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 are named differently 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

Examples

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

Links

15edo Chord Names in Xenpaper