Attempt to explain
Vilen
I can’t content with explanations of some phenomena in music which I
find in literature. These explanations include references on
unexplained qualities of intervals, chords and so on. Or a serious
music theory (H.Riemann) derives scale from chords, which notes it
takes from the scale. Because of it I try to find some explanations
myself.
Why is major mode better as minor one? As first cause the fact that it
has leading note is named. It is said that leading note attracts tonic
note. How it can be explained? The tonic note has 2.-overtone, which
is fixed in mind (tonality) and if leading note is continuation of
notes with increasing pitches then because of its nearness to 2-
overtone arises forecast of tonic note and its appearance calls a
pleasant sensation.
Let us consider case of perfect cadence in major mode with chords
g,b,d,f and c,e,g. It includes 2 semitones intervals which in case of
right voice leading create forecast of notes c, e and sensation of
perfect cadence.
In minor mode perfect cadence includes chords e,g,b,d - a,c,e and have
1 coincidence e-e and one semitone nearness b-c. If consider m7 tonic
chord a,c,e,g then it has 2 coincidences and 1 semitone nearness and
all the same evaluated worse as perfect major cadence. It is important
to note that major cadence has semitone interval to middle chord note
and, possibly, because of it this note is recommended to retain in
major chord always.
Commonly the resolving of tritone dissonance b-d is considered as
source of perfect cadence’s force. Some facts contradict that.
Firstly tritone dissonance is one between second and third harmonics
of its notes and second harmonic may be weak.
Secondly it is interesting to analyze the using of tritone (Lydian)
interval by classic composers Bach, Haydn, Mozart and Beethoven. They
used his interval “as pathway from one key to the next” (http://
www.schillerinstitut.dk/bach.html). Let us consider such leap with
following passage to fifth.
In this case the fifth is higher on one semitone as Lydian interval
and following passage to fifth is movement in the same direction.
Identical there is movement in same direction by leap on Lydian
interval downwards with following passage to fifth below.
For comparison leap on 8 semitones upwards gives dissonance between
second and third harmonics as by Lydian leap on 6 semitones, i.e.
equivalent dissonance. Yet the following passage to fifth below goes
in opposite direction. Same situation arises by 8 semitones leap
downwards:
following one semitone passage to fifth below goes in opposite
direction.
Thus the overwhelming using of Lydian leap indicates on essential
importance of continuation of same direction movement for one semitone
passage. There is so called “soft landing”.
Yuri Vilenkin
Hans Aberg
> Why is major mode better as minor one?
I'm not sure that find major "better" have a rational, objective
explanation for that.
But there is the phenomenon of difference (combination, resultant)
tones. The cochlea produced the sensation of the frequency |f0 - f1] if
tones f0 and f1 are played. So it is a physiological phenomenon, not
acoustical, despite the fact that it is also called "acoustic root".
Now, the Just major chord 4:5:6 has the property that in all inversions,
the lowest difference tone is an octave of the root of the chord. In
4:5:6, the lowest difference tone is 1, two octaves below 4. In 5:6:8,
the lowest difference tone is 1, two octaves below 8. In 3:4:5, the
lowest difference tone is 1, two octaves below 4.
So even if the Just major chord is inverted, its named root gets
emphasizes in the bass by an acoustic root. The minor chord does not
that have that property.
> As first cause the fact that it
> has leading note is named. It is said that leading note attracts tonic
> note. How it can be explained?
Perhaps some experts here can give suggestsions of that.
But with the major chord in hand, one wants to be able to emphasize the
the fifths above and below the tonic - the dominant and the subdominant.
The Just major chord on all those three notes generate the Just major
scale. Even if not playing this Just intonation scale exactly, one
attempts to approximate it. For example, during the Renaissance,
quarter-comma meantone, which sets the major third equal to 5/4 (close
to E31), was popular.
I think that this (extended) meantone might be the basis for deciding
the consonance-dissonance CPP theory. For example, the interval ratio
7/4 is approximated at about 1 cent by the interval 6# (augmented 6th).
But is without the major/minor scales system, which makes it hard to use
despite being harmonically convergent or consonant within this tuning.
So in fact, it is limited as a predominant in the form of the German
sixth chord and some others.
Hans
Steve Latham
> Why is major mode better as minor one?
>
It is not.
Starting a hypothesis, or argument, or experiment like this only leads
to finding information that supports the hypothesis while ignoring
that which counters it.
BEFORE you start looking at WHY Major is better than minor, you first
have to PROVE that Major is better than minor.
Otherwise, your method is unscientific and illogical, and your
evidence is suspect.
Steve
LJS
> following passage to fifth.
> In this case the fifth is higher on one semitone as Lydian interval
> and following passage to fifth is movement in the same direction.
> Identical there is movement in same direction by leap on Lydian
> interval downwards with following passage to fifth below.
> For comparison leap on 8 semitones upwards gives dissonance between
> second and third harmonics as by Lydian leap on 6 semitones, i.e.
> equivalent dissonance. Yet the following passage to fifth below goes
> in opposite direction. Same situation arises by 8 semitones leap
> downwards:
> following one semitone passage to fifth below goes in opposite
> direction.
> Thus the overwhelming using of Lydian leap indicates on essential
> importance of continuation of same direction movement for one semitone
> passage. There is so called “soft landing”.
>
> Yuri Vilenkin
I don't think that Better is the best choice of words. You may mean
"seems to work better" when looking at your premise. I, as you may or
may not know, like to think of scales being a product of the harmonic
structure inherent in the Harmonic Series arrangements of chords of
two fundamentals a fifth apart.
It would be a lot to ask, but I find it difficult to understand a lot
of what you are saying because of the scientific and ratio oriented
terminology you are using as well as your translation of your thoughts
into English from your native language. (more on that in a bit!). I
am, however, interest in what you have to say and I can see that you
have given it a lot of thought.
What I would like to see is a graph or chart that would show the exact
placement of the frequencies that are the result of the structures and
ratios that you are using and their relationship to the actual
placement of the frequencies as they exist in both the Harmonic series
(when reduced into the the octave range) AND the 12-tet placement of
the frequencies. For me, and probably others, this would take away a
lot of the confusion of the ratios and would allow me and other
musicians to understand what you are actually saying and give us a way
to relate the more musical way that we think to the more scientific
way that you are presenting the material. Music maybe abstract
mathematics but us non-scientific musicians don't think in ratios, we
think in notes and intonation.
If it is too much work, I understand, but I think you will get more
productive input if we had a tool to see more clearly what you are
specifically saying.
Back to the ESL:
First of all, I have great respect for your ability to communicate in
English. I have lived in Spanish, French, Hindi variations, and
Chinese speaking countries and although there are many good musicians
in all of the places that I lived, verbal discussion was always
limited because of my inability to translate my thoughts into that
other language.
As I remember, your earlier writings were constructed better
grammatically, but I never noticed so much what you were saying as I
did not see much depth in your writing. Now I see that you are being a
bit less concerned with the grammar and choice of words and you are
taking chances as you write more of what you think and feel. In this
post, I see a much higher level of understanding in your writing. I am
used to reading ESL speech and writing because of my worldwide travels
teaching music. The most difficult thing is to get the student to just
talk or write and get his IDEAS out and worry about correcting the
nuances of a stupid and complicated grammatical language such as
English. Chinese, for example does not even provide for case agreement
with nouns and verbs. It all comes from the context and sometimes with
a "signal" word (or even an semi-spoken character) that provides this
information and the sentence structure is not so important as the
words and characters that are included in the group of words or
characters.
Congratulations on your progress in mastering my language. I am
particularly glad that you are as my skills in this area are not very
good. You have made great progress and you are now showing a lot more
depth in your writing even though your grammar lags behind your
ability to communicate. I can certainly ask for clarification of some
of the nuances if necessary. I am really interested in what you have
to say rather than how you translate it. You don't really have to, but
I can see that if you continue to write in English, you will begin to
make great strides to becoming very fluent. Thanks.
LJS
Jon Slaughter
The major mode is the natural mode. It is the scale produced by the 2 most
related tones to the tonic.
C->G
F->C
So the 3 main tones are C F G.
Those 3 tones are neither major nor minor. But do you agree these tones are
the physically the most related to C? Is C# more related to C than F? If
you don't agree with this you don't understand physics or the the overtone
series and no bother to discuss any further. (the only question would be the
term "Relation" which is consonance)
Now, taking the next logic step we look at the overtone series for the next
new tone to extend this group. i.e., if we want to extend the "scale" we
look to the overtone series because it shows us the most natural relation
between pitches. I doubt you agree with this but it is a sign of
incompetence. Why? Because it is both physical, mathematical, and historical
and no other logical system exists that is based in those.
i.e., For C, what we call the tonic, the next most related tone is E. You
have any other better choices? If not then accept it is E.
So the scale is now
C E F G
Now we have a major scale. It's not Eb. Of course you don't agree with this
analysis?
C E F G is the most natural 4 group of notes with C being the tonic.
Now we can add A and B by repeating the logic above.
We then have
C E F G A B
The tones we are missing is D. This is a bit more challening to make a
logical choice but if we have to choose between Db, D, Eb we see that D is
the most natural as it is the logical choice from looking at G. (hence
probably the reason why the dominant is generally the key that is most
modulated to from the tonic)
We see that D is related much more closely to C than Db or Eb.
In any case it is natural to have the major mode. Again, is is
mathematically, physically, and historically the natural choice.
The minor mode is a mode of the major scale. It is a direct consequence of
the major mode and not vice versa.
Now, it's not "better" in any sense except one of most natural. "Better" is
an aethestic.
If you don't agree show me a logical and natural construction of the minor
mode that is just as simple as the major mode.
Jack Campin - bogus address
> Vilen wrote:
>>> Why is major mode better as minor one?
Vilen was more sensibly looking at the use of the different modes
in a very narrow range of musical idioms when making that assertion.
It's not totally silly to think the major mode offered possibilities
to Haydn and Mozart that others didn't - after all, they used it more
often.
On a wider historical scale, that's nonsensical. The most widespread
mode in the music of Europe and Western Asia since the beginning of
music theory has been the Dorian. It wasn't "Mode I" for nothing in
the mediaeval scheme both in Western and Byzantine chant, and it's
overwhelmingly the commonest 7-note mode in the folk music of the
Turkic and Finno-Ugrian peoples. (Major is rare in both, *very* rare
in all Middle Eastern folk cultures).
The worldwide pattern is for less developed cultures, on the whole,
to make music in scales that span a range far less than an octave,
and with no one scale predominating. This is still the pattern in
some relatively advanced societies, as with the folk music of Egypt,
Kurdistan and Azerbaijan. The range can get *very* small, as in one
genre of Melanesian song that uses only three adjacent semitones.
The overtone series doesn't come into it when you never sing *any*
harmonics. It's irrelevant to most of the music humanity has ever
produced.
> The minor mode is a mode of the major scale. It is a direct consequence
> of the major mode and not vice versa.
The major mode hardly existed in European music before the Renaissance.
It's not ancestral to anything.
> If you don't agree show me a logical and natural construction of the
> minor mode that is just as simple as the major mode.
Who needs it? History is what it is. There are analyses of the
nahawand scale of Arabic music (one form of the minor scale) that
predate any known music in the major by centuries. The ancient
Greeks had a highly sophisticated theory of their music that never
mentioned the major scale.
==== j a c k at c a m p i n . m e . u k === <http://www.campin.me.uk> ====
Jack Campin, 11 Third St, Newtongrange EH22 4PU, Scotland == mob 07800 739 557
CD-ROMs and free stuff: Scottish music, food intolerance, and Mac logic fonts
****** I killfile Google posts - email me if you want to be whitelisted ******
Vilen
Why is major mode better as minor one?
>It is not.
>Starting a hypothesis, or argument, or experiment like this only leads
>to finding information that supports the hypothesis while ignoring
>that which counters it.
My aim was not to prove superiority of major. My question about it was
rhetorical. Essentially I wanted to analyse cases in which major mode
is better (let us remember the use of “ tierce de Picardie in minor
mode ) in order to find understandable common rules.
>BEFORE you start looking at WHY Major is better than minor, you first
>have to PROVE that Major is better than minor.
>Otherwise, your method is unscientific and illogical, and your
>evidence is suspect.
I think that superiority of major is common view. You deny it
(superiority). It is logical to suppose that you have definite
criterion. What?
Best Regards
Yuri Vilenkin
Nonna Vilenkina
>Now, the Just major chord 4:5:6 has the property that in all inversions,
>the lowest difference tone is an octave of the root of the chord. In
>4:5:6, the lowest difference tone is 1, two octaves below 4. In 5:6:8,
>the lowest difference tone is 1, two octaves below 8.
In last case the lowest difference tone is three octaves below 8.
