[Smt-talk] Classical Form and Recursion

Ildar Khannanov solfeggio7 at yahoo.com
Wed Apr 8 08:38:15 PDT 2009

Dear Fred,
thank you very much for your encouraging  response. Indeed, tension/relaxation is intuitive in many musical cultures. It also exists in some educational systems as a logical component. I would like to bring an example of Boleslav Yavorsky's theory of lad rhythm, in which he defines the triton-based system, the product of equal division of an octave, an analogue of Arthur Berger's concept of  octatonic. One would expect this system to be devoid of tension-relaxation (after all, we are talking her about artificial modality, sets, collections, etc.) but he manages to retain the idea of resolution of the tritones. He call them sopryazhenie, which means simultaneous tension, coordination by tension. Tension in Russian is napryazhenie. So, even in cold spaces of artificial modality, there is tension and relaxation. When in late Scriabin, say in his Etude op 63 no 3, or in Guirlandes op 73, tension does not receive relaxation, the tritone is still
 ultimately tensed up and is waiting for a resolution.
Of course, in music of Palestrina and in Gregorian chant tension/relaxation model does not seem to play a major role, but in these cases we deal with textual-musical forms (the term of Valentina Kholopova), and in them tension and relaxation is done primarily in the lyrics. For example, teh sequence Victimae paschali  has a place of ultimate tension, on words Mors et Vita duello. However, even in this sequence, there is also a pattern in pitch structure which displays tension and relaxation: the first phrase begins on  Re and ends on Re, the second phrase begins on La and ends on Re, the third phrase begins on La and ends on La, the fourth phrase begins on LA and ends on Re, the fifth phrase, obviously an auxiliary one, begins on Fa and ends on Do, and the last phrase begins on Mi and ends on Re. The dialectics of finalis and repercussa, mediated by the Do as an embryonic form of the third function, is clearly expressed in Victimae paschali. 
Palestrina's motet Nigra sum opens with a strangely familiar progression I  IV ( v ) V  I. 
I am not implying Riemann here, just the idea of tension and relaxation curve.
Best wishes,
Ildar Khannanov
Peabody Conservatory

--- On Wed, 4/8/09, Fred Lerdahl <awl1 at columbia.edu> wrote:

From: Fred Lerdahl <awl1 at columbia.edu>
Subject: Re: [Smt-talk] Classical Form and Recursion
To: "smt-talk Talk" <smt-talk at societymusictheory.org>
Date: Wednesday, April 8, 2009, 8:42 AM

Ildar Khannanov writes:

> You have mentioned that the studies oftonal  tension cover music from Bach to Messiaen. I can argue that tension/relaxation can be applied also to earlier and later periods. I have heard many times from my colleauges that tension/relaxation model applies mostly to 19th century music and it does not rise up to the level of Schenkerian abstraction. Or, some say that there was no harmony in the 18th-century music, let alone in the 17th and earlier centuries. What do you think about my idea that tension/relaxation as a category directly relates to harmony in a wider sense and as such it is universal  and can be attributed to Greek music as well as Bach and Messiaen?

Intuitions of tension and relaxation seem to be widespread if not universal, and they are by no means confined to music. In our tonal tension project, Krumhansl found mutually consistent responses using two contrasting experimental methods, indicating that these intuitions are robust.

So I agree that tension applies to all kinds of music. It would be valuable (if daunting) to investigate empirically how indigenous listeners in different musical idioms register intuitions of tension. Assuming consistent and robust responses, the modeling of tension across idioms would require theoretical modifications according to features of the idioms. For Machaut, for example, one would alter somewhat both the pitch space and the measures of surface dissonance. For Balinese gamelan, one would incorporate timbral features; these might outweigh the role of a comparatively simple Balinese pitch space. For West African drumming, a theory of rhythmic tension would have to be developed (such a theory is needed for standard tonal music, too).

I don't know much about ancient Greek music, but Costas Tsougras has developed an elegant model applicable to 20th-century popular Greek music in his "Modal Pitch Space" (Musicae Scientiae, 7.1, 57-86 [2003]).

Fred Lerdahl
Columbia University
awl1 at columbia.edu

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