User:Fitzgerald Lee/15edo Chord Names

Chord Names

Triads shown here are the ones built from thirds, or from a second or fourth with a fifth.

Triads
Triad	Approx. JI	Shorthand	Name
[0,3,6]	21:24:28	Cf	Semaphore
[0,3,7]	7/6/5	Cu	Utonal Diminished
[0,4,7]	5:6:7	Co	Otonal Diminished
[0,3,8]	7:8:10	Ct	Triforce
[0,4,8]	35:42:50	Cd	Diminished
[0,5,8]	10/8/7	Cw	Wolf
[0,2,9]	18:20:27	C2	Suspended Second
[0,3,9]	6:7:9	Cs	Subminor
[0,4,9]	6/5/4	Cm	Minor
[0,5,9]	4:5:6	C	Major
[0,6,9]	6:8:9	C4	Suspended Fourth
[0,5,10]	20:25:32	Ca	Augmented

Tetradic extensions have different intervals to use, depending on the top note of the triad in root position.

Tetradic extensions (top note 6\15)
Interval	Approx. JI	Shorthand	Name
8\15	10/7	d	Diminished Fifth
9\15	3/2	5	Perfect Fifth
10\15	8/5	m	Minor Sixth
11\15	5/3	6	Major Sixth

Tetradic extensions (top note 7\15)
Interval	Approx. JI	Shorthand	Name
9\15	3/2	5	Fifth
10\15	8/5	m	Minor Sixth
11\15	5/3	6	Major Sixth
12\15	7/4	h	Harmonic Seventh

Tetradic extensions (top note 8\15)
Interval	Approx. JI	Shorthand	Name
10\15	8/5	m	Minor Sixth
11\15	5/3	6	Major Sixth
12\15	7/4	h	Harmonic Seventh
13\15	9/5	n	Neutral Seventh
X	X	7	Seventh

X: Extend the chord by the corresponding third in the chord (only applicable to triforce, diminished and wolf chords).

Tetradic extensions (top note 9\15)
Interval	Approx. JI	Shorthand	Name
11\15	5/3	6	Sixth
12\15	7/4	h	Harmonic Seventh
13\15	9/5	n	Neutral Seventh
14\15	15/8	M	Major Seventh
X	X	7	Seventh

X: Extend the chord by the corresponding third in the chord (only applicable to subminor, minor and major chords).

Tetradic extensions (top note 10\15)
Interval	Approx. JI	Shorthand	Name
12\15	7/4	6	Sixth
13\15	9/5	n	Neutral Seventh
14\15	15/8	7	(Major) Seventh

Assuming the root note is C,
[0,3,8,11] → Ct6
[0,4,8,12] → Cd7
[0,5,9,13] → Cn
Etc.