner as they appear
in
the tertiary array) is commonly referred to as a "major triad." Thus
there
are three major triads in this major-scale array, which are located at
I, IV, and V in the harmonic structure. If you are unclear on the
meaning
of the word "located," refer to Part (1), where this is explained. _Do
not
continue until you understand this vital concept_. Similarly, referring
to
Table 3.2(b), there are just two major triads in this minor-scale array,
and they are located at V and VI.
The array elements (II:3), (III:3), and (VI:3) are triads which have the
pitch interval pattern <34>. As most of you know, this pitch interval
pattern is commonly referred to as a "minor triad." Similarly, referring
to
Table 3.2(b), the array elements [I:3] and [IV:3] are also minor triads.
The array elements (VII:3), [II:3], and [VII:3] are triads which have
the
pitch interval pattern <33>. As you may know (although the percentage in
favor of this is not that high), this pitch interval pattern is commonly
referred to as a "diminished triad."
And finally, the array element [III:3] is a triad having the pitch
interval
pattern <44>. As you may know (although the percentage in favor of this
is
probably even lower than for the diminished triad), this pitch interval
pattern is commonly referred to as an "augmented triad."
Summarizing these results to include the triads within both key arrays:
-----------------------------------------------------------------------
<43> Major Triads at I and IV and V in a major key
V and VI in a minor key
<34> Minor Triads at II and III and VI in a major key
I and IV in a minor key
<33> Diminished Triads at VII in a major key
II and VII in a minor key
<44> Augmented Triad at III in a minor key
Table 3.3 THE LINK BETWEEN 3-TONE CHORDS AND STRUCTURAL LOCATION
=======================================================================
The same type of analysis for all of the 4-tone chords (they are not
"named" here, since this is not required for purposes of the current
discussion) in both key arrays is presented below in Table 3.4. It shows
that there are seven different pitch interval patterns (versus four with
3-tone chords). They are located as follows:
-----------------------------------------------------------------------
<434> at I and IV in a major key
VI in a minor key
<343> at II and III and VI in a major key
IV in a minor key
<433> at V in a major key
V in a minor key
<334> at VII in a major key
II in a minor key
<344> at I in a minor key
<443> at III in a minor key
<333> at VII in a minor key
Table 3.4 THE LINK BETWEEN 4-TONE CHORDS AND STRUCTURAL LOCATION
-----------------------------------------------------------------------
The information presented above in Table 3.3 and 3.4 may be displayed in
a
much more useful form by replacing the Ancient labels in Table 1.1 with
ordinal numerals to identify the roots and using my "popular-style"
chord
notation (discussed in Part (4)) to denote the _chord form_ at each
structural location.
-----------------------------------------------------------------------
(1) {1} {2} {3} {4} {5} {6} {12}
(2) C G Dm Am Em Bm- F
(3) C:7 G7 Dm7 Am7 Em7 Bm7- F:7
(a) C-Major
(1) {1} {2} {3} {6} {9} {10} {12}
(2) Cm G Dm- Bm- Ab Eb+ Fm
(3) Cm:7 G7 Dm7- Bm6- Ab:7 Eb:7- Fm7
(b) C-Minor
Table 3.5 THE KEYS OF C-MAJOR AND C-MINOR
------------------------------------------------------------------------
Line (1) shows the root
Line (2) shows the 3-tone chord built upon the root in Line (1).
Line (3) shows the 4-tone chord built upon the root in Line (1).
-----
Notes about chord notation:
Briefly, a + sign at the end of a chord symbol denotes a raised fifth
degree, a - sign a the end of a chord symbol denotes a lowered fifth
degree, a 7 denotes a lowered 7th degree, a :7 denotes a natural 7th
degree, and an m denotes a pitch interval of three semi-tones between
the
root-tone and the tone next highest in pitch.
-----
For example, in the key of C-major, a 4-tone chord used at location {3}
is
Dm7, a minor-mode 7th chord (Ancient minor 7th) containing tones DFAC.
Or,
in the key of C-minor, a 3-tone chord used at location {12} is Fm, a
minor
triad containing tones FAbC, etc.
In case you have missed it, the point which I am making here is that the
"key" blueprint can be expressed as a link between chord form and
structural location, _without any reference to Ancient labels_. Seeing
is
believing; nary a Roman Numeral in sight!!!
SUMMARY
In the Ancient tertiary construction process, a tone combination is
constructed by stacking up tones upon a root-tone which corresponds with
a
degree of a diatonic major or (harmonic) minor scale. Using this
process,
it is possible to construct upon a given root-tone a maximum of five
combinations, containing 3, 4, 5, 6, and 7 tones.
Since there are only seven roots in the diatonic subset, this
construction
process creates two different 5x7 arrays (which our Ancient Theorist
refers
to as a "key"), corresponding with the two types of diatonic scales.
An element in an array is a tone combination. The pitch interval
patterns
of these various tone combinations (the harmonious ones being referred
to
as "chords") are not unique to a particular structural location. That
is,
some of these combinations have pitch interval patterns which are found
at
more than one location.
CONCLUSION
The Ancient tertiary construction process, represented by the two key
arrays of Table 3.3, accomplishes two _distinctly different_ purposes:
(1) It provides a variety of "harmoniously-blending" compositional
building blocks. Such a building block is commonly referred to
as a "chord." As a byproduct of the shotgun approach, it also
provides a whole potload of tone combinations which do not blend
together harmoniously.
(2) It provides a restrictive link between chord form and structural
location. Our Ancient Theorist refers to this particular type of
link as a "key."
The purpose of this article has been to address item (1); the creation
of
various chord forms, using this Ancient chord construction process. In
Part
(4), I will discuss a different method of chord construction, which does
not rely upon the creation of a restrictive (stylistic) link between
chord
form and structural location.
