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 3/2 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 and pentadic extensions have different intervals to use, depending on the top note of the triad in root position. Extensions shown below are assuming that tetradic and pentadic extensions extend by thirds (except 6th chords, which usually only extends by a fourth to a 6/9 chord but is still notatable in this system).

Tetradic and pentadic 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
12\15	7/4	h	Harmonic Seventh
13\15	9/5	n	Neutral Seventh
14\15	15/8	M	Major Seventh
16\15	32/15	m	Minor Ninth

Tetradic and pentadic 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
13\15	9/5	n	Neutral Seventh
14\15	15/8	M	Major Seventh
16\15	32/15	m	Minor Ninth
17\15	20/9	9	Major Ninth

Tetradic and pentadic 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
14\15	15/8	M	Major Seventh
X	X	7	Seventh
16\15	32/15	m	Minor Ninth
17\15	20/9	9	Major Ninth
18\15	16/7	s	Subminor Tenth

X: The seventh which is derived from going the corresponding third up from the fifth (only applicable to Triforce, Diminished and Wolf chords).

Tetradic and pentadic 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
16\15	32/15	m	Minor Ninth
17\15	20/9	M	Major Ninth
18\15	16/7	s	Subminor Tenth
19\15	12/5	m	Minor Tenth

X: The seventh which is derived from going the corresponding third up from the fifth (only applicable to subminor, minor and major chords).

Tetradic and pentadic 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
16\15	32/15	m	Minor Ninth
17\15	20/9	9	Major Ninth
18\15	16/7	s	Subminor Tenth
19\15	12/5	m	Minor Tenth

Examples

Assuming the root note is C,
[0,3,8,11] → Ct6
[0,4,8,12] → Cd7
[0,5,9,13] → Cn
[0,3,6,9,13] → Cf5n
[0,4,9,14,19] → CmMm
[0,5,9,12,17] → Ch9
Etc.

Links

15edo Triad and Tetrad Names in Xenpaper