Polytemporality in Music

In the context of the virtual residency programme 2020, composer and music theorist Adrian Kleinlosen talked with the composer Karin Wetzel about the phenomenon of “polytemporality” in music.

Adrian Kleinlosen (AK): Dear Karin, you wrote your doctorate on the theme of the poly-work in the 20^th and 21^st centuries, on the musical phenomenon that denotes the simultaneous performance of at least two works. As I understand the concept, it is not enough, however, that multiple works are performed at the same time. Rather, the works must be conceived in such a way that they can be performed only in combination with very specific works – precisely those works with which they, as precompositional construction, develop structural points of intersection. Performing a Beethoven piano sonata and a piece by Billie Eilish at the same time could hardly be designated as a poly-work in an emphatic sense.

Karin Wetzel (KW): I see it just the same. Performing both pieces at the same time should be viewed instead as a simultaneous performance in John Cage’s sense. The poly-work begins in the precompositional process. On the one hand, it seeks to finalize single strands of the work so that they can also be performed independently; on the other hand, they should be open enough to each other that they can forge something together. Of course this can make the process of composition very complex. I discussed this process in my dissertation. It was fascinating for me to learn whether the composers composed their poly-works simultaneously or successively, or whether it was a matter of a mix of both compositional processes.

Have you yourself written a poly-piece or thought about doing so? If so, how did the compositional process take shape or how would you approach it?

AK: No, I have neither composed nor conceived a poly-work. There are several reasons for this, the principal one being simply that I work on my pieces very long. On my most recent piece – which will be 14 minutes long – I’ve been working already for some two and half years. For a poly-work I would need, then, indeed a couple of centuries, which unfortunately exceeds my lifespan. Something that I have occupied myself with for quite some time is the concurrence of several rhythmic strands that are in themselves already very complicated.

Concerning this theme, what I would like to talk about with you is the phenomenon of “polytemporality” in music. Firstly, I would like to define polytemporality as the simultaneity of at least two tempos. But just as the concept of polyphony means not solely the presence of several parts but rather the presence of several independent parts, the outline of the concept of polytemporality would be incomplete if one didn’t add that the tempos, too, have to be independent to a certain extent. In my opinion, this kind of independence reveals itself, in turn, in the relations between the tempos, which have to exhibit a certain degree of complexity. Tempos that stand to each other in the relations 2:1, 4:1, 8:1 etc. do not fulfil, then, the demand of independence.

How would you define “polytemporality”?

KW: I think one should distinguish more specifically between polytempo and polytemporality, that is, one should conceive of the concept of polytemporality more broadly than the pure numerical ratio of tempos. The temporal arrangement of a piece encompasses more than merely the indicated tempo. Also metre, rhythm, formal rhythm and the dramaturgy of events play a role. These are all intertwined to form the temporal character of a piece. And this intertwining of the diverse components then leads to a specific “temporality”. Even when the tempo relations are related to each other in a simple way or are actually identical, the temporality can be different – perhaps the metre is offset and/or the rhythmic configurations deviate significantly from one another. Of course, in purely mathematical terms, the metric intersections of diverse tempos are highly predictable and frequent in the simple relations. Probably a common underlying pulse can be identified, which, of course, also has something unifying to it. The more differently and loosely the tempos relate to each other, the more interesting are the metric intersections and the question concerning how to deal with them. Does one ignore them, or do they have formal consequences? And here, of course, it also becomes interesting for the poly-work, because if a temporal tension exists between the simultaneous strands of the work, and the relation between the works tends towards non-synchronization, then a very special dynamic can arise.

How do you see it?

AK: Your distinction between polytempo and polytemporality makes sense to me and I would like to go along with it. If I may make a suggestion: I would replace the concept of polytempo with “polytempic”. While “polytempo” refers more to the concrete event, “polytempic” would designate the phenomenon as such. (We may think of the distinction in German between Rhythmus and Rhythmik, Harmonie and Harmonik, etc.^[1])

KW: That is certainly sensible.

AK: But what about works in which diverse tempos follow each other successively? In your opinion, can one speak of polytempic in such cases? Or would a different concept be more suitable?

KW: Those are changes in tempo. The appeal of simultaneity lies in the colliding of what is different in the same time frame and it represents a counter model to the purely successive and linear development and sequence. What is heterogeneous can thus be experienced at the same time and linked with one another. It is especially the tension generated between the different strands that can be directly perceived.