----------------
Albert Silverman
Joey Goldstein
THE ALTERED CHORD SET
by Albert Silverman
July 17, 1998
-------------------------------------
As I explained in Part (6) of this series, subtitled "The Essential
Chord
Set," the complete gamut of possible dynamic effects in a dominant-tonic
progression can be demonstrated with just _four basic chord forms_. They
are listed below in Table 7.1, in decreasing order of dynamic tension.
name construction popular-style
formula notation
---------------------------------------------------------
(1) major-mode 7th 1,3,5,-7 7
(2) minor-mode 7th 1,-3,5,-7 m7
(3) major triad 1,3,5 (none)
(4) minor triad 1,-3,5 m
Table 7.1 THE ESSENTIAL CHORD SET
The construction of chords in isolation is discussed in Part (4) RevA of
this series.
This article discusses chords having a "chromatic alteration" of the
fifth
degree. This is a raising or lowering of the fifth degree by one
semi-tone.
As I explained in Part (4) RevA, every chord is constructed from the
diatonic major scale based upon the constructional reference tone, with
chromatic alteration as may be required.
What does the word "required" mean, in the context of the Modern method
of
chord construction which I presented in Part (4) RevA? With regard to a
chord in the essential chord set, it means one of two things: (1) the
lowering of the third degree to create a chord in the minor mode, and/or
(2) the lowering of the seventh degree to create a 7th chord.
Apart from these essential-set "chromatic alterations" (by the way DO
NOT
ask our Ancient Theorist about the meaning of "chromatic alteration,"
since
he does not understand Modern chord construction), there is a third,
relatively infrequent type of chromatic alteration that is sometimes
applied to the FIFTH degree of certain chords. This third type of
chromatic
alteration is the subject of this article.
EVERY chord possesses a fifth degree. Unless it has been chromatically
altered, it will be the fifth degree in the diatonic scale of Modern
construction. For example, every C-chord in the essential chord set will
contain tone G, which is the natural (unaltered) fifth degree of the
diatonic C-major scale.
WHY ALTER THE FIFTH DEGREE?
In view of the fact that the essential chord set provides all of the
possible diatonic dynamic effects (i.e., those which can be traced to semi-
tone intervals in the tonic diatonic major scale), what is gained by the
chromatic alteration of the fifth degree?
The answer to this question is in two parts, one which involves sound
quality, the other which involves chord dynamics. First, there will
sometimes be a prominent (i.e., long-duration) melody tone which differs
by
only one semi-tone in pitch from the pitch of the unaltered fifth
degree.
These two tones sounded together will produce a harsh discord, which is
usually undesirable. For example, tone G# may be a prominent melody
tone.
If the accompanying chord is a C-chord of the essential set, it will
contain tone G, the unaltered fifth degree. Melody tone G# sounded along
with chord tone G will then produce a harsh discord.
The general solution to this (usually) unwanted discord is to
chromatically
alter the fifth degree of the accompanying chord in order to match the
clashing melody tone, thus preventing the harsh discord. In the above
example, chord tone G would be raised by one semi-tone to G#. Similarly,
if
the discordant melody tone is Gb, chord tone G would be lowered to Gb,
preventing the harsh discord.
A new set of eight "altered" chords can be created by raising and
lowering
the fifth degree of the four chord forms in the essential set. The word
"altered" as used here applies specifically to an alteration of the
FIFTH
degree. As it happens, three of these altered chord forms are of little
or
no practical utility as units of composition. Thus the practical set of
altered chords consists of only FIVE of these eight chords.
The chromatic alteration of the fifth degree does not ADD to the number
of
tones in the chord. Thus, a triad with an altered fifth degree still
contains three tones, and a 7th chord with an altered fifth degree still
contains four tones. An uninverted altered major-mode 7th chord,
however,
no longer contains a pitch interval patterns consisting of only three or
four semi-tones; hence this pitch interval pattern will not be found in
the
major or minor key arrays. For example, the C-major-mode 7th chord with
a
raised fifth degree contains tones CEG#Bb. Its pitch interval pattern is
<432>, which cannot be reached via the Ancient tertiary construction
process.
The pitch interval patterns of the remaining altered chords, however, do
conform with pitch interval patterns that are created in the Ancient
tertiary construction process. For example (refer to Table 3.2), the
chord
[III:3] is a major triad with a raised fifth degree, the chord [VII:3]
is a
minor triad with a lowered fifth degree, and the chord [II:4] is a minor-
mode 7th chord with a lowered fifth degree.
The practically-useful set of five altered chords (two with raised fifth
and three with lowered fifth) is shown below in Table 7.2:
name construction MY
formula popular-style
notation
------------------------------------------------------------------------
(1) major-mode 7th with raised fifth 1,3,+5,-7 7+
(2) major-mode 7th with lowered fifth 1,3,-5,-7 7-
(3) minor-mode 7th with lowered fifth 1,-3,-5,-7 m7-
(4) major triad with raised fifth 1,3,+5 +
(5) minor triad with lowered fifth 1,-3,-5 m-
Table 7.2 THE ALTERED CHORD SET
Note that, as I mentioned in Part (4) RevA, a + or - sign at the end of
MY
"popular-style" chord notation denotes a raised or lowered fifth degree,
respectively. This is a simpler notation scheme than that which is
regularly found in "popular" chord charts. These charts usually use
notations such as b5 or #5 or flat5 or sharp5, etc. to denote an altered
fifth degree.
As an example of the construction of an altered chord, consider the
construction of the chord Dm7-, which is a minor-mode 7th chord with a
lowered fifth degree. How does the name "half-diminished" grab you for
this
particular chord? You say that this is "art," which means that is
satisfactory to use "labels" as chord names, without any connection to
reality? I see.
As indicated in the construction formula, this chord contains the first
(tone D), the lowered third (tone F), the lowered fifth (tone Ab), and
the
lowered seventh (tone C) degrees of the diatonic D-major scale. That is,
Dm7- contains tones DFAbC. Believe it or not!
DYNAMIC PROPERTIES OF ALTERED CHORDS
The second part of the answer to the question "Why alter the fifth
degree
of a chord?" involves the dynamic properties of an altered chord. With a
single exception (the minor triad with a lowered fifth degree), a
chromatic
alteration of the fifth degree creates in this tone a tendency in the
direction of the alteration. In contrast, _the unaltered fifth degree is
always dynamically neutral_; i.e., it has neither tendency nor persistence.
