User:MisterShafXen/27L 14s

27L 14s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 27 large steps and 14 small steps, repeating every octave. 27L 14s is related to 1L 9s, expanding it by 31 tones. Generators that produce this scale range from 87.8 ¢ to 88.9 ¢, or from 1111.1 ¢ to 1112.2 ¢.

↖ 26L 13s	↑ 27L 13s	28L 13s ↗
← 26L 14s	27L 14s	28L 14s →
↙ 26L 15s	↓ 27L 15s	28L 15s ↘

Scale structure
Step pattern	...41 steps...
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	3\41 to 2\27 (87.8 ¢ to 88.9 ¢)
Dark	25\27 to 38\41 (1111.1 ¢ to 1112.2 ¢)
TAMNAMS information
Related to	1L 9s (antisinatonic)
With tunings	9:2 to 14:3
Related MOS scales
Parent	14L 13s
Sister	14L 27s
Daughters	41L 27s, 27L 41s
Neutralized	13L 28s
2-Flought	68L 14s, 27L 55s
Equal tunings
Equalized (L:s = 1:1)	3\41 (87.8 ¢)
Supersoft (L:s = 4:3)	11\150 (88.0 ¢)
Soft (L:s = 3:2)	8\109 (88.1 ¢)
Semisoft (L:s = 5:3)	13\177 (88.1 ¢)
Basic (L:s = 2:1)	5\68 (88.2 ¢)
Semihard (L:s = 5:2)	12\163 (88.3 ¢)
Hard (L:s = 3:1)	7\95 (88.4 ¢)
Superhard (L:s = 4:1)	9\122 (88.5 ¢)
Collapsed (L:s = 1:0)	2\27 (88.9 ¢)
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Scale properties