AK: Let’s now consider some examples of polytemporality in old and new music. The opera “Die Soldaten” by Bernd Alois Zimmermann suggests itself to me as a prime example, especially in its first version in which Zimmermann developed seven distinct tempo layers, five of which are at times superimposed upon each other. I also think of “Studies for Player Piano” by Conlon Nancarrow. Already in the second of these 49 études for player piano, the two parts play in a speed ratio of 3:5. From here it is only a small step to electroacoustic music, the possibilities of which seem nearly limitless: While the superposition of seven different tempos may seem impracticable to an orchestra, with a computer, by contrast, the superposition of hundreds of different tempos becomes a banality.

And what is possible is also done: In my work “mv1:i” for bassoon, piano and electronics, each part – which is in itself already organized polyphonically – has its own tempo. These parts are then superimposed upon one another: The bassoonist must master up to three simultaneous parts, the pianist up to four, and the electronic part consists of up to six distinct parts.

But which works come to mind when you think of the phenomenon of musical polytemporality? And what about your own compositional work: Are there passages with polytemporal character in your works?

KW: For me, a very interesting example for the interaction of polytempic and poly-work is the “Anea Crystal Cycle” for two string quartets by Chaya Czernowin. The first quartet, which is written in simple fractions, is contrasted with the other quartet in a complicated double-fraction notation. Added to this are different tempos that switch at different points in time. The independence of the quartets is constituted on the material level and also even more so on the temporal-organizational level. This accentuates the autonomous character of the single strands of the work.

I myself have composed a poly-work for violin with the title “Dividuum”. It is a free combination of two solo pieces that can be performed independently of each other, and which join together into a third solo piece. The two underlying solo pieces have different tempos. Of course, this is mainly a conceptual idea. What concerns me is the question whether and how diverse timelines can be performed by one individual. In present-day life, one is confronted time and again with the question: How does one balance allegedly irreconcilable diverse temporal demands? One must pose this question, and sometimes it works better, sometimes worse. This symbiosis of both solo pieces into a third solo piece is thus never 100% + 100%. Perhaps it will be only 40% + 82 %. The result is always imperfect, but for me it reflects this difficult balancing act of the compatibility of different things – a phenomenon that is so ubiquitous.

AK: Lastly I’d like to raise the question whether the phenomenon of polytemporality appears in European art music for the first time in the 20^th century or whether it can be found already in works of earlier periods.

I’m inclined to the former: Were not the parts of the ars subtilior, which stand to one another in occasionally complex numerical relations and for which Johannes Ciconia’s three-part canon “Le ray au soleyl” may be taken as a model, invariably subsumed to a superordinate tempo? Shouldn’t one speak here of “polymetric” instead of polytemporality? And, pursuing this question further, wouldn’t such an attribution also be valid for the greater part of New Music? Then the above supposition should be condensed to the following claim: Since its first appearance within European art music of the 20^th century, musical polytemporality is a phenomenon that appertains to only very few compositions.

Let’s take the work of Brian Ferneyhough as an example. Is his music polytemporal? I would say: no. As complicated as the single parts may be arranged, they coincide again and again in common focal points, are thus not polymetrically organized. Also tempo and signatures are the same for all parts. Thus we may call Ferneyhough’s music neither “polytempic” nor “polysignaturic”. Ultimately the tuplets that characterize Ferneyhough’s notation – mostly numerical relations placed in brackets such as 8:7 or 11:8 – always point to the beat. Thus Ferneyhough’s music is also not “polypulsive”. What is left? A superposition of many different rhythms: Ferneyhough’s music is polyrhythmic.

KW: Sometimes it’s also a question for the notation and practical considerations of performance concerning which temporal parameter is differentiated. Polytempic and polyrhythm are sometimes transferrable to one another. What is more feasible in the end? A delicate rhythmic arrangement based on a common beat or the synchronization of different tempos? Transferring polytempos onto paper in notes is also demanding. Meanwhile there is a programme that can help with notational and practical difficulties of performance.^[2]

AK: And here it becomes apparent once again how the implementation of a concept is dependent on the development of technical equipment. While only very few instrumental and vocal works up to now are polytemporally organized – which can undoubtedly also be accounted for by the exorbitant effort this entails for composers and interpreters – this could change in the foreseeable future thanks to such programmes.

KW: That may be the case. On the one hand, they simplify certain composition processes and make them efficient. On the other hand, efficiency ought not lead to neutralizing the actual tension between the diverse temporal strands. For me the appeal lies in preserving this temporal tension.

Translated from the German by Aaron Shoichet

[1] Note of the translator: There is no satisfactory equivalent in the English language for this distinction.

[2] See The Polytempo Network and The Polytempo Composer by Philippe Kocher, https://polytempo.zhdk.ch/.