For example, in the chord CEG#, which is a C-major triad with a raised
fifth degree G#, tone G# has an upward semi-tone tendency toward tone A.
Similarly, in the chord DFAbC, which is a D-minor-mode 7th with a
lowered
fifth degree Ab, tone Ab has a downward semi-tone tendency toward tone
G.
In contrast, in the unaltered chord CEG, tone G is dynamically neutral.
And
in the unaltered chord DFAC, tone A is dynamically neutral.
The additional tendency of an altered fifth degree often reinforces a
tendency of one of the other chord tones, thus increasing the dynamic
tension in the altered chord. In such a case, the altered fifth degree
seeks a resolution in a tone which is also sought by one of the other
tones
with a diatonic tendency.
In other cases, the tendency of the altered fifth degree will seek a
tone
which is not sought by the tendency of a tone in the unaltered chord. In
any case, however, an altered fifth degree cannot possess a tendency if
the
unaltered chord has no tendency tone; i.e., if the unaltered chord is a
minor triad.
The chromatic alteration process creates a _non-diatonic tendency tone_.
This is a tone whose tendency cannot be traced to a semi-tone interval
of
the tonic diatonic major scale. For example, in the dominant-tonic
progression GBD#-->GCE (G+-->C), tone B progresses to tone C, in
accordance
with the upward diatonic semi-tone tendency. That is, the interval (B-C)
is
a semi-tone interval of the diatonic C-major scale. In contrast, the semi-
tone progression D#-->E does NOT correspond with a semi-tone interval in
the diatonic C-major scale.
The dynamic properties of the set of five practically-useful altered
chords
are discussed below.
========================================================================
(1) Major-mode 7th with raised fifth
------------------------------------
The raised fifth degree possesses an upward tendency toward the third
degree of the tonic chord. This tendency reinforces the downward
tendency
of the lowered 7th degree toward the same tone.
For example, in the dominant-tonic progression GBD#F-->GCE (G7+ -->C),
tone
D#, the raised fifth degree, has an upward tendency toward tone E, the
third degree of the C-major triad. This tendency reinforces the downward
tendency of tone F, the lowered 7th degree, toward the same tone.
(2) Major-mode 7th with lowered fifth
-------------------------------------
The lowered fifth degree possesses a downward tendency toward the
root-tone
of the tonic chord. This tendency reinforces the upward tendency of the
third degree toward this same tone.
For example, in the dominant-tonic progression GBDbF-->GCE (G7- -->C),
tone
Db, the lowered fifth degree, has a downward tendency toward tone C, the
root-tone of the tonic major triad. This tendency reinforces the upward
tendency of tone B, the third degree, toward the same tone.
(3) Minor-mode 7th with lowered fifth
-------------------------------------
The lowered fifth degree possesses a downward tendency toward the
root-tone
of the tonic chord. The minor-mode 7th with an unaltered fifth degree
has
no tone with a tendency toward this tone. That is, the tonic root-tone
remains dynamically undefined in progression from the minor-mode 7th
chord.
Thus the tendency of the lowered fifth degree provides a very important
dynamic enhancement: a perfect definition of the tonic 7th chord.
For example, in the dominant-tonic progression DFAbC-->DFGB (Dm7-
-->G7),
tone Ab, the lowered fifth degree, has a downward tendency toward tone
G,
the root-tone of the tonic G7 chord. Note that this tone is not defined
in
progression from the Dm7 chord.
(4) Major triad with raised fifth
---------------------------------
The raised fifth degree possesses an upward tendency toward the third
degree of the tonic chord. This tone is not defined in the progression
from
a major triad. Thus the tendency of the raised fifth degree provides a
very
important dynamic enhancement: a perfect definition of the tonic major
triad.
(5) Minor triad with lowered fifth
----------------------------------
The minor triad with a lowered fifth degree is an exceptional case, in
that
the lowered fifth degree does NOT possess a downward tendency toward the
tonic root-tone. The reason for this is that the lowered third degree of
the minor triad has no diatonic tendency. Hence the lowered fifth degree
in
the altered minor triad cannot possess a tendency, because there is no
tendency in the unaltered chord.
SUMMARY
The fifth degree of a chord may be raised or lowered by one semi-tone
(i.e., "chromatically altered") for two reasons. First, it may happen
that
a melody tone will exist in a semi-tone relationship with the fifth
degree
of the chord of accompaniment. If this melody tone is sufficiently long
in
duration, it will create a harsh discord when sounded along with the
fifth
degree of the chord of accompaniment. This clash is usually undesirable
and
can be prevented by altering the fifth degree of the accompanying chord
to
match the otherwise-discordant melody tone.
The second reason for altering the fifth degree of a chord is that it
provides an enhancement of the dynamic properties. The semi-tone
tendency
of an altered fifth degree may either reinforce a diatonic tendency
(i.e.,
it may seek the same tone as that sought by the diatonic tendency) or it
may seek a tone which is not sought in an unaltered chord, because the
unaltered fifth degree is dynamically neutral.
In the case of diatonic reinforcement, the dynamic tension of the
dominant
chord is strengthened, but without changing the dynamic definition of
the
tonic chord of resolution. When there is no diatonic reinforcement, the
dynamic definition of the tonic chord is improved, over and above that
which is provided from an unaltered chord. By "improved," it is meant
that
more tones of the tonic chord are dynamically defined.
The tendency of an altered fifth degree is NOT a diatonic tendency
since,
in progression from this tone to the tone sought in the tonic chord, the
melodic semi-tone interval does not exist in the tonic diatonic major
scale.
Eight altered chords can be created by raising and lowering the fifth
degree of the four chords in the essential chord set. However, only five
of
the resulting chords are of practical utility. These five chords are
referred to as the "altered chord set."
CONCLUSION
Taken together with the essential chord set, the altered chord set
provides
a complete set of just NINE chord forms, with which ANY chord-based
composition may be analyzed.
This set of nine chord forms does not include chords with "added" tones,
which are _non-essential_ in their harmonic function. Such tones will be
discussed in Part (8).
