Abstract principle: Beethoven's 5th Symphony
Albert Silverman
ABSTRACT PRINCIPLE: BEETHOVEN'S 5TH SYMPHONY
by Albert Silverman
--------------------------------------------
In previous articles, I explained:
(1) the dynamic function of the chord having the pitch interval pattern of
the Ancient so-called "diminished 7th" chord
(2) the "rootless dynamic function"
As I have pointed out, no tone of the "diminished 7th" chord (whose
symmetrical-interval-pattern construction I denote as "m6-"), _a derivative
of the minor triad_, possesses a diatonic tendency. This means that it has
no dynamic tension, barring the existence of "prepared" melodic tendency.
In theory, any tone can be given a prepared melodic tendency; this is done
by using an appropriate phrasing in context. Significantly, such a prepared
tendency may be contrary to the normal (diatonic) tendency of that tone,
identified in connection with a specific pitch interval pattern. In such an
event, the chord is said to be functioning in a "rootless" dynamic mode.
This means that it lies outside the harmonic structure; i.e., it lacks a
functional root location.
In practice, however, only a few chord forms are suited for functioning in
a rootless dynamic mode. The most common of these is the m6- chord, which
frequently functions in a rootless mode. In this mode, it possesses an
unmistakable, strong dynamic tension.
Occasionally, a chord which possesses the pitch interval pattern of a
major-mode 7th chord (the Ancient "dominant 7th") will function in a
rootless dynamic mode. This is the case in the following example from the
Second Movement of Beethoven's 5th Symphony, which illustrates the rootless
dynamic function of such a chord, during the process of changing from one
"key" to another (known as an Ancient "modulation"). Also illustrated in
this same example is its predecessor, an m6- chord which functions in a
normal diatonic manner (i.e., without dynamic tension).
IMPORTANT NOTE:
Rather than using the terminology "root-tone of central significance" or
"preferential root-tone," I will henceforth use the more-convenient Ancient
terminology "key," in reference to this particular tone. Admittedly, this
entails a significant risk, in view of the fact that, in addition to this
tone, Ancient "key" includes a major/minor scale designator, which _implies
a link between chord form and structural location_. Since linking chord
form with structural location is a STYLISTIC restriction, rather than being
theoretically relevant, my reference to "key" necessarily excludes any
Ancient scale designator.
Thus, for example, when I refer (in a theoretical discussion) to the "key
of C," I mean only that C is the preferential root-tone. This does not
imply anything about the use of specific chord forms at specific structural
locations.
========================================================================
Beethoven: Symphony #5, 2nd Movement
Line #1: |1 |2 ||3 |4 ||5 |
Line #2: Eb G |AbAbBb|CAb Bb||CCDb|EbEb F ||GbEb F |
Line #3: 16 32 32|8 8 8 |416 32 32||888 |4 16 32 32||4 16 32 32|
---------------------------------------------------------------|
Line #4: | ||Gb |
Line #5 |Eb ||Eb |
Line #6 |C ||C |
Line #7 |Ab ||A |
---------------------------------------------------------------|
Line #8: |Ab ||(Am6-) |
Line #9: |{1} ||{8} |
Line #1: |6 |7 ||8 |9 ||10 |11 |
Line #2: |GbEb F|F# ||G E CD|CrE G ||CCD|EC D |
Line #3: |4 16 32 32|48 ||16 32 32 88|8816 32 32||888|416 32 32|
-----------------------------------------------------------------|
Line #4: | |F# ||G |
Line #5 | |Eb ||E |
Line #6: | |C ||C |
Line #7: | |Ab ||G |
-----------------------------------------------------------------|
Line #8: | |(Ab7)||C |
Line #9: | |{?} ||{1a} |
Notes:
Line 1 numbers the measures. Phrases are delineated by double bar lines.
Line 2 shows the melody ("r" denotes a rest).
Line 3 shows the time durations of the melody tones in line #2.
