User:MisterShafXen/15L 39s

15L 39s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 15 large steps and 39 small steps, with a period of 5 large steps and 13 small steps that repeats every 400.0 ¢, or 3 times every octave. 15L 39s is related to 6L 3s, expanding it by 45 tones. Generators that produce this scale range from 155.6 ¢ to 160 ¢, or from 240 ¢ to 244.4 ¢.

↖ 14L 38s	↑ 15L 38s	16L 38s ↗
← 14L 39s	15L 39s	16L 39s →
↙ 14L 40s	↓ 15L 40s	16L 40s ↘

Scale structure
Step pattern	...54 steps...
Equave	2/1 (1200.0 ¢)
Period	1\3 (400.0 ¢)
Generator size
Bright	7\54 to 2\15 (155.6 ¢ to 160.0 ¢)
Dark	3\15 to 11\54 (240.0 ¢ to 244.4 ¢)
TAMNAMS information
Related to	6L 3s (hyrulic)
With tunings	7:4 to 2:1
Related MOS scales
Parent	15L 24s
Sister	39L 15s
Daughters	54L 15s, 15L 54s
Neutralized	30L 24s
2-Flought	69L 39s, 15L 93s
Equal tunings
Equalized (L:s = 1:1)	7\54 (155.6 ¢)
Supersoft (L:s = 4:3)	23\177 (155.9 ¢)
Soft (L:s = 3:2)	16\123 (156.1 ¢)
Semisoft (L:s = 5:3)	25\192 (156.2 ¢)
Basic (L:s = 2:1)	9\69 (156.5 ¢)
Semihard (L:s = 5:2)	20\153 (156.9 ¢)
Hard (L:s = 3:1)	11\84 (157.1 ¢)
Superhard (L:s = 4:1)	13\99 (157.6 ¢)
Collapsed (L:s = 1:0)	2\15 (160.0 ¢)
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Scale properties

