# BRTOK, part II



## millionrainbows (Jun 23, 2012)

In this quote by Ernö Lendvai, he reveals the most profound aspect of Bartók's system:

"A secret of Bartók's music, and perhaps the most profound, is that the 'closed' world of the GS (Golden Section) (1,2,3 and 6 being 'closed' or 'inward-directed' intervals, as opposed to 4ths and 5ths) is counterbalanced by the 'open' sphere of the acoustic system. The former always pre-supposes the presence of the complete system -- it is not accidental that we have always depicted chromatic formations in the closed circle of fifths. In the last, all relations are dependent on one tone since the natural sequence of overtones emerges from one single root: therefore it is open. Thus, the diatonic system has a fundamental 'root' note, and the chromatic system a 'central' note...Bartók's GS system always involves the concentric expansion or contraction of intervals..."

So we can see from this exposition of the intervals that modern music started moving away from traditional tonality by way of exploiting the INHERENT SYMMETRIES in the 12-note scale.

In the bigger picture, what these small, recursive intervals do is allow the creation of pitch cells; these are aggregates of notes which expand around an axis of symmetry. Thus, localized areas of tonal centricity can be created on any note.

An analogy would be, traditional tonality is like a tree which grows up in one direction from one 'rooted' spot; in the chromatic approach, tonality becomes radiant 'flowers' of pitch, centering on any possible note in the vertical spectrum.

Another aspect of Bartók's approach which has puzzled many is the fact that he still uses the fifth & fourth as generators of traditional tonality, sometimes mixing the two approaches.

All of these ideas were 'in the air' so to speak, around the turn of the century, and were not unique to Bartók; examples of symmetry began showing up as early as R. Strauss, in his 'Elektra' and 'Metamorphosen,' before he retreated back into conservative classicism. Debussy, as most of us know, used the whole-tone scale in his music, most notably the prelude 'Voiles' from Book I. The 6-note whole-tone scale itself is a symmetrical projection of the major second, and there are only two of them; Debussy exploits this characteristic to create 2 areas of contrasting tonality. Schoenberg was influenced by this idea as well; in an old post of mine from an Amazon thread, "Schoenberg's Op. 26 Wind Quintet", I pointed this out:
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[The row is (first hexad) Eb-G-A-B-C#-C, which gives an augmented/whole-tone scale feel, with a "resolution" to C at the end, then (second hexad) Bb-D-E-F#-G#-F, which is very similar in its augmented/whole-tone scale structure, which only makes sense: there are only two whole-tone scales in the chromatic collection, each a chromatic half-step away from the other. I've heard Debussy use the two whole-tone scales in this manner, moving down a half-step to gain entry to the new key area. This is why Schoenberg used a "C" in the first hexad, and the "F" in the second; these are "gateways" into the chromatically adjacent scale area. Chromatic half-step relations like these can also be seen as "V-I" relations, when used as dual-identity "tri-tone substitutions" as explained following.
Another characteristic of whole-tone scales is their use (as in Thelonious Monk's idiosyncratic whole-tone run) as an altered dominant, or V chord. There is a tritone present, which creates a b7/3-3/b7 ambiguity, exploited by jazz players as "tri-tone substitution". The tritone (if viewed as b7-3 rather than I-b5) creates a constant harmonic movement, which is what chromatic jazzers, as well as German expressionists, are after.
So Schoenberg had several ideas in mind of the tonal implications when he chose this row.]
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Also, from this we can see that, historically, it was the tritone (in both V7-I's and in diminished seventh chords) which was the first emergent symmetry which led to the expansion of tonality; this interval was the color tone in the V7-I progression, being the major third and flat-seven, which would then exchange places for the next cycle. This gave rise to new roots, moving chromatically instead of by fifths. This was tied-in (as mentioned above) with 'flat-nine' dominant altered chords, which are closely related to the diminished seventh. The use of 'flat-nine dominants' as true V chords appears as early as Beethoven and Bach. The vii degree of the major scale, a diminished triad, has always been treated as an incomplete dominant ninth with G as the 'imaginary' root, and resolved as a V7 chord would be (to C).
So, it can be seen from all this that 'tonality' underwent great changes around the dawn of the 20th century; and one should not confuse this expanded chromatic version of tonality with Schoenberg's 12-tone method, which just confuses the issue.

Quoting Lendvai: "In fact, I am more critical of Schoenberg than I ever was before; his method treated dissonances like consonances, and renounced a tonal center. But dissonance is not the same as consonance; it has different acoustical and physiological effects. Therefore, dissonance ought not be treated as if it were identical with consonance. Plus, Schoenberg's renunciation of a tonal center does not follow from any previously stated proposition, and is merely an assertion of his dogmatic belief that the negation of tonality was 'historically inevitable.'"

However, that's a whole 'nother can of worms.

In closing, this quote by co-authors George Perle and Paul Lansky:

"Perhaps the most important influence of Schoenberg's method is not the 12-note idea itself, but along with it the individual concepts of permutation, inversional symmetry, invariance under transformation, etc.....Each of these ideas by itself, or in conjunction with many others, is focused upon with varying degrees...by...Bartók, Stravinsky, Berg, Webern, Varèse, etc...In this sense the development of the serial idea may be viewed not as a radical break with the past but as an especially brilliant coordination of musical ideas which had developed in the course of recent history. The symmetrical divisions of the octave so often found in Liszt and Wagner, for example, are not momentary abberations in tonal music which led to its ultimate destruction, but, rather, important musical ideas which, in defying integration into a given concept of a musical language, challenged the boundaries of that language."


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