Extended meantone notation

Standard meantone notation uses 7 base note letters, plus sharps and flats.

... Gbb Dbb Abb Ebb Bbb Fb Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E# B# F## C## G## D## A## ...

However, when transferred onto a 31edo scale, it looks like this:

C Dbb C# Db C## D Ebb D# Eb D## E Fb E# F Gbb F# Gb F## G Abb G# Ab G## A Bbb A# Bb A## B Cb B# C

Note that the base note letters alternate.

The 31edo sharp can be split in half, so in 31edo this is solved by semisharps and semiflats, sometimes notated with ups and downs.

The meantone circle of fifths however, has no single semisharp/semiflat. In extended meantone notation, a sharp is split into 2 different parts that can be added to produce a sharp.

# — sharp, 7 fifths up
b — flat, 7 fifths down
Y — semisharp 1, 12 fifths down
Z — semiflat 1, 12 fifths up
y — semisharp 2, 19 fifths up
z — semiflat 2, 19 fifths down

Unlike a single semisharp/semiflat, this can be generalized to other meantone tunings:

• 7edo (sharp is tempered out, semisharp 1 is positive and semisharp 2 is negative)
• 12edo (sharp is equal to semisharp 2, semisharp 1 is tempered out)
• 19edo (sharp is equal to semisharp 1, semisharp 2 is tempered out)
• 26edo (semisharp 1 is greater than sharp, and semisharp 2 is negative)
• 31edo (semisharp 1 is equal to semisharp 2)
• 43edo (semisharp 1 is smaller than semisharp 2)
• 50edo (semisharp 1 is greater than semisharp 2)

There are of course notational equivalences.

• B#Y and B##z are equal to C
• CyY is equal to C# (because the two semisharps add up)
• DbbZ and Dbbby are equal to C

Semisharp 1 can be considered to be 36/35, 50/49 or 64/63, while semisharp 2 is 49/48, assuming septimal meantone. 9–odd–limit intervals and their notation relative to C:

 1/1 — C

 3/2 — G
 4/3 — F

 5/4 — E
 5/3 — A
 8/5 — Ab
 6/5 — Eb

 7/4 — A#, or BbZ
 7/6 — D#, or EbZ
 7/5 — F#, or GbZ
 8/7 — Ebb, or DY
12/7 — Bbb, or AY
10/7 — Gb, or F#Y

 9/8 — D
 9/5 — Bb
 9/7 — Fb, or EY
16/9 — Bb
10/9 — D
14/9 — G#, or AbZ

Two semisharp 1 or two semisharp 2 cannot be stacked to produce a sharp. 11–limit and 13–limit notation can vary.

Y, Z, y and z is placeholder notation and should be replaced with better notation. It should be in ASCII, so that it can be easily written on a keyboard, like # and b are.