Intervals of 15L 39s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Minor 1-mosstep	m1ms	s	0.0 ¢ to 22.2 ¢
	Major 1-mosstep	M1ms	L	22.2 ¢ to 80.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 44.4 ¢
	Major 2-mosstep	M2ms	L + s	44.4 ¢ to 80.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0 ¢ to 66.7 ¢
	Major 3-mosstep	M3ms	L + 2s	66.7 ¢ to 80.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	L + 3s	80.0 ¢ to 88.9 ¢
	Major 4-mosstep	M4ms	2L + 2s	88.9 ¢ to 160.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	L + 4s	80.0 ¢ to 111.1 ¢
	Major 5-mosstep	M5ms	2L + 3s	111.1 ¢ to 160.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	L + 5s	80.0 ¢ to 133.3 ¢
	Major 6-mosstep	M6ms	2L + 4s	133.3 ¢ to 160.0 ¢
7-mosstep	Diminished 7-mosstep	d7ms	L + 6s	80.0 ¢ to 155.6 ¢
	Perfect 7-mosstep	P7ms	2L + 5s	155.6 ¢ to 160.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	2L + 6s	160.0 ¢ to 177.8 ¢
	Major 8-mosstep	M8ms	3L + 5s	177.8 ¢ to 240.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	2L + 7s	160.0 ¢ to 200.0 ¢
	Major 9-mosstep	M9ms	3L + 6s	200.0 ¢ to 240.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	2L + 8s	160.0 ¢ to 222.2 ¢
	Major 10-mosstep	M10ms	3L + 7s	222.2 ¢ to 240.0 ¢
11-mosstep	Perfect 11-mosstep	P11ms	3L + 8s	240.0 ¢ to 244.4 ¢
	Augmented 11-mosstep	A11ms	4L + 7s	244.4 ¢ to 320.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	3L + 9s	240.0 ¢ to 266.7 ¢
	Major 12-mosstep	M12ms	4L + 8s	266.7 ¢ to 320.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	3L + 10s	240.0 ¢ to 288.9 ¢
	Major 13-mosstep	M13ms	4L + 9s	288.9 ¢ to 320.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	3L + 11s	240.0 ¢ to 311.1 ¢
	Major 14-mosstep	M14ms	4L + 10s	311.1 ¢ to 320.0 ¢
15-mosstep	Minor 15-mosstep	m15ms	4L + 11s	320.0 ¢ to 333.3 ¢
	Major 15-mosstep	M15ms	5L + 10s	333.3 ¢ to 400.0 ¢
16-mosstep	Minor 16-mosstep	m16ms	4L + 12s	320.0 ¢ to 355.6 ¢
	Major 16-mosstep	M16ms	5L + 11s	355.6 ¢ to 400.0 ¢
17-mosstep	Minor 17-mosstep	m17ms	4L + 13s	320.0 ¢ to 377.8 ¢
	Major 17-mosstep	M17ms	5L + 12s	377.8 ¢ to 400.0 ¢
18-mosstep	Perfect 18-mosstep	P18ms	5L + 13s	400.0 ¢
19-mosstep	Minor 19-mosstep	m19ms	5L + 14s	400.0 ¢ to 422.2 ¢
	Major 19-mosstep	M19ms	6L + 13s	422.2 ¢ to 480.0 ¢
20-mosstep	Minor 20-mosstep	m20ms	5L + 15s	400.0 ¢ to 444.4 ¢
	Major 20-mosstep	M20ms	6L + 14s	444.4 ¢ to 480.0 ¢
21-mosstep	Minor 21-mosstep	m21ms	5L + 16s	400.0 ¢ to 466.7 ¢
	Major 21-mosstep	M21ms	6L + 15s	466.7 ¢ to 480.0 ¢
22-mosstep	Minor 22-mosstep	m22ms	6L + 16s	480.0 ¢ to 488.9 ¢
	Major 22-mosstep	M22ms	7L + 15s	488.9 ¢ to 560.0 ¢
23-mosstep	Minor 23-mosstep	m23ms	6L + 17s	480.0 ¢ to 511.1 ¢
	Major 23-mosstep	M23ms	7L + 16s	511.1 ¢ to 560.0 ¢
24-mosstep	Minor 24-mosstep	m24ms	6L + 18s	480.0 ¢ to 533.3 ¢
	Major 24-mosstep	M24ms	7L + 17s	533.3 ¢ to 560.0 ¢
25-mosstep	Diminished 25-mosstep	d25ms	6L + 19s	480.0 ¢ to 555.6 ¢
	Perfect 25-mosstep	P25ms	7L + 18s	555.6 ¢ to 560.0 ¢
26-mosstep	Minor 26-mosstep	m26ms	7L + 19s	560.0 ¢ to 577.8 ¢
	Major 26-mosstep	M26ms	8L + 18s	577.8 ¢ to 640.0 ¢
27-mosstep	Minor 27-mosstep	m27ms	7L + 20s	560.0 ¢ to 600.0 ¢