Lines 4-7 show the component chord tones. Line #7 also gives the bass
tone
Line 8 shows the constructional notation for the chord forms in lines 4-7.
A
chord notation enclosed in parentheses denotes that it is an
_enharmonic equivalent notation_ for the chord in lines 4-7.
Line 9 shows the functional root locations of the chords in lines 4-7.
========================================================================
The key (there, I said it!!) of Ab has been established ahead of the short
section shown here. The first four measures are heard in this key, in the
harmony of Ab, which is therefore denoted by the functional root location
{1}. In measure 5, there is a 4-tone, symmetrical-interval-pattern chord,
with tone A in the bass. For what it is worth (which isn't very much, by
the way!), the SCALE interval (A-Gb), between the bass and melody tones, is
an Ancient "diminished 7th."
In its CONSTRUCTION (from the 1st, lowered 3rd, lowered 5th, and 6th)
degrees of the diatonic A-major scale, this chord is noted as (Am6-) which,
in the tempered scale, is the enharmonic equivalent of the chord containing
the four tones ACEbGb. The parentheses denote that the constructional chord
notation is the enharmonic equivalent of the actual chord that appears in
the score.
Due to the nature of the melodic phrasing, the tone progression Ab-->A in
the bass in measures 4-5 does not endow tone A with an upward prepared
melodic tendency. Hence the chord ACEbGb lacks dynamic tension (believe it
or not!), Ancient protests to the contrary notwithstanding. Since this
chord is functioning diatonically, it possesses a functional root. The
functional root location {8} reflects a chord with a constructional root-
tone "A," which is HEARD in the previously-established key of Ab. Check
this out by noting the number of harmonic steps, measured along the circle
of fifths, to move from "A" to "Ab".
The chord of exceptional interest in this example is that in measure 7,
containing tones AbCEbF#. This chord has the unique pitch interval pattern
of a major-mode 7th chord (the Ancient "dominant 7th"). It is CONSTRUCTED
from the first, third, fifth, and lowered seventh degrees of the diatonic
Ab-major scale (tones AbCEbGb), and it therefore has the _sound quality_ of
a dominant 7th chord. Since tone F#, in the score, is the enharmonic
equivalent of tone Gb, used in the chord construction, the chord is noted
as (Ab7). For what it is worth (which is not very much), note that the
SCALE interval (Ab-F#) is an Ancient "augmented sixth."
Note the enharmonic change of spelling from Gb to F# in measures 6-7. The
reason for this "strange" (oops!) situation is the fact that tone Gb
"belongs" in the original Ancient key of Ab, while tone F# leads
melodically to tone G in measure 8, in the new key of C. The change of
spelling from Gb to F# reflects this transition (an Ancient modulation)
between the keys of Ab and C. The (Am6-) chord in measures 5-6, which
precedes the (Ab7) chord in measure 7, is a transitional chord between
these two keys.
The dynamic function of the (Ab7) chord is of exceptional importance in the
transition between these two "distantly-related" keys (four steps along the
circle of fifths). In measures 6-7, the melodic phrasing is such that the
semi-tone progression A-->Ab, in the bass, _endows tone Ab with a downward
prepared tendency toward tone G_. Hence the chord AbCEbF# has a dynamic
tension, resulting from this ONE tendency tone.
Tone F# does NOT possess an upward tendency toward tone G, even though it
progresses melodically to this tone, in measures 7-8. The reason, of
course, is that tone F# is simply an enharmonic spelling of tone Gb (which
is without tendency) in measure 6. There is no way on earth that this
simple _enharmonic change in spelling_ can endow tone F# with a tendency,
despite the appearance in the score, which suggests that this is the case.
Note also the "strange" (oops!) tone progression Eb-->E in line 5, in
measures 7-8. From this upward semi-tone progression, it would appear that
tone Eb should be spelled as D#. However, the spelling of tone Eb is
carried over from its spelling in the initial Ab-major triad, which
introduces a dilemma that cannot be resolved by a spelling in accordance
with the melodic progression.