Intervals of 27L 14s

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 29.3 ¢
	Major 1-mosstep	M1ms	L	29.3 ¢ to 44.4 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	44.4 ¢ to 58.5 ¢
	Major 2-mosstep	M2ms	2L	58.5 ¢ to 88.9 ¢
3-mosstep	Diminished 3-mosstep	d3ms	L + 2s	44.4 ¢ to 87.8 ¢
	Perfect 3-mosstep	P3ms	2L + s	87.8 ¢ to 88.9 ¢
4-mosstep	Minor 4-mosstep	m4ms	2L + 2s	88.9 ¢ to 117.1 ¢
	Major 4-mosstep	M4ms	3L + s	117.1 ¢ to 133.3 ¢
5-mosstep	Minor 5-mosstep	m5ms	3L + 2s	133.3 ¢ to 146.3 ¢
	Major 5-mosstep	M5ms	4L + s	146.3 ¢ to 177.8 ¢
6-mosstep	Minor 6-mosstep	m6ms	3L + 3s	133.3 ¢ to 175.6 ¢
	Major 6-mosstep	M6ms	4L + 2s	175.6 ¢ to 177.8 ¢
7-mosstep	Minor 7-mosstep	m7ms	4L + 3s	177.8 ¢ to 204.9 ¢
	Major 7-mosstep	M7ms	5L + 2s	204.9 ¢ to 222.2 ¢
8-mosstep	Minor 8-mosstep	m8ms	5L + 3s	222.2 ¢ to 234.1 ¢
	Major 8-mosstep	M8ms	6L + 2s	234.1 ¢ to 266.7 ¢
9-mosstep	Minor 9-mosstep	m9ms	5L + 4s	222.2 ¢ to 263.4 ¢
	Major 9-mosstep	M9ms	6L + 3s	263.4 ¢ to 266.7 ¢
10-mosstep	Minor 10-mosstep	m10ms	6L + 4s	266.7 ¢ to 292.7 ¢
	Major 10-mosstep	M10ms	7L + 3s	292.7 ¢ to 311.1 ¢
11-mosstep	Minor 11-mosstep	m11ms	7L + 4s	311.1 ¢ to 322.0 ¢
	Major 11-mosstep	M11ms	8L + 3s	322.0 ¢ to 355.6 ¢
12-mosstep	Minor 12-mosstep	m12ms	7L + 5s	311.1 ¢ to 351.2 ¢
	Major 12-mosstep	M12ms	8L + 4s	351.2 ¢ to 355.6 ¢
13-mosstep	Minor 13-mosstep	m13ms	8L + 5s	355.6 ¢ to 380.5 ¢
	Major 13-mosstep	M13ms	9L + 4s	380.5 ¢ to 400.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	9L + 5s	400.0 ¢ to 409.8 ¢
	Major 14-mosstep	M14ms	10L + 4s	409.8 ¢ to 444.4 ¢
15-mosstep	Minor 15-mosstep	m15ms	9L + 6s	400.0 ¢ to 439.0 ¢
	Major 15-mosstep	M15ms	10L + 5s	439.0 ¢ to 444.4 ¢
16-mosstep	Minor 16-mosstep	m16ms	10L + 6s	444.4 ¢ to 468.3 ¢
	Major 16-mosstep	M16ms	11L + 5s	468.3 ¢ to 488.9 ¢
17-mosstep	Minor 17-mosstep	m17ms	11L + 6s	488.9 ¢ to 497.6 ¢
	Major 17-mosstep	M17ms	12L + 5s	497.6 ¢ to 533.3 ¢
18-mosstep	Minor 18-mosstep	m18ms	11L + 7s	488.9 ¢ to 526.8 ¢
	Major 18-mosstep	M18ms	12L + 6s	526.8 ¢ to 533.3 ¢
19-mosstep	Minor 19-mosstep	m19ms	12L + 7s	533.3 ¢ to 556.1 ¢
	Major 19-mosstep	M19ms	13L + 6s	556.1 ¢ to 577.8 ¢
20-mosstep	Minor 20-mosstep	m20ms	13L + 7s	577.8 ¢ to 585.4 ¢
	Major 20-mosstep	M20ms	14L + 6s	585.4 ¢ to 622.2 ¢
21-mosstep	Minor 21-mosstep	m21ms	13L + 8s	577.8 ¢ to 614.6 ¢