	Major 27-mosstep	M27ms	8L + 19s	600.0 ¢ to 640.0 ¢
28-mosstep	Minor 28-mosstep	m28ms	7L + 21s	560.0 ¢ to 622.2 ¢
	Major 28-mosstep	M28ms	8L + 20s	622.2 ¢ to 640.0 ¢
29-mosstep	Perfect 29-mosstep	P29ms	8L + 21s	640.0 ¢ to 644.4 ¢
	Augmented 29-mosstep	A29ms	9L + 20s	644.4 ¢ to 720.0 ¢
30-mosstep	Minor 30-mosstep	m30ms	8L + 22s	640.0 ¢ to 666.7 ¢
	Major 30-mosstep	M30ms	9L + 21s	666.7 ¢ to 720.0 ¢
31-mosstep	Minor 31-mosstep	m31ms	8L + 23s	640.0 ¢ to 688.9 ¢
	Major 31-mosstep	M31ms	9L + 22s	688.9 ¢ to 720.0 ¢
32-mosstep	Minor 32-mosstep	m32ms	8L + 24s	640.0 ¢ to 711.1 ¢
	Major 32-mosstep	M32ms	9L + 23s	711.1 ¢ to 720.0 ¢
33-mosstep	Minor 33-mosstep	m33ms	9L + 24s	720.0 ¢ to 733.3 ¢
	Major 33-mosstep	M33ms	10L + 23s	733.3 ¢ to 800.0 ¢
34-mosstep	Minor 34-mosstep	m34ms	9L + 25s	720.0 ¢ to 755.6 ¢
	Major 34-mosstep	M34ms	10L + 24s	755.6 ¢ to 800.0 ¢
35-mosstep	Minor 35-mosstep	m35ms	9L + 26s	720.0 ¢ to 777.8 ¢
	Major 35-mosstep	M35ms	10L + 25s	777.8 ¢ to 800.0 ¢
36-mosstep	Perfect 36-mosstep	P36ms	10L + 26s	800.0 ¢
37-mosstep	Minor 37-mosstep	m37ms	10L + 27s	800.0 ¢ to 822.2 ¢
	Major 37-mosstep	M37ms	11L + 26s	822.2 ¢ to 880.0 ¢
38-mosstep	Minor 38-mosstep	m38ms	10L + 28s	800.0 ¢ to 844.4 ¢
	Major 38-mosstep	M38ms	11L + 27s	844.4 ¢ to 880.0 ¢
39-mosstep	Minor 39-mosstep	m39ms	10L + 29s	800.0 ¢ to 866.7 ¢
	Major 39-mosstep	M39ms	11L + 28s	866.7 ¢ to 880.0 ¢
40-mosstep	Minor 40-mosstep	m40ms	11L + 29s	880.0 ¢ to 888.9 ¢
	Major 40-mosstep	M40ms	12L + 28s	888.9 ¢ to 960.0 ¢
41-mosstep	Minor 41-mosstep	m41ms	11L + 30s	880.0 ¢ to 911.1 ¢
	Major 41-mosstep	M41ms	12L + 29s	911.1 ¢ to 960.0 ¢
42-mosstep	Minor 42-mosstep	m42ms	11L + 31s	880.0 ¢ to 933.3 ¢
	Major 42-mosstep	M42ms	12L + 30s	933.3 ¢ to 960.0 ¢
43-mosstep	Diminished 43-mosstep	d43ms	11L + 32s	880.0 ¢ to 955.6 ¢
	Perfect 43-mosstep	P43ms	12L + 31s	955.6 ¢ to 960.0 ¢
44-mosstep	Minor 44-mosstep	m44ms	12L + 32s	960.0 ¢ to 977.8 ¢
	Major 44-mosstep	M44ms	13L + 31s	977.8 ¢ to 1040.0 ¢
45-mosstep	Minor 45-mosstep	m45ms	12L + 33s	960.0 ¢ to 1000.0 ¢
	Major 45-mosstep	M45ms	13L + 32s	1000.0 ¢ to 1040.0 ¢
46-mosstep	Minor 46-mosstep	m46ms	12L + 34s	960.0 ¢ to 1022.2 ¢
	Major 46-mosstep	M46ms	13L + 33s	1022.2 ¢ to 1040.0 ¢
47-mosstep	Perfect 47-mosstep	P47ms	13L + 34s	1040.0 ¢ to 1044.4 ¢
	Augmented 47-mosstep	A47ms	14L + 33s	1044.4 ¢ to 1120.0 ¢
48-mosstep	Minor 48-mosstep	m48ms	13L + 35s	1040.0 ¢ to 1066.7 ¢
	Major 48-mosstep	M48ms	14L + 34s	1066.7 ¢ to 1120.0 ¢
49-mosstep	Minor 49-mosstep	m49ms	13L + 36s	1040.0 ¢ to 1088.9 ¢
	Major 49-mosstep	M49ms	14L + 35s	1088.9 ¢ to 1120.0 ¢
50-mosstep	Minor 50-mosstep	m50ms	13L + 37s	1040.0 ¢ to 1111.1 ¢
	Major 50-mosstep	M50ms	14L + 36s	1111.1 ¢ to 1120.0 ¢
51-mosstep	Minor 51-mosstep	m51ms	14L + 37s	1120.0 ¢ to 1133.3 ¢
	Major 51-mosstep	M51ms	15L + 36s	1133.3 ¢ to 1200.0 ¢
52-mosstep	Minor 52-mosstep	m52ms	14L + 38s	1120.0 ¢ to 1155.6 ¢
	Major 52-mosstep	M52ms	15L + 37s	1155.6 ¢ to 1200.0 ¢
53-mosstep	Minor 53-mosstep	m53ms	14L + 39s	1120.0 ¢ to 1177.8 ¢
	Major 53-mosstep	M53ms	15L + 38s	1177.8 ¢ to 1200.0 ¢
54-mosstep	Perfect 54-mosstep	P54ms	15L + 39s	1200.0 ¢

