Arabic Diatonic in standard 31-tET notation

The Arabic Diatonic can be notated, for example, as

Ab A# Cb Db Eb E# Gb (Ab)

or

A# Cb C# D# E# Gb G# (A#)

In fact, both of these can be accessed from a simple 19-tone meantone
instrument, centered around D, which would extend to six sharps and
six flats, and thus allow the eight 12-tone modes from Arian through
Scorpian to be played in the key of C . . .

I'm thinking, though, of labeling my keyboard (for 31-tET use) with
21 notes: 7 flats, 7 sharps, and 7 naturals (on every other white
key) . . . This will allow the ten 12-tone modes from Arian through
Capricornian in the key of D, and six (?) transpositions of Arabic
Diatonic . . .

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> The Arabic Diatonic can be notated, for example, as
>
> Ab A# Cb Db Eb E# Gb (Ab)
>
> or
>
> A# Cb C# D# E# Gb G# (A#)
>
> In fact, both of these can be accessed from a simple 19-tone
meantone
> instrument, centered around D, which would extend to six sharps and
> six flats, and thus allow the eight 12-tone modes from Arian
through
> Scorpian to be played in the key of C . . .
>
> I'm thinking, though, of labeling my keyboard (for 31-tET use) with
> 21 notes: 7 flats, 7 sharps, and 7 naturals (on every other white
> key) . . . This will allow the ten 12-tone modes from Arian through
> Capricornian in the key of D, and six (?) transpositions of Arabic
> Diatonic . . .

I'm uploading my best attempt to map a 24-tone chain of fifths to the
standard keyboard. I've shown, with six colors, the six
transpositions of the Arabic Diatonic that can be notated without
double sharps or double flats (assuming the generating fifths are 31-
tET fifths). While the mapping is somewhat logical, in some places
the notes are not in order of pitch . . . I'd love to see suggestions
for improvement.