>In 3:4:5, the lowest difference tone is 1, two octaves below 4.
In inversion 6:8:10 the lowest difference tone is 2 but of the same
pitch class.
For minor chord we have:
In root position- 10:12:15 with the lowest difference tone 2;
In first inversion- 12:15:20 with the lowest difference tone3;
In second inversion-7.5:12:15 with the lowest difference tone3.
I.e the perceptible virtual pitch alters for some inversions of minor
chord. If it can disturb music idea then let Steve count one point to
major.
Best Regards
Yuri Vilenkin
Hans Aberg
My dictionary says that the difference tones were discovered by G.
Tartini in 1714 and described in his "Trattori di musica" from 1754, and
that it can be easily heard on harmonium, organ, and violin. Also called
Tartini's tone, ir Italian "terzo suono" - third tone. (There are
summation tones as well, but they are more difficult to recognize.)
On pipe organs, one can make an acoustic bass: instead if a 32-foot
stop, one makes a 2:3 differential tone between a 16-foot and a 10 2/3
foot stop. Cheaper.
So it was well known. The might have considered it when defining the
root of a chord, and finding that the major chord and the major scale
are optimal.
Then then harmony and making it optimal is just one aspect of music.
However, another factor might be that optimal harmony allows for more
instruments playing together. The large CPP orchestras of late 19th
century impressed around the world, and was a factor in trying find
harmony for regional music (for example, Persian, according to Farhat's
thesis).
Stravinsky's "Rite of Spring" was originally written for a large
orchestra, but reorchestrated for a smaller one. Then alzo electrical
amplification starts to become common, making optimized harmony less
important.
Hans
Alain Naigeon
640d9731-a028-42f5...@h2g2000vbd.googlegroups.com...
On 24 Okt., 17:23, Steve Latham <llat...@odu.edu> wrote:
>BEFORE you start looking at WHY Major is better than minor, you first
>have to PROVE that Major is better than minor.
>Otherwise, your method is unscientific and illogical, and your
>evidence is suspect.
I think that superiority of major is common view.
Another common view : major is gay, minor is sad;
A third common view : sad music is better.
So... what about the truth contained in common views?
--
Fran�ais *==> "Musique renaissance" <==* English
midi - facsimiles - ligatures - mensuration
http://anaigeon.free.fr | http://www.medieval.org/emfaq/anaigeon/
Alain Naigeon - anai...@free.fr - Oberhoffen/Moder, France
http://fr.youtube.com/user/AlainNaigeon
tom_k
"Alain Naigeon" <anai...@free.fr> wrote in message
news:4ae428bd$0$714$426a...@news.free.fr...
> "Vilen" <vi...@online.de> a �crit dans le message de news:
> 640d9731-a028-42f5...@h2g2000vbd.googlegroups.com...
> On 24 Okt., 17:23, Steve Latham <llat...@odu.edu> wrote:
>
>>BEFORE you start looking at WHY Major is better than minor, you first
>>have to PROVE that Major is better than minor.
>>Otherwise, your method is unscientific and illogical, and your
>>evidence is suspect.
>
> I think that superiority of major is common view.
>
> Another common view : major is gay, minor is sad;
> A third common view : sad music is better.
>
superior!!
> So... what about the truth contained in common views?
There doesn't appear to be much "truth" here. It seems some 19th century
composers (Beethoven > Liszt > Wagner> Franck, etc.) realized this as they
gradually began to combine the major & minor modes into one tonality, just
as the church modes were merged into major and minor 300 years earlier.
Since Vilen isn't "trying to prove the superiority" of major, the real
question seems to be why some folks seem to think in these terms in the
first place.
Tom
Joey Goldstein
What I would say is that in the area of creating, confirming and
maintaining a key feeling (i.e. tonal centre with a tonic, a chord whose
root is that tonic, and similar chords available whose roots are a P5th
above and below that tonic) the major triad is an easier target to
maintain than the minor triad.
The first problem with minor triads as tonic chords is that the
intervals in minor triads all have different acoustical roots, whereas
all the intervals in the major triad have the same acoustical root. So
right off the bat the minor triad is not as suitable a target for
becoming a home chord as the major triad is.
The 2nd problem is the lack of a leading tone or of a V7 chord within
the natural minor scale. In major keys the leading tone and the V7 chord
are the two main pointers that composers have used to point to and
confirm the I chord as home. These pointers are missing in the natural
minor scale so they had to be grafted onto it via musica ficta.
But as far as major being better than minor from an aesthetics pov,
that's just silly.
--
Joey Goldstein
<http://www.joeygoldstein.com>
<http://homepage.mac.com/josephgoldstein/AudioClips/audio.htm>
joegold AT primus DOT ca
LJS
> tom_k wrote:
> > "Alain Naigeon" <anaig...@free.fr> wrote in message
> >news:4ae428bd$0$714$426a...@news.free.fr...
> >> "Vilen" <vi...@online.de> a écrit dans le message de news:
> >> 640d9731-a028-42f5-ab8d-5bd53e4ca...@h2g2000vbd.googlegroups.com...
Someone correct me if this is not accurate:
I believe that cadences were set up during the contrapuntal time late
enough to be using Musica Ficta. As the tensions were created and as
they resolved through suspensions, and the creation of the tritone and
other cadential factors, the Dominant 7th chord started to appear.
Then there came the "switch" from contrapuntal thinking and by that
time, the working cadences started to have all the elements of the IV-
V-I cadence with and without the cadential 6/4.
If this is more or less accurate, then the establishment of a key that
has all those descriptive phrases in the reply has no relevance to the
tonic being Major OR Minor. It just would not be a factor. A simple iv-
V7- sets up the tonic note. the color of the scale used once you are
in that key depends solely on the scale used over that established
tonic. Using this premise, there would be no difference in creating
and maintaining a sense of key for major or for minor. That concept
just would not apply as stated in the reply.
LJS
Jon Slaughter
> Jon Slaughter wrote:
>> Vilen wrote:
>>>> Why is major mode better as minor one?
>> The major mode is the natural mode.
>
> Vilen was more sensibly looking at the use of the different modes
> in a very narrow range of musical idioms when making that assertion.
> It's not totally silly to think the major mode offered possibilities
> to Haydn and Mozart that others didn't - after all, they used it more
> often.
>
> On a wider historical scale, that's nonsensical. The most widespread
> mode in the music of Europe and Western Asia since the beginning of
> music theory has been the Dorian. It wasn't "Mode I" for nothing in
> the mediaeval scheme both in Western and Byzantine chant, and it's
> overwhelmingly the commonest 7-note mode in the folk music of the
> Turkic and Finno-Ugrian peoples. (Major is rare in both, *very* rare
> in all Middle Eastern folk cultures).
>
Actually the modes used today are not even close approximations of what was
used by the greeks there is very few documents surviving that even come
close.
In any case your believe that history predicates logic is entirely ignorant.
Does a child determine what is correct? Should we accept a childs concept of
physics because the child was before the man? Do you think because a
culture is primitive that it somehow must know the correct interpretation?
Do you not believe that intellectual understanding advances in time and not
backwards? Do cultures become more ignorant or less over time(in general)?
> The worldwide pattern is for less developed cultures, on the whole,
> to make music in scales that span a range far less than an octave,
> and with no one scale predominating. This is still the pattern in
> some relatively advanced societies, as with the folk music of Egypt,
> Kurdistan and Azerbaijan. The range can get *very* small, as in one
> genre of Melanesian song that uses only three adjacent semitones.
And in almost all these cultures they base there music off the fundamental
P4-T-P5 relationship, do they not? If you agree with this then you must
agree with my first analysis as they coincide. Adding the M3rd is the next
logical step. It does not mean these cultures made that step. They could
have been so rooted in their own development and because of other cultural
reasons as to not advance(such as a strict religious dogma that prevented
them from artistic freedom).
>
> The overtone series doesn't come into it when you never sing *any*
> harmonics. It's irrelevant to most of the music humanity has ever
> produced.
Your absolutey wrong in both cases. It is an ignorant statement and I
believe if you put more effort into it then you would see it. The overtone
series dictates to all just as the law of gravity... you can refuse to
ignore it just as any other primitive person... it's your choice. But the
overtones dictate no matter what. It is a mathematical principle which you
should study upon more. The beatings produced by two pure sinusoids still
happens as prescribed by the overtone series. In this case few intervals are
involved and a less complex interaction exists but an interaction exists
nonetheless.
>> The minor mode is a mode of the major scale. It is a direct
>> consequence of the major mode and not vice versa.
>
> The major mode hardly existed in European music before the
> Renaissance.
> It's not ancestral to anything.
Even if these were true, which it is not, it would not prove anything.
Again, could a primitive culture understand quantum mechanics? Ok, so
quantum mechanics must be wrong since it was not created by a primitive
culture? In fact the major modes existed in greek to a very large extend.
Lydian was a very popular mode almost as popular as dorian. Even though we
have very little understanding of how they actually used these modes.
>
>> If you don't agree show me a logical and natural construction of the
>> minor mode that is just as simple as the major mode.
>
> Who needs it? History is what it is. There are analyses of the
> nahawand scale of Arabic music (one form of the minor scale) that
> predate any known music in the major by centuries. The ancient
> Greeks had a highly sophisticated theory of their music that never
> mentioned the major scale.
This is complete ignorance. I suggest you actually study some history of the
greek modes. How bout you read plato who specifically mentions the major
modes in his republic.
Again though, it is irrelevant. We don't discount science because in the
distant past it did not exist, do we? I guess with your logic we do... What
a sad state of affairs.
The fact of the matter is that because of the conclusions from the overtone
series suggestions that certain cultures "got it right" while others did
not. You do not want to accept this because you believe that music is
completely subjective. This is fine because music is completely
subjective... but has nothing to do with the overtone series. The overtone
series only says what is natural. If music coincides with the overtone
series it is more natural than others. This is neither good nor bad but
something you don't understand.
Similarly how it is natural for people to fall down to earth and not float
upwards. It is natural because of the law of gravity. You want to believe
that there is no such law because of your preconcieved notion of "natural"
as better. A primitive culture may have "got it wrong" but this does not
mean it is bad. This is because music is an aethestic and does not have any
physical consequences such as the law of gravity.
In any case you still won't get it because of your bias and
misunderstanding.
Alain Naigeon
89mdnXNPbLBI5nnX...@giganews.com...
>
> "Alain Naigeon" <anai...@free.fr> wrote in message
> news:4ae428bd$0$714$426a...@news.free.fr...
>> "Vilen" <vi...@online.de> a �crit dans le message de news:
>> 640d9731-a028-42f5...@h2g2000vbd.googlegroups.com...
>> On 24 Okt., 17:23, Steve Latham <llat...@odu.edu> wrote:
>>
>>>BEFORE you start looking at WHY Major is better than minor, you first
>>>have to PROVE that Major is better than minor.
>>>Otherwise, your method is unscientific and illogical, and your
>>>evidence is suspect.
>>
>> I think that superiority of major is common view.
>>
>> Another common view : major is gay, minor is sad;
>> A third common view : sad music is better.
>>
> By that logic, then it follows that since minor is better, it must be
> superior!!
>
>> So... what about the truth contained in common views?
>
> There doesn't appear to be much "truth" here.
Tom, that's exactly what I meant, though not as explicitely
as you've just done ;-)
Jon Slaughter
> What I would say is that in the area of creating, confirming and
> maintaining a key feeling (i.e. tonal centre with a tonic, a chord
> whose root is that tonic, and similar chords available whose roots
> are a P5th above and below that tonic) the major triad is an easier
> target to maintain than the minor triad.
>
> The first problem with minor triads as tonic chords is that the
> intervals in minor triads all have different acoustical roots, whereas
> all the intervals in the major triad have the same acoustical root. So
> right off the bat the minor triad is not as suitable a target for
> becoming a home chord as the major triad is.
And this relates to the overtone series... It can be proven directly from it
why what you said is "natural". Can you logically show why your statement
makes sense not using the overtone series?
>
> The 2nd problem is the lack of a leading tone or of a V7 chord within
> the natural minor scale. In major keys the leading tone and the V7
> chord are the two main pointers that composers have used to point to
> and confirm the I chord as home. These pointers are missing in the
> natural minor scale so they had to be grafted onto it via musica
> ficta.
And this also supports why the minor mode is artificial. It was modified in
a way to resemble the major mode. If it were the other way around one would
except the major mode to have a minor dominant or at least some borrowing
from the minor mode while the minor mode would have stood intact. Of course
now days one can somewhat freely mix the two modes.
>
> But as far as major being better than minor from an aesthetics pov,
> that's just silly.
Of course... at least for the most part. The overtone series tells us what
is "natural". By this I simply mean what is natural in the sense of the
physical world. Similarly how objects fall to earth and not float away. It
is natural to have such things because of the "law" of gravity. Natural
does not mean better except when better mean more natural.
