24edo chord names
Various 24edo triads, 6th and 7th chords, named via ups and downs. Not meant to be exhaustive, but this list does demonstrate the basic rules for naming. ^M6 and vm7 are the same interval, and chords that use that interval can be named as either a 6th chord or a 7th chord.
Highly implausible chords are named as a more plausible homonym, e.g. 0–5–15 = Cvm(^5) becomes 15–24–29 = ^G^, where "a" stands for augmented and "d" stands for diminished.
| Thirds → | vm3 | m3 | ~3 | M3 | ^M3 | P4 | ~4 | |
|---|---|---|---|---|---|---|---|---|
| Triads with P5 | Cvm | Cm | C~ | C | C^ | C4 | C~4 | |
| Other triads |
v5 | Cvm(v5) | Cm(v5) | C~(v5) | C(v5) | C^(v5) | C4(v5) | C~4(v5) |
| d5 | Cvd | Cd | C^d | C(b5) | C^(b5) | C4(b5) | C~4(b5) | |
| ^5 | (^G^) | Cm(^5) | C~(^5) | C(^5) | C^(^5) | C4(^5) | C~4(^5) | |
| a5 | Cvm(#5) | (Ab) | Cva | Ca | C^a | (Fm) | C~4(#5) | |
| Tetrads with P5 |
~6 | Cvm~6 | Cm~6 | C~6 | C,~6 | C^,~6 | C4~6 | C~4~6 |
| M6 | Cvm,6 | Cm6 | C~,6 | C6 | C^,6 | C4,6 | C~4,6 | |
| ^M6 vm7 |
(Cvm^6) Cvm7 |
Cm^6 Cmv7 |
C~^6 C~v7 |
C,^6 C,v7 |
C^6 (C^v7) |
C4^6 C4v7 |
C~4^6 C~4v7 | |
| m7 | Cvm,7 | Cm7 | C~,7 | C7 | C^,7 | C4,7 | C~4,7 | |
| ~7 | Cvm~7 | Cm~7 | C~7 | C,~7 | C^,~7 | C4~7 | C~4~7 | |
| M7 | CvmM7 | CmM7 | C~M7 | CM7 | C^,M7 | C4M7 | C~4M7 | |
| ^M7 | Cvm^M7 | Cm^M7 | C~^M7 | C,^M7 | C^M7 | C4^M7 | C~4^M7 | |
A punctuation comma (",") is spoken as "add", thus C^,7 is "C-up add-seven". The only exception is when a comma separates two numbers, as in C4,7 which is "C four-seven". A comma is written, and "add" is spoken, whenever not doing so would cause confusion with another chord. C^,~6 is clear without a comma if limiting oneself to 24edo. However, some edos like 58-edo have an upmid 3rd and 6th, and C^~6 would be P1 ^~3 P5 ^~6.