I'm glad you like the symbols, Igliashon. The more I look at them, the more they makes sense to me too. In one sense they are the most common symbols used in Sagittal, the same Spartan symbols used for 11-limit JI-based notations for EDOs, and so they have the same size order, and the same approximate size when the fifths are near just. And yet, by having that extra little left scroll they cannot be confused with them. The existing higher-prime-comma meanings of these left-scroll symbols are very rarely used because they notate complex ratios.
are way up in the Promethean (high precision JI) extension.
is in the Trojan (12n-edo) extension, but it is only used to notate 108-edo and 120-edo.
And the more I investigate your idea of apotome and limma fraction notations for small EDOs (particularly those with bad fifths), the more I love it. I think it was brilliant of you to think that it might be possible to do it with only four symbol pairs in addition to conventional sharps and flats -- half and quarter apotome symbols and half and quarter limma symbols.
I would not have thought it possible. But since you told us that it is, I'm guessing this is how you do it (although you would be using ASCII placeholders rather than Sagittals). I've shown the compound accidentals in the left-right order they would appear on the staff:
1/5, 1/6, 1/7 apotome 1/4, 1/5 limma
1/4, 1/3, 2/7 apotome 1/3, 2/5 limma
2/5, 3/7 apotome 1/2 limma
1/2 apotome 2/3, 3/5 limma
3/5, 4/7 apotome
3/4, 2/3, 5/7 apotome
4/5, 5/6, 6/7 apotome
As it happens, there are two other Promethean-extension symbols with left scrolls,
, that would allow us to extend the system as follows:
1/8, 1/9, 1/10 apotome, 1/7 limma
1/5, 1/6, 1/7, 2/9 apotome 1/4, 1/5, 1/6, 2/7 limma
1/4, 1/3, 2/7, 3/10 apotome 1/3, 2/5, 3/7 limma
2/5, 3/7, 3/8, 4/9 apotome 1/2 limma
1/2 apotome 2/3, 3/5, 4/7 limma
3/5, 4/7, 5/8, 5/9 apotome 3/4, 4/5, 5/6, 5/7 limma
3/4, 2/3, 5/7, 7/10 apotome
4/5, 5/6, 6/7, 7/9 apotome
7/8, 8/9, 9/10 apotome
The 1/8-apotome symbol
allows us to notate EDOs with up to 10 steps per apotome, the smallest being 71-edo, where the previous set only allows up to 7 steps per apotome, the smallest being 42-edo. But I freely admit that
whose long ASCII is )~| , is very hard to distinguish from
whose long ASCII is )/| .
The 3/4-limma symbol
allows for some enharmonic spelling in the limma-notated EDOs 23, 28 and 35, and it replaces
in apotome-notated EDOs and thereby eliminates one case of accidentals altering in opposite directions.