31edo chord names

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Ups and downs notation

Various 31edo 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 ~3 M3 ^M3 v4 P4 ~4
triad Cvm Cm C~ C C^ Cv4 C4 C~4
~6 Cvm~6 Cm~6 C~6 C,~6 C^,~6 Cv4~6 C4~6 C~4~6
M6 Cvm,6 Cm6 C~,6 C6 C^,6 Cv4,6 C4,6 C~4,6
^M6 Cvm^6 Cm^6 C~^6 C,^6 C^6 Cv4^6 C4^6 C~4^6
vm7 Cvm7 Cmv7 C~v7 C,v7 C^v7 Cv4v7 C4v7 C~4v7
m7 Cvm,7 Cm7 C~,7 C7 C^,7 Cv4,7 C4,7 C~4,7
~7 Cvm~7 Cm~7 C~7 C,~7 C^,~7 Cv4~7 C4~7 C~4~7
M7 CvmM7 CmM7 C~M7 CM7 C^,M7 Cv4M7 C4M7 C~4M7
^M7 Cvm^M7 Cm^M7 C~^M7 C,^M7 C^M7 Cv4^M7 C4^M7 C~4^M7

A comma (the actual punctuation mark ",") is spoken as "add", thus C,v7 is "C add-down-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 or an "add" if limiting oneself to 31edo. However, some edos like 58-edo have an upmid 3rd and 6th, and C^~6 would be P1 ^~3 P5 ^~6.

Note that 4:5:6:7 = C E G vBb is named C,v7 not Cv7 because Cv7 is an alternate name for C~v7. To get a shorter name for this important chord, one could call it a harmonic7 chord, or one could borrow from color notation to call it a har7 chord, written Ch7. Names for subharmonic chords can be similarly shortened.

chord notes ups and downs name color name
4:5:6:7 C E G vBb C add-down-7 C,v7 C har7 Ch7
7:6:5:4 C vEb vGb vBb C downminor7 downflat-5 Cvm7(vb5) C sub7 Cs7
12:10:8:7 C Eb G ^A C minor up-6 Cm^6 C sub6 Cs6

Extended jazz symbol set

No*ie's original proposition (2024-03-02).

No*ie proposes the following symbols:

Chord quality Symbol Comments
Inframinor I The horizontal and vertical bars of the letter I may be drawn to scale with the subminor symbol for more visual consistency
Subminor = Akin to two parallel minus signs
Ultramajor U The letter U may be drawn with horizontal and vertical bars for more visual consistency with other symbols
Harmonic seventh H7
Subdiminished / sin(bv5)
Half Diminished / m7(b5)
Half Subdiminished / sin7(bv5)
Augmented +
Superaugmented / saj(#+5) 王 (or *) Akin to the plus sign with two extra lines

These symbols can also be used with other tuning systems where these interval qualities are relevant.

See also