Albert Silverman
Joey Goldstein
Date: 11 Jul 1999 21:58:49 GMT
From: slv...@netcom.com (Albert Silverman)
Organization: home in La Mesa, California
Newsgroups: rec.music.theory
A VAST WASTELAND OF MUSICAL IGNORANCE
by Albert Silverman
July 11, 1999
-------------------------------------
INTRODUCTION
There exists throughout the Western world a Vast Wasteland of ignorance of
"chord-based" musical composition. "Ignorance," as it is referred to here,
means the lack of a CONSCIOUS (a key word) knowledge of the principles of
this music. With very few exceptions, the "understanding" of the
construction of this music, by those who compose it (and/or improvise upon
the work of others) cannot be put into words which offer a _rational,
coherent, and relevant_ explanation of it. Additionally, the overwhelming
majority of "academically-trained" instrumental performers, music teachers,
musicologists, etc., know nothing significant (i.e., relevant) about the
nature of chord-based music.
This is indeed a strange situation, isn't it? Yet there *IS* an explanation
for this tragic state of affairs, and it is furnished in this article.
Contrary to the claims of those who are responsible for perpetuating this
state of affairs, the explanation is *NOT* that "music is an art, art has
no logic, and by definition, if it is logical, it is not art"!
HISTORY AS A *BLOCK* TO MUSICAL UNDERSTANDING
It has often been said that "history is a great teacher." But not in music,
where exactly the opposite happens to be true! For reasons explained below,
musical history turns out to be an extremely effective BLOCK to the
comprehension of chord-based music! This is not saying that understanding
musical history is a comprehensional block in itself. Rather, the basic
failure of (theoretical) music education is that the Academic Musical
Establishment very long ago created this block (and has continued to
maintain it over hundreds of years) by failing to PROPERLY teach the
evolution from earlier musical forms into the chord-based composition which
began in the common-practice period.
At the heart of this failure is the perception, by the Academic Musical
Establishment, that its charter is to preserve the Ancient Identity of
music _as an "art" form_. In accordance with this conception of the
Historical Destiny of music, it MUST be taught with the express intent of
avoiding any "revision" of musical history. Thus, even though the changed
nature of musical composition with the passage of time warrants (indeed,
screams and shouts for) a drastic revision in the approach to explaining
the relevant principles, music continues to be taught from a historical
perspective, far beyond the point where the Ancient Concepts have any
COMPOSITIONAL RELEVANCE. It is as though maintaining the quaint and Archaic
terminology and "ideas," _for the sake of historical preservation_, is the
only thing that really counts. And let the REAL compositional principles be
damned!
----------
Webster's dictionary defines "theory" as:
"A more or less plausible or scientifically acceptable general
principle offered to explain phenomena."
----------
For example, in the field of science, the phenomena which are explained by
different theories are such things as (in physics) the motion of bodies,
the nature of vibrations, the nature of chemical reactions, etc., etc. In
other words, the explanation which is provided by the theory helps one to
understand the nature of some particular phenomena.
That is, the above definition of theory implies that
THEORY IS SYNONYMOUS WITH UNDERSTANDING.
************************************************************************
This is apparently a revolutionary idea in musical Academic Circles
(where they are all running around, like......). Echoing Archaic
Academic Authority, this notion of theory promoting the understanding
of musical principles was vehemently denied, in a public discussion on
the internet, by one inconsequential Perfesser of music theory and
composition at a large midwestern university, while vigorously
defending the teaching of Musical History as "theory," _for the
express purpose of avoiding any revision of Musical History_!!
************************************************************************
In accordance with Webster's definition of theory, one is certainly
entitled to expect that there will be a separate theory of chord-based
composition. Why? Because _the principles of this music differ
SIGNIFICANTLY from the principles of earlier music_.
But unfortunately, this is a mistaken expectation. As a result of this
Academic Focus upon preserving Musical History _at the expense of
comprehension_, the relevant principles of chord-based composition,
presented in a rational and coherent fashion, are
NOWHERE IN SIGHT
in the academic journals, textbooks and classrooms. Hence there is no
reason to expect anything OTHER than the existence of a Vast Wasteland of
Musical Ignorance. This "community" (welcome to our Wonderful land!) is as
inevitable as night following day.
=========================================================================
THE EVOLUTION OF CHORD-BASED MUSIC FROM EARLIER FORMS
"Chord-based" music (i.e., music in which the chord is employed as an
_organizational building block_) evolved from music in which the "chord"
was perceived as a temporary coincidence of simultaneously-sounded
melodies. In this earlier music, melodies were generally composed from the
tones of a single "diatonic scale." Hence it was only natural to attempt to
explain the later chord-based music in terms of melodies composed from a
single diatonic scale.
Melodies in the earlier, coincident-melody music were generally phrased
independently of one another. Due to the independent phrasing of the
various melodies, _it was impossible to define a "chord" as a unit of
musical organization. As musical composition evolved, however, a very
significant change took place in the nature of melody. Bar-lines (marking
rhythmic accents) appeared, along with a rhythmic regularity (often
referred to as the "tyranny of the bar-line") which _established the
melodic PHRASE as the driving force in chord-based composition_.
Reflecting this new dominance of the rhythmically-regular phrase, the
nature of a piece which contained multiple melodies changed profoundly.
Specifically, in the new musical order of things, one melodic line assumed
a prominence and the remaining melodic lines (or fragmentary vestiges, if
indeed any other melodies were audibly perceptible) _assumed a subordinate
role to this prominent melody line_.
Characterizing this new order was the fact that the phrasing of these
subordinate melodies was _dependent upon the phrasing of the melody to
which they were subordinate. Due to this phrasing subordination, it was
possible to create a "chord" as a unit of organization; i.e., as a
"structural building block." The vital point is that, within this new
organization, the structural building block _was no longer associated with
any specific diatonic scale_. This represented a sea-change in musical
viewpoint, even though Ancient Academic Authority refused to formally
acknowledge it.
************************************************************************
That is, the diatonic scale as a tool for the creation of melody, in the
earlier music, was cast in a FAR DIFFERENT (and much more complex) role,
within a "harmonic structure" in which the chord was now an _organizational
unit_, rather than being a temporary coincidence of simultaneously-sounded
melodies created from a single diatonic scale.
