|
| From: | Saul Tobin |
| Subject: | Re: irrational meters |
| Date: | Tue, 17 Jan 2023 16:57:39 -0800 |
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).
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
| [Prev in Thread] | Current Thread | [Next in Thread] |