Doesn't "Night Fantasies" by Elliott Carter use an extremely obscure structural polyrhythm? Not an actual irrational meter but similar idea.
On Tue, Jan 17, 2023 at 4:47 PM H. S. Teoh via LilyPond user discussion < lilypond-user@gnu.org> wrote: > On Tue, Jan 17, 2023 at 07:08:41PM -0500, David Zelinsky wrote: > > Kieren MacMillan <kie...@kierenmacmillan.info> writes: > > > > > Hi Silvain, > > > > > >> I wonder about the term “irrational” meter. Should not we say > > >> “irregular” ?? as in mathematics, an irrational number is a number > > >> which cannot be represented as a fraction... > > > > > > As both a published composer *and* a published number theorist, I > > > wholeheartedly concur with your intuition — I’ve been pushing for > > > decades against “irrational” as a descriptor for time signatures > > > [except where it actually applies, of course, as in π/4]. > > > > > > “Irregular” is better… but ultimately I prefer “non-dyadic” to > > > describe any time signature where the bottom number (a.k.a. > > > “denominator”, a label I also avoid) is not an integer power of 2. > [...] > > As another professional number theorist and musician (though not a > > composer), I also find this use of "irrational" to mean "non-dyadic" > > very grating. But I once said as much on the Music Engraving Tips > > facebook group, and got summarily shot down as ignorant and elitist. > > The argument, such as it was, held that this is about *music*, not > > *mathematics*, so there's no reason to adopt mathematicians' quirky > > terminology. This left me rather speechless, so I gave up. However, > > if I ever have reason to discuss this type of meter, will always call > > it "non-dyadic". > [...] > > This is off-topic, but it would be interesting if somebody composed a > piece with an actually irrational meter, like π/4 or 3/π. Only thing > is, it would be impossible for human performers to play correctly, since > there isn't any way to count the beats correctly (counting beats implies > a rational fraction, since by definition it's impossible to count up to > an irrational ratio by counting finite parts). > > But perhaps a more practicable approach is to use an irrational fraction > as an endless source of diverse beat divisions that has no long-term > patterns (because another property of an irrational number is that its > base-n expansion does not produce a repeating sequence). For example, > one could take the digits of π (in whatever base one fancies) and use > that as the number of beats to divide each bar into. In base 10, the > first bar would be 3/4, the second bar 1/4, the third 4/4, then 1/4, > then 5/4, etc.. Or, if one wishes, use pairs of digits for time > signatures: 3/1, 4/1, 5/9, ... etc.. It doesn't have to be base 10, of > course. Base 12 would yield 3/1, 8/4, 8/0, and so on (not sure how to > interpret 8/0, but I'm sure someone could come up with something). > > > T > > -- > "The whole problem with the world is that fools and fanatics are always so > certain of themselves, but wiser people so full of doubts." -- Bertrand > Russell. "How come he didn't put 'I think' at the end of it?" -- Anonymous > >
