On Mahnkopf’s ‘Theory of Polyphony’

After a very stimulating discussion the other day with fellow composers Peter Clark and Michael Mathieson-Sandars around Claus-Steffen Mahnkopf’s article ‘Theory of Polyphony’ in the book Polyphony and Complexity (first book in the series New Music and Aesthetics in the 21st Century), I thought I’d try to write up some of my thoughts about it.

Now my distaste for Mahnkopf’s unnecessarily obfuscatory writing style aside, and my overall disagreement with his generally formalist, idealist bent, the article does contain some valuable contributions to thinking about counterpoint. I want to deal here both with what I find valuable in his article, and what I disagree with, as well as what seems contradictory or unclear.

Difference and totality. Mahnkopf’s concept of polyphony is one of ‘difference’. In fact it is about ‘difference qua difference’: “it is difference as such that gives rise to the polyphonic perspective” (p. 39). The epigraph for the article is a quote from Derrida’s Writing and Difference: “… [I]n the absence of a center or origin, everything becomes discourse–provided we can agree on this word–that is to say, a system in which the central signified, the original or transcendental signified, is never absolutely present outside of a system of differences.” (quoted on page 38). Now the stuff about ‘discourse’ aside, the assertion that the centre is not present except mediated through a system of local difference is absolutely true of all reality, and certainly an important perspective to have when composing polyphony today. The problem is when you start to assume that the centre or totality simply doesn’t exist and that therefore you are opened up into a space of pure difference. To my mind, Mahnkopf equivocates or is unclear on this point. He on the one hand wants to say that there is no unity in true polyphony, that such a unity would be a function of the listening subject (I’ll come back to this): “a unity that transcends all differences and which is therefore no longer materially present. Its immanent musical content therefore reaches beyond that which is musically “given”: an ideal, the “thought” that synthesises the polyphonic listening experience” (p. 45). On the other hand, he wants to suggest that some kind of relationship exists between difference and unity within the work: “In musical terms, it is a critical point whether or not difference is emphasized within the unity of differing elements (or whether or not the uniformity of these differences is suppressed by unity). It is only this fundamental option that can give rise to polyphony as a musical paradigm at all” (p. 39). So this seems to suggest that there is a question of the relative weighting of unity and difference and that it is a matter of the articulation of a totality made from relatively autonomous parts that are not wholly subsumed.

So either there is a liberal, postmodern-type pure difference (or diversity), or there is something much closer to Adorno’s dialectical approach. We can’t be sure Mahnkopf’s position. Here is Adorno, being much less confused and confusing than Mahnkopf:

While all the elements interpenetrate, they also remain distinct, and the unity comes into being only though the function each of them has and by virtue of which it influences the others. It is not an immediate unity, but a unity of opposites. (‘The function of counterpoint in new music’, p. 129)

Mahnkopf wants to differentiate himself from this because of a misguided critique of the dialectic (and organicism) he inherits from Derrida whereby “only the difference between difference and unity as an emphatic difference (and not as a return to unity) can act as a basis of a differential theory (which dialectic merely claims to be)” (p. 39).

Diagonal listening. All this aside, effectively Mahnkopf goes on to outline a theory of polyphonic listening that is quite dialectical. He calls it ‘diagonal listening’ which is a fair enough term for it, since it is neither purely vertical listening nor horizontal. For Mahnkopf, and it is almost a truism, listening to polyphony forces one to oscillate back and forward between parts and whole, never fully settling on the one or the other. A significant degree of unconscious listening takes place since the listener can’t focus on everything simultaneously, but presumably everything is relevant to everything else, so pre- or un-conscious “modes of cognition and perception” fill in the gaps.

For Mahnkopf diagonal listening is a mediation (notice the dialectical terminology!): “a mediation between vertical and horizontal differences through a (in Derrida’s sense) delay in the (diagonal) correspondences, a displacement occurring between levels of significance” (p. 41). Or: “It offers neither the whole … nor to “mere” individual voices its undivided attention, as it would if they were autonomous, isolated, and separated from their tectonic context” (p. 41). Nice dialectic of part and whole!

