Re: irrational meters

[David Wright]

On Wed 18 Jan 2023 at 08:22:19 (+0000), Mark Knoop wrote:
> At 16:46 on 17 Jan 2023, "H. S. Teoh" via LilyPond user discussion wrote:
> > On Tue, Jan 17, 2023 at 07:08:41PM -0500, David Zelinsky wrote:
> >> Kieren MacMillan <kieren@kierenmacmillan.info> writes:
> >>>
> >>>> 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).
> 
> Perhaps one should define "correctly" before assuming impossibility. By
> any definition of correctly which makes sense in this context (i.e.
> precise rhythmic execution), it is arguably equally impossible to play
> music in a *dyadic* meter correctly.

I understood TSH's "correctly" to mean "precisely", and I would say
that by convention, one is not expected to play music in a dyadic
meter with precision. For example, most people are familiar with the
Viennese Waltz and its anticipated second beat, or the ebb and flow of
most solo piano music, and so on.

OTOH specifying a (mathematically) irrational meter implies a
precision that I would agree is virtually impossible to perform
without artificial aids like computer synthesis.

Cheers,
David.