The most "natural" music would be simply that of the unison. But it is not
the best. The reason is because we, as humans, need change to be
interested. There must be enough relationship to what is natural to have it
make sense(more likely to be "consistent") and enough variety to create
change(so it is new and different).
The most basic pitch class is P4-T-P5. Without this it is extremely
unnatural. Without any context this would be unacceptable. As you add more
tones you get further away from being natural and more variety can
exist(hence the choice between the 3rds and others). Primitive cultures,
being free to choose because there are no ramifications, had the choice to
choose which every pitch class they wanted. Almost all got the P4-T-P5 right
and added the other tones as they did. Again, neither bad nor good but what
is just physically the most natural. Even if they choose something entirely
different does not mean it is bad but just unnatural.
But to reiterate, having the most natural is not always the best. This is
the problem most of you guys don't get. You want to ignore the ramifications
of the overtone series... but it is because of your belief that if the OT
had any ramifications they must dictate or judge what is created. They do
not dicate but they do judge in terms of naturalness. Some people find that
aesthetic as better than of unnaturalness while it is the opposite for
others.
For example, some like paintings that are extremely detailed and natural...
lets say photographic(not sure what they call it) while others like
paintings that make no sense to most people... maybe stuff drawn with poo
from a monkey by the monkey.
I guess there are a lot of non-musical reasons why people choose to either
go along with the "naturalness" imposed by the overtone series(which,
physically, does dictate a lot of stuff) and go against it. Ultimately most
people choose some middle ground. Again, because there are no consequences
to the choice you will find people all over.
What do I mean by "naturalness"? Simply the consonance/disonance. That is
all the overtone series dictates. It tells us what is consonant and what is
disonant. In fact we can even put numbers to it. It doesn't tell us how to
interpret or how we should feel or which is better or not(again, unless
better means to agree with the overtone series).
It is natural that when you through a ball that the ball eventually goes
down and not up. This is not always the best thing(such as if the ball was a
spacecraft). Gravity dictates to us what is "natural" but, as always,
natural is not always what we want.
Joey Goldstein
> Joey Goldstein wrote:
>> What I would say is that in the area of creating, confirming and
>> maintaining a key feeling (i.e. tonal centre with a tonic, a chord
>> whose root is that tonic, and similar chords available whose roots
>> are a P5th above and below that tonic) the major triad is an easier
>> target to maintain than the minor triad.
>>
>> The first problem with minor triads as tonic chords is that the
>> intervals in minor triads all have different acoustical roots, whereas
>> all the intervals in the major triad have the same acoustical root. So
>> right off the bat the minor triad is not as suitable a target for
>> becoming a home chord as the major triad is.
>
> And this relates to the overtone series... It can be proven directly
> from it why what you said is "natural". Can you logically show why your
> statement makes sense not using the overtone series?
Of course not.
The phenomenon of acoustical root is brought about because of the
overtone series.
>> The 2nd problem is the lack of a leading tone or of a V7 chord within
>> the natural minor scale. In major keys the leading tone and the V7
>> chord are the two main pointers that composers have used to point to
>> and confirm the I chord as home. These pointers are missing in the
>> natural minor scale so they had to be grafted onto it via musica
>> ficta.
>
> And this also supports why the minor mode is artificial. It was modified
> in a way to resemble the major mode.
Yes. But no so much as just to "resemble" it.
Musica ficta is introduced so that minor keys feeling can be maintained
as concretely as their major key cousins.
> If it were the other way around
> one would except the major mode to have a minor dominant or at least
> some borrowing from the minor mode while the minor mode would have stood
> intact. Of course now days one can somewhat freely mix the two modes.
I don't know that that necessarily follows.
Steve Latham
>
> What I would say is that in the area of creating, confirming and
> maintaining a key feeling (i.e. tonal centre with a tonic, a chord whose
> root is that tonic, and similar chords available whose roots are a P5th
> above and below that tonic) the major triad is an easier target to
> maintain than the minor triad.
????
Only if you start with that assumption.
Remember, targets at first were single tones, then perfect 5ths. By
the time 3rds get added, there doesn't seem to be any preference for a
major triad over a minor one.
If anything, it's the LEADING TONE that's more important in making the
final chord the target.
There's enough music in Minor modes (modal and tonal) that shows
establishment of a minor tonality and thus making a minor chord a
target harmony is no more difficult than Major.
>
> The first problem with minor triads as tonic chords is that the
> intervals in minor triads all have different acoustical roots, whereas
> all the intervals in the major triad have the same acoustical root. So
> right off the bat the minor triad is not as suitable a target for
> becoming a home chord as the major triad is.
Joey, you're trying to explain something that does not actually
happen. Minor chords are, I would guess given the entire body of
music, which I've not yet studied in toto, as likely a final chord as
a Major chord.
This is a flawed argument. When you start with "minor is not suitable"
you can't just start spouting off acoustical roots as the reason,
unless you can prove that composers didn't find minor tonics suitable
for that very reason. In the absence of written documentation from
various composers that says "I don't find the minor tonic as a
suitable target because...." then you really only have extant music to
look at. And given the fact that there are more than a couple of Minor
targets, the logical assumption is that they found them "suitable
enough".
>
> The 2nd problem is the lack of a leading tone or of a V7 chord within
> the natural minor scale. In major keys the leading tone and the V7 chord
> are the two main pointers that composers have used to point to and
> confirm the I chord as home. These pointers are missing in the natural
> minor scale so they had to be grafted onto it via musica ficta.
Not in Phrygian. Why?
Because that's not the reason.
>
> But as far as major being better than minor from an aesthetics pov,
> that's just silly.
With that I agree.
Though most of the cool music is in minor :-)
Steve
tom_k
> "tom_k" <tko...@comcast.net> a �crit dans le message de news:
> 89mdnXNPbLBI5nnX...@giganews.com...
>>
>> "Alain Naigeon" <anai...@free.fr> wrote in message
>> news:4ae428bd$0$714$426a...@news.free.fr...
>>> "Vilen" <vi...@online.de> a �crit dans le message de news:
>>> 640d9731-a028-42f5...@h2g2000vbd.googlegroups.com...
>>> On 24 Okt., 17:23, Steve Latham <llat...@odu.edu> wrote:
>>>
>>>>BEFORE you start looking at WHY Major is better than minor, you first
>>>>have to PROVE that Major is better than minor.
>>>>Otherwise, your method is unscientific and illogical, and your
>>>>evidence is suspect.
>>>
>>> I think that superiority of major is common view.
>>>
>>> Another common view : major is gay, minor is sad;
>>> A third common view : sad music is better.
>>>
>> By that logic, then it follows that since minor is better, it must be
>> superior!!
>>
>>> So... what about the truth contained in common views?
>>
>> There doesn't appear to be much "truth" here.
>
> Tom, that's exactly what I meant, though not as explicitely
> as you've just done ;-)
>
Sorry if I misunderstood you, Alain.
Tom
tom_k
"Jon Slaughter" <Jon_Sl...@Hotmail.com> wrote in message
news:hc2bcp$b03$1...@news.eternal-september.org...
>>
>
> Actually the modes used today are not even close approximations of what
> was used by the greeks there is very few documents surviving that even
> come close.
True.
> In fact the major modes existed in greek to a very large extend. Lydian
> was a very popular mode almost as popular as dorian. Even though we have
> very little understanding of how they actually used these modes.
But you just said that the Greek "modes" have nothing to do with the
"church" modes - and now you claim that what the Greeks called Lydian =
Major?? You might want to review the Greek system of tetrachords for a
start.
> How bout you read plato who specifically mentions the major modes in his
> republic.
Jon, can you provide a source for this assertion? If the Greeks employed
the major scale, I'm sure lots of musicolgists would love to know about it!
Tom
Jon Slaughter
Well, "feelings" of what? Thats what I mean by resembles. The harmonic
movement of dominant to tonic is very strong in major and was used as the
model for minor.
>
>> If it were the other way around
>> one would except the major mode to have a minor dominant or at least
>> some borrowing from the minor mode while the minor mode would have
>> stood intact. Of course now days one can somewhat freely mix the two
>> modes.
>
> I don't know that that necessarily follows.
Maybe not necessarily but it is a probability considering the consequences.
It may or may not be true but no other logical explanation exists that makes
sense... at least from what I have read. Things like that don't happen by
happenstance and it's not a random occurance that just happened to create a
whole aethestic art around it. I don't know if we will ever know exactly how
it came about but it makes sense considering there is no real counter
evidence to suggest otherwise.
Joey Goldstein
> On Oct 25, 12:52 pm, Joey Goldstein <nos...@nowhere.net> wrote:
>
>> What I would say is that in the area of creating, confirming and
>> maintaining a key feeling (i.e. tonal centre with a tonic, a chord whose
>> root is that tonic, and similar chords available whose roots are a P5th
>> above and below that tonic) the major triad is an easier target to
>> maintain than the minor triad.
>
> ????
>
> Only if you start with that assumption.
>
> Remember, targets at first were single tones, then perfect 5ths. By
> the time 3rds get added, there doesn't seem to be any preference for a
> major triad over a minor one.
If you can trey to put historical practise and statistics aside and look
at contemporary practise within maj/min tonality, maybe you'll see more
of what I'm trying to get at.
I.e.
It's just as tricky today to create and sustain a minor key feeling as
it was at any other point in music's development (in which the concept
of "minor key" makes any sense to be talking about). It's less tricky to
create a major key feeling. That's what I'm suggesting.
And although I'm invoking contemporary notions of key, I'm trying to
limit this discussion to traditional notions of what a minor key is. Eg.
A modern piece in phrygian mode is not really a piece in "a minor key".
It's not in a "key" at all really.
The main techniques that delineate a key-based tonal centre from a modal
tonal centre are the use of leading tones and V7 chords. Stick a V7
chord into a modal phrygian texture and it's not a phrygian texture
anymore, it's then a minor key.
The same is true for the aeolian mode, aka the natural minor scale.
Start using leading tones and V7 chords and it's not modal music
anymore, it's a minor key.
But leading tones and V7 chords are not wholly diatonic to the aeolian
scale. I know it's common practice to call the harmonic minor and
melodic minor scales "diatonic scales" and to call the maj 6th and the
maj 7th "diatonic to the minor key", but we all know, or should know,
that these sounds are not really found in "the diatonic sale". They
have to be grafted in artificially.
No such extra artifice is required to turn ionian into a major key. All
the elements are already present.
> If anything, it's the LEADING TONE that's more important in making the
> final chord the target.
True. But the ambiguous nature, as far as acoustical root is concerned,
of the minor triad is also a factor. It's not the deciding factor, but
it is a factor.
Eg. If you end a piece in major on a partial voicing of I it is several
times less confusing to the ear than if you end a piece in minor on a
partial voicing of Im. The only reason for this is that each of the
intervals of the minor triad has a different acoustical root whereas all
of the intervals of the major triad have the same acoustical root.
> There's enough music in Minor modes (modal and tonal) that shows
> establishment of a minor tonality and thus making a minor chord a
> target harmony is no more difficult than Major.
Just because people happened to do it statistically does not mean that
it was just as easy to do. I think that statistically speaking you might
even find more key-based music in minor keys than in major keys.
One reason for this is that music in minor keys tends to be more complex
harmonically and melodically than music in major keys, and this owes
again to the ambiguities that minor key music is imbued with.
>> The first problem with minor triads as tonic chords is that the
>> intervals in minor triads all have different acoustical roots, whereas
>> all the intervals in the major triad have the same acoustical root. So
>> right off the bat the minor triad is not as suitable a target for
>> becoming a home chord as the major triad is.
>
> Joey, you're trying to explain something that does not actually
> happen. Minor chords are, I would guess given the entire body of
> music, which I've not yet studied in toto, as likely a final chord as
> a Major chord.
True. But composers have gone to great lengths to inject techniques that
are completely self-contained in major key harmony into minor key
harmony where they didn't exist. In minor keys, if you take away the
hallmarks of major-key harmony, namely the leading tone and the V7
chord, you don't really have "minor-key harmony" anymore. You've then
got an aeolian modal texture. And chromatic movement away from the basic
aeolian pitch collection will destroy that feeling of the aeolian tonal
centre. To re-establish the aeolian tonal centre you'll need to start
from scratch again, most likely with some sort of a drone. (see below)
> This is a flawed argument. When you start with "minor is not suitable"
I never said "minor is not suitable".
What I said is that it is more difficult to establish and to maintain.
And that is not a flawed argument. It's a fact of musical life.
> you can't just start spouting off acoustical roots as the reason,
Well, sorry. But it is one of the reasons.