************************************************************************
Incredibly, however, contrary to this radically different role played by the
diatonic scale in chord-based music, harmonic theory is being MIStaught
today within Musical Academia. That is, the diatonic scale is STILL
being cast in a role _which is no longer applicable and has not been
applicable from the inception of the Classical period_, which marked the
shift to chord-based composition. This sort of Academic Intransigence is
largely responsible for the Vast Wasteland in which you are wandering
around aimlessly.
----------
Reflecting the historical origin of music as a confluence of "voices," the
commonly-accepted method for explaining chord-based music is to use a model
consisting of a single melody line (normally the soprano voice)
"accompanied" by chords. Although this model is far superior to the view of
a chord as a temporary coincidence of simultaneous-sounded melodies, since
it implies that a chord is a unit of organization, it nevertheless fails
when it comes to acknowledging the existence of _multiple melodies_.
-----
In a nutshell:
A model for chord-based music MUST recognize the chord as a unit of
organization, while at the same time providing for the possible
existence of multiple melodies.
-----
The single-melody-with-chordal-accompaniment model for chord-based music,
which has been roundly criticized because it does not take into account the
existence of counterpoint, is a simplistic attempt to reconcile chord-based
music with music that has evolved from melodies being sung simultaneously
by several voices. Music which fits this model is commonly referred to as
"homophonic" music, which literally means "same voice."
Fortunately, this defect in the traditional "homophonic" model is easily
remedied by a modification _which includes counterpoint within chord-based
theory_. This modification is based upon the fact that, _in chord-based
music, all melodies are phrased in the same manner_. In other words, while
there may be one melody which is more prominent (usually in the soprano
voice), there may simultaneously be other "contrapuntal" melodies; but it
is REQUIRED that these other melodies (if any) be phrased in subordination
to the prominent melody.
************************************************************************
With this modification, based upon the _dependent phrasing of
auxiliary melodies or melodic fragments (as is most often the case)_,
the single melody which is implied in the term "homophonic" is
extended to include the existence of MULTIPLE MELODIES, while in no
way invalidating the concept of the chord as a unit of organization.
************************************************************************
Here, then, is the key to understanding the music of J.S. Bach, composed in
the Classical (as opposed to the Baroque) period. This is indeed CHORD-
BASED music. At the same time, it is highly contrapuntal music. It is
impossible to over-emphasize the fact that "chord-based" and "contrapuntal"
are
***NOT***
mutually exclusive concepts. If you want to escape from that Vast Wasteland
of Musical Ignorance, then it is essential (one of a long line of essential
concepts to learn!) to understand this fact. If you don't understand it,
then go back and read it again and again and again and......, until you do.
But if you don't WANT to understand it, then why are you reading this?
Polyphony
"Polyphonic" music is distinguished from "homophonic" music, in that
multiple melodies in the former are _independently phrased_. For this
fundamental reason, polyphonic music and chord-based music are mutually
exclusive. Hence it is a GRIEVOUS ERROR to lump the two together under the
common heading of "counterpoint."
This error results from a reliance upon Ancient Academic Authority which,
for reasons explained above, has muddied the waters in an attempt to avoid
a revision of musical history. Historically, multiple melodies mean
"counterpoint." Therefore, furthering the interest of confusion (so what
else is new?) and destruction of comprehension........
Are you "doctors" and/or "teachers" and/or.....listening out there in that
VAST WASTELAND?
----------------
Albert Silverman
July 11, 1999
--
Joey Goldstein
CHORDS WITH ADDED TONES
by Albert Silverman
July 19, 1998
-------------------------------------
BACKGROUND AND REVIEW
The set of four essential chord forms was presented In Part (6). The
reason
that this set is referred to as "essential" is that it provides for all
of
the possible DIATONIC dynamic effects involved in the harmonic process.
These are the dynamic effects _which can be attributed to the two
semi-tone
intervals of the diatonic major scale_, and which are the theoretical
foundation of the "dominant-tonic" harmonic progression discussed in
Part (5).
-----
Hence, at least in theory
A harmonic analysis of any chord-based composition can be
conducted using ONLY these four essential chord forms.
-----
In practice, however, a simple modification of a chord from the
essential
set may sometimes be desirable to avoid a harsh discord between a melody
tone and the fifth degree of the accompanying chord. This discord will
occur if the melody tone and the fifth degree of the chord differ by one
semi-tone. It is avoided by "chromatically altering" (i.e., raising or
lowering by one semi-tone) the fifth degree of the accompanying chord.
As it happens, a chromatic alteration of the fifth degree may (depending
upon the particular chord form) also provide an important dynamic
"enhancement" that is not present with an unaltered fifth degree. An
altered fifth degree possesses a tendency in the direction of the
alteration, PROVIDED that the unaltered chord has at least one tendency
tone. Due to this proviso, a minor triad with an altered fifth degree
cannot provide any dynamic definition of the tonic triad. Despite this
dynamic deficiency, a minor triad with an altered fifth degree and an
added
sixth degree (the Ancient "diminished 7th" chord) is commonly used for
its
distinctive tonal coloration.
The tendency of an altered fifth degree is NON-diatonic; i.e., it cannot
be
attributed to a semi-tone interval of the diatonic major scale. As I
explained in Part (6), the only chord form of the essential set which
perfectly defines a tonic chord (i.e., which has tendencies and
persistencies that seek all of the tones of the tonic chord) is the
[dominant 7th]. However, if we admit the non-diatonic tendency of an
altered fifth degree into our chordal vocabulary, we then get a perfect
definition of the tonic chord from both the major triad with a raised
fifth
degree and the minor-mode 7th with a lowered fifth degree.
Thus, in the dominant-tonic progression CEG#-->CFA (C+-->F), the tonic
F-major triad is perfectly defined by the root-tone persistence C-->C
and
the upward tendencies E-->F and G#-->A. And in the dominant-tonic
progression DFAbC-->DFGB (Dm7- --> G7), the tonic major-mode G7th chord
is
perfectly defined by the root-tone persistence D-->D, the lowered third
degree persistence F-->F, and the downward tendencies Ab-->G and C-->B.
