Could end up having all sorts of unfortunate ironies...

It's when those tuplets start nesting that I have a problem. Just too darn ornithological.  

I hope we don't let this thread drag on too far. I'm off to warm some soup.

I've always bore something of a grudge against Xenakis for his rather drawn-out approach to explaining the rather more notational aspects of mathematics in that theory book of his rather than focussing on the musical aspects.  Cough.  This rather turned me off the idea of listening to his music (I tried to listen to one CD, but couldn't get over how much I disliked his extended discourse on associativity...I probably need to see a therapist...).

Though, on the music-analysis side Dmitri Tymoczko seems to be having a reasonable amount of fun at the moment.


Or a very, very tiny and rather contrived subset of 'composers/theorists' (see Mazzola.  Their (Mazzola's school) work isn't entirely without merit, from what portion I've been able to understand of it).

I definitely like the whole "science" as a tool aspect of the applications of science to music; I think that's definitely the best branch for opening things up; I would have expected Sethares's recentish developments to have spurred on a whole industry of microtonal theory (and can't understand why all these music theorists with their theories that easily generalize to non-standard tunings mightn't try to test out their theories in these contexts to see if their discoveries in the 12-note scale aren't mostly fortuitous (I am mainly thinking of Mazzola here)).  But not just yet, it seems.

Xenakis has said much about the "musical aspects" in his other books and interviews. Formalized Music is subtitled "Thought and Mathematics in Composition" and it does what it says on the tin. I think it's clear even from this book that, for Xenakis, the mathematical techniques he used in his compositions were axiomatically those of the natural phenomena which those mathematical techniques are otherwise used to describe, so that, so to speak, the mathematics as such cancels out from the equation and you have music which sounds direct and unmediated. This is also why much of his electronic music dispenses with the techniques he used in his notated music, in favour of concrete sounds, ie. an even more direct use of "natural phenomena" which in a certain sense have the mathematics already built into them.

Think you might have misunderstood one or other of the terms, increpatio - not sure which, but 'polyrhythms' and 'irrational rhythms' are quite different things.

'Polyrhythm' (whether regular or irregular) refers to the combination, i.e. the simultaneity and interaction, of two or more different rhythmic strands. 'Irrational rhythm' (whether one thinks it's a good term or needs changing) has never been used to refer to this; it refers to the use, within a single rhythmic strand, of rhythmic values which can only be notated by a symbol denoting e.g. '5 in the time of 4', '17 in the time of 13' or whatever. I can see how this might sound like a form of polyrhythm but the difference is that when you say 'X in the time of Y', the Y refers to a notional number of beats (as measured against the tempo indication for the passage in question), rather than to an audible pulse actually being realised in a simultaneously present strand.

Which could almost be said of the role of mathematics in natural science too? The puzzle about its role in science being how mathematics can (apparently) be both 'contentless' (i.e. analytic and necessarily true) and at the same time possess great descriptive and explanatory power. It's spooky stuff.


Or, in another certain sense , not yet abstracted from them?

To return for a moment to the (in some circles) somewhat vexed matter of "tuplets", the two reasons why I find the term more acceptable than the so far posited alternatives are
(a) it's a succinct one-word term
(b) it sounds commensurate with / analogous to terms such as "triplets" and "quintuplets" which are unlikely to be dropped from the vocabulary.
"Nesting tuplets", whilst also acceptable, might benefit from a better alternative, such as, for example, "layered tuplets", if only to lead away from the possible impression that they were first discovered by Messiaen; the notions that such tuplets might at some point leave the nest or that the may be subdivided into fledgeling and mature tuplets might tend to support such an alternative term to that which I 'umbly propose here - and it has to be said that even greater confusion would arise if we got onto such things as "lesser spotted tuplets" (i.e. those with more rests than note-heads) or "tuplets of prey" - still more so if lengths of beamed tuplet groups were to be measured in wingspans...

Best,

Alistair