> unless you can prove that composers didn't find minor tonics suitable
> for that very reason. In the absence of written documentation from
> various composers that says "I don't find the minor tonic as a
> suitable target because...." then you really only have extant music to
> look at. And given the fact that there are more than a couple of Minor
> targets, the logical assumption is that they found them "suitable
> enough".
Again, try to put the history aside.
Let's say that you want to create a feeling of a minor key, today.
Can you do it without using a leading tone or a V7 chord?
My answer would be yes, but I've talked to many classical guys who would
say no. They would call a tonal centre associated with a minor triad
that did not use any leading tone movement to the root of that triad a
modal piece of music, akin to folk music.
And it's my contention that if you begin with an aeolian tonal centre
and then start bringing in harmonies from outside of the aeolian sale,
in almost any capacity, then that feeling of a modal aeolian tonal
centre will be lost rather quickly and will be supplanted by a feeling
of some other different tonal centre.
Yet if we do start using leading tones and V7 chords it's quite a bit
easier to get that Im feeling back after wandering away. But if you do
it that way it's not an aeolian tonal centre anymore. It's then a minor
key, because that leading tone and that V7 chord had to be grafted into
the texture artificially.
>> The 2nd problem is the lack of a leading tone or of a V7 chord within
>> the natural minor scale. In major keys the leading tone and the V7 chord
>> are the two main pointers that composers have used to point to and
>> confirm the I chord as home. These pointers are missing in the natural
>> minor scale so they had to be grafted onto it via musica ficta.
>
> Not in Phrygian. Why?
I don't follow this question, not the answer below.
> Because that's not the reason.
>
>> But as far as major being better than minor from an aesthetics pov,
>> that's just silly.
>
> With that I agree.
>
> Though most of the cool music is in minor :-)
>
> Steve
Joey Goldstein
Jon.
Major keys and minor keys are a fairly recent device in the development
of music over the eons.
They may seem inevitable to us today, but that is by no means the truth.
If the musicians after Pythagoras' time had not decided that they wanted
to hear more compatible tones sounding simultaneously, i.e. more complex
harmonies, then they never would have experimented with tempering the
intervals within the diatonic scale so that they could have chords with
nicer sounding 3rds in them, and we never would have even progressed to
triads let alone the maj/min key system.
Who knows what we'll do next as we try to go beyond maj/min tonality and
into even more complex combinations of tones?
None of this is a given, or we'd know already what we're going to do
next and Pythagoras would have known what we were going to do.
Jon Slaughter
> "Jon Slaughter" <Jon_Sl...@Hotmail.com> wrote in message
> news:hc2bcp$b03$1...@news.eternal-september.org...
>>>
>>
>> Actually the modes used today are not even close approximations of
>> what was used by the greeks there is very few documents surviving
>> that even come close.
>
> True.
>
>> In fact the major modes existed in greek to a very large extend.
>> Lydian was a very popular mode almost as popular as dorian. Even
>> though we have very little understanding of how they actually used
>> these modes.
>
> But you just said that the Greek "modes" have nothing to do with the
> "church" modes - and now you claim that what the Greeks called
> Lydian = Major?? You might want to review the Greek system of
> tetrachords for a start.
No I didn't say that. If you read the last sentence you might understand
why. We generally assume that lydian is major and we do have some historical
evidence(But it could have been misinterpreted).
>
>> How bout you read plato who specifically mentions the major modes in
>> his republic.
>
> Jon, can you provide a source for this assertion? If the Greeks
> employed the major scale, I'm sure lots of musicolgists would love to
> know about it!
Have you read plato's republic? He specifically discusses the musical modes
and there characteristics and when and how they should be used. Note, I said
major mode and not major scale. Given that there are only 3 minor modes and
3 major modes do you not agree that if 4 modes are mentioned then it is a
must that at least one would be major? (assuming locrian is out of the
picture. If locrian was used to express happiness then thing is totally
wrong with the picture)
In any case I can give other ample evidence but probably shouldn't since
your question was rhetorical.
Was Aristoxenus greek? I believe he was the guy where we get most of our
understand about music of the greeks?
"..that a whole-tone above the Dorian is the Phrygian, and that the Lydian
lies another whole-tone above the Phrygian."
This alone proves, assuming the modes actually means a sort of "rotation" of
the scale(which is most probable). Why? Because even if the names were not
correct we do not have 3 minor modes in a row. At most you have 2, hence in
this case at least one of those modes must be major.
Sure there are some assumption being made but no worse than what you have
made.
"Classifier: Apollonius <called> the Classifier, because, being naturally
talented, he distinguished in the Library the different genres [of literary
compositions] according to their musical mode: in fact, among the
various odes, he put together those which were supposed to be performed
to a Dorian mode, and he did the same for those performed
to a Phrygian, Lydian, Mixolydian and Ionic mode too."
Again, your believe that only a minor mode existed is complete nonsense. In
fact it's ridiculous to believe that for festive ocassions they would use
minor modes for the melodies and never reach into the major modes.
It is my guess that dorian is actually our lydian(or at least the closest
one) and phrygian is is mixolydian and the lydian is aeolian. Because of the
limited documentation we have passed down and the potential for errors(after
all, we already see a change from the church modes and the greek modes)
http://en.wikipedia.org/wiki/Musical_mode
"In fact, the church modes originated in the 9th century. Authors from that
period created confusion by trying to use a text by Boethius, a scholar from
the 6th century who had translated Greek music theory treatises by
Nicomachus and Ptolemy into Latin"
"probably translating the Greek word t??p?? (tropos), which he also rendered
as Latin tropus (Bower 1984, 253)�in connection with the seven diatonic
octave species, so the term was simply a means of describing transposition
and had nothing to do with the church modes"
It would do you good to read that site then read a bit from plato's
republic. In many of the greek texts we generally see "dorian" melodies
associated with happy occasions. While modern dorian could potentially be
used for such I think there is potential for other possibilities. Similarly
how phrygian is also considered in many festive situations. I'm not a
musicologist nor a ancient greek scholar. One could attribute my opinions as
simply cultural differences but it would be hard for me to comprehend our
locrian mode as being their dorian. Hence there is some evidence to suggest
that our phyrgian is not a happy and festive mode and hence was probably not
their phrygian.
Would you accept that if, say, our musical system was passed on to a future
generation only by a single bach piece that it would be impossible to
determine the "mode". If they only knew that it was music and the dots meant
pitch they could not conclude what mode it was in? After all, one would
first have to get the clef correct for the mode to be right but how could
they with such limited information? I'm not questioning the results of all
the "scholars" though as many of them have spent a few days on it. Like you
they make a lot of assumptions though. It is my best guess they are right
though but in any case it is irrelevant to the application of the overtone
series to the naturalness of the major scale.
Jack Campin - bogus address
> > mode in the music of Europe and Western Asia since the beginning of
> > music theory has been the Dorian. It wasn't "Mode I" for nothing in
> > the mediaeval scheme both in Western and Byzantine chant, and it's
> > overwhelmingly the commonest 7-note mode in the folk music of the
> > Turkic and Finno-Ugrian peoples. (Major is rare in both, *very* rare
> > in all Middle Eastern folk cultures).
> Actually the modes used today are not even close approximations of what
> was used by the greeks there is very few documents surviving that even come
> close.
I didn't mention ancient Greek modes in that paragraph, so you comment
is irrelevant. And there is plenty of documentation of what their modal
systems were like, as just about any serious book on the history of music
will tell you.
The major was not "natural" to anybody in ancient Greece, and it wasn't
natural to anyone doing liturgical music in either the Western or the
Byzantine traditions. It isn't natural to a modern Turkish folk singer
and it's a minor feature of modern Hungarian folk song. So much for any
claims to universality.
> In any case your believe that history predicates logic is entirely
> ignorant.
I can't imagine what you mean by "history predicates logic". It's
gibberish.
> Do you not believe that intellectual understanding advances in time and not
> backwards? Do cultures become more ignorant or less over time(in general)?
We learn new stuff, we forget old stuff. How many antimicrobial plants
can you identify in your environment, and how many do you know how to
prepare for medicinal use? Can you tell the time by the stars?
Some cultures have managed to forget less of what you're talking about
here. I watched the finale of a Turkish TV quiz show two or three years
ago. The crunch questions played fragments of a few recent pop hits and
then asked the contestants *what makam each of them was in* (choice of
four boxes). The point being that this was a tough question but not a
totally insane one.
>> The worldwide pattern is for less developed cultures, on the whole,
>> to make music in scales that span a range far less than an octave,
>> and with no one scale predominating. This is still the pattern in
>> some relatively advanced societies, as with the folk music of Egypt,
>> Kurdistan and Azerbaijan. The range can get *very* small, as in one
>> genre of Melanesian song that uses only three adjacent semitones.
> And in almost all these cultures they base there music off the fundamental
> P4-T-P5 relationship, do they not?
No they don't. Not even in some very sophisticated ones. The slendro
scales of Indonesian music are approximately 5-tone equally tempered.
They have a range of several octaves available to them, but don't use
pure fourths and fifths at all. The art music traditions of the Middle
East construct scales in tetrachords (sometimes trichords or pentachords)
which don't have to contain any pure fourth or fifth. Usually they do,
but some like the saba tetrachord don't, and saba features in all these
traditions from the early Middle Ages to the present day. (Usually it's
extended with another tetrachord in such a way that the complete scale
has a pure fifth but doesn't have either a pure fourth or a pure octave).
Nobody playing or listening to that sort of music thinks there's anything
wrong with saba because it doesn't fit your scheme of things.
If 4ths and 5ths were as culture-free as you're implying, they'd feature
in everybody's music, back to when we found out how to make fire. They
don't. So they're culturally specific artifacts.
> Adding the M3rd is the next logical step.
Maybe "logical" in your peculiar logic, but not in the logic of
history. It didn't happen like that anywhere.
>> The overtone series doesn't come into it when you never sing *any*
>> harmonics. It's irrelevant to most of the music humanity has ever
>> produced.
> Your absolutey wrong in both cases. It is an ignorant statement and
> I believe if you put more effort into it then you would see it. The
> overtone series dictates to all just as the law of gravity.
Dictates what, exactly? Doesn't seem to have stopped the ancient Greeks
coming up with a scale like the intense chromatic. Didn't stop some of
the cultures of southern Africa from using 7-tone equally tempered scales
so you could start any of their songs on any pitch.
> you can refuse to ignore it just as any other primitive person.
Can we pretend you just never said that? (Think about the implications,
they are not pretty).
> it's your choice. But the overtones dictate no matter what. It is
> a mathematical principle which you should study upon more.
I've done all that mathematics, years ago. Enough to know how little
relevance it has to musical aesthetics and historical development at
the very basic level you're talking about. (It does relate to the
harmonic techniques of certain specific kinds of music, but even for
those, not in the uniform way you're suggesting).
> The beatings produced by two pure sinusoids still happens as
> prescribed by the overtone series.
What has that got to do with somebody singing a monophonic melody with
a range of a third? How are they supposed to use the information?
> This is complete ignorance. I suggest you actually study some history
> of the greek modes. How bout you read plato who specifically mentions
> the major modes in his republic.
Does he now. Where? (I've read it, several times. I have both the
Jowett and Bloom translations upstairs. Let's see you try to prove
that).
Jon Slaughter
If you mean by key a "tonal" thing then yes, you are right. But as a scale
you are wrong. Pythagoras worked out all the consonant tones from day one
and figured out the overtone series. I don't know what he did before or
after or if he really did this but this is what our history tells us. The
greeks were highly scientific and music was treated in a scientific way. It
is doubtful it was all happenstance as you are suggesting. They may not have
had the luxury of the past to give them direction but they did have
direction... the only direction they could have had... which was from
science. (hence why music was treated as a scientific device because it was
precisely that to them)
In fact, it seems that they treated music in a much more scientific way than
we do. They might not have the concepts that we have such as tonality,
pandiatonism, chromatism, etc but they approached it in a mathematical way.
This is precisely how I try to approach it too. It could have all been like
you are suggesting but if it were then music is meaningless and we are
simply perpetuating a random event. Of course history suggests otherwise and
it is only a matter of understanding that history to figure the most likely
truth.
Joey Goldstein
Assuming that by "a "tonal" thing" you mean a key, then yes that's what
I meant. Lol.
By key I mean the type of tonal centre used in the music of the
classical style which is still being used in various guises in today's
music, as opposed to music which used other types of tonal centres like
Medieval modal music and whatever types of tonal centres predated that.
> But as a
> scale you are wrong.
Hmm. I was aware of the Greeks referring to scales with small or large
3rds, but I was not aware that they used the terms "major" and "minor"
to describe them. Is this true?
> Pythagoras worked out all the consonant tones from
> day one
What do you man by "consonant tones" here?
Do you mean the pleasing and displeasing intervals that can be formed
from the Greek diatonic scale of pure 5ths?
