41edo Chord Names

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Various 41edo 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.

vm3 m3 ^m3 ~3 vM3 M3 ^M3 v4 P4 ^4 ~4
triad Cvm Cm C^m C~ Cv C C^ Cv4 C4 C^4 C~4
~6 Cvm~6 Cm~6 C^m~6 C~6 Cv,~6 C,~6 C^,~6 Cv4~6 C4~6 C^4~6 C~4~6
vM6 Cvm6 Cmv6 C^mv6 C~v6 Cv6 C,v6 C^v6 Cv4v6 C4v6 C^4v6 C~4v6
M6 Cvm,6 Cm6 C^m,6 C~,6 Cv,6 C6 C^,6 Cv4,6 C4,6 C^4,6 C~4,6
^M6 Cvm^6 Cm^6 C^m6 C~^6 Cv^6 C,^6 C^6 Cv4^6 C4^6 C^4^6 C~4^6
vm7 Cvm7 Cmv7 C^mv7 C~v7 Cv7 C,v7 C^v7 Cv4v7 C4v7 C^4v7 C~4v7
m7 Cvm,7 Cm7 C^m,7 C~,7 Cv,7 C7 C^,7 Cv4,7 C4,7 C^4,7 C~4,7
^m7 Cvm^7 Cm^7 C^m7 C~^7 Cv^7 C,^7 C^7 Cv4^7 C4^7 C^4^7 C~4^7
~7 Cvm~7 Cm~7 C^m~7 C~7 Cv,~7 C,~7 C^,~7 Cv4~7 C4~7 C^4~7 C~4~7
vM7 CvmM7 CmvM7 C^mvM7 C~vM7 CvM7 C,vM7 C^vM7 Cv4vM7 C4vM7 C^4vM7 C~4vM7
M7 Cvm,M7 CmM7 C^m,M7 C~M7 Cv,M7 CM7 C^,M7 Cv4M7 C4M7 C^4M7 C~4M7
^M7 Cvm^M7 Cm^M7 C^mM7 C~^M7 Cv^M7 C,^M7 C^M7 Cv4^M7 C4^M7 C^4^M7 C~4^M7

A comma (the actual punctuation mark ",") is spoken as "add", thus Cv,7 is "C-down 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.

P1-vm3-P5-M7 is named vm,M7 = downminor add major 7. One might think that the "add" could be omitted, and it could be named vmM7. But there's a rule that in a 7th chord, an initial arrow affects both the 3rd and the 7th. So vmM7 is a minor-major chord with both the 3rd and 7th downed, i.e. P1-vm3-P5-vM7.

See also:

The last link is fairly exhaustive, and covers augmented and diminished chords.