Generator chain of 15L 39s

Bright gens	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.
22	Augmented 10-mosdegree	A10md	Augmented 28-mosdegree	A28md	Augmented 46-mosdegree	A46md
21	Augmented 3-mosdegree	A3md	Augmented 21-mosdegree	A21md	Augmented 39-mosdegree	A39md
20	Augmented 14-mosdegree	A14md	Augmented 32-mosdegree	A32md	Augmented 50-mosdegree	A50md
19	Augmented 7-mosdegree	A7md	Augmented 25-mosdegree	A25md	Augmented 43-mosdegree	A43md
18	Augmented 0-mosdegree	A0md	Augmented 18-mosdegree	A18md	Augmented 36-mosdegree	A36md
17	Augmented 11-mosdegree	A11md	Augmented 29-mosdegree	A29md	Augmented 47-mosdegree	A47md
16	Major 4-mosdegree	M4md	Major 22-mosdegree	M22md	Major 40-mosdegree	M40md
15	Major 15-mosdegree	M15md	Major 33-mosdegree	M33md	Major 51-mosdegree	M51md
14	Major 8-mosdegree	M8md	Major 26-mosdegree	M26md	Major 44-mosdegree	M44md
13	Major 1-mosdegree	M1md	Major 19-mosdegree	M19md	Major 37-mosdegree	M37md
12	Major 12-mosdegree	M12md	Major 30-mosdegree	M30md	Major 48-mosdegree	M48md
11	Major 5-mosdegree	M5md	Major 23-mosdegree	M23md	Major 41-mosdegree	M41md
10	Major 16-mosdegree	M16md	Major 34-mosdegree	M34md	Major 52-mosdegree	M52md
9	Major 9-mosdegree	M9md	Major 27-mosdegree	M27md	Major 45-mosdegree	M45md
8	Major 2-mosdegree	M2md	Major 20-mosdegree	M20md	Major 38-mosdegree	M38md
7	Major 13-mosdegree	M13md	Major 31-mosdegree	M31md	Major 49-mosdegree	M49md
6	Major 6-mosdegree	M6md	Major 24-mosdegree	M24md	Major 42-mosdegree	M42md
5	Major 17-mosdegree	M17md	Major 35-mosdegree	M35md	Major 53-mosdegree	M53md
4	Major 10-mosdegree	M10md	Major 28-mosdegree	M28md	Major 46-mosdegree	M46md
3	Major 3-mosdegree	M3md	Major 21-mosdegree	M21md	Major 39-mosdegree	M39md
2	Major 14-mosdegree	M14md	Major 32-mosdegree	M32md	Major 50-mosdegree	M50md
1	Perfect 7-mosdegree	P7md	Perfect 25-mosdegree	P25md	Perfect 43-mosdegree	P43md
0	Perfect 0-mosdegree Perfect 18-mosdegree	P0md P18md	Perfect 18-mosdegree Perfect 36-mosdegree	P18md P36md	Perfect 36-mosdegree Perfect 54-mosdegree	P36md P54md
−1	Perfect 11-mosdegree	P11md	Perfect 29-mosdegree	P29md	Perfect 47-mosdegree	P47md
−2	Minor 4-mosdegree	m4md	Minor 22-mosdegree	m22md	Minor 40-mosdegree	m40md
−3	Minor 15-mosdegree	m15md	Minor 33-mosdegree	m33md	Minor 51-mosdegree	m51md
−4	Minor 8-mosdegree	m8md	Minor 26-mosdegree	m26md	Minor 44-mosdegree	m44md
−5	Minor 1-mosdegree	m1md	Minor 19-mosdegree	m19md	Minor 37-mosdegree	m37md
−6	Minor 12-mosdegree	m12md	Minor 30-mosdegree	m30md	Minor 48-mosdegree	m48md
−7	Minor 5-mosdegree	m5md	Minor 23-mosdegree	m23md	Minor 41-mosdegree	m41md
−8	Minor 16-mosdegree	m16md	Minor 34-mosdegree	m34md	Minor 52-mosdegree	m52md
−9	Minor 9-mosdegree	m9md	Minor 27-mosdegree	m27md	Minor 45-mosdegree	m45md
−10	Minor 2-mosdegree	m2md	Minor 20-mosdegree	m20md	Minor 38-mosdegree	m38md
−11	Minor 13-mosdegree	m13md	Minor 31-mosdegree	m31md	Minor 49-mosdegree	m49md
−12	Minor 6-mosdegree	m6md	Minor 24-mosdegree	m24md	Minor 42-mosdegree	m42md
−13	Minor 17-mosdegree	m17md	Minor 35-mosdegree	m35md	Minor 53-mosdegree	m53md
−14	Minor 10-mosdegree	m10md	Minor 28-mosdegree	m28md	Minor 46-mosdegree	m46md
−15	Minor 3-mosdegree	m3md	Minor 21-mosdegree	m21md	Minor 39-mosdegree	m39md
−16	Minor 14-mosdegree	m14md	Minor 32-mosdegree	m32md	Minor 50-mosdegree	m50md
−17	Diminished 7-mosdegree	d7md	Diminished 25-mosdegree	d25md	Diminished 43-mosdegree	d43md
−18	Diminished 18-mosdegree	d18md	Diminished 36-mosdegree	d36md	Diminished 54-mosdegree	d54md
−19	Diminished 11-mosdegree	d11md	Diminished 29-mosdegree	d29md	Diminished 47-mosdegree	d47md
−20	Diminished 4-mosdegree	d4md	Diminished 22-mosdegree	d22md	Diminished 40-mosdegree	d40md
−21	Diminished 15-mosdegree	d15md	Diminished 33-mosdegree	d33md	Diminished 51-mosdegree	d51md
−22	Diminished 8-mosdegree	d8md	Diminished 26-mosdegree	d26md	Diminished 44-mosdegree	d44md