Or do you mean what we generally mean today as consonant, namely the
intervals as found in the overtone series?
My understanding is that the only intervals in the Greek diatonic scale
that went well together were octaves, fifths, 4ths and maj 9ths (maybe
min 7ths too). I don't believe that they were too fond on the large and
small 3rds and 6ths that exist within that scale. That's why later
generations of musicians sought to temper the intervals of the Greek
diatonic scale, so that 3rds would be more consonant and therefore more
useful for music making.
But I could be wrong.
> and figured out the overtone series.
I was not aware that they had figured out the entire overtone series, or
if they had that they thought of it as such.
I know that they were involved with dividing vibrating strings into
various equal divisions, but I'm not aware how many divisions they
thought were relevant to their music or to their musical understanding.
> I don't know what he did
> before or after or if he really did this but this is what our history
> tells us. The greeks were highly scientific and music was treated in a
> scientific way.
>
> It is doubtful it was all happenstance as you are
> suggesting.
Well, while the discovery of the sound of what we now call the P5th
interval was based on scientific enquiry, what musicians decided to do
with that sound is "art", not happenstance.
The creation of the diatonic scale is art based on a scientific idea,
the same way that the fractal pictures we see today are.
There was no pure scientific reason really that I can see to go stacking
6 P5ths on top of each other and to then transpose the resulting pitches
so that they spanned a single octave, although there were logical
reasons why it made sense to stop at 6 P5ths (or at 11 P5ths in the case
of the Greek chromatic scale). They just liked the sounds they were getting.
The tempering of the diatonic scale and the creation of Tonal harmony
was also art, not science, not happenstance.
There are scientific principles at work behind all art and many
scientists insist that science is art too. But they are not really
exactly the same things, IMO.
[Religion was also man's earliest attempt at science, and look what it
got us. That's irrelevant, but I felt like saying it anyway.]
> They may not have had the luxury of the past to give them
> direction but they did have direction... the only direction they could
> have had... which was from science. (hence why music was treated as a
> scientific device because it was precisely that to them)
>
> In fact, it seems that they treated music in a much more scientific way
> than we do. They might not have the concepts that we have such as
> tonality, pandiatonism, chromatism, etc but they approached it in a
> mathematical way. This is precisely how I try to approach it too. It
> could have all been like you are suggesting but if it were then music is
> meaningless and we are simply perpetuating a random event. Of course
> history suggests otherwise and it is only a matter of understanding that
> history to figure the most likely truth.
Jon Slaughter
Obviously they did not have the same notion of key but had "something" that
has an innate relation. They had the idea of tonis, which, I guess, could
be concieved as a precursor to tonality.
>> But as a
>> scale you are wrong.
>
> Hmm. I was aware of the Greeks referring to scales with small or large
> 3rds, but I was not aware that they used the terms "major" and "minor"
> to describe them. Is this true?
I actually don't know. I can only describe what I know by using language I
know. I do not even know if the pitch classes they used can even be
categorized in any way that our music theory allows. I do know from what I
read that basically they had the modal system we use today as far as pitch
class is concerned. I also know they modified the intervals because, after
all, they didn't have the equaltemperament idea yet.
The original supposition still stands though. I do not know of one case
where humanity has progressed towards the primitive except in the cases
where catastrophic events forced such things(but those have been only local
setbacks).
The point being is that we don't start out with a more accurate theory and
then develope a less accurate one from it. Quantum mechanics came out of
newtonian mechanics and not the other way around... it is impossible... at
least implausible.
So to point to historic cultures as proof that the overtone's do not have
relation to music is ignorant. We can't expect them to have gotten it right.
It takes time and evolution perfect such things. We don't even have it
right.. but we are closer than they are.
I feel those arguing against it is mainly a way to preserve their need to
preserve cultural signifance in music. e.g., the indians created their music
and if they are primitive and primitive music was not as perfect then it is
not good music. This is somewhat true but history is very important and
necessary. Without such music we could not perfect it. Also since music is
an aethetic it has value in that reguard independent of how "perfect" it is.
In fact I would say that because music is a very complex interaction between
physical and psychological things it is impossible to actually objectively
"grade" it. What we can say though is that if some cultures musical identity
has not progressed then the music is primitive.
Surely you would agree that if a culture's music was what it was in the
begining when the culture was primitive then the music would be primitive?
Of course this is very difficult to judge since there are no primitive
cultures left(a few are close and their music is not highly developed).
While it is not scientific proof it is better than nothing...
>
>> Pythagoras worked out all the consonant tones from
>> day one
>
> What do you man by "consonant tones" here?
> Do you mean the pleasing and displeasing intervals that can be formed
> from the Greek diatonic scale of pure 5ths?
> Or do you mean what we generally mean today as consonant, namely the
> intervals as found in the overtone series?
> My understanding is that the only intervals in the Greek diatonic
> scale that went well together were octaves, fifths, 4ths and maj 9ths
> (maybe min 7ths too). I don't believe that they were too fond on the large
> and small 3rds and 6ths that exist within that scale. That's why later
> generations of musicians sought to temper the intervals of the Greek
> diatonic scale, so that 3rds would be more consonant and therefore
> more useful for music making.
> But I could be wrong.
>
Pythagoras took several strings and stretched them. He let them vibrate
freely. He noted that as when he changed the length(or tension as it doesn't
matter) that he could create such a condition that the strings would be
heard as identical. We call this the unision. He then proceded and found the
octave, the 5th, etc.. When he did this he realized that some relations
sounded more "alike" than others. He called this consonance(I don't know who
actually created the term).
If he were to rank them(no doubt he did), he found that the relations were
most "consonant" with the unision then octave and progressively became less
consonant. He then figured out a mathematical way to state this:
If F is you the fundamental frequency of the referenced string then the most
consonant to least consonant's are
1F 2F 3F 4F 5F ....
1F was the unison, 2F the octave, 3F the P5th, 5F the double octave, etc...
So consonances is a mathematical relationship to the fundamental.
You might ask, what about the frequency 1.2342F? Is that consonant or
dissonant? We can determine this using the above principle by extending
through octaves. In this case 1.2342F = 12342F (at some octave) and hence it
would be extremely far from the fundamental and not be consonant. This is
artificial though and actually not true since our ears are not perfect.
What we later found out(not sure where it started) was that when two
strings(or pipes or whatever) are sounded that are not close in frequency
one gets beating. This beating is actually the envelope of the total sound
and is created from the destructive interference. The beats are exactly at
the difference in frequency. (because an actual sound is generally a complex
of harmonics it is more difficult but is based on that principle)
What we hear as the "beats" is really what is meant by consonances. Beating
is bad and is heard as a dissonance or a disagreement between the sounds. A
minor 3rd has more dissonance than the major. It is pleasurable if you
prefer agreement. But pleasure is subjective. Consonance is mathematical.
Helmholtz in fact gave a method to give the consonance of a complex of
pitches.(such as measuring the consonance of a chord)
Because a real sound is made up of overtones we actually need to compute the
beatings of all the relations between the sounds. (up to a point at least as
eventually the beatings are so fast as to be heard as actual tones)
The ET is a compromise as it introduces slight differences that our ears
generally except but realize that most music sounds much better in just
intontation which is the scale produced by exactly integer ratios. The
problem, as you already know, has to do with creating a scale where each
note can be used as the tonic which is not the case with JI.
Now, about the chain of P5's. If it actually was used the logic probably
went something like this: Start with C. If we take the octave we get C
again. It produces nothing. So the next logical choice is the P5. It gives
us G which is the first new tone. G is very consonant with C. In fact it is
the most consonant tone that is distinct from C. Hence it holds special
"powers"(remember, pythagoras was basically a mystic). But why is C special?
We could have started with G? If we did we would get D. Why not D? We get A.
Hence the logic, which is simply based off beliving that the P5 is the most
fundamental interval that produces something new(which it is with respect to
the overtone series) gives you all the notes(in fact an infinite number but
we have to stop at some point to make sense of it all).
We could apply the same logic to the semitone and this gives us the
chromatic scale. Or we could apply it so the interval of 1.2342F which gives
a class of pitches that we could use to make music. We could use F + 100k
but unfortunately this means that we have to fix the fundamental for
everyone if we want to have melodies that can be transposed. (e.g., for F =
A we get a completely different sounding melody than for F = C even though
they use the same pitch class)
The historic event is how pythagoras discovered the overtone series and how
the P5 as the signal most important interval that created something new. The
next being the P4 by the exact same logic and assuming that the fundamental
was "movable"(relativity basically). After than we can use the same basic
logic to get the next new pitch which is the M3rd. Those 2 ideas gives us
the diatonic scale and all the modes.
P5 idea gives us the P4 relation by inversion. (C is to G as F is to C and F
is the P4 of C)
M3rd is found by finding the next new tone as was done to find the P5. (we
could then get the m6ths from this also)
We could apply this again for the M2nd.
Any way we cut it we can use the overtone series to get what we want.
Because it is known that pythagoras did something like this we don't have to
know exactly what to give a best guess that our musical system is based on
the overtones. That is, our system would be totally different if it were
not... that the overtones are fundamental to our current musical practices.
In pythagoras's time it may have been different... as it takes time to
perfect our understanding of things...
But realize also that almost all our musical instruments are based on the
overtone series too. Pipes? exactly from what pythagoras discovered(F =
k*sqrt(T/l) I think is the formula) Strings? Same thing. What else is there?
drums? Ok, thats different... totally different. But it actually supports my
claim.
In actuality the very hole flute like instruments had holes that were not
aligned by the overtone series. I read somewhere that the performers had to
have a lot of techniques to get the notes right... in any case it is
irrelevant as those instruments were primitive and quickly replaced by
instruments based on pythagoras's findings.
>> and figured out the overtone series.
>
> I was not aware that they had figured out the entire overtone series,
> or if they had that they thought of it as such.
> I know that they were involved with dividing vibrating strings into
> various equal divisions, but I'm not aware how many divisions they
> thought were relevant to their music or to their musical
> understanding.
It doesn't matter. He quickly found the relation to the integers. It is
actually very beautiful because it is the most simple way.
For a drum head you have something totally different. You do have vibrations
but they are much more complex. The frequency spectrum of a drum beat is
much more complex and has nothing to do with simple integer ratio's. If you
record a simple note of an instrument and look at the spectrogram(shows us
the frequencies) you will see that the note has a frequency at almost
exactly integer multiples of the lowest frequency. (if your interested I can
do that for you)
Basically pythagoras found this out without using computers, ADC's, FFT's,
etc...
>> I don't know what he did
>> before or after or if he really did this but this is what our history
>> tells us. The greeks were highly scientific and music was treated
>> in a scientific way.
>>
>> It is doubtful it was all happenstance as you are
>> suggesting.
>
> Well, while the discovery of the sound of what we now call the P5th
> interval was based on scientific enquiry, what musicians decided to do
> with that sound is "art", not happenstance.
> The creation of the diatonic scale is art based on a scientific idea,
> the same way that the fractal pictures we see today are.
> There was no pure scientific reason really that I can see to go
> stacking 6 P5ths on top of each other and to then transpose the
> resulting pitches so that they spanned a single octave, although there
> were logical
> reasons why it made sense to stop at 6 P5ths (or at 11 P5ths in the
> case of the Greek chromatic scale). They just liked the sounds they were
> getting. The tempering of the diatonic scale and the creation of
> Tonal harmony was also art, not science, not happenstance.
> There are scientific principles at work behind all art and many
> scientists insist that science is art too. But they are not really
> exactly the same things, IMO.
> [Religion was also man's earliest attempt at science, and look what it
> got us. That's irrelevant, but I felt like saying it anyway.]
I understand that one can do whatever they like. I am simply saying that the
discovery of the overtone series and because it is the basis of sound(at
least simple sound such as strings and pipes) it influenced all music there
after.
Now, we can argue all day long about if the music is good or not depending
on how well it fits with the overtone series. I personally take the stance
that the everything we hear is based in it and bad music simply does not
fit. Bad can be good in the right context but in general we, as humans,
expect sound to fit in the overtone series. Our ears are conditions by
genetics and physics to understand sound that way. Music is an exploitation
of this and the psychological conditions of emotion.
So our music is a little bit of science and a little bit of psychology. But
the science is just as important. Both are necessary... well, it's not
necessary but innate.
The overtone series is as fundamental as the law of gravity. You don't
neglect gravity just because past civilizations didn't have a scientific
understanding of it? They understood it more or less... They understood the
overtone series more or less. It's just that we happen to understand it
more(again, because knowledge generally increases). It's nothing good or
bad... future civilizations will understand music better than us. This is
because because as humans we build off the past. We don't have to rediscover
everything at each step.
Think about it this way: You have the cave man paintings on the wall. This
is "Art" and has historical importance. But it is not the same as a van go.