	Major 21-mosstep	M21ms	14L + 7s	614.6 ¢ to 622.2 ¢
22-mosstep	Minor 22-mosstep	m22ms	14L + 8s	622.2 ¢ to 643.9 ¢
	Major 22-mosstep	M22ms	15L + 7s	643.9 ¢ to 666.7 ¢
23-mosstep	Minor 23-mosstep	m23ms	15L + 8s	666.7 ¢ to 673.2 ¢
	Major 23-mosstep	M23ms	16L + 7s	673.2 ¢ to 711.1 ¢
24-mosstep	Minor 24-mosstep	m24ms	15L + 9s	666.7 ¢ to 702.4 ¢
	Major 24-mosstep	M24ms	16L + 8s	702.4 ¢ to 711.1 ¢
25-mosstep	Minor 25-mosstep	m25ms	16L + 9s	711.1 ¢ to 731.7 ¢
	Major 25-mosstep	M25ms	17L + 8s	731.7 ¢ to 755.6 ¢
26-mosstep	Minor 26-mosstep	m26ms	17L + 9s	755.6 ¢ to 761.0 ¢
	Major 26-mosstep	M26ms	18L + 8s	761.0 ¢ to 800.0 ¢
27-mosstep	Minor 27-mosstep	m27ms	17L + 10s	755.6 ¢ to 790.2 ¢
	Major 27-mosstep	M27ms	18L + 9s	790.2 ¢ to 800.0 ¢
28-mosstep	Minor 28-mosstep	m28ms	18L + 10s	800.0 ¢ to 819.5 ¢
	Major 28-mosstep	M28ms	19L + 9s	819.5 ¢ to 844.4 ¢
29-mosstep	Minor 29-mosstep	m29ms	19L + 10s	844.4 ¢ to 848.8 ¢
	Major 29-mosstep	M29ms	20L + 9s	848.8 ¢ to 888.9 ¢
30-mosstep	Minor 30-mosstep	m30ms	19L + 11s	844.4 ¢ to 878.0 ¢
	Major 30-mosstep	M30ms	20L + 10s	878.0 ¢ to 888.9 ¢
31-mosstep	Minor 31-mosstep	m31ms	20L + 11s	888.9 ¢ to 907.3 ¢
	Major 31-mosstep	M31ms	21L + 10s	907.3 ¢ to 933.3 ¢
32-mosstep	Minor 32-mosstep	m32ms	21L + 11s	933.3 ¢ to 936.6 ¢
	Major 32-mosstep	M32ms	22L + 10s	936.6 ¢ to 977.8 ¢
33-mosstep	Minor 33-mosstep	m33ms	21L + 12s	933.3 ¢ to 965.9 ¢
	Major 33-mosstep	M33ms	22L + 11s	965.9 ¢ to 977.8 ¢
34-mosstep	Minor 34-mosstep	m34ms	22L + 12s	977.8 ¢ to 995.1 ¢
	Major 34-mosstep	M34ms	23L + 11s	995.1 ¢ to 1022.2 ¢
35-mosstep	Minor 35-mosstep	m35ms	23L + 12s	1022.2 ¢ to 1024.4 ¢
	Major 35-mosstep	M35ms	24L + 11s	1024.4 ¢ to 1066.7 ¢
36-mosstep	Minor 36-mosstep	m36ms	23L + 13s	1022.2 ¢ to 1053.7 ¢
	Major 36-mosstep	M36ms	24L + 12s	1053.7 ¢ to 1066.7 ¢
37-mosstep	Minor 37-mosstep	m37ms	24L + 13s	1066.7 ¢ to 1082.9 ¢
	Major 37-mosstep	M37ms	25L + 12s	1082.9 ¢ to 1111.1 ¢
38-mosstep	Perfect 38-mosstep	P38ms	25L + 13s	1111.1 ¢ to 1112.2 ¢
	Augmented 38-mosstep	A38ms	26L + 12s	1112.2 ¢ to 1155.6 ¢
39-mosstep	Minor 39-mosstep	m39ms	25L + 14s	1111.1 ¢ to 1141.5 ¢
	Major 39-mosstep	M39ms	26L + 13s	1141.5 ¢ to 1155.6 ¢
40-mosstep	Minor 40-mosstep	m40ms	26L + 14s	1155.6 ¢ to 1170.7 ¢
	Major 40-mosstep	M40ms	27L + 13s	1170.7 ¢ to 1200.0 ¢
41-mosstep	Perfect 41-mosstep	P41ms	27L + 14s	1200.0 ¢