Apperceptive overload. All this comes about because the listener is overloaded with information (and bearers of information). For Mahnkopf polyphony is the music of “apperceptive overload” and vice versa. He explains it thus:

“Whereas the active ear can cling to a harmonically framed monody, so to speak “singing along” with it, it reaches the limits of how much information can be assimilated and how many perceptual and experiential levels it can occupy at one time when confronted with polyphonic music” (p. 41).

While Mahnkopf doesn’t spell it out clearly in this article I think he’d agree that a critical point is to what end apperceptive overload is pursued. For Mahnkopf it is clearly as a means to force the listener into a state of diagonal listening. If apperceptive overload is pursued for its own sake, and pushed to the extreme, it is possible that it would obliterate this diagonal listening, the dialectic of part and whole, and produce a vertical structure that is essentially reductive and reified, a kind of banal noise. A lesson for complexists!

What is not polyphony: antiphony. Just as absolute complexity destroys polyphony, on another plane the mere layering of musical structures is anti-contrapuntal:

Polyphony is therefore a qualitative term, one which necessarily connotes the (somewhat paradoxical) notion of a binding heterogeny [dialectical totality!], both “ideally” and technically. Counter-polyphonic stances–whether conceived as aleatory, “tachistic” (Cage), as a negational combination of consciously irreconcilable elements founded on “polystylistic semantics” (Bernd Alois Zimmerman), as a statistical-stochastic leveling-out of dissonances to produce mass phenomena without internal functional relationships (Xenakis)–lead to the consciously random co-existence of materials, precisely because they neutralize all differences and shift the focus of the listening experience from the directness of the diagonal level to the “bird’s eye view” of the exterior, be it “harmonically” framed or simply uncrafted. (p. 46)

This is an excellent defence of polyphony as a dialectical system of relations. The lines within a polyphony must be both different and similar, in order for diagonal listening to be possible:

It seems beyond doubt, however, that the field of polyphonic representation requires a relative material homogeneity, and also requires that the material should not already contain too high a level of dissociation; otherwise the diagonal force-fields [an Adornian term which I think is perfectly apt here] would lose their energy, an energy which can only result from the interaction between related, “erotically” associated materials [why this I’m not sure], however heteromorphic they may be. (p. 46)

Or even better, if we’re looking at the dialectical reflection of external relations upon internal relations:

[In impressionism and spectralism] the aim is to create a naturalistic objective, self-identical monad through musically immanent precision, whereas the polyphonic tradition strives for the greatest possible number of “outward” relationships in a fibrous network of formations that are reciprocally reactive, and thus of permanently impaired identity. (p. 45, my emphasis)

Those musics that do not do this and simply layer musical structures over the top of each other could be said to be ‘antiphonic’ and not ‘polyphonic’ (Mahnkopf mentions that Boulez once made this distinction, p. 51 n. 32). This is a useful term, and something I will certainly take up. Of course the boundaries between polyphony and antiphony are porous…

Listening and the subject. Now, this again raises the question of totality. And I should stop banging on about it, because it’s largely semantic and clarifying it may not necessarily have any impact on my composing, but from the standpoint of the philosophy of counterpoint, it is important. Despite all of the above, in which Mahnkopf recognises that there must in a sense be a ‘system’ of interrelations between the lines in order for the music to be polyphonic (that there be diagonal listening), he nonetheless posits that the unity of the work is an ‘ideal’ one located in the listening subject:

a unity that transcends all differences and which is therefore no longer materially present. Its immanent musical content therefore reaches beyond that which is musically “given:” an ideal, the “thought” that synthesizes the polyphonic listening experience by reacting to the apperceptive overload with diagonal bracing, this on the basis of an affinity between the “unity” of the musical dimension and that of the self. (p. 45)

