Juhani wrote:I can't help thinking that there's an overwhelming number of difficult-to-decipher, difficult-to-write-in-shorthand symbols in the Promethean level and that there's an overwhelming number of symbols to memorize. I'm very uncomfortable with the multitude of commas that one is required to learn (in the single-symbol version). I doubt many Just Intonation composers and performers even consider those commas or think in terms of them; these commas have to do with the logic of the Sagittal system, and with JI and temperament theory.
Yes. Forget Promethean. If we use a single-Sagittal notation at all, it should be Olympian, which consists mostly of Spartan symbols with accents. I would not expect performers to think in terms of the comma that is exactly represented by any accented symbol. I'd expect them to ignore the accents and think in terms of the approximate pitch alteration implied by the core symbol, then adjust by ear if necessary.
I fear the multi-Sagittal accidentals would quickly become awkward. Johnston's notation does have the problem of long horizontal clusters of symbols but it uses also symbols as attachments ( would be used as the stem of instead of having them side by side etc.), so this only applies to multiples of the same symbol ( +++ for 81^3, 77 for 49 etc.).
I think we try it and see. I think we should begin with an almost symbol-for-symbol transliteration of Johnston's notation, with the exception of using the Pythagorean nominals instead of the JI major. There are many intermediate stages available in Sagittal between one-symbol-per-prime and one-symbol per note.
Of course Sagittal can combine comma symbols with sharps and flats to make a single symbol too, but you have to be willing to use the Sagittal form of the sharp and flat, and then you're into the pure Sagittal. We've never liked symbols like Gould's quartertones or Sabat & von Schweinitz' 5-commas because they make the accidentals so tall that you can't place them above one another in chords, and because they put the arrowheads a long way above or below the notehead they apply to, possibly beside another notehead entirely. I really don't think the horizontal stacks of Sagittals will end up much wider that those of the Johnstons, on average.
It's difficult to say if there are singers or string players who'd prefer the former [multi-Sagittal] over the latter [single-Sagittal], as there is no JI repertoire published in Sagittal, except in Sagittal study materials and demos (as far as I know).
All the more reason to try both forms of Sagittal (and possibly some in-between).
It is a fact, on the other hand, that the scores of Johnston, Sabat etc. are written for musicians who tune the intervals by ear or are at least expected to do so, note against note, which is why the notation tells the tuning path exactly. That's why in Johnston, for example, a different symbol is used for 33:32 and 36:35 even if they're both quarter-tones and differ only about 4 cents.
I assume you're aware these are different in Sagittal too. versus or .
They're to all practical purposes the same interval. Sometimes they're even combined to the same accidental so that they cancel each other out (33:32 up and 36:35 down). It would be just fine to sing the uninflected note, but the singer wouldn't know how to find it if her note is the 11/8 of the 7th harmonic that's been sounding in the bass, say.
Yes. That's a good point. So if that bass note was notated C or C it would make sense to notate the upper note as F or F. The Olympian single-symbol alternative would be F.
That's the philosophy behind these JI notation systems: it's quite different from that of Sagittal, as I understand.
I believe Sagittal can serve that JI notation philosophy just as well as Johnston and Sabat & von Schweinitz notations can. We always intended it could be used that way (as per the bold entries in Table 1). We just didn't spend any time on it in the paper, thinking it was obvious how to use it in that manner, and preferring to show the options that aren't available with other JI notations.
But a cellist friend of mine played a solo piece by Sims, in extended JI notated as 72-equal, and he found it quite annoying that the notation didn't tell which just interval each note represents. Originally, he tried finding the 72 equal steps and only later realized that the music is supposed to be played in pure intervals, but it took a lot of trial, error and analyzing. He'd prefer a Johnston-notated version of the Sims piece.
Good point. Sagittal can certainly be used, with multiple symbols per note, to show the JI structure of a chord or arpeggio.
The situation is somewhat similar here, the main difference being that in JI Sagittal (without the accents), the notation gives rational approximations for ratios, rather than the irrational ones of equal divisions.
Right. But that's only one option for how to use Sagittal accidentals for notating JI. It was actually me, not Cam, who suggested we should not use any approximations. If we're doing multi-Sagittal, we define to be exactly the 26:27 thirdtone and we use or (depending on context) for the almost-identical 7-limit thirdtone.