Generator chain of 27L 14s

Bright gens	Scale degree	Abbrev.
67	Augmented 37-mosdegree	A37md
66	Augmented 34-mosdegree	A34md
65	Augmented 31-mosdegree	A31md
64	Augmented 28-mosdegree	A28md
63	Augmented 25-mosdegree	A25md
62	Augmented 22-mosdegree	A22md
61	Augmented 19-mosdegree	A19md
60	Augmented 16-mosdegree	A16md
59	Augmented 13-mosdegree	A13md
58	Augmented 10-mosdegree	A10md
57	Augmented 7-mosdegree	A7md
56	Augmented 4-mosdegree	A4md
55	Augmented 1-mosdegree	A1md
54	Augmented 39-mosdegree	A39md
53	Augmented 36-mosdegree	A36md
52	Augmented 33-mosdegree	A33md
51	Augmented 30-mosdegree	A30md
50	Augmented 27-mosdegree	A27md
49	Augmented 24-mosdegree	A24md
48	Augmented 21-mosdegree	A21md
47	Augmented 18-mosdegree	A18md
46	Augmented 15-mosdegree	A15md
45	Augmented 12-mosdegree	A12md
44	Augmented 9-mosdegree	A9md
43	Augmented 6-mosdegree	A6md
42	Augmented 3-mosdegree	A3md
41	Augmented 0-mosdegree	A0md
40	Augmented 38-mosdegree	A38md
39	Major 35-mosdegree	M35md
38	Major 32-mosdegree	M32md
37	Major 29-mosdegree	M29md
36	Major 26-mosdegree	M26md
35	Major 23-mosdegree	M23md
34	Major 20-mosdegree	M20md
33	Major 17-mosdegree	M17md
32	Major 14-mosdegree	M14md
31	Major 11-mosdegree	M11md
30	Major 8-mosdegree	M8md
29	Major 5-mosdegree	M5md
28	Major 2-mosdegree	M2md
27	Major 40-mosdegree	M40md
26	Major 37-mosdegree	M37md
25	Major 34-mosdegree	M34md
24	Major 31-mosdegree	M31md
23	Major 28-mosdegree	M28md
22	Major 25-mosdegree	M25md
21	Major 22-mosdegree	M22md
20	Major 19-mosdegree	M19md
19	Major 16-mosdegree	M16md
18	Major 13-mosdegree	M13md
17	Major 10-mosdegree	M10md
16	Major 7-mosdegree	M7md
15	Major 4-mosdegree	M4md
14	Major 1-mosdegree	M1md
13	Major 39-mosdegree	M39md
12	Major 36-mosdegree	M36md
11	Major 33-mosdegree	M33md
10	Major 30-mosdegree	M30md
9	Major 27-mosdegree	M27md
8	Major 24-mosdegree	M24md
7	Major 21-mosdegree	M21md
6	Major 18-mosdegree	M18md
5	Major 15-mosdegree	M15md
4	Major 12-mosdegree	M12md
3	Major 9-mosdegree	M9md
2	Major 6-mosdegree	M6md
1	Perfect 3-mosdegree	P3md
0	Perfect 0-mosdegree Perfect 41-mosdegree	P0md P41md
−1	Perfect 38-mosdegree	P38md
−2	Minor 35-mosdegree	m35md
−3	Minor 32-mosdegree	m32md
−4	Minor 29-mosdegree	m29md
−5	Minor 26-mosdegree	m26md
−6	Minor 23-mosdegree	m23md
−7	Minor 20-mosdegree	m20md
−8	Minor 17-mosdegree	m17md
−9	Minor 14-mosdegree	m14md
−10	Minor 11-mosdegree	m11md
−11	Minor 8-mosdegree	m8md
−12	Minor 5-mosdegree	m5md
−13	Minor 2-mosdegree	m2md
−14	Minor 40-mosdegree	m40md
−15	Minor 37-mosdegree	m37md
−16	Minor 34-mosdegree	m34md
−17	Minor 31-mosdegree	m31md
−18	Minor 28-mosdegree	m28md
−19	Minor 25-mosdegree	m25md
−20	Minor 22-mosdegree	m22md
−21	Minor 19-mosdegree	m19md
−22	Minor 16-mosdegree	m16md
−23	Minor 13-mosdegree	m13md
−24	Minor 10-mosdegree	m10md
−25	Minor 7-mosdegree	m7md
−26	Minor 4-mosdegree	m4md
−27	Minor 1-mosdegree	m1md
−28	Minor 39-mosdegree	m39md
−29	Minor 36-mosdegree	m36md
−30	Minor 33-mosdegree	m33md
−31	Minor 30-mosdegree	m30md
−32	Minor 27-mosdegree	m27md
−33	Minor 24-mosdegree	m24md
−34	Minor 21-mosdegree	m21md
−35	Minor 18-mosdegree	m18md
−36	Minor 15-mosdegree	m15md
−37	Minor 12-mosdegree	m12md
−38	Minor 9-mosdegree	m9md
−39	Minor 6-mosdegree	m6md
−40	Diminished 3-mosdegree	d3md
−41	Diminished 41-mosdegree	d41md
−42	Diminished 38-mosdegree	d38md
−43	Diminished 35-mosdegree	d35md
−44	Diminished 32-mosdegree	d32md
−45	Diminished 29-mosdegree	d29md
−46	Diminished 26-mosdegree	d26md
−47	Diminished 23-mosdegree	d23md
−48	Diminished 20-mosdegree	d20md
−49	Diminished 17-mosdegree	d17md
−50	Diminished 14-mosdegree	d14md
−51	Diminished 11-mosdegree	d11md
−52	Diminished 8-mosdegree	d8md
−53	Diminished 5-mosdegree	d5md
−54	Diminished 2-mosdegree	d2md
−55	Diminished 40-mosdegree	d40md
−56	Diminished 37-mosdegree	d37md
−57	Diminished 34-mosdegree	d34md
−58	Diminished 31-mosdegree	d31md
−59	Diminished 28-mosdegree	d28md
−60	Diminished 25-mosdegree	d25md
−61	Diminished 22-mosdegree	d22md
−62	Diminished 19-mosdegree	d19md
−63	Diminished 16-mosdegree	d16md
−64	Diminished 13-mosdegree	d13md
−65	Diminished 10-mosdegree	d10md
−66	Diminished 7-mosdegree	d7md
−67	Diminished 4-mosdegree	d4md

