User:Moremajorthanmajor/15edX

15edX is the scale which occurs as the dominant minor edX (equal division of a tenth interval). It also gives the period of the 15th-decade Alfincavallo branch of the Carrera temperament family.

Intervals

Decade					Period	Notes
6\5					96	Intense Aeolian-Subpental Dorian mode begins
	17\14				97.143
11\9					97.7	Intense Aeolian-Subpental Dorian mode ends, Subpental Dorian mode begins
	16\13				98.4615
		21\17			98.8235
			26\21		99.0476
5\4					100	Subpental Dorian mode ends, Pental Dorian mode begins
	19\15				101.3
14\11					101.81	Pental Dorian mode ends, Superpental Dorian mode begins
	23\18				102.2
9\7					102.857	Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins
	31\24				103.3
22\17					103.5294	Mohajira Dorian-Mixolydian mode ends, Beatles Dorian-Mixolydian mode begins
	35\27				103.703
13\10					104	Beatles Dorian-Mixolydian mode ends, Subpental Mixolydian mode begins
17\13					104.615
21\16					105	Subpental Mixolydian mode ends, Pental Mixolydian mode begins
	25\19				105.263
4\3					106.6	Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins
				31\23	107.826
			27\20		108
		23\17			108.235
	19\14				108.571
15\11					109.09	Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins
	26\19				109.474
11\8					110	Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins
	18\13				110.769
		25\18			111.1
7\5					112.5	Mixolydian-Ionian mode ends

Relative cents

Degrees	Enneatonic		Intense Aeolian-Subpental Dorian	Dorian	Dorian-Mixolydian	Subpental-Soft Superpental Mixolydian	Intense Superpental Mixolydian ~ Mixolydian-Ionian
1	G#/Jb	G#/Ab	96.6	100	103.3	106.6	110
2	J	A	193.3	200	206.6	213.3	220
3	J#/Ab	A#/Bb	290	300	310	320	330
4	A	B	386.6	400	413.3	426.6	440
5	B	C	483.3	500	516.6	533.3	550
6	B#/Cb	C#/Qb	580	600	620	640	660
7	C	Q	676.6	700	723.3	746.6	770
8	C#/Qb	Q#/Db	773.3	800	826.6	853.3	880
9	Q	D	870	900	930	960	990
10	D	S	966.6	1000	1033.3	1066.6	1100
11	D#/Eb	S#/Eb	1063.3	1100	1136.6	1173.3	1210
12	E		1160	1200	1240	1280	1320
13	E#/Fb		1256.6	1300	1343.3	1386.6	1430
14	F		1353.3	1400	1446.6	1493.3	1540
15	G		1450	1500	1550	1600	1650

By a surprising coincidence, the 15ed of the Pyrite tenth (7φ+6)\(5φ^2)edo is almost exactly every third degree of 34edo. Additionally, those of the modal Golden and Pyrite tenths are almost exactly +1/28-syntonic comma 4ed(5/4) (Intense Aeolian-Subpental Dorian), 9ed(5/3)/equal multiples of 18/17 (Subpental Dorian), 13ed(15/7) (Pental Dorian), 2ed(9/8) (Superpental Dorian), -1/12-syntonic comma 3ed(6/5) (Dorian-Mixolydian), 14ed(7/3)/equal multiples of 17/16/100π\3 cents (Subpental Mixolydian), 3ed(6/5) (Pental Mixolydian), 4ed(9/7)/+1/36-syntonic comma 14ed(12/5) (Soft Superpental Mixolydian), 12ed(32/15) (Intense Superpental Mixolydian) and 8ed(5/3)/-1/9 schismic 9ed(16/9)/14ed(22/9) (Mixolydian-Ionian) respectively.

See also

• 15ed5/2 - equal division of the classic major tenth
• 15ed7/3 - equal division of the septimal minor tenth