Sunday, August 01, 2010

Curses & Snake Oil, Practice & Theory

Alex Ross has a pair of posts (here and here) about a harmonic progression with some significant history, moving, for example, from F# Major to d minor, two chords with no common tones.

As it happens — the lattice of coincidence being what it is —, in Budapest last week, I picked up a copy of Ernő Lendvai's Verdi and Wagner, a volume intended to be the first of several on "Bartók and the 19th century". Lendvai is best known to musicians for his thesis that major structural divisions in Bartók's music correspond to Fibbonaci proportions and the golden section. I've never been convinced that this thesis is precisely true, but find it unremarkable that such proportions in a rough form are present as it simply makes sense that major events in the course of a musical work would be successfully programmed to maximize our attention by appearing somewhere between the half-way point and the end, and a sequence like 1:2, 2:3, 3:5, 5:8, 8:13, ... hovers right in that region.* I suspect that a great deal of hovering around these ratios has been and will be tolerated in the exact divisions of a single musical work, so much so that an over-obsession with precision is probably unneccessary; moreover, in Lendvai's own accounting of Bartók's actual proportions, there is enough variability — particularly due to tempi — that considerable fuzziness in the ratios of real elapsed time are inevitable. This series of books, however, was intended to focus on Bartók's relationship to a harmonic tradition, in particular that of the major later 19th century opera composers, Verdi and Wagner. (It's worth adding here that the two more immediate influences on the younger Bartók's practice were Richard Strauss and Franz Liszt, who could be considered as mediator's between Bartók and those operatic styles.) I bought the book with nothing more in mind than having some streetcar riding material, but it did turn out to be fascinating reading, although in ways Lendvai certainly did not intend. What Lendvai did intend was to describe later 19th century harmonic practice in terms of the interraction between the diatonic and the chromatic, the one irregularly, assymmetricly, divided, the other evenly and symmetrical. So far, so good. But Lendvai's treatment rapidly goes beyond this, constructing an elaborate system with idiosyncratic terminology and then going well beyond his system proper by associating literal "meanings" for particular harmonic relationships with excourses into topics like key characteristics. The bulk of the volume is given over to a description of Verdi's Falstaff.

As far as I'm concerned, music theory of this sort is close to snake oil, with its effectiveness as analysis approximating a placebo effect more than a real account of what our ears and brains do with musical sounds. That said, the fact that real musicians have taken and do take such constructions seriously, as an impetus to the production of real — and often very fine — music, means that it is a real part of the culture around the music and, at the very least, we have an ethnographic obligation to take it seriously as well, at the very least as a locally coventional — if, ultimately, in terms of the psychoacouctical and neurological foundations of musical perception, arbitrary — means of giving constraint and order to musical materials. Lendvai's "theory" is, ultimately, a doctrine, positing for the late 19th century an extension and equivalent to the earlier doctrines of musical figures and affects.

Now, the chord progression which Ross has noted might be described in terms of any number of theoretical "systems" — Lendvai's among them — and individual composers may well work productively with such systems, and it has certainly established itself in the repertoire as a recognizeable figure with an associated affect, but there is probably no real need to call up either an elaborate theoretical apparatus or an existing repertoire of usage to identify the salient qualities of the progression: the two chords are connected by a smooth ("parsimonious" is the term of art) voice leading,** yet — depending upon how one deals with "enharmonically equivalent" tones — do not come from a common diatonic collection. Most tonal music bops along within the same diatonic collection, venturing from time to time to collections that share most tones, so a sudden jump like this one plays with our habits and expectations. The effect — and possibly, affect — is thus both smooth and startling.

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* When one traces the development of the Sonata form, one finds a similar refinement of proportions, successively moving the point of furthest harmonic remove from the center of the simple AABB Sonata further back into a development section.
** It is not a coincidence that the examples here are taken from vocal ensemble and opera, in which changes of texture, i.e. not maintaining a constant four-voice ensemble, are frequent.

1 comment:

Paul Beaudoin said...

I have had two compositions teachers who were firm believers in GS/Fibonacci, but I continue to be surprised at how many feel this is "bunk." Quite often I think composers are inspired by theory - even if they don't follow the rigor of it. In the case of Lendvai/Bartok, it was perhaps more of an inspiration to composers, like Ligeti, who found the theory a kind of spark for the imagination. Later, Ligeti himself disclosed how important the writings of AM Jones was in his discovery of African polyrhythms.

Case in point, I was lucky to have Ligeti read an analytical paper I wrote on his 'Cello Concerto. It remains one of my biggest pleasures to know that many months after I received a post card from him about it.

Charles Bouleau has a wonderful book that explores the geometric shaping of visual art in his "The Painter's Secret Geometry."

While we probably find it difficult to hear GS/Fibonacci sequences a priori, I do think there is merit in the kinds of ways it offers composers a way to mark the landscapes of their compositions.

Rabattement anyone?