Thanks for making me see sense.רועיסיני wrote: ↑Thu Jun 22, 2023 2:42 amI think that's really going against the spirit of sagittal and a lot of things established so far. The one hard and fast rule in sagittal is that of apotome complements, and I see no reason to break it here. Even the Trojan double shaft accidentals where is used for 66.7¢ although - + = 83.3¢ and other similar quirks involving and are advertised on the PDF in all their glory, and even the notation for 72, which is one of the first things a newcomer is supposed to learn in sagittal, has inconsistent double shaft flag arithmetic, and 128 approximates the fifth with a worse relative error than 72. Also, 53's notation uses where no flag combination is reused and this does not prevent it from being a great notation.Dave Keenan wrote: ↑Sat Jun 17, 2023 1:54 pm What if we just said that double shaft symbols (and by extension X-shaft symbols) don't have fixed rational definitions, i.e. there are no fixed apotome-complementary pairs of symbols, and you can always just make them recapitulate the single-shaft flag combinations, like this:1 2 3 4 5 6 7 8 9 10 11 12 13What problems would that cause?
I deliberately did not look at George's notation for 128edo while designing a 128edo notation as part of an overall magenta apotome-fraction system. Nor did I consider apotome complements. I see now, that versus is the only difference between George's notation and mine.I will note that George suggested using for 2\128, which makes at least 9 and 11 degrees use the same combinations as 2 and 4. Why didn't you choose it here?
Here are the reasons I did not choose for 2\128:
1. When tempering 3's only, it does not map to 2/13-apotome across the whole range of magenta fifth sizes (not above 703.9 ¢). In particular, it does not map to 2/13-apotome in the case of 121edo which is just barely outside the magenta range and might usefully be included within it in future. is mapped to 3\121 by both the patent map and 3's-only.
2. In the overall magenta scheme, it seems better to reserve for slightly larger apotome fractions like 3/17, 2/11, 3/16 (0.167, 0.182, 0.188). You can see, in the nested arches of symbols above, that we have a size progression: ( ) . I have put brackets around because they reverse this order across a significant part of the magenta range. has the smallest slope of the two. You can see from the chart above, that the natural boundary between and in the magenta range is around 0.17-apotome. 2/13 is 0.154.
3. While not actually producing inconsistent flag arithmetic, the only way to make it consistent is to assign <> = 0 which implies that <> = = 4, when in fact 7/11C (the primary comma for ) is 5/13-apotome across most of the magenta range (including 128 and 121edos). We'd need <> = 0 because we have = - ( - ) = 5 - (6 - 3) = 2. This is a fairly minor objection since no one is likely to notice this.
4. With instead of the flag-count is not monotonic with size. Again, a small disadvantage.
None of these are fatal to the use of for 2\128, but the only reason I see to prefer it over for 2\128 is to have one less flag combination in the revo flavour. But some people have no interest in the revo flavour.
Of course some people have no interest in evo. Should we recommend different evo and revo single-shaft sequences for the same tuning? I fear I may have set a bad precedent with 130 and 142edo in the pdf. If we don't do that, how should we decide?
I want to say that revo inherently requires a user to learn more symbols than evo, therefore if they are willing to take that hit, can't they take a little more for the sake of the simplest possible evo notation? Or putting it another way, since evo users likely choose evo for it's smaller learning curve, shouldn't we give them the simplest possible evo notation?