41L 12s

↖ 40L 11s	↑ 41L 11s	42L 11s ↗
← 40L 12s	41L 12s	42L 12s →
↙ 40L 13s	↓ 41L 13s	42L 13s ↘

Scale structure
Step pattern	...53 steps...
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	31\53 to 24\41 (701.9 ¢ to 702.4 ¢)
Dark	17\41 to 22\53 (497.6 ¢ to 498.1 ¢)
TAMNAMS information
Related to	5L 2s (diatonic)
With tunings	9:4 to 7:3
Related MOS scales
Parent	12L 29s
Sister	12L 41s
Daughters	53L 41s, 41L 53s
Neutralized	29L 24s
2-Flought	94L 12s, 41L 65s
Equal tunings
Equalized (L:s = 1:1)	31\53 (701.9 ¢)
Supersoft (L:s = 4:3)	117\200 (702.0 ¢)
Soft (L:s = 3:2)	86\147 (702.0 ¢)
Semisoft (L:s = 5:3)	141\241 (702.1 ¢)
Basic (L:s = 2:1)	55\94 (702.1 ¢)
Semihard (L:s = 5:2)	134\229 (702.2 ¢)
Hard (L:s = 3:1)	79\135 (702.2 ¢)
Superhard (L:s = 4:1)	103\176 (702.3 ¢)
Collapsed (L:s = 1:0)	24\41 (702.4 ¢)
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41L 12s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 41 large steps and 12 small steps, repeating every octave. 41L 12s is related to 5L 2s, expanding it by 46 tones. Generators that produce this scale range from 701.9 ¢ to 702.4 ¢, or from 497.6 ¢ to 498.1 ¢. Its chroma-positive generator is a almost-perfect fifth of no more than 31\53 (701.9 ¢), where the large step is identified with the pythagorean comma, and the small step is identified with the countercomp comma. Pythagorean tuning can generate this MOS scale with a hardness of 1.1822.