These two dynamic enhancements, as it were, which are provided by the non-
diatonic tendency of the altered fifth degree are very important. In
particular, these dynamic enhancements are useful even though the fifth
degree may not be altered for the purpose of avoiding a harsh discord
between a melody tone and an unaltered fifth degree. Altered chords
possessing such dynamic enhancement are very common in more
sophisticated
"popular" music. In particular, the minor-mode 7th with a lowered fifth
degree is frequently used.
In summary, the altered set of five chord forms is a very important
(although not structurally "necessary") addition to the chordal
vocabulary,
for the following reasons:
(1) to avoid a harsh discord with a particular melody tone
(2) to provide a perfect dynamic definition of the tonic chord in two
specific cases (the major triad with a raised fifth degree and the
minor-mode 7th with a lowered fifth
(3) to provide a distinctive tonal coloration in the "diminished 7th" chord
(a minor triad with a lowered fifth degree and an added sixth degree)
---------------
In a nutshell:
Four essential chords plus five altered chords, taken together,
comprise a "basic chord set" which is suitable for the harmonic
analysis of ALL chord-based composition.
---------------
This basic set of nine chord forms is shown below in Table 8.1. The four
chord forms in the essential set are shown in lines (1)-(4) and the five
chord forms in the altered set are shown in lines (5)-(9).
name construction MY
formula popular-style
notation
_______________________________________________________________________
(1) major-mode 7th 1,3,5,-7 7
(2) minor-mode 7th 1,-3,5,-7 m7
(3) major triad 1,3,5 (none)
(4) minor triad 1,-3,5 m
-----------------------------------------------------------------------
(5) major-mode 7th with lowered fifth 1,3,-5,-7 7-
(6) major-mode 7th with raised fifth 1,3,+5,-7 7+
(7) minor-mode 7th with lowered fifth 1,-3,-5,-7 m7-
(8) major triad with raised fifth 1,3,+5 +
(9) minor triad with lowered fifth 1,-3,-5 m-
________________________________________________________________________
Table 8.1 THE BASIC CHORD SET (FOUR ESSENTIAL PLUS FIVE ALTERED)
**MEMORIZE THEM**
"ADDED" (NON-ESSENTIAL) TONES
Note that the chords within this basic set contain only three or four
tones. This is because the triad is the unit of chord-based composition.
There are two triads in the essential set: one in the major mode and one
in
the minor mode.
Additionally, the lowered 7th degree, when added to a triad to create a
7th
chord, functions as a "helper" tone to provide an improved dynamic
definition of the tonic chord. THIS is the harmonic purpose of the 7th
chord, containing an auxiliary fourth tone; there are two 7th chords in
the
essential set: one in the major mode and one in the minor mode.
The construction formulas in Table 8.1 reveal that the following seven
tones are components of these nine chords:
1, -3, 3, -5, 5, +5, -7
These tones are all "essential," since they play a fundamental role in
the
TRIADIC harmonic process (which includes the four tone chord with a
lowered
seventh degree). In many pieces, however, there are prominent (long-
duration) melody tones which are not one of these seven tones (or their
enharmonic equivalents). These missing tones are:
-2, 2, 4, 6, 7
These five tones are "non-essential," since they play no fundamental
harmonic role; i.e., they serve no triadic "structural" purpose.
Alternatively, they are commonly referred to as "added" tones. The
purpose
of such tones is twofold: (1) variety in tone color (2) melodic.
Because such tones serve no structural harmonic function, they need not
be
accounted for in a purely harmonic (as opposed to melodic ) analysis.
However, chord notations are commonly used in improvisational
performance.
In this practical (as opposed to analytical) application, it is
necessary
to include, in the chord notation, added tones that do not appear in
"the"
melody. Otherwise, these tones will not be played.
A triad with an added tone
--------------------------
The second and sixth degrees
The most common added tones are the second and sixth degrees. Here, the
"popular" system of chord notation suffers from its association with
Ancient Theory. Thus we find, for example, that a second degree somehow
seems invariably to be noted as a "ninth," based upon the Ancient
tertiary
construction into the second octave, despite the fact that it is simply
an
added second degree. The system of Ancient nomenclature/notation, based
upon the tertiary construction process, is totally inadequate and does
not
deserve any serious consideration. Sorry about that, AT.
In a sensible system of chord notation, based upon chord construction in
isolation, as explained in detail in Part (4) of this series, a tone
added
to a triad is noted by the scale degree following the mode designator,
if
minor, or following the root-tone designator, if the mode is major. In
most
cases, the notation using this scheme is the same as the common
(popular)
chord notation.
For example, a C-major triad with an added sixth degree (tones CEGA) is
noted as C6, which is the common notation used in popular chord charts.
However, I note a D-minor triad with an added second degree (tones DEFA)
as
Dm2. In this case, the popular notation, suffering an Ancient Hangover,
would usually identify the added second degree as some sort of "ninth"
chord.
It is sometimes argued, by those who defend the Ancient "ninth"
nomenclature, that this supposedly designates the tone dispersal along
the
musical staff. For example, if tone C is the constructional reference
tone,
then supposedly a tone designated as a "ninth" specifically should
differ
from tone C by a pitch interval of fourteen semi-tones, which is tone D
an
octave and two semi-tones above tone C.
This is nonsensical, however, since the performer, in improvisation from
a
chord chart using popular-style chord notations, determines how the
various
chord tones are to be dispersed along the musical staff. Hence,
regardless
of the octave in which the tone may be played, the chord notation should
reflect the pitch interval, _in the primary octave_, which a tone makes
with the constructional reference tone.
As another example, I note an F-minor triad with a lowered fifth degree
and
an added sixth degree (tones FAbCbD) as Fm6-. For reasons which are too
gruesome (and hardly worth the effort) to explain here, this tone
combination is referred to in popular terminology as a "diminished 7th"
chord. This terminology was of course invented by our Ancient Theorist.