In any chord that is functioning in a normal diatonic mode, its
constructional root-tone _cannot possess a tendency_; in fact, this tone
has a weak persistence. Since tone Ab, the constructional root-tone of the
(Ab7) chord, possesses a downward tendency in context, it follows that this
chord is functioning in a "rootless" dynamic mode. The rootless nature of
the dynamic function is shown by the bracketed question mark in line 9.
In measure 8, the C-major triad at the beginning of the phrase introduces
the new key of C. It is noted as {1a} in line 9, the "a" subscript being
necessary to indicate the existence of a new key. Even though the new key
is C, the Ancient "key signature" remains at four flats, denoting the
initial Ancient key of "Ab-major."
CONCLUSION
This example illustrates the use of _dynamic functional analysis_, which is
based upon the principles of chord relationships (TRIADIC THEORY). As such,
it has an _excellent aural correlation_ with the music. This analytical
technique bears little resemblance to the theoretical irrelevance of
Ancient Art/History, a STYLISTIC approach to analysis which is universally
taught within Musical Academia under the guise of "theory."
Albert Silverman
Zack Leven
In article <slvrmnE7...@netcom.com>, slv...@netcom.com (Albert
Silverman) wrote:
> This analytical technique bears little resemblance to the
> theoretical irrelevance of Ancient Art/History, a STYLISTIC
> approach to analysis which is universally taught within
> Musical Academia under the guise of "theory."
Translation:
Silverman is saying that the irrelevance of "Ancient" Art/History is only
theoretical, and not yet been proven. He goes on to say that when you go to
music school and study theory, you're actually studying art/history, which
is actually just an approach to analysis. He doesn't specify what
Art/History is analyzing.
This guy's talkin' crazy.
-Zack-
Albert Silverman
In article <zack-17039...@zackintosh.concord.org>,
Zack Leven <za...@concord.org> wrote:
>In article <slvrmnE7...@netcom.com>, slv...@netcom.com (Albert
>Silverman) wrote:
>
>> theoretical irrelevance of Ancient Art/History, a STYLISTIC
>> approach to analysis which is universally taught within
>> Musical Academia under the guise of "theory."
>
>
>Silverman is saying that the irrelevance of "Ancient" Art/History is only
>theoretical, and not yet been proven.
Silverman is saying nothing of the kind!
Quite imaginative and original, but out of touch with reality.
For Leven's information, even though he doesn't seem to want it,
Silverman is saying that Ancient Art/History is explaining compositional
STYLE, as opposed to explaining (vis-a-vis the subject of harmony) the
THEORY of chord relationships.
But since it is perfectly clear that Leven does not understand the vital
distinction between THEORY and STYLE (and he is hardly alone), he is
certainly in no position to act as a speculative "translator" of
Silverman's statements!
Perhaps Leven should ASK what Silverman is saying, when he doesn't have
the slightest idea?
>He goes on to say that when you go to
>music school and study theory, you're actually studying art/history, which
>is actually just an approach to analysis.
He does not go on to say anything of the sort.
He goes on to say that one cannot possibly understand the principles of
chord relationships (REAL, honest-to-goodness theory) by studying Ancient
art/history, which is what one is generally taught in a "theory" course
in Musical Academia. If you don't believe this, just ask The Perfesser,
who has clearly stated that this is what he teaches.
He cannot understand why it is so difficult for Leven to distinguish
between musical art/history and the theoretical principles of chord
relationships. There is a very wide chasm between the two.
>He doesn't specify what
>Art/History is analyzing.
He specifies that Art/History is "analyzing" music in accordance with an
incomprehensible maze of irrational, inconsistent, and irrelevant concepts.
>
>This guy's talkin' crazy.
Leven should be so crazy!
Albert Silverman
(Al is in Wonderland!)
And HOW!
