Group composition

I recently read through Richard Toop’s 2002 Kürten lectures on Stockhausen. I’ve never really been a big fan of Stockhausen – seeing him, as many do, as something of a caricature – but I’ve been reviewing the serialist project lately and finding that there’s a wealth of stimulating stuff there for me, not least of all in the kind of things Stockhausen developed across his output.

I’ll briefly touch on some of the later approaches Stockhausen took, but for now I wanna get to the bottom of why ‘group composition’ is super relevant for what I’m doing.

Group composition

Toop suggests that whereas ‘point composition’ was more of a stylistic matter – a question of sonic result – ‘group composition’ was more of a method of composition. (p. 3)

Group composition was not so much a matter of building a rigorous method where everything would be justified (as is the caricature of serialism), but of pushing composition into new spaces.

It’s not just a method of ‘disciplined composition’; above all, it’s a way of exploring unknown artistic territory with three primary objectives:

  1. To cover as much territory as possible in a non-arbitrary way;
  2. To establish coherent and artistically meaningful procedures for dealing with what one finds, and to unify these procedures wherever possible;
  3. To retrieve the findings into the world of art in terms of ‘works’, even if this involves partly redefining he notion of art. (pp. 3-4)

This clearly fits in with what I was saying in my last blog post, right down to the spatial metaphor of ‘unknown artistic territory’.

Toop gives a wonderful little explanation on exactly what group composition is as opposed to point composition, but I won’t copy it all out. The main thing about group composition, according to Toop, is that “it has to do with proportioning” (p. 4).

Which is to say that whereas in point composition a number sequence such as 3 2 4 1 5 would give a shape to a parameter over a series of single notes (e.g. a middle note, a lower note, a higher note, etc etc), in group composition, such a number sequence would define the regions of notes upon which a parameter would act (a group of 3 then a group of 2 then of 4 etc etc). Each ‘group’ in the series would have a common identity in one parameter. So, to be really obvious, all 3 notes in group 1 could have, for instance, a particular pitch (g#, why not), then both notes in group 2 would have another pitch (let’s say c#), and then all four notes in group 3 would have yet another pitch (how about e), and so on. The pitches themselves would have to be determined according to another sequence of numbers…

Broader applications

Now the implications of this are immensely far reaching and are not at all bound to the approach taken to this group composition in, for instance, the Klavierstücke. The point is a group could be anything, conceived of at any time-scale, upon which anything that could be parametrised in a composition would have its function. (Stockhausen’s Studie II from 1954 is a really great example of a work conceived, from the bottom up, in terms of ‘groups’. Toop looks at this in his article). The phenomenal appearing of groups can be contradicted by different partitioning of the same note sequence in different parameters (as the colour-talea division in Medieval music, see Klavierstücke VIII), undermining the clear identity of said group. Or it could be reinforced by having multiple parameters structured according to the same group structure. The degree of self-identity itself can be a parameter that is applied to a group structure.

It is in this sense that I’m particularly interested by how Badiou’s theory of the phenomenon in LOW could relate to the concept of the ‘group’ in this music.

The other thing about group composition is that there is no reason to think solely in terms of diachronic sequences of groups of pitches. Instead one could treat them vertically, and not bound to quantifiable collections of notes, but simply to different strata in the work. For example in my new piece, Kampflieder I have five strata (five ‘groups’) each of which has a different number of instruments: 1, 2, 3, 4, 5. To this structure I add differential sequences of relative self-identity in different parameters numbered 1-5 where 1 is minimal and 5 is maximal self-identity (I can thank Richard Barrett for this idea, since prior to having a lesson with him, I was defining these parametric differences much more intuitively). I’ve kinda explained this elsewhere

What this gives you is a very coherent way of establishing the stratification of lines in a musical ‘texture’, and then exploring their individual developments as well as their interrelations. Which really is my definition of counterpoint at the moment.

And again, this is why the connection to LOW and Badiou’s determination of the ‘phenomenon’ is interesting:

We have called the ‘phenomenon’ of a multiple-being, relative to the world in which it appears, the giving of the degrees of identity that measure its relationship of appearance to all the other beings of the same world (or, more precisely, of the same object-of-the-world). (LOW, p. 207)

This approach has pushed me to come up with textures I wouldn’t normally come up with. Hopefully much more interesting textures – and that’s the point.

But, as I said above, thinking in groups can also apply to much larger time scales then a brief collection of notes. So you can have groups that are whole formal ‘sections’.

The biggest interest and tension for me at the moment is this between characterising big formal groups (and thus the constituents within them, enough to make it clear that this section is indeed a section), and characterising the primary strata. Richard Barrett’s music, for example, to my mind tends toward very clear horizontal group determinations, even when he is working with vertical strata, and so the counterpoint is somewhat reduced. This is the old vertical-horizontal contradiction common to contrapuntal thought going back centuries, but now within a more rationalised, emancipated framework.

And a final, related, thought on groups. For a while recently I was composing across phrases. That is to say, I would have continuous processes (let’s say a wonky rhythmic diminution) that would last a whole section, which would ignore phrase divisions. Phrase divisions would be considered as just one parameter amongst many, and did not have a determining function over other processes. This is in contrast to thinking in terms of ‘phrases’ as ‘groups’. In the former, the basic unit is a long-range stream of information, the character of a phrase was not so firm, and could shift part-way through depending on the process; in the latter, the basic element is the group and its identity is as weak or strong depending on how it was specifically structured. At the moment I’m caught between the two approaches… We’ll see where this goes.