Not only did our artistic expressions increase so has our social
awareness(more or less at least). Without the technological means van go
could not have created his paintings. Without the social need for such
things(if he was too busy trying to fend of the dinosuars) then it wouldn't
exist either.
The overtone series allowed us to develop more precise intruments... but to
build a whole structure that was congruent with that basic concept.
Pythagoras could easily have said "I hate conformity so I will not use the
P5 as the basis" and chose a random interval. He didn't because humans have
more of a need for unity than variety. You can only have so much unity(you
can't create anything more unified than the unision) but you can have an
infinite amount of variety.
Also don't forget that the overtone series led us to ET which lead to a
whole new system of harmonic understanding, atonality, etc... This couldn't
have happened without the overtone series and it's no doubt why other
cultures do not have such an expanded harmonic framework. They simply got it
"wrong" and were led down a dead end. Again, the music itself is still
historically and culturally significant and is variety. In fact, our
current western system may be a dead end...
Joey Goldstein
And here I thought that you were arguing that the maj/min key system was
"based on" the overtone series, which is something that I disagree with.
If you're only arguing that the sensation of a tonal centre, in general,
is based-on the OTS then I'd agree.
Part of the problem is that you and I use the phrase "based on" differently.
>>> But as a
>>> scale you are wrong.
>>
>> Hmm. I was aware of the Greeks referring to scales with small or large
>> 3rds, but I was not aware that they used the terms "major" and "minor"
>> to describe them. Is this true?
>
> I actually don't know. I can only describe what I know by using language
> I know. I do not even know if the pitch classes they used can even be
> categorized in any way that our music theory allows. I do know from what
> I read that basically they had the modal system we use today as far as
> pitch class is concerned. I also know they modified the intervals
> because, after all, they didn't have the equaltemperament idea yet.
>
> The original supposition still stands though. I do not know of one case
> where humanity has progressed towards the primitive except in the cases
> where catastrophic events forced such things(but those have been only
> local setbacks).
How 'bout cable news?
Or pop music?
All we can say is that current Western musical technology and theory is
more complex than earlier theories and technologies. Whether or not this
complexity is in and of itself an improvement is totally subjective
though. I don't think that Indian classical musicians see Western music
as being superior to their own music or their own music theories. In
some ways Western music is primitive compared to their music.
Many of your comments seem to express a type of cultural arrogance that
is kind of distasteful to me and I'm guessing to other readers here as
well. Western music is not superior to the music of all other cultures.
Rhythmically speaking it's miles behind Indian music and African music.
It's main contribution to the world of music is harmonic progression
IMO. That's no small feat mind you, but that doesn't make it superior in
and of itself.
> The point being is that we don't start out with a more accurate theory
> and then develope a less accurate one from it. Quantum mechanics came
> out of newtonian mechanics and not the other way around... it is
> impossible... at least implausible.
>
> So to point to historic cultures as proof that the overtone's do not
> have relation to music is ignorant.
Hmm. I haven't done that and I haven't noticed anybody else doing that.
Many of your comments are also ignorant, btw. And you've been throwing
that "i" word around a lot lately. Be careful. People in glass houses, etc.
> We can't expect them to have gotten
> it right. It takes time and evolution perfect such things. We don't even
> have it right.. but we are closer than they are.
Closer to what?
You can't try to judge ancient music with modern criteria, and visa
versa. It's quite likely that modern music is missing just as much
valuable stuff that was present in ancient music as it has improved upon it.
> I feel those arguing against it
Arguing against what?
You keep making comments that seem to making it your position that the
OTS is responsible for absolutely everything in music, and *that's*
ignorant.
> is mainly a way to preserve their need
> to preserve cultural signifance in music. e.g., the indians created
> their music and if they are primitive and primitive music was not as
> perfect then it is not good music. This is somewhat true but history is
> very important and necessary. Without such music we could not perfect
> it. Also since music is an aethetic it has value in that reguard
> independent of how "perfect" it is.
>
> In fact I would say that because music is a very complex interaction
> between physical and psychological things it is impossible to actually
> objectively "grade" it. What we can say though is that if some cultures
> musical identity has not progressed then the music is primitive.
Progress is not always for the best.
> Surely you would agree that if a culture's music was what it was in the
> begining when the culture was primitive then the music would be
> primitive?
I guess so. But that might not be a bad thing. And I don't really see
how this particular tangent of yours is relevant.
> Of course this is very difficult to judge since there are no
> primitive cultures left(a few are close and their music is not highly
> developed).
But some primitive music is very highly developed.
> While it is not scientific proof it is better than nothing...
What is proof of what?
Consonance is the sound of intervals with simple frequency ratios.
> You might ask, what about the frequency 1.2342F? Is that consonant or
> dissonant? We can determine this using the above principle by extending
> through octaves. In this case 1.2342F = 12342F (at some octave) and
> hence it would be extremely far from the fundamental and not be
> consonant. This is artificial though and actually not true since our
> ears are not perfect.
You mention 12TET a bit below.
You are aware I hope that every interval in 12TET, except the octave,
consists of pairs of tones with extremely complex frequency ratios, yet
we still treat them *as if* they are consonances. Evidently there is a
threshold of for out-of-tune intervals that we are willing to forgive.
and evidently any definition of consonance, like mine above, is
subjective to some degree.
> What we later found out(not sure where it started) was that when two
> strings(or pipes or whatever) are sounded that are not close in
> frequency one gets beating.
Why do you say "later".
Why wouldn't Pythagoras' crowd have known about this?
> This beating is actually the envelope of the
> total sound and is created from the destructive interference. The beats
> are exactly at the difference in frequency. (because an actual sound is
> generally a complex of harmonics it is more difficult but is based on
> that principle)
>
> What we hear as the "beats" is really what is meant by consonances.
I assume that's some sort of a typo above. Please clarify what you meant
to type.
> Beating is bad and is heard as a dissonance or a disagreement between
> the sounds.
Careful with those value judgments.
I think that classical Gamelan music requires beating between many of
the intervals in the scales they use.
> A minor 3rd has more dissonance than the major. It is
> pleasurable if you prefer agreement. But pleasure is subjective.
> Consonance is mathematical. Helmholtz in fact gave a method to give the
> consonance of a complex of pitches.(such as measuring the consonance of
> a chord)
I think you'll find, although I'm not totally sure myself because I
don't have a good enough tone generator on my iMac, that
overtone-series-based intervals, including maj 3rds min 3rds min 7ths,
and possibly all the rest, do not beat. So, if beating is your standard
for consonance I think you need another standard.
All that I think can be said is that the simplest frequency ratios have
the smoothest sound and that the most complex ratios have the roughest
sound. The fact that our ears seem to accept the ridiculously complex
frequency ratios in 12TET as being reasonable facsimiles for the
simplest of ratios is a puzzle though.
> Because a real sound is made up of overtones we actually need to compute
> the beatings of all the relations between the sounds. (up to a point at
> least as eventually the beatings are so fast as to be heard as actual
> tones)
>
>
> The ET is a compromise as it introduces slight differences
They're not that slight if you're looking at the actual frequency
ratios. But we do experience them *as if* they're slight.
> that our ears
> generally except but realize that most music sounds much better in just
> intontation which is the scale produced by exactly integer ratios. The
> problem, as you already know, has to do with creating a scale where each
> note can be used as the tonic which is not the case with JI.
>
>
> Now, about the chain of P5's. If it actually was used
You have doubts that the diatonic scale is the result of stacking P5ths?
> the logic
> probably went something like this: Start with C. If we take the octave
> we get C again. It produces nothing. So the next logical choice is the
> P5. It gives us G which is the first new tone. G is very consonant with
> C. In fact it is the most consonant tone that is distinct from C. Hence
> it holds special "powers"(remember, pythagoras was basically a mystic).
> But why is C special? We could have started with G? If we did we would
> get D. Why not D? We get A.
I have no idea why you think they must have started with what we today
now call "C". Could be one of those cultural biases of yours again?
They probably started with the lowest pitch they could produce so that
the successive P5th above that were manageable and audible. They
probably gave the notes names later on in the process.
I believe our current "A" is called "A" because it (i.e. 27.5 hz) is the
lowest practical pitch from which we can work. Somewhere below 27.5 hz
we start hearing individual beats rather than a pitch.
> Hence the logic, which is simply based off beliving that the P5 is the
> most fundamental interval that produces something new(which it is with
> respect to the overtone series) gives you all the notes(in fact an
> infinite number but we have to stop at some point to make sense of it all).
>
> We could apply the same logic to the semitone and this gives us the
> chromatic scale.
We could?
What freq ratio would you be using for the semitone that allows you to
stack 11 of them to create the chromatic scale?
Pythagoras' people stacked 5ths to get the Pythagorean version of the
chromatic scale.
> Or we could apply it so the interval of 1.2342F which
> gives a class of pitches that we could use to make music. We could use F
> + 100k but unfortunately this means that we have to fix the fundamental
> for everyone if we want to have melodies that can be transposed. (e.g.,
> for F = A we get a completely different sounding melody than for F = C
> even though they use the same pitch class)
You don't seem to be taking into account that the scales produced by the
Pythagorean formula you cite are not the scales that we use today for
music making. But your point above is on track. We could have done lots
of different things from the things we did do. The Western scale system
in use today was never pre-ordained merely by the existence of the OTS
or by Pythagoras' work.
> The historic event is how pythagoras discovered the overtone series and
> how the P5 as the signal most important interval that created something
> new.
I agree. Th P5th is the basis of Western music as a whole. But that does
not mean that the system of maj/min tonality is "based-on" the OTS. It
means that the most important interval in maj/min Tonality is based on
the OTS. There's a difference.
> The next being the P4 by the exact same logic and assuming that the
> fundamental was "movable"(relativity basically). After than we can use
> the same basic logic to get the next new pitch which is the M3rd. Those
> 2 ideas gives us the diatonic scale and all the modes.
If you believe that the inclusion of just intonated 3rds was
pre-ordained for Western music then you must also believe that we're
heading towards a system where we'll be using just intonated 2nds and
7ths and tritones as well. Your thesis can only be proven correct if
this actually occurs. [Actually, this is a bad argument on my part
because 12TET 2nds 7ths and tritones are experienced already as
reasonable facsimiles of their OTS generated cousins.]
And with computer aided tone generators there are musicians exploring
this world as we speak. The biggest problem for me is that you need a
computer to be able to play this music. But whether someone like you,
with all of your apparent biases, accepts this as being the correct
direction for music to be going in will remain to be seen. You seem to
think that music was pre-ordained to be as it is now. Why then should it
change?
I think it likely that much of today's music would have seemed like
noise to the musicians of Bach's day, which is kind of an irrelevant
statement but seems to tie in here somewhere.
Just thinking out loud here I guess.
> P5 idea gives us the P4 relation by inversion. (C is to G as F is to C
> and F is the P4 of C)
> M3rd is found by finding the next new tone as was done to find the P5.
> (we could then get the m6ths from this also)
>
> We could apply this again for the M2nd.
>
> Any way we cut it we can use the overtone series to get what we want.
We can modify the OTS to get what we want to hear.
If the OTS itself was all we wanted then all music would be in the
lydian b7 scale.
We have to modify the OTS because what we want to hear does not exist in
and of itself within the OTS.
The modification of nature to meet man's needs is known as artistry. The
maj/min key system is art and was not pre-ordained by any scientific
study of the OTS anymore than hexachloraphine was pre-ordained by the
discovery of the table of elements.
> Because it is known that pythagoras did something like this we don't
> have to know exactly what to give a best guess that our musical system
> is based on the overtones. That is, our system would be totally
> different if it were not... that the overtones are fundamental to our
> current musical practices. In pythagoras's time it may have been
> different... as it takes time to perfect our understanding of things...
>
> But realize also that almost all our musical instruments are based on
> the overtone series too.
Right. Almost all Western instruments that is.
> Pipes? exactly from what pythagoras
> discovered(F = k*sqrt(T/l) I think is the formula) Strings? Same thing.
> What else is there? drums? Ok, thats different... totally different. But
> it actually supports my claim.
>
> In actuality the very hole flute like instruments had holes that were
> not aligned by the overtone series. I read somewhere that the performers
> had to have a lot of techniques to get the notes right... in any case it
> is irrelevant as those instruments were primitive and quickly replaced
> by instruments based on pythagoras's findings.
>
>>> and figured out the overtone series.
>>
>> I was not aware that they had figured out the entire overtone series,
>> or if they had that they thought of it as such.
>> I know that they were involved with dividing vibrating strings into
>> various equal divisions, but I'm not aware how many divisions they
>> thought were relevant to their music or to their musical
>> understanding.
>
>
> It doesn't matter.
It matters in that if you're going to take it upon yourself to discuss
these things in public it might be wise to get your facts straight.
