Juhani wrote: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.
Ah, yes. Thank you for reminding me of that.
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).
Yes. That is one of the most powerful features of Sagittal.
I assume
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.
Yes. That is one literal reading. But I tend to read it like this: That's a 35 or 13 symbol, but they have added a right accent, so for some reason they
really care about that 0.4 cent difference (which usually no one can hear) and they want an
extremely precise 13.
I would not recommend using the accented symbol for 13, as in any given situation only one of the 35 or 13 meanings will be tunable by ear, and only one of them will make a simple ratio with the local tonic or the root of the chord, and if you got the wrong one, no one would know anyway since it's only 0.4 of a cent. And I understand that it's not really the kind of symbol you had in mind when you asked if there was a dedicated symbol for 13. So in that sense, no, there is no dedicated symbol for 13.
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.
Yes, certainly. That would be a good thing to do. You could even define
as a the 35-comma (35:36) and
as the 13-comma (26:27).
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. ... 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.
I agree with all that you say here. But you can see that we had a difficult job, to satisfy everyone. Some people say there are too many symbols. By ignoring the tiny interval of 4095:4096, and other even smaller intervals, we were able to achieve a significant reduction in the number of symbols needed, and hence the number of different flag types that needed to be distinguished. Then we added the right accents for those who
thought they really needed to distinguish between things that were 0.4 cents apart.
I note that
is not a combination of a 7-comma flag and a 5-comma flag.
is a 7:11-comma and
is a 55-comma. But of course the result is still logically a 35-comma and you just have to learn that it's also the 13-comma (26:27).
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.
Although we wanted to show that Johnston-like one-symbol-per-prime usage was possible for those who
thought they needed it, we didn't really want to encourage it, because we don't believe it is the best way. For example, while something like
is fine, what about the poor performer who sees
. It is far from obvious what direction the overall alteration is. So we defined
=
. There's even a kind of visual logic to that, and it's then obvious that it represents a small upward alteration.