The natural 7th degree
Another tone which is commonly added to a triad is a NATURAL 7th degree.
Since the notation 7 is used to denote a LOWERED 7th degree, a
notational
method must be found to distinguish between these two types of 7th
degrees.
As should be expected, our Ancient Theorist once again comes charging in
to
the rescue to screw up the terminology and provide an incomprehensible
challenge. This is his way of thumbing his nose at logic and consistency.
Thus, in popular terminology, a triad with an added, natural 7th degree
is
called a "major 7th" chord, which of course makes Ancient "sense." I
note
this particular chord as :7, with the colon separator being used to
denote
a natural 7th degree. Thus, for example, I note the tone combination
CEGB
as C:7. This notation is far superior to a notation such as "maj7" or a
triangle(!), or whatever strikes one's irrational fancy. It is much more
efficient, taking up very little space in a chord chart.
Adding a tone to a 7th chord
----------------------------
When a tone is added to a 7th chord (i.e., to a four-tone chord
containing
a LOWERED 7th degree), the combination of this tone and the lowered 7th
degree is denoted by a numeral which is seven larger than the degree of
the
added tone. Since this one numeral denotes the existence of BOTH tones,
the
numeral 7 does not appear in the notation.
For example, a second degree and a lowered 7th degree existing together
in
the same chord are noted by the numeral 9. Similarly, a sixth degree and
a
lowered 7th degree existing together in the same chord are noted by the
numeral 13, etc. Thus the notation C9 refers to the chord CDEGBb (D is
the
second degree), the notation C13 refers to the chord CEGABb (A is the
sixth
degree), etc. Note, in particular, that this notation _says NOTHING
about
the dispersal of the component tones along the musical staff_. Sorry
about
that, AT.
In summary, a numeral higher than 7 always denotes the existence of TWO
tones, one of which is an added tone and the other of which is a lowered
7th degree.
The added, lowered second degree
A lowered second degree is frequently added to a major-mode 7th chord.
Although this tone has no structural function, it nevertheless possesses
a
non-diatonic (by definition) tendency which seeks the fifth degree of
the
tonic chord. Thus it increases the dynamic tension by reinforcing the
persistence of the root-tone. This is the only case in which an added
tone
possesses a tendency.
For example, the chord GBDFAb is a G7 chord with an added, lowered
second
degree Ab (in the diatonic G-major scale of construction). Tone Ab has a
downward tendency toward tone G, which is the fifth degree of a tonic C-
chord. Hence it reinforces the persistence of the root-tone, G-->G.
I use the special notation -9 to denote this particular chord. Thus I
note
the chord GBDFAb as G-9, etc.
The added fourth degree
A fourth degree added to a major-mode seventh chord is the source of
much
confusion, due to the potential discord between the natural third and
fourth degrees. If the pitch interval between these two tones is only
one
semi-tone, the harsh discord will usually dictate against their being
sounded simultaneously. If it is wished to employ the fourth degree
without
such a discord, it is common practice to _replace the third degree with
the
fourth degree, rather than to sound them both simultaneously.
For example, the tone combination GBCDF, which is a G7 chord with an
added
fourth degree C, is highly discordant when tones B and C are sounded
together, only one semi-tone apart in pitch level. However, if tone C
replaces tone B (the natural third degree in the diatonic G-major
scale),
the resulting tone combination GCDF has a pleasing sound.
The discord between these two tones can be sharply reduced by increasing
the pitch interval between them to at least eleven semi-tones. For
example,
if tone C is played in the bass and tone B is at least eleven semi-tone
tones higher in pitch, there will be no harsh discord.
I prefer not to differentiate, in the chord notation, between a fourth
degree which replaces the natural third degree and a fourth degree which
is
sounded simultaneously with the natural third degree. Therefore, I use
the
notation 11 to denote either case, leaving it up to the performer to
decide
how large a pitch interval that is used to separate these two tones.
Thus,
I note BOTH the tone combinations GBCDF and GCDF as G11.
If the fourth degree is supposed to be played in the bass, I use the
accepted / notation at the end of the chord notation. Thus, for example,
I
use the notation G11/C to denote the tone combination GBCDF with tone C
played in the bass.
There is no comparable discord problem when a fourth degree is added to
a
minor-mode 7th chord. This is because the smallest pitch interval
between
the LOWERED third degree and fourth degree is two semi-tones, no matter
how
these two tones are dispersed along the staff. Often it is desired for
the
added fourth degree to be played in the bass; this can be ensured by
using
the / notation. For example, the notation Dm11/G refers to the tone
combination DFGAC, with tone G played in the bass. In contrast, the
notation Dm11 denotes the same tone combination, but without any
preferential bass tone.
Multiple added tones
--------------------
If no lowered 7th degree is present, I note each added by a numeral
which
designates its scale degree. Under such circumstances, a 7 denotes a
NATURAL 7th degree. For example, the chord CDEGB is noted as C27. The 7
cannot denote a lowered 7th degree, since this chord would be noted as C9.
When two tones are added to a 7th chord, the lowest added tone is
combined
with the lowered 7th degree, while the other added tone is designated by
its scale degree. For example, the chord CDEGABb is noted as C96.
SOME EXAMPLES OF CHORDS WITH ADDED TONES
MY construction common name added
popular-style construction tone(s)
notation formula
----------------------------------------------------------------------
-9 1,-2,3,5,-7 minor ninth -2
9 1,2,3,5,-7 ninth 2
13 1,3,5,6,-7 thirteenth 6
2 1,2,3,5 2
m2 1,2,-3,5 2
6 1,3,5,6 sixth 6
m6 1,-3,5,6 minor sixth 6
:7 1,3,5,7 major seventh 7
m:7 1,-3,5,7 7
26 1,2,3,5,6 2,6
m26 1,2,-3,5,6 2,6
27 1,2,3,5,7 major ninth 2,7
11 1,3,4,5,-7 4
11 1,4,5,-7 suspension 4
m11 1,-3,4,5,-7 4
4 1,4,5 4
96 1,2,3,5,6,-7 2,6
9+ 1,2,3,+5,-7 2
m6- 1,-3,-5,6 diminished seventh 6
-----------------------------------------------------------------------
SUMMARY
All of the diatonic dynamic effects (i.e., those which can be attributed
to
the two semi-tone intervals of the diatonic scale) in the harmonic
process
can be demonstrated with the set of four essential chord forms.