The same could be said about me too though.
> He quickly found the relation to the integers. It is
> actually very beautiful because it is the most simple way.
There is no other way.
I don't think of pitched sound as being "simple" myself.
I think of it as being quite special and unusual. Most sound is not
pitched. I think that scientists have been intrigued by pitched sound in
the same way that they've been intrigued by other natural oddities like
magnetism.
> Now, we can argue all day long about if the music is good or not
> depending on how well it fits with the overtone series.
There's lots of good music that doesn't "fit" the overtone series.
> I personally
> take the stance that the everything we hear is based in it
Ah. Well there you go again making a really huge sweeping generalization
that is not really tenable as stated.
> and bad music
> simply does not fit.
??? Doesn't fit what?
> Bad can be good in the right context but in general
> we, as humans, expect sound to fit in the overtone series.
Sweeping generalization again. Check out some Gamelan music or some
carillon bells ringing in a church tower.
> Our ears are
> conditions by genetics and physics to understand sound that way. Music
> is an exploitation of this and the psychological conditions of emotion.
To some degree that is true. Not to the degree that I think you mean though.
> So our music is a little bit of science and a little bit of psychology.
I'd say art rather than psychology.
> But the science is just as important. Both are necessary...
Of course.
> well, it's
> not necessary but innate.
>
> The overtone series is as fundamental as the law of gravity. You don't
> neglect gravity just because past civilizations didn't have a scientific
> understanding of it?
Saying that all music is "based on" the overtone series is a little bit
like saying that all building construction is "based on" gravity.
Certainly an architect needs to account for gravity when he designs his
building but that doesn't mean that the building is "based on" gravity.
> They understood it more or less... They understood
> the overtone series more or less. It's just that we happen to understand
> it more(again, because knowledge generally increases). It's nothing good
> or bad... future civilizations will understand music better than us.
> This is because because as humans we build off the past. We don't have
> to rediscover everything at each step.
>
> Think about it this way: You have the cave man paintings on the wall.
> This is "Art" and has historical importance. But it is not the same as a
> van go.
That's your opinion. I'll bet Van Gogh would have probably disagreed
with you.
> Not only did our artistic expressions increase so has our social
> awareness(more or less at least). Without the technological means van go
> could not have created his paintings. Without the social need for such
> things(if he was too busy trying to fend of the dinosuars) then it
> wouldn't exist either.
>
> The overtone series allowed us to develop more precise intruments...
No it didn't.
The overtone series doesn't *do* anything.
It's we who do the doing. The OTS is merely a phenomenon whose
characteristics we exploit to make our art.
> but
> to build a whole structure that was congruent with that basic concept.
> Pythagoras could easily have said "I hate conformity so I will not use
> the P5 as the basis" and chose a random interval. He didn't because
> humans have more of a need for unity than variety. You can only have so
> much unity(you can't create anything more unified than the unision) but
> you can have an infinite amount of variety.
He picked the P5th because he like the way it sounded and it also
resonated with him philosophically. It also has the same effect on lots
of other people, thus its popularity within cultures whose music happens
to utilize it.
> Also don't forget that the overtone series led us to ET which lead to a
> whole new system of harmonic understanding, atonality, etc...
And *you* see this as positive progress. There are lots of folks out
there who disagree. They're in the minority, but they're out there.
History is written by the people who are the victors. It's entirely
possible that the future of music might not go in the direction that you
think it should inevitably go in. Nothing in art is inevitable.
> This
> couldn't have happened without the overtone series and it's no doubt why
> other cultures do not have such an expanded harmonic framework.
Why is harmony the pinnacle of music making?
> They
> simply got it "wrong" and were led down a dead end.
Yep. There's that cultural arrogance.
> Again, the music
> itself is still historically and culturally significant and is variety.
> In fact, our current western system may be a dead end...
Not if you believe that 12TET and Britney Spears is an improvement over
Pythagorean diatonicism and Bach.
No time to proof read this. Hope it's not too filled with mistakes and
typos and logical inconsistencies.
LJS
>
> Steve
Thank you Steve, I think that this fills in any facts that Tom and I
didn't quite cover.
Your documentation and scope seems to be improving. Glad to see it.
Jack Campin - bogus address
> out the overtone series.
Our total knowledge of statements reasonably well attested as being by
Pythagoras amounts to two short sentences, neither of them about music.
> I don't know what he did before or after or if he really did this
No you don't.
> but this is what our history tells us.
It's what urban legend tells us. We have so little reliable information
about what Pythagoras did, wrote, said or thought that a treatise about
music from is him about as likely to exist as an instructional DVD about
carpentry narrated by Jesus.
Not only is Pythagoras's own work almost entirely legendary, so is that
of his followers for the next few generations. People in later ages
attributed ideas to Pythagoras to claim respectability for stuff they
were just making up on the spot. Like you're doing.
> The greeks were highly scientific
They also believed that lightning was the sperm of Zeus, that the ocean
was higher than the mountaintops and that the brain was for keeping your
blood cool. Well, maybe that is the only use you have for yours.
> and music was treated in a scientific way.
Some of them tried. The more important thing was musical practice,
much of which didn't fit any theory they could construct, and which
has persisted as a continuous tradition to the present day in the
microtonal modal music of the Middle East.
> They may not have had the luxury of the past to give them direction
They did. Greek theory was based on Egyptian and Mesopotamian theory,
just as their musical practice was. The more we find out about their
predecessors the less they seem to have innovated.
> but they did have direction... the only direction they could have
> had... which was from science. (hence why music was treated as a
> scientific device because it was precisely that to them)
They had no concept of "science". Music theory was one of the
antecedents of science, not the other way round.
> it seems that they treated music in a much more scientific way than
> we do. They might not have the concepts that we have such as tonality,
> pandiatonism, chromatism, etc but they approached it in a mathematical
> way.
They had a lot *more* concepts than we do, some of which were useful
(they could at least record the fact that a lot of their music used
microtones, even if they couldn't say anything useful about it) and
some of which seem utterly alien to us, like the correspondences
between the notes of the scale and the planets, the elements or the
Ptolemaic spheres (an idea which alchemical tradition retained until
the Renaissance).
Vilen
>I don't think that Better is the best choice of words. You may mean
>"seems to work better" when looking at your premise.
It is perfectly right. I understood even that my “choice of words” is
some careless, intended to formulate otherwise but forgave. Indeed, I
consider cases when there is one direction movement to known
(established) note through note in one semitone nearness from target
note. In two cases the patterns are considered in which major mode has
acknowledged advantages against natural minor and third case is about
use of Lydian interval and isn’t tied with theme major-minor. So the
question what is in general better major or minor wasn’t essential. It
seems to me that it is often discussed but all the same serves further
discussion.
Best Regards
Yuri Vilenkin
tom_k
"Jon Slaughter" <Jon_Sl...@Hotmail.com> wrote in message
> We generally assume that lydian is major and we do have some historical
> evidence(But it could have been misinterpreted).
You can assume what you what but you have no evidence that the Greek's
Lydian has any relationship to a major mode, scale or whatever.
> Have you read plato's republic? He specifically discusses the musical
> modes and there characteristics and when and how they should be used.
> Note, I said major mode and not major scale. Given that there are only 3
> minor modes and 3 major modes do you not agree that if 4 modes are
> mentioned then it is a must that at least one would be major? (assuming
> locrian is out of the picture. If locrian was used to express happiness
> then thing is totally wrong with the picture)
You are still confusing Greek and Gregorian modes. If you want to say that
the Greeks used the interval of a major 3rd, fine. But where does Plato
talk about "major modes"?
> Again, your believe that only a minor mode existed is complete nonsense.
> In fact it's ridiculous to believe that for festive ocassions they would
> use minor modes for the melodies and never reach into the major modes.
You assume that since I don't believe Major existed I believe the Greek
modes were Minor? If I said that, please reference the post.
Greek scales (modes) were combinations of tetrachords - their basic building
blocks. "Major and Minor" emerge many centuries later and don't enter into
it - they did not yet exist. You might just as well argue that the Romans
preferred 4 speed rather than 3 speed transmissions on their chariots; or
that the only reason that 16th century musicians eschewed the electric
guitar was the lack of an extention chord!
> "In fact, the church modes originated in the 9th century. Authors from
that
> period created confusion by trying to use a text by Boethius, a scholar
> from the 6th century who had translated Greek music theory treatises by
> Nicomachus and Ptolemy into Latin"
And you seem to be continuing that confusion to justify major over minor for
some reason! If you want to talk about the major midieval/renaissance modes
vs. the minor ones, fine. If there is any evidence that Ionian, Lydian &
Mixolydian were "more natural" or favored over Dorian, Phyrgian & Aeolian,
it would make for an interesting discussion.
But bringing the Greeks and their linking of music and philosophy into it is
a complete red herring.
> Would you accept that if, say, our musical system was passed on to a
> future generation only by a single bach piece that it would be impossible
> to determine the "mode". If they only knew that it was music and the dots
> meant pitch they could not conclude what mode it was in? After all, one
> would first have to get the clef correct for the mode to be right but how
> could they with such limited information?
While I'm not sure what you are getting at, what if "our musical system was
passed on to a future
generation only by a single" Webern piece? In other words, "our musical
system" is a bit too broad - much broader than that of the Greeks.
> I'm not questioning the results of all the "scholars" though as many of
> them have spent a few days on it. Like you they make a lot of assumptions
> though. It is my best guess they are right though but in any case it is
> irrelevant to the application of the overtone series to the naturalness of
> the major scale.
Now I'm confused. Is it Plato or the OTS which proves the superiority of
the major scale?
Tom
Jon Slaughter
Vilen
> Though most of the cool music is in minor :-)
The best is the enemy of the good. Let the minor mode is more powerful
but more difficult to use instrument.
Few people can write cool works. Apparently people who can write them
can rather manage with more complex instrument. Majority of people
would obtain better results with major. It must be better for them.
Yuri Vilenkin
Orangeboxman
> Steve Latham wrote:
...
> The major mode is the natural mode.
I do not consider any mode to be natural.
By my own criteria, Mixolydian would be closer than major.
Orangeboxman
> enough to be using Musica Ficta. As the tensions were created and as
> they resolved through suspensions, and the creation of the tritone and
> other cadential factors, the Dominant 7th chord started to appear.
> Then there came the "switch" from contrapuntal thinking and by that
> time, the working cadences started to have all the elements of the IV-
> V-I cadence with and without the cadential 6/4.
>
> If this is more or less accurate, then the establishment of a key that
> has all those descriptive phrases in the reply has no relevance to the
> tonic being Major OR Minor. It just would not be a factor. A simple iv-
> V7- sets up the tonic note. the color of the scale used once you are
> in that key depends solely on the scale used over that established
> tonic. Using this premise, there would be no difference in creating
> and maintaining a sense of key for major or for minor. That concept
> just would not apply as stated in the reply.
>
> LJS
I agree with this. Major and minor modes are essentially Mixolydian,
Aeolean and Dorian modes in which the cadential fictae have been
extended to the beginning. I realize how bizarre this explanation
might sound, but it is the one that makes the most sense,
historically.
The effect is that, aside from their persistent cadential quality,
major and minor preserve most of the qualities of the modes from which
they are derived.
Orangeboxman
as concretely as their major key cousins.
Incorrect.
Both modes emerge at the same historical time, and by the same means.
One is a shadow of the other only in modern thinking.
Orangeboxman
and figured out the overtone series.
Pythagoras did not work out the overtone series.
He identified superparticular ratios as being consonant up to 4:3, but
not beyond.
And the connection to overtones, while real, was not part of his
reasoning, because overtones, themselves, were never part of his
vocabulary.
Attributing Helmholz' work to Rameau is a common enough error... but
to Pythagoras?
Joey Goldstein
Please see my reply to Steve Latham.
Orangeboxman
Sure. Which one?
I forgot to mention that on pianos, the major 3rd is actually an
acoustically rougher interval than the minor 3rd.
Are the major and minor triads we're supposed to be considering in the
ongoing discussion piano triads or some other kind of triad?
LJS
This is somewhat off the direct line of this thread, but not by much.
If I remember the earlier parts of this thread it was concerning the
melodic evolution of the cadences through musica ficta and how this is
what really established the minor cadences and that the Harmonic
Series worked better for major than it did for minor to establish it
( the HS) as being responsible for the major dominant and minor tonic
and a few other things as well.
Back to Pythagoras, and this is the slightly off topic part.
I have no problems with your statements as to P. and the ratios. I
don't bellieve that he had anything to do with the HS as such. BUT as
I have talked about in the past (starting with the question "Is the
Harmonic Series Tonic or Dominant?"
