
From:  LukasFabian Moser 
Subject:  Re: TimeSignature with note in denominator 
Date:  Sat, 13 Nov 2021 22:13:36 +0100 
Useragent:  Mozilla/5.0 (X11; Linux x86_64; rv:78.0) Gecko/20100101 Thunderbird/78.13.0 
Hi Carl,
Although the time signature looks like a fraction, it is not. A fraction has numbers in the denominator and the numerator (and strictly speaking, a fraction properly has integers in the numerator and denominator  if they are not integers, it's a quotient, not a fraction, IIUC). And the time signature has an integer in the "numerator" and a duration in the "denominator". I'm not sure it is worth the work to get semantically correct, but semantically, \time 4/4 should not be a fraction of two integers; it should be a pair of a count and a duration.
I think you are right that the notion of time signatures being represented by formal fractions ("formal" meaning that 4/4 is not identical to 2/2) is wrong and that one should talk about a count and a duration. But it's an error with a huge tradition, not just in LilyPond, but in talking about music in general. Everybody talks and writes of "3/4 time" (and some people even write their time signatures with a fraction line), and I'd be very surprised to hear someone say  very correctly, admittedly  "what time signature? Ah, right, three crotchets per bar". (I'm using the English names, because in the American and German nomenclature, the difference is much more subtle: "Three quarters" vs. "Three quarter notes".)
So, I very much think that LilyPond should continue to support formal fractions of positive integers for time signature declarations. But your argument provides additional incentive to also support time signature declarations of the form (index? ly:duration?) and more generally (index? ly:music?). Although it would be nice, from a user's perspective, to do both using just the one \time command, I still doubt that this would be feasible.
And if we had semantically correct time signature entry, Kieren's wish for a different display for the duration would be relatively straightforward, although we would potentially have an "isoduration" problem that is analogous to the "chord name semantics" problem  there is no difference in duration between 4~4 and 2, so we couldn't preserve 4~4. Similarly, we could not tell the difference between 8.~8 and 8~8., although I can't imagine how the difference between these two representations would be important; both represent a duration of 5 eighthnotes.
I think you mean 5 16ths? The difference might, for example, be in the beat structure. I could imagine differences like 16[ 16] 16[ 16 16] vs. 16[ 16 16] 16[ 16], and also that beam subdivision might enter the scene: There should be a difference between \time \kieren 1 { 8.~8 } and \time \kieren 1 { 8. 8 } that I could imagine might just be "disconnected groups" vs. "two groups with a single connecting beam", etc.
Lukas
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