Irrational time signature - full durations cause unwanted tuplets

[luisfncosta]

Hi guys!

Sorry to post again after asking a question a few days ago, but I'm experimenting with rhythm, time signatures, and ratios, and I found a new problem.

In the patch below, my intention is to have several irrational time signatures, where each bar has only one note that lasts a full bar. Therefore, a 1/1 time signature has a duration of 1/1, a 22/9 time signature has a duration of 22/9, and so on.

Since the duration of each note is equal to the length of the bar, I don't understand why there are tuplets.

I thought it was a thinking problem about irrational time signatures and proportions, but I think there is an issue in bach.score that I can't figure out.

Thanks in advance and keep the good work! Best,
Luís

Code: Select all

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[danieleghisi]

Well, this borders on philosophical
There are tuplets because if you have a bar of, say, 13/12, that bar contains a whole note plus *one* octave of a triplet, which makes for an incomplete tuplet.
If you come from OpenMusic this may sound weird, because open music does it differently: If I remember correctly it remaps everything as if the whole note was 8/12 (8 being the nearest power of two below 12), so that 12/12 would be a dotted whole, and 13/12 would be a dotted whole plus a quaver.
This is a (personally unintuitive) way to make modulation, implying that you must think everything differently depending on the dyadicity of the denominator. As a matter of fact, it's a way of writing 13/8 with a tempo change.

bach doesn't go that way, bach keeps it simple: 1/1 or 8/8 or 12/12 or n/n is always a whole. So 13/12 is a whole plus an incomplete triplet; that's it.
Most of the scores I know go down this path (and, for what is worth, https://youtu.be/cQ9yI4dtuGQ?si=9KkYPxLrKVAB4YtX&t=138)

[luisfncosta]

Thank you for the reply, Daniele!

I see. bach stays true to the n/n as a whole note. In fact, with non-dyadic time signatures, you don't have rhythmic figures for durations like 1/12 or so, so I understand the use of tuplets.

I have used non-dyadic denominators before, but in different ways. In one of my pieces, I chose the numerator 4 as a whole note. Everything was like conventional time signatures with different speeds. All the musician had to do was listen to the click track and it was clearer to him. In another piece of mine, I used 2/6 with two quarter notes because it was easier to think of them as an incomplete quarter notes triplet. I think it's the same idea that Thomas Adès uses in Traced Overhead (https://youtu.be/a5G_I-pWR8Q?t=90). But of course this is all a notational adjustment for musicians. When we think of 6/6, that would be 6 quarter notes (dotted whole note) instead of one whole note, and that's not correct. As far as I understand from what you said, this is the approach of OpenMusic.

If I may, I would like to suggest some possibilities for bach.score for you to consider whether it makes sense to add it or not:
- Allow to have this kind of setting as I and Adès used. It's not correct, but a notational adjustment for the musician.
- Allow that the division stays true to a conventional duration plus something. It's very weird to see a 22/23 time signatures as whole note inside of a 23:22. It would be better to have a whole note plus a 1/22.
- I know it's possible to have additive time signatures, but only with a fixed denominator. What about additive time signatures with changing denominators? You can see this in the first bar of Czernowin's Sahaf (https://youtu.be/AjIiJo5Gzo0?t=37). The score also has fractional time signatures. Although they could be written more simply, this could be a notational accommodation for the musician.

This is indeed a question that borders on the philosophical and the limitations of our notation system. I'll think about what suits my needs this time.

Thanks again for your time and keep up the good work!

Luís