>
>-Zack-
Zack Leven
>But since it is perfectly clear that Leven does not understand the vital
>distinction between THEORY and STYLE (and he is hardly alone), he is
>certainly in no position to act as a speculative "translator" of
>Silverman's statements!
What Leven understands is this thing that I like to call the English
language. Maybe you should try studying it a little - I think it will help
you to explain your "theories" by leaps and bounds. But just in case you you
decide to put it off, here's your first lesson:
pretentious - adj.
1. Claiming or demanding a position of distinction or merit, especially when
unjustified.
2. Making or marked by an extravagant outward show; ostentatious.
-Zack-
Al E.
here's your first lesson:
>pretentious - adj.
>1. Claiming or demanding a position of distinction or merit, especially when
>unjustified.
>2. Making or marked by an extravagant outward show; ostentatious.
>-Zack-
Hear, hear!! That's an attaboy, Zack!!
Zack Leven
In article <5gnq96$4ch$1...@msunews.cl.msu.edu>, eber...@pilot.msu.edu (Nathan
Eberhardt) wrote:
> From one of Leven's recent articles on "Re: Theory and
> Composition":
>
> "It's one thing to bash theory, but it's another thing
> altogether to bash people who don't know anything about
> theory. I know it sounds pretensious to site credentials..."
> ~~~~~~~~~~~ I'm glad you also learned how to spell the word
> after you looked it up, Leven. :-)
>
>
> -Nathan...
Touche'.
-z-
Michael P. Mossey
In article <slvrmnE7...@netcom.com>,
Albert Silverman <slv...@netcom.com> wrote:
>But since it is perfectly clear that Leven does not understand the vital
>distinction between THEORY and STYLE (and he is hardly alone), he is
>certainly in no position to act as a speculative "translator" of
>Silverman's statements!
>
>the slightest idea?
Yes, this vital distinction between theory and style is difficult to
grasp, but I thought I might help out. I thought that presenting a
form of dialogue might help. I hope that everyone finds it much
easier to understand Al's theory after reading this.
Theory and Style
================
A lesson in the form of a conversion between teacher and students.
Characters: Mr. Ass and students 1, 2, 3, and 4.
(Character names are fictional and any resemblance of a name to any
individual, living, dead, living but confused, or otherwise, and any
resemblance of the letters A-S-S to the initials of any individual
[for example, and this is only hypothetically speaking, Al Silverman,
Supergenius] is purely coincidental and completely unintended.)
[This play takes place in a wooded area filled with various plants.
All the characters except Student 1 wear hats.]
Mr. Ass: Here is a gibber bush. It has green leaves, the twigs sprout
in groups of three. Here is an oober bush. It has yellow leaves and
the twigs sprout individually.
Students (together): Ok.
Mr. Ass: Let's test your UNDERSTANDING. Here is another bush. What
color are its leaves?
Students (together): Green!
Mr. Ass: How many twigs in each group?
Students (together): Three!
Mr. Ass: What kind of bush is it?
Students (together): A gibber bush!
Mr. Ass: Very good. And now, this bush over here, with yellow leaves
and individually sprouted twigs, what is this?
Students (together): An oober bush!
Mr. Ass: Very, very good! You are really showing TRUE UNDERSTANDING
and the ability to THINK FOR YOURSELVES. Very, very good.
Student 1: Excuse me, Mr. Ass, this bush here has lime-green leaves
and twigs in groups of three. Lime-green instead of green. I guess
this is a third kind of bush.
Mr. Ass: No, no, oh no, NO! It's an gibber bush, you are just
confusing THEORY with STYLE. THEORETICALLY all gibber bushes have
some form of green leaf; STYLISTICALLY the green may vary in shade.
Please, do not confuse the study of THEORY with STYLE.
Students (together): Yes, Mr. Ass.
Mr. Ass: Now let me explain a tendency of gibber bushes: they have red
bark and attract ants.
