"Sabat et al notations don't have a single symbol for 35:36 or any of the other combinations of primes for which Sagittal has single symbols."
Johnston has 5-limit nominals, so actually the single symbol for prime 7 is indeed for 35:36 but then 63:64 is notated with a combination of 35:36 and 80:81.
Even if Sagittal has more symbols for various commas, and they're single symbols, I still read them as following the logic of a combination of other comma symbols (two
's make a
and so on). See below.
"it is neither "multiply by 32:33" nor "multiply by 33:32" because multiplication is not defined on colon ratios.
means multiply by 33/32.
means multiply by 32/33."
OK, I read now that that's how it is in mathematics but I learned the colon ratios differently in school (ie. as ordered, not unordered), and I also have ratio calculator software where a:b is used for a/b.
"Otic"? Do you mean "acoustics"? Sorry, odd typo. Logic.
means 8192:8505 corrected by a 4095:4096 comma? But then the accidental is still derived in a complicated path from a 7-limit interval. That's what I mean by the logic of the accidentals. Assuming I never use the 7-limit comma 8192:8505
I can tell the musicians that this is the accidental used for 13-limit intervals. All the other symbols for low-prime-limit intervals have their own symbol (5-comma, 7-comma, 11-comma), and how signs are combined to a single symbol is often clear (
for two syntonic commas etc.). I would have liked a separate symbol for 13 that is distinct from a combination of lower-limit intervals. I predict musicians won't always be satisfied with learning a symbol by heart but will try to understand it, like me, as a combination of symbols (intervals). And that's not how a 13:8 limit interval is played or sung. A musician playing in just intonation, from a Johnston score, for example, sees a 13-accidental and tunes the 13/8 interval by ear - NOT by tuning two 3/2's, one 5/4 and one 7/4 down, as the Sagittal symbol seems to be saying. But as I said, I can simply tell the musicians that this
is used for 13, don't worry why it looks like that. Maybe I'd add the number 13 above the note to remind that you're supposed to find the 13th harmonic here. I don't find that ideal, though.
"The symbols to use for that purpose have their descriptions given in bold in Table 1 on page 9. If you prefer to use Sagittal in that manner, then you would notate sharp-26:27-down as
and 35:36 as
." Table 1 doesn't show examples of those combinations of separate glyphs. It seems that's indeed what I'm after but then I'd need loads of new combined symbols in the font.