Because terminology amuses me here. Years ago, I learned that time signatures were decidedly not fractions but ratios from a one Richard Hoffman. But even before that I learned ratios consisted of antecedents and consequents, which also seems to overlap musical structural terminology in a weird way making that also fairly useless as a nomenclature.
Shane On Wed, Jan 18, 2023 at 9:38 AM David Wright <[email protected]> wrote: > 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 <[email protected]> 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. >