Modes of 15L 39s

UDP	Cyclic order	Step pattern
51|0(3)	1	LssLsssLssLsssLsssLssLsssLssLsssLsssLssLsssLssLsssLsss
48|3(3)	8	LssLsssLsssLssLsssLssLsssLsssLssLsssLssLsssLsssLssLsss
45|6(3)	15	LsssLssLsssLssLsssLsssLssLsssLssLsssLsssLssLsssLssLsss
42|9(3)	4	LsssLssLsssLsssLssLsssLssLsssLsssLssLsssLssLsssLsssLss
39|12(3)	11	LsssLsssLssLsssLssLsssLsssLssLsssLssLsssLsssLssLsssLss
36|15(3)	18	sLssLsssLssLsssLsssLssLsssLssLsssLsssLssLsssLssLsssLss
33|18(3)	7	sLssLsssLsssLssLsssLssLsssLsssLssLsssLssLsssLsssLssLss
30|21(3)	14	sLsssLssLsssLssLsssLsssLssLsssLssLsssLsssLssLsssLssLss
27|24(3)	3	sLsssLssLsssLsssLssLsssLssLsssLsssLssLsssLssLsssLsssLs
24|27(3)	10	sLsssLsssLssLsssLssLsssLsssLssLsssLssLsssLsssLssLsssLs
21|30(3)	17	ssLssLsssLssLsssLsssLssLsssLssLsssLsssLssLsssLssLsssLs
18|33(3)	6	ssLssLsssLsssLssLsssLssLsssLsssLssLsssLssLsssLsssLssLs
15|36(3)	13	ssLsssLssLsssLssLsssLsssLssLsssLssLsssLsssLssLsssLssLs
12|39(3)	2	ssLsssLssLsssLsssLssLsssLssLsssLsssLssLsssLssLsssLsssL
9|42(3)	9	ssLsssLsssLssLsssLssLsssLsssLssLsssLssLsssLsssLssLsssL
6|45(3)	16	sssLssLsssLssLsssLsssLssLsssLssLsssLsssLssLsssLssLsssL
3|48(3)	5	sssLssLsssLsssLssLsssLssLsssLsssLssLsssLssLsssLsssLssL
0|51(3)	12	sssLsssLssLsssLssLsssLsssLssLsssLssLsssLsssLssLsssLssL

Scale tree

Scale tree and tuning spectrum of 15L 39s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
7\54						155.556	244.444	1:1	1.000	Equalized 15L 39s
					37\285	155.789	244.211	6:5	1.200
				30\231		155.844	244.156	5:4	1.250
					53\408	155.882	244.118	9:7	1.286
			23\177			155.932	244.068	4:3	1.333	Supersoft 15L 39s
					62\477	155.975	244.025	11:8	1.375
				39\300		156.000	244.000	7:5	1.400
					55\423	156.028	243.972	10:7	1.429
		16\123				156.098	243.902	3:2	1.500	Soft 15L 39s
					57\438	156.164	243.836	11:7	1.571
				41\315		156.190	243.810	8:5	1.600
					66\507	156.213	243.787	13:8	1.625
			25\192			156.250	243.750	5:3	1.667	Semisoft 15L 39s
					59\453	156.291	243.709	12:7	1.714
				34\261		156.322	243.678	7:4	1.750
					43\330	156.364	243.636	9:5	1.800
	9\69					156.522	243.478	2:1	2.000	Basic 15L 39s Scales with tunings softer than this are proper
					38\291	156.701	243.299	9:4	2.250
				29\222		156.757	243.243	7:3	2.333
					49\375	156.800	243.200	12:5	2.400
			20\153			156.863	243.137	5:2	2.500	Semihard 15L 39s
					51\390	156.923	243.077	13:5	2.600
				31\237		156.962	243.038	8:3	2.667
					42\321	157.009	242.991	11:4	2.750
		11\84				157.143	242.857	3:1	3.000	Hard 15L 39s
					35\267	157.303	242.697	10:3	3.333
				24\183		157.377	242.623	7:2	3.500
					37\282	157.447	242.553	11:3	3.667
			13\99			157.576	242.424	4:1	4.000	Superhard 15L 39s
					28\213	157.746	242.254	9:2	4.500
				15\114		157.895	242.105	5:1	5.000
					17\129	158.140	241.860	6:1	6.000
2\15						160.000	240.000	1:0	→ ∞	Collapsed 15L 39s