Modes of 27L 14s

UDP	Cyclic order	Step pattern
40|0	1	LLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLs
39|1	4	LLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLsLLs
38|2	7	LLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLsLLsLLs
37|3	10	LLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLsLLsLLsLLs
36|4	13	LLsLLsLLsLLsLLsLLsLLsLLsLLsLsLLsLLsLLsLLs
35|5	16	LLsLLsLLsLLsLLsLLsLLsLLsLsLLsLLsLLsLLsLLs
34|6	19	LLsLLsLLsLLsLLsLLsLLsLsLLsLLsLLsLLsLLsLLs
33|7	22	LLsLLsLLsLLsLLsLLsLsLLsLLsLLsLLsLLsLLsLLs
32|8	25	LLsLLsLLsLLsLLsLsLLsLLsLLsLLsLLsLLsLLsLLs
31|9	28	LLsLLsLLsLLsLsLLsLLsLLsLLsLLsLLsLLsLLsLLs
30|10	31	LLsLLsLLsLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLs
29|11	34	LLsLLsLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLs
28|12	37	LLsLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLs
27|13	40	LsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLs
26|14	2	LsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLsL
25|15	5	LsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLsLLsL
24|16	8	LsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLsLLsLLsL
23|17	11	LsLLsLLsLLsLLsLLsLLsLLsLLsLLsLsLLsLLsLLsL
22|18	14	LsLLsLLsLLsLLsLLsLLsLLsLLsLsLLsLLsLLsLLsL
21|19	17	LsLLsLLsLLsLLsLLsLLsLLsLsLLsLLsLLsLLsLLsL
20|20	20	LsLLsLLsLLsLLsLLsLLsLsLLsLLsLLsLLsLLsLLsL
19|21	23	LsLLsLLsLLsLLsLLsLsLLsLLsLLsLLsLLsLLsLLsL
18|22	26	LsLLsLLsLLsLLsLsLLsLLsLLsLLsLLsLLsLLsLLsL
17|23	29	LsLLsLLsLLsLsLLsLLsLLsLLsLLsLLsLLsLLsLLsL
16|24	32	LsLLsLLsLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsL
15|25	35	LsLLsLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsL
14|26	38	LsLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsL
13|27	41	sLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsL
12|28	3	sLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLsLL
11|29	6	sLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLsLLsLL
10|30	9	sLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLsLLsLLsLL
9|31	12	sLLsLLsLLsLLsLLsLLsLLsLLsLLsLsLLsLLsLLsLL
8|32	15	sLLsLLsLLsLLsLLsLLsLLsLLsLsLLsLLsLLsLLsLL
7|33	18	sLLsLLsLLsLLsLLsLLsLLsLsLLsLLsLLsLLsLLsLL
6|34	21	sLLsLLsLLsLLsLLsLLsLsLLsLLsLLsLLsLLsLLsLL
5|35	24	sLLsLLsLLsLLsLLsLsLLsLLsLLsLLsLLsLLsLLsLL
4|36	27	sLLsLLsLLsLLsLsLLsLLsLLsLLsLLsLLsLLsLLsLL
3|37	30	sLLsLLsLLsLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLL
2|38	33	sLLsLLsLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLL
1|39	36	sLLsLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLL
0|40	39	sLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLLsLL

Scale tree

Scale tree and tuning spectrum of 27L 14s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
3\41						87.805	1112.195	1:1	1.000	Equalized 27L 14s
					17\232	87.931	1112.069	6:5	1.200
				14\191		87.958	1112.042	5:4	1.250
					25\341	87.977	1112.023	9:7	1.286
			11\150			88.000	1112.000	4:3	1.333	Supersoft 27L 14s
					30\409	88.020	1111.980	11:8	1.375
				19\259		88.031	1111.969	7:5	1.400
					27\368	88.043	1111.957	10:7	1.429
		8\109				88.073	1111.927	3:2	1.500	Soft 27L 14s
					29\395	88.101	1111.899	11:7	1.571
				21\286		88.112	1111.888	8:5	1.600
					34\463	88.121	1111.879	13:8	1.625
			13\177			88.136	1111.864	5:3	1.667	Semisoft 27L 14s
					31\422	88.152	1111.848	12:7	1.714
				18\245		88.163	1111.837	7:4	1.750
					23\313	88.179	1111.821	9:5	1.800
	5\68					88.235	1111.765	2:1	2.000	Basic 27L 14s Scales with tunings softer than this are proper
					22\299	88.294	1111.706	9:4	2.250
				17\231		88.312	1111.688	7:3	2.333
					29\394	88.325	1111.675	12:5	2.400
			12\163			88.344	1111.656	5:2	2.500	Semihard 27L 14s
					31\421	88.361	1111.639	13:5	2.600
				19\258		88.372	1111.628	8:3	2.667
					26\353	88.385	1111.615	11:4	2.750
		7\95				88.421	1111.579	3:1	3.000	Hard 27L 14s
					23\312	88.462	1111.538	10:3	3.333
				16\217		88.479	1111.521	7:2	3.500
					25\339	88.496	1111.504	11:3	3.667
			9\122			88.525	1111.475	4:1	4.000	Superhard 27L 14s
					20\271	88.561	1111.439	9:2	4.500
				11\149		88.591	1111.409	5:1	5.000
					13\176	88.636	1111.364	6:1	6.000
2\27						88.889	1111.111	1:0	→ ∞	Collapsed 27L 14s