It's going to take me a little while to digest all your comments. Thank you for such detailed replies.

What I meant by Sagittal notation "tempering out" certain commas is in the extended diamond, I was seeing a lot of "approximations" (using schismas and schisminas) rather than exact representations, e.g. notating a higher prime ratio as being a much lower prime one modified by accent marks, e.g. 37:25 as a

fifth, that is, 40:27 lowered by a schisma, or, indistinguishable from a diminished sixth, or 37:33 notated as a

major second, the same as 28:25 without the lowered schisma, and the same as 21:20 plus an apotome. 21:20, a

minor second and 20:19, a

minor second, are also separated notationally by a schisma, which is a 5-prime interval, though the difference here involves prime factors 2, 3, 5, 7 and 19 [400:399=(2^4.5^2)/(3.7.19)]. Pretty much my point about (virtual) "tempering" is, the notation generally uses combinations of simple lower prime symbols to represent higher prime identities, meaning some unison vector is being assumed (generally within the realm of 0-0.2c or so in JI). As seen in 2460edo, where the mina represents one of any variety of prime factors between very close ratios.

Also, any reason why 494 was chosen as the EDO to represent Promethean? The schisma is not tempered out, and exists as 1\494. The schismina seems to be tempered out though. 612 looks very handy for Herculean however, with the schisma very closely approximated by and mapped to 1\, incredibly near-just fifths, 12edo available, as well as meantones a tiny bit lower than 1/3-comma~19edo, higher than 2/7-comma~50edo, lower than 1/6-comma~55edo, and 12edo, etc, and gentle fifths rather close to where Margo Schulter likes them, with a virtually just 22:21 minor second, and close 13:11, 13:7, 21:13, etc. I quite like having the ability to add or subtract schismas to help with well temperaments, timbre/colour manipulation and scale structure, but I'm not that concerned with schisminas, so this seems like a good balance. I started obsessing over 581edo earlier this year, but this may be another handy cousin, and one that ties in better with the notation.

Are all primes above 23 only "approximatable"? That is, there exist symbols to exactly represent intervals involving primes up to and including 23, but as far as I can see, symbols involving primes 29, 31, etc are approximations, using other primes' symbols inflected by accent marks, again this is part of the microtempering I was trying to explain.

Interesting point about Promethean, I was thinking the Promethean notation for the diamond would be available simply by removing all accent marks, as Herculean would be from removing only schisminas. Is this not the case?

I'll think about making a more practical chart for 13-prime JI, and 13-prime 45-odd limit seems like a good idea, though my own interests have led me to generally include primes 17, 19, 23 and occasionally 29 and 31 in how I think about JI. It surely will simplify the total number of unique symbols in the chart, which might be one reason it took so long. I agree that intervals with primes higher than 13 have currently a rather limited fanbase, but I didn't want to exclude them here in this first jumbo attempt.

Actually, it would be good to include single-Sagittal notations for all ratios in the 13-smooth 45 odd limit that can be notated exactly using a Spartan symbol and up to two right accents (schismina accents). And the note would say that these accents can be dropped from the performance notation if errors of 0.4 cents per accent are not significant.

You don't mean Athenian here do you? I see no reason to limit ourselves to Spartan symbols when notating extended 13-prime JI, I find 14:13, 13:11, 33:28, 33:26, 14:11, etc, pretty core ratios that should be able to be notated how they're often used as seconds, thirds, etc. But I do see your point in catering for the 70-90%, rather than getting too technical trying to cover 99.9%.

Multi-spartan is definitely an option, I can work on that. But I'm sticking to D as 1/1 for now, because it makes the most sense notationally, and it's in the middle of the gamut of keys people usually use, in the middle of the most popular 12-tone meantone gamuts Eb-G# and Ab-C#, and in the middle of a very popular 17-tone chain of fifths from Gb-A# that has occupied the vast majority of notated music. Notating things from C will get you a few too many flats in general, plus the diamond won't be notationally symmetric making calculations harder. I wish Scala allowed you to change 1/1 to keys other than C, D would be a great one.

I fear that many will find the number of different symbols used, including diacritics, to be overwhelming.

Agreed. But I decided to start here at the complex level, and from there I can simplify. Makes more sense for me than going the other way, where I'd need to redefine quite a few ratios as I went.

Sorry, I've written this all in bits and pieces in the wrong order, it might not make too much sense. Still very keen to hear more from you and anyone else interested and/or knowledgeable, and try a few more things out.