P. came up with the first three elements of the harmonic. and he
stopped there for work on his cycle of 5ths. I don't believe that he
looked at the entire series or that he even had the technology to be
aware of the ratios of all of the harmonic series. And what had come
before him did not seem to need the whole HS to be analyzed in the
manner that he did. There are more than one way to get that cat skin
for your slippers.
BUT the connection to the HS is still extremely likely and I
personally aver that it was the force behind his discovery and his
problems with the Wolf. (It was also before Peter and the Wolf!)
The fact is that the HS was around then as it always has been and
always will be. The HS shaped the music and the tunings when they did
it by ear and when he started to experiment with the ratios that had
been used in his time, they led him to the first three (really the
second 2) elements of the HS. This solved his problem and without more
sophisticated instruments OR the need to go any further, being a
practical man, he went with this discovery and as history shows, he
did quite well with it as fare as theory goes. (I understand his
"perfection" concepts and the presence of the wolf caused him some
problems with the elders, I don't know for sure, I am not quite that
old)
So. I find it quite believable that if he (P.) discovered that "just
happened" to be the first three elements of the HS, he was working
with the HS weather he realized it or not. He researched until he
found something that worked and went with it. IF he had been listening
to the music of the CPP, not only would he have been a time traveler,
but he would have probably gone on and discovered at least the first 5
elements and maybe the first 9 elements. BUT this is pure speculation.
The Fact is that his discovery IS the first three elements of the HS.
One caution however. That post by Steve, (if I saw the correct one) is
one of the rare instances that Steve has posted in a Joey/LJS "thread"
and this post is in total agreement with MY previous thread but is put
more into terms that Joey could understand (and then too, it came from
Steve and not from me! lol) I believe that I complimented Steve on his
expansion of his perspective after he made that reply. Now if Joey
realizes that this reply by Steve is perfectly congruent with my
earlier post, YOU may find your self threatened with the dreaded "kill
file" and your credentials will probably be questioned. so, shhh!
Don't tell him!
LJS
Orangeboxman
The harmonic series exists in and of itself, whereas tonics and
dominants don't exist without each other for reference,
and both tonics and dominants require at least a set of dyads in each
case (the harmonic series being one tone, not two).
LJS
Ah! In order to consider this, you have to go to the higher levels of
understanding of the principles of Tonic and Dominant as defined by
Bloom. I am talking about speculative analysis and a more abstract way
of looking at the phenomen.
Yes, it does exist in and of itself, but there is more to it than
that. If you listen, you can actually hear the notes of the series.
Stick a mike in the sound board and EQ it to bring out the higher
overtones if you have difficulty hearning this) . Then take the tones
that you hear and listen carefully. Is it a stable sonority? or do you
hear it as having tension?
The harmonidc series is not one tone. It is a series of tones produced
as a string (or air column vibrates at different rates superimposed
over each other. I am sure you know the tones. IF you really want to
hear it clearly, you can set it up on something like LaScala that Hans
talks about all the time. (I think this can do it, or you can use as
many tone generators as the resultant elements of the series that you
want to listen to. When you put these tones together, you will not
have the same tunings as on the keys of the piano and the resulting
intonation will have real perfect fifths, octaves and fourths. Pure
thirds (and you can really start to understand Fux and the Thirds as
being consonant when you hear them here, and then when you get past
the C G E you hear that 7th element which is between the major 6th and
the minor 7th.
This is the key to the question. (the question is not for those
thinking inside a small box, one needs go take it as what it is, a
series of tones that is present in nature. The series may be present
in ONE NOTE or one string, but there certainly are different tones and
as the name implies. They are harmonic in nature so together they
present a series of tones that can be treated as if they are a chord.
In fact, it would be really hard to argue that these tones do not
produce a chord. Even the human voice is capable of creating these
chords as in the music of those Tibetan Monks that have toured
demonstrating this effect.
So, to answer the question, listen to the tones produced by the
harmonics of one string and see if you hear them as Tonic or
Dominant.
If you decide to discuss this, I will then share my thoughts and give
you the reasons and defend all relevant comments on the subject. If
not. Maybe later when you have thought about it more, you might see
the possibilities of what this may actually mean and how it has
affected music through the ages.
LJS
btw, this is not my original idea. Well the question might be but I
got it from a lecture by a super esteemed musician, composer and
theoretician. .
Joey Goldstein
> >Please see my reply to Steve Latham.
>
> Sure. Which one?
I believe that there's only two times in this thread that I replied to
Steve. it's in one of those.
> I forgot to mention that on pianos, the major 3rd is actually an
> acoustically rougher interval than the minor 3rd.
>
> Are the major and minor triads we're supposed to be considering in the
> ongoing discussion piano triads or some other kind of triad?
Sorry. I've lost track of what it is you're even talking about because
you haven't included any of the relevant text.
Joey Goldstein
Lol.
Good luck talking with LJS about this.
Be prepared for a long and winding thread about nothing.
Hans Aberg
> I forgot to mention that on pianos, the major 3rd is actually an
> acoustically rougher interval than the minor 3rd.
This is not true. In E12, the Just minor third 6/5 is 15.641 cents off
(higher than ET, and the Just major third 5/4 is -13.686 cents off
(lower than ET).
> Are the major and minor triads we're supposed to be considering in the
> ongoing discussion piano triads or some other kind of triad?
Most guys here use CPP harmony theory adapted to E12. There are just a
few differences, like the augmented sixth, and pivoting on the
diminished 7th chord.
Hans
Orangeboxman
It's not merely a question of intonation.
The piano is a special case because of its notable inharmonicity. The
major 3rds are especially rough unless your piano has strings of
infinite length and thinness. This is a question I pretty much nailed
shut in my thesis while explaining that Helmholz failed to understand
the dissonance of the augmented triad because, contrary to basically
everything else he did, ever, he somehow decided to use the piano as a
reference instrument in assessing this chord.
Inharmonic timbres basically always have the harmonics stretched,
rather than compressed, so the major 3rd will be rougher the less
harmonic the timbre is.
The consonance of the major 3rd is an even more modern idea than the
consonance of the minor third.
The Pythagoras didn't use the just major 3rd, but instead had 81:64
where the just interval was later used.
Because the interval for the smaller third was less complex, the
smaller third would have to be regarded as more consonant until
basically the Renaissance, even aside from questions like string
dimensions. The major 3rd in Chinese music has always been regarded as
weak an emotional. Really, if the major 3rd is such a great interval,
why don't more of those huge church organs have an nice set of stops
at the corresponding part of the harmonic series?
Orangeboxman
understanding of the principles of Tonic and Dominant as defined by
Bloom. I am talking about speculative analysis and a more abstract way
of looking at the phenomen.
Forget Bloom. Tonics and dominants are not acoustic phenomena.
They are cognitive phenomena. The harmonic series is acoustic.
It is the tree falling in the forest whether you are there to hear it
or not,
and whether anyone yet exists to hear it or not.
>Yes, it does exist in and of itself, but there is more to it than
that. If you listen, you can actually hear the notes of the series.
The series is not notes. The series is frequencies.
The notes are in your mind.
Stick a mike in the sound board and EQ it to bring out the higher
overtones if you have difficulty hearning this) . Then take the tones
that you hear and listen carefully. Is it a stable sonority? or do you
hear it as having tension?
I hear it is having tension when it is not resolved, as it is not
resolved on the piano,
or when it is an out-of-phase travesty of the harmonic series such is
produced on organs.
>The harmonidc series is not one tone.
It IS a tone. It is a tone produced by a series of frequencies to
which inharmonic members approach as they decay.
If you didn't think the piano was God's reference tool for the natural
acoustics of the universe, this wouldn't be so confusing, probably.
Hans Aberg
>>> I forgot to mention that on pianos, the major 3rd is actually an
>>> acoustically rougher interval than the minor 3rd.
>> This is not true. In E12, the Just minor third 6/5 is 15.641 cents off
>> (higher than ET, and the Just major third 5/4 is -13.686 cents off
>> (lower than ET).
> It's not merely a question of intonation.
>
> The piano is a special case because of its notable inharmonicity. The
> major 3rds are especially rough unless your piano has strings of
> infinite length and thinness. This is a question I pretty much nailed
> shut in my thesis while explaining that Helmholz failed to understand
> the dissonance of the augmented triad because, contrary to basically
> everything else he did, ever, he somehow decided to use the piano as a
> reference instrument in assessing this chord.
>
> Inharmonic timbres basically always have the harmonics stretched,
> rather than compressed, so the major 3rd will be rougher the less
> harmonic the timbre is.
But inharmonic instruments are stretch tuned, compensating for that. And
the minor third will still be worse than the major one.
The inharmonicity of a concert grand is just a few cents per octave, and
very small in the middle region where most harmony is played.
> The consonance of the major 3rd is an even more modern idea than the
> consonance of the minor third.
> The Pythagoras didn't use the just major 3rd, but instead had 81:64
> where the just interval was later used.
> Because the interval for the smaller third was less complex, the
> smaller third would have to be regarded as more consonant until
> basically the Renaissance, even aside from questions like string
> dimensions. The major 3rd in Chinese music has always been regarded as
> weak an emotional. Really, if the major 3rd is such a great interval,
> why don't more of those huge church organs have an nice set of stops
> at the corresponding part of the harmonic series?
If you check the size of the minor second in a tempered picth system,
then in Pythagorean tuning tuning it is about 90 cents, in E12 it is 100
cents, in quarter-comma meantone which sets the major third exactly it
5/4 it is about 117 cents, and in the meantone that sets the mior third
exactly 6/5 it is about 126 cents.
The major and minor third will approximate the Just 5-limit somewhere
bwteen these two last tunings. The further you go towards the
Pythagorean side, the greater the difference with the minor third the worst.
In music using the Pythagorean tunings, the thirds are usually not very
important in harmony - pitches sounding together. Instead the pure 4th
and 5ths are more important.
Hans
LJS
> >Ah! In order to consider this, you have to go to the higher levels of
>
> understanding of the principles of Tonic and Dominant as defined by
> Bloom. I am talking about speculative analysis and a more abstract way
> of looking at the phenomen.
>
> Forget Bloom. Tonics and dominants are not acoustic phenomena.
> They are cognitive phenomena. The harmonic series is acoustic.
> It is the tree falling in the forest whether you are there to hear it
> or not,
> and whether anyone yet exists to hear it or not.
Hmm, Bloom's levels of understanding exists weather the tree falls or
not. Just like the HS, you hear the "tones", "notes" or "frequencies",
you are hearing the sounds that combine to give the sonority of the
HS. I hope this is just a semantic problem with the terms as I do not
intend to get into this discussion if we are going to nit-pick
semantic differences. What terms would you like to use. "Frequencies"
will be very cumbersom. What other term do you want to use?
>
> >Yes, it does exist in and of itself, but there is more to it than
>
> that. If you listen, you can actually hear the notes of the series.
>
> The series is not notes. The series is frequencies.
> The notes are in your mind.
yes, actually in the subconscious every time you hear a tone, or note
or actually just about any musical or other type of sound. If you
prefer to call them frequencies instead of notes, OK, no problem. When
I say "notes" in this thread, just realize that I am defining them as
"frequencies". I don't see any reason to type out 11 letters instead
of 4 when the frequencies do in fact represent things that we know in
everyday life as "notes".
>
> Stick a mike in the sound board and EQ it to bring out the higher
> overtones if you have difficulty hearning this) . Then take the tones
> that you hear and listen carefully. Is it a stable sonority? or do you
> hear it as having tension?
>
> I hear it is having tension when it is not resolved, as it is not
> resolved on the piano,
That would be an indication of a Dominant sonority. If it feels as
though it needs to resolve, it is a 1st class sonority. If it sounds
like it has already
> or when it is an out-of-phase travesty of the harmonic series such is
> produced on organs.
Are you speaking of the single pipe of an Organ? If not, then the
context for your 'out of phase' observation is not relevant to my
statements.
>
> >The harmonic series is not one tone.
>
> It IS a tone. It is a tone produced by a series of frequencies to
> which inharmonic members approach as they decay.
This, I hope, is still that semantic thing. Are you saying that the
harmonic series is not one frequency?
>
> If you didn't think the piano was God's reference tool for the natural
> acoustics of the universe, this wouldn't be so confusing, probably.
What in my post could possibly prompt this statement? I am not
confused at all. In no way what soever did I suggest the piano except
as a source to hear the HS.
(What was that reference you made about trolls in another post?)
LJS
Orangeboxman
What are 'nit picky semantic distinctions' to the average music theory
student are,
to the metatheorist and the perception/cognition researcher the
difference between
talking about what you're trying to talk about, and actually talking
about something
completely different (and getting it wrong).
The harmonic series is not a musical object. It is a mathematical
object which is used to explain physical events which are then used,
in turn, to explain musical events which are related to, but not the
same as perceived musical events.
The series is a series of frequencies, audible or otherwise.