Additionally, a harsh discord between a melody tone and a chord tone can
be
prevented, and possibly a dynamic enhancement (improved definition of
the
tonic chord in a dominant-tonic progression) obtained, by including the
set
of five altered chords in the chordal vocabulary.
These two chord sets, taken together, use tones 1,3,-3,-5,5,+5,-7.
The remaining tones, -2,2,4,6,9 are "non-essential" tones, since they do
not contribute in the harmonic process. Rather, they are used for
melodic
and/or tonal coloration purposes.
A purely harmonic (as opposed to melodic) analysis need not account for
these non-essential tones. However, if the purpose is create a chord
chart
for use in improvisational performance, it is necessary to include non-
essential tones in the chord notations, unless these tones specifically
appear in "the" melody.
Albert Silverman
Joey Goldstein
--
Joey Goldstein
http://www.joeygoldstein.com
joegold AT sympatico DOT ca
don groves
nos...@nowhere.net hath writ:
> You seemed interested in Albert's "theories". Here thay are. Enjoy.
Thanks, Joey. Are you saving these for some reason other than to
generate toilet paper?
--
dg (domain=ccwebster)
Melodious Thunk
> You seemed interested in Albert's "theories". Here thay are. Enjoy.
Since you've taken the trouble to collect 'em, are you up to making a version *without* the
diatribes against the "ancients?"
I'd like to know what he's saying (about chords), but have trouble reading his posts.
Joey Goldstein
Helps quiet the newbies.
> --
> dg (domain=ccwebster)
Bob Pease
"Joey Goldstein" <nos...@nowhere.net> wrote in message
news:4224C334...@nowhere.net...
The banal disguised as profound.
RJ P
don groves
news02.socal.rr.com>, Melodious Thunk at rep...@website.com hath
writ:
I've made up a single text file from Joey's reposts of Al and if
I've the time, I'll try to do that very thing. I'd like to try
to understand what he's saying also, but the stuff is 50% crapola
about the "ancients".
--
dg (domain=ccwebster)
USM
> In article <422497db$1...@mk-nntp-2.news.uk.tiscali.com>,
> USM <TheUl...@SexMagnet.com> wrote:
>> Matthew Fields wrote:
>>
>>>
>>> Al's account of subdominant functions as 11 steps removed from tonic
>>> is *much more complex* and indirect than the usual account.
>>
>> Maybe so. I`m certainly no expert, and when i do make music i don`t
>> use theory (i don`t write or score as i expect you do, i just
>> sequence numbers). My only point that was that a single sentance
>> axiom has a certain mnemonic conveniance. If you already understand
>> the point he`s making in your own terms, then no doubt your
>> established veiw will persist. You could though, offer an
>> alternative sentance that does the same job in the significantly
>> less complex way you suggest....?
>>
>
> Sure. Subdominants are one fifth below the tonic, not 11 fifths above
> it.
I geuss so... i`d have to confess to having little understanding of theory
as it applies *inside* the octave, but then all the more reason to accompany
criticisms with examples.... However he does seem to be outlining a broader
concept, of which this is just one aspect. I geuss my ignorance of the
issue may be a good test bed for which veiw i`m able to understand first...?
Certainly, "one fifth down" seems prefferable to "11 fifths up"...
USM
> In article <4224a...@mk-nntp-2.news.uk.tiscali.com>,
> USM <TheUl...@SexMagnet.com> wrote:
>> don groves wrote:
>>
>>>
>>> I don't recall saying he's wrong, so why are you acting like I
>>> did. I merely asked for conrete examples to clear up my
>>> confusion about his meaning(s). Do you have any?
>>
>> No i`m sorry i was getting a bit extra there, and my interference
>> wasn`t needed anyway - i only meant that Al was "right" to object
>> that your innitial response somewhat confused the terms "principle"
>> and "style". I didn`t mean to express the opinion that Al`s theory
>> was "right", only that his distinction between terms was valid.
>> Appologies..
>>
>>
>
> But actually Al is wrong about this, as are you. Music theory is
> theory of actual music, which always has a style. Styles may be more
> or less closely related to each other, but there simply are no
> principles of music which are true of all styles.
Ethnomusicologists, and indeed archeologists, would disagree. In fact, your
reliance on Al`s usage of the term "principal of music" falls out of context
in this broader concept of "all styles" - clearly, in common usage of the
term there are many universal principles of music - i make frequent mention
of them. Al`s idea clearly refers to Western tonality, it is not intended
as a principle of any arbitrary tonal system. If you can prove Al wrong,
then do so rationally, not by attempting to muddy the water until nobody can
understand the issue..... that`s bad form, and indicative of muddled
thinking.
As me, Al and others here have constantly pointed out - music theory is NOT
"theory of actual music" - it is an evolved attempt at establishing a
meaningful language to correctly contextualize musics mechanisms, rules and
interrelationships, *including* stylistic variation - as such it has evolved
through many misconceived principles and subsequent styles. Your statement
above could be taken to imply that a seperate set of musical principles is
required for every observable (or concievable) style - clearly an absurdity.
Both you and Joey seem terrified of the prospect of musical universals - yet
you produce music - so how on earth do you know that other people are going
to comprehend your work, unless you`re willing to credit them with the same
perceptual faculties that enabled you to write the music in the first place?
All of your music relies on the universal principles of music - they`re
inherent in all of us. Your common fall-back insult of musician vs.
non-musician betrays a fundamental misunderstanding of these universal
principals. But in all fairness, you`ve probably had to endure a lifetime
of people telling you that you`re "talented"... perhaps that`s why you`re
so offended by the fact that lower animals process music, at least at a most
basic level, in much the same way as us.... Either way - the term "music
theory" refers to an evolved language, and not a theory of music. It is not
intended as a theory of music, and hasn`t been so for over a century. And
if "music... always has a style" then how do you explain Enya?