On the facebook "22-Tone workgroup", Cryptic Ruse mentioned that he was working on a non-JI-based general notation system for EDOs 72 and below, based on accidentals for fractions of the Pythagorean apotome (7 fifths, octave-reduced) and Pythagorean limma (5 fourths, octave-reduced), and asked what Sagittal accidentals would be most suitable for 1/4-apotome, 1/2-limma and 1/4-limma. The Sagittal apotome symbol is of course
) and the medium-precision 1/2-apotome is
. My choice for a 1/4-apotome symbol is the 7-comma symbol
because the exact relationship
is highly suggestive of
although this is only approximate in standard Sagittal.
With pure fifths, the difference between the apotome (116.7 c) and the limma (90.2 c) is the Pythagorean comma or 3-comma (23.5 c). This is symbolised exactly as
in Sagittal, so the limma is exactly
. But we wouldn't use diacritics for EDOs of this size. We'd just use
for the limma. The 1/4-limma (22.6 c) happens to be between the 5-comma and the 3-comma in size, so we'd use the 5-comma symbol
for the 1/4-limma, and the double-5-comma symbol
for the 1/2-limma.
full sharp paosharp
half pakai or vai phai or fai
quarter tai pai