On Tue, Jan 17, 2023 at 07:08:41PM -0500, David Zelinsky wrote:
> Kieren MacMillan <kieren@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).
Speaking of non-human performers, you’ll find examples in the player piano studies of Conlon Nancarrow.
Best,
David