Student 2: Here is a curious thing. It is a bush with yellow leaves,
like an oober bush, but it also has twigs in groups of three, red
bark, and ants crawling on it. In most respects, it seems like a
gibber bush. I know you said that yellow leaves means it's an oober
bush, but perhaps could this be...
Mr. Ass: no no no! Look, if it has yellow leaves, it's an oober bush.
This is a stylistic variant of an oober bush that has red bark, twigs
in groups of three, and attracts ants. Please show some UNDERSTANDING.
[Student 3 gets out a chemistry set and begins processing samples from
the bush in question.]
Student 3: Look at this, Mr. Ass, this bush is poisonous...and so is
the first gibber bush you showed us. Maybe it's pretty important to
call this a gibber bush to make sure everyone knows it's poisonous...
Mr. Ass: It's an oober bush!
[Student 4 kneels down to study the leaves of the bush in question.]
Student 4: Hey, I see here yellow-green spots on the leaves. Perhaps
we could regard the leaf as a variant on the green leaves of the
gibber bush...
Mr. Ass: No, no, it's an oober bush! Wait, I just had an insight!
It's not a bush at all! Yes, that's the answer. I'm pretty clever,
aren't I!
Students (together): Ooooh...
[Mr. Ass rips the bush in question out of the ground and begins to
stomp on it.]
Mr. Ass: Not a bush! Not a bush! Not a bush!
[For the first time Mr. Ass notices that everyone but Student 1 wears
a hat.]
Mr. Ass (to Student 1): I notice that everyone's head functions to
support a hat but yours. I suspect you don't belong with this class.
Get out! Go! Scram!
Student 1: But, Mr. Ass, but...
Mr. Ass: Wait! I have a better idea. You are HEADLESS. Yes, that's
it, you are lacking a FUNCTIONALLY DYNAMICALLY STRUCTURAL HEAD. Which
is not to say you are lacking a head altogether, since you do possess
a CONSTRUCTIONAL head.
Students (together): Ooooh...
Mr. Ass: I hope, students, that you are beginning to acquire a TRUE
UNDERSTANDING of these matters. I hope you are beginning to see the
power of intelligent abstract thinking.
[Student 2 begins digging at the dirt between bushes.]
Mr. Ass: What are you doing?
Student 2: Well, I just wanted to compare the roots of these two kinds
of bushes. Wow, look at this, I think the bushes share a root system.
Mr. Ass: Now you stop that this instant...
Student 2: Yes, look at this! Both types of bushes are actually
branches of a single plant.
Mr. Ass: Put that dirt back right now!
Student 3: Hmm, maybe we could say that each bush is a stylistic
variant of the same plant?
[Mr. Ass practically explodes.]
Mr. Ass: Noooo! THEORY not STYLE. STYLE not THEORY. THEORY not
STYLE. STYLE not THEORY. THEORY not...
[All the students start digging between many plants.]
Mr. Ass: All of you are INDOCTRINATED. Yes, that's it, you can't
think for yourselves any more.
[Mr. Ass shakes his head as he walks away. The students continue
digging.]
T H E E N D
I hope that helps to clarify the vital distinction between theory and
style. Please, don't hesitate to ask questions...we need to expose
your stupidity as soon as possible.
M. Mossey
Albert Silverman
Well, it looks like you've been "ingesting" the proper medication to cure
the affliction which has thus far prevented the Rolling Stones from
accepting your past applications!
If you apply once again (and show those needle marks as proof), I'm sure
that they will reconsider. I understand that they are currently in need
of a "stoned" tambourine player, and you will fill that vacancy
(just look at those eyes!) perfectly.
However, you will have to give up your coveted new position in the Kookoo
Quartet, in order to contribute your talents full-time to the Stoned.
Oh, and by the way, be sure to clue them in on your new theory, which
will have the Stoned Rolling on the floor.
Yes, the Rolling Stoned DO gather Mossey, who can roll with the best of
them. I admit that I was wrong.