Again, an equivocation. He clearly is trying to say that the unity of the work is located outside of the work in an ‘ideal’ (which is perhaps best conceived of as a Kantian regulative idea to which the listening subject aspires through diagonal listening). At the same time he mentions that this comes about through an affinity with the “unity” on the musical level. It’s a bit of a dodgy sleight of hand: are the scare quotes meant to imply that there in fact isn’t a unity on the musical level, in which case how is the unity of the listening experience in affinity with it, or are they merely to say that it isn’t a simple unity, but in fact a complex unity of opposites, in which case it is still a unity present in the work and the listening experience does not add it.

In any case, this does raise the question of the subject of polyphony today. A few quick remarks: 1) the subject of counterpoint from Bach to Schoenberg was a thematic one, the theme–as François Nicolas points out–being the figure of self-consciousness or the subject insofar as it effected its surrounding structure as it effected itself (cf. Marx’s third thesis on Feuerbach). 2) this is now no longer possible in athematic music. 3) nonetheless music that is asubjective has gone over to the order of things, so a subject must be sought. 4) surely the listening subject exists and the effect of truly polyphonic music (via diagonal listening) would be that of a dereification of the experience of the listening subject; 5) nonetheless, for Adorno, the subject would have to be located at the level of the music itself, it would be sedimented there, the dereification of experience would be in the work, insofar as the listener can let themselves go into the music (a great discipline).

This solves nothing, and I’ll come back to this question in the future, but for now I just want to say that Adorno solves the ambiguity in Mahnkopf’s formulation, and that in order to do this both the subject and the unity must be found at the level of the work itself. Granted the subject is complex and divided and the unity is a complex unity of opposing forces; a force-field.

Ok. I need to go and compose now, so I’ll wrap up the last few points very quickly.

Parametric polyphony vs. Expressionist counterpoint? Something that comes out of this is Mahnkopf’s constructivist bent. For Mahnkopf, as a ‘post-serialist’, polyphony is something to be determined by careful and systematic distribution of parameters (cf. Nicolas on serialism and parametric thinking). Adorno’s subject is at least partly (or perhaps principally) intuitive… It is based in the category of experience and the ‘mimetic comportment’ of art. Of course in a rational society art cannot simply continue with pre-rational forms, but at the same time it cannot, without losing its essence, be totally rationally controlled. The idea is to present the possibility of a reconciled subject, a reconciliation of reason and intuition, within a context where no such reconciliation is possible (to the point where, under modern capitalism pure reason turns into its opposite: pure barbarism). And this is precisely why a counterpoint that emphasises difference and complex totalities is important today: the lines cannot add up to a simple whole without being false to the social whole in which they are situated.

For me, if diagonal listening provides the experience of an unreconciled reconciliation, its structuration must also be by way of an unreconciled reconciliation of reason and intuition; of formalist, parametric thinking and expressionist, spontaneous thinking. Just as the lines within a polyphonic texture must be preserved in their dissonance with each other, so must the intuitive flowing of the work be preserved in its dissonance with its rational control. Otherwise, the effect of diagonal listening would have been produced by a cold, calculating and reified reason that is precisely lacking in hope of an integrated whole. It is one in which the experience of a dialectic in the polyphony is a false one, since it is produced by false means.

It is as though one has an authentic (dialectical) experience of subjectivity that has been perfectly refined and delivered by administrative technocrats. A truly distopian scenario.

Polyphony/polymorphy. Not really something that needs elaborating, polyphony is the simultaneous existence of relatively autonomous lines and polymorphy concerns the degree to which these lines are differently formed.

Polywork. I won’t take this up here, since it does not concern my practice at this stage. However, I’m suspicious of this concept since it contains the exact ambivalence around the question of unity and totality that is throughout Mahnkopf’s general theory.

Polyvectoriality. I’ll come back to this on an post about my latest piece, since it concerns the method of composing lines separately from each other before bringing them back into relation.

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