u/stalefleas

looking at scales in 31edo

we can take basic modes (major, dorian, phrygian, etc) and we can expand on these

if (in edosteps) s = 2, m = 3, n = 4, M = 5, S = 6

the most basic scales of 31edo might be

major
M M m M M M m
C D E F G A B C

minor
M m M M m M M
C D Eb F G Ab Bb C

neutral
M n n M M n n
C D Ed F G Ad Bd C

supermajor
M S s M S M s
C D Et F G At Bt C

subminor
M s S M s M S
C D Edb F G Adb Bdb C

of course, minor is just a mode of major, so we might compound these to basic "diatonic". but, subminor is not a mode of supermajor (they are both subsets of diasem, but i haven't found this too helpful, personally.) they are, i suppose, different chiralities of the same rank-3 step pattern (notice supermajor has S s while subminor has s S)

if we consider the basic modes of 31edo, we can consider not only the modes of 12edo, but also scales of similar but exaggerated or subdued contour in 31edo. so, for instance, there is the dorian mode which is

1 2 b3 4 5 6 b7

but there is also a subdorian mode which would be

1 2 db3 4 5 6 db7

and also a half-dorian mode which would be

1 2 d3 4 5 6 d7

but also a sort of flipping of the dorian shape, which would be tempting to call "anti-dorian" if there were not already a host of anti-diatonic scales in other tunings that includes this name

1 2 t3 4 5 6 t7

we might just flip the name dorian to "rodian" instead, and apply this similar system to the other modes

if we sequentially examine the basic modes and their exaggerated / subdued / flipped forms, we have the following:

exaggerated - prepended by super or sub

supermajor (1 2 t3 4 5 t6 t7)
subdorian (1 2 db3 4 5 6 db7)
subphrygian (1 db2 db3 4 5 db6 db7)
superlydian (1 2 3 #t4 5 6 7)
submixolydian (1 2 3 4 5 6 db7)
subminor (1 2 db3 4 5 db6 db7)
sublocrian (1 db2 db3 4 db5 db6 db7)

subdued - prepended by "half"

half-dorian (1 2 d3 4 5 6 d7)
half-phrygian (1 d2 d3 4 5 d6 d7)
half-lydian (1 2 3 t4 5 6 7)
half-mixolydian (1 2 3 4 5 6 d7)
half-locrian (1 d2 d3 4 d5 d6 d7)

flipped - prefix is flipped, or something similar

rodian (1 2 t3 4 5 6 t7)
gryphian (1 t2 t3 4 5 t6 t7)
dylian (1 2 3 d4 5 6 7)
moxidylian (1 2 3 4 5 6 t7)
colrian (1 t2 t3 4 t5 t6 t7)

the subdued forms of major and minor are both neutral, and the flipped version of major is minor, so they've been omitted here

using this naming system, most of the basic modes of 31edo can be described using these names + an additional alteration, similar to the melodic minor modes of 12edo

for example, if we examine the modes of the subminor scale, we have the following:

M s S M s M S - subminor
1 2 db3 4 5 db6 db7
C D Edb F G Adb Bdb

1 db2 b3 4 db5 db6 b7 - sublocrian b3, b7
C Ddb Eb F Gdb Adb Bb

1 t2 t3 4 5 t6 t7 - gryphian
C Dt Et F G At Bt

1 2 db3 d4 5 6 db7 - subdorian d4
C D Edb Fd G A Bdb

1 s2 s3 4 5 s6 b7 - subphrygian b7
C Ddb Edb F G Adb Bb

1 2 t3 #t4 5 t6 t7 - supermajor #t4
C D Et F#t G At Bt

1 t2 t3 4 5 t6 b7 - colrian b7
C Dt Et F Gt At Bb C

as you can see, even with an extended system of names, mode 2 here is pretty messy, with 2 alterations. while a cleaner name would be preferred, i've yet to find one

edited to add:

subminor & supermajor are a chiral pair, as are subdorian & rodian, and submixolydian & superlydian