Intervals

Intervals of 41L 12s

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 22.6 ¢
	Major 1-mosstep	M1ms	L	22.6 ¢ to 29.3 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	29.3 ¢ to 45.3 ¢
	Major 2-mosstep	M2ms	2L	45.3 ¢ to 58.5 ¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	58.5 ¢ to 67.9 ¢
	Major 3-mosstep	M3ms	3L	67.9 ¢ to 87.8 ¢
4-mosstep	Minor 4-mosstep	m4ms	3L + s	87.8 ¢ to 90.6 ¢
	Major 4-mosstep	M4ms	4L	90.6 ¢ to 117.1 ¢
5-mosstep	Minor 5-mosstep	m5ms	3L + 2s	87.8 ¢ to 113.2 ¢
	Major 5-mosstep	M5ms	4L + s	113.2 ¢ to 117.1 ¢
6-mosstep	Minor 6-mosstep	m6ms	4L + 2s	117.1 ¢ to 135.8 ¢
	Major 6-mosstep	M6ms	5L + s	135.8 ¢ to 146.3 ¢
7-mosstep	Minor 7-mosstep	m7ms	5L + 2s	146.3 ¢ to 158.5 ¢
	Major 7-mosstep	M7ms	6L + s	158.5 ¢ to 175.6 ¢
8-mosstep	Minor 8-mosstep	m8ms	6L + 2s	175.6 ¢ to 181.1 ¢
	Major 8-mosstep	M8ms	7L + s	181.1 ¢ to 204.9 ¢
9-mosstep	Minor 9-mosstep	m9ms	6L + 3s	175.6 ¢ to 203.8 ¢
	Major 9-mosstep	M9ms	7L + 2s	203.8 ¢ to 204.9 ¢
10-mosstep	Minor 10-mosstep	m10ms	7L + 3s	204.9 ¢ to 226.4 ¢
	Major 10-mosstep	M10ms	8L + 2s	226.4 ¢ to 234.1 ¢
11-mosstep	Minor 11-mosstep	m11ms	8L + 3s	234.1 ¢ to 249.1 ¢
	Major 11-mosstep	M11ms	9L + 2s	249.1 ¢ to 263.4 ¢
12-mosstep	Minor 12-mosstep	m12ms	9L + 3s	263.4 ¢ to 271.7 ¢
	Major 12-mosstep	M12ms	10L + 2s	271.7 ¢ to 292.7 ¢
13-mosstep	Minor 13-mosstep	m13ms	10L + 3s	292.7 ¢ to 294.3 ¢
	Major 13-mosstep	M13ms	11L + 2s	294.3 ¢ to 322.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	10L + 4s	292.7 ¢ to 317.0 ¢
	Major 14-mosstep	M14ms	11L + 3s	317.0 ¢ to 322.0 ¢
15-mosstep	Minor 15-mosstep	m15ms	11L + 4s	322.0 ¢ to 339.6 ¢
	Major 15-mosstep	M15ms	12L + 3s	339.6 ¢ to 351.2 ¢
16-mosstep	Minor 16-mosstep	m16ms	12L + 4s	351.2 ¢ to 362.3 ¢
	Major 16-mosstep	M16ms	13L + 3s	362.3 ¢ to 380.5 ¢
17-mosstep	Minor 17-mosstep	m17ms	13L + 4s	380.5 ¢ to 384.9 ¢
	Major 17-mosstep	M17ms	14L + 3s	384.9 ¢ to 409.8 ¢
18-mosstep	Minor 18-mosstep	m18ms	13L + 5s	380.5 ¢ to 407.5 ¢
	Major 18-mosstep	M18ms	14L + 4s	407.5 ¢ to 409.8 ¢
19-mosstep	Minor 19-mosstep	m19ms	14L + 5s	409.8 ¢ to 430.2 ¢
	Major 19-mosstep	M19ms	15L + 4s	430.2 ¢ to 439.0 ¢
20-mosstep	Minor 20-mosstep	m20ms	15L + 5s	439.0 ¢ to 452.8 ¢
	Major 20-mosstep	M20ms	16L + 4s	452.8 ¢ to 468.3 ¢
21-mosstep	Minor 21-mosstep	m21ms	16L + 5s	468.3 ¢ to 475.5 ¢
	Major 21-mosstep	M21ms	17L + 4s	475.5 ¢ to 497.6 ¢
22-mosstep	Perfect 22-mosstep	P22ms	17L + 5s	497.6 ¢ to 498.1 ¢
	Augmented 22-mosstep	A22ms	18L + 4s	498.1 ¢ to 526.8 ¢
23-mosstep	Minor 23-mosstep	m23ms	17L + 6s	497.6 ¢ to 520.8 ¢
	Major 23-mosstep	M23ms	18L + 5s	520.8 ¢ to 526.8 ¢
24-mosstep	Minor 24-mosstep	m24ms	18L + 6s	526.8 ¢ to 543.4 ¢
	Major 24-mosstep	M24ms	19L + 5s	543.4 ¢ to 556.1 ¢
25-mosstep	Minor 25-mosstep	m25ms	19L + 6s	556.1 ¢ to 566.0 ¢
	Major 25-mosstep	M25ms	20L + 5s	566.0 ¢ to 585.4 ¢
26-mosstep	Minor 26-mosstep	m26ms	20L + 6s	585.4 ¢ to 588.7 ¢
	Major 26-mosstep	M26ms	21L + 5s	588.7 ¢ to 614.6 ¢
27-mosstep	Minor 27-mosstep	m27ms	20L + 7s	585.4 ¢ to 611.3 ¢
	Major 27-mosstep	M27ms	21L + 6s	611.3 ¢ to 614.6 ¢
28-mosstep	Minor 28-mosstep	m28ms	21L + 7s	614.6 ¢ to 634.0 ¢
	Major 28-mosstep	M28ms	22L + 6s	634.0 ¢ to 643.9 ¢
29-mosstep	Minor 29-mosstep	m29ms	22L + 7s	643.9 ¢ to 656.6 ¢
	Major 29-mosstep	M29ms	23L + 6s	656.6 ¢ to 673.2 ¢
30-mosstep	Minor 30-mosstep	m30ms	23L + 7s	673.2 ¢ to 679.2 ¢
	Major 30-mosstep	M30ms	24L + 6s	679.2 ¢ to 702.4 ¢
31-mosstep	Diminished 31-mosstep	d31ms	23L + 8s	673.2 ¢ to 701.9 ¢
	Perfect 31-mosstep	P31ms	24L + 7s	701.9 ¢ to 702.4 ¢
32-mosstep	Minor 32-mosstep	m32ms	24L + 8s	702.4 ¢ to 724.5 ¢
	Major 32-mosstep	M32ms	25L + 7s	724.5 ¢ to 731.7 ¢
33-mosstep	Minor 33-mosstep	m33ms	25L + 8s	731.7 ¢ to 747.2 ¢
	Major 33-mosstep	M33ms	26L + 7s	747.2 ¢ to 761.0 ¢
34-mosstep	Minor 34-mosstep	m34ms	26L + 8s	761.0 ¢ to 769.8 ¢
	Major 34-mosstep	M34ms	27L + 7s	769.8 ¢ to 790.2 ¢
35-mosstep	Minor 35-mosstep	m35ms	27L + 8s	790.2 ¢ to 792.5 ¢
	Major 35-mosstep	M35ms	28L + 7s	792.5 ¢ to 819.5 ¢
36-mosstep	Minor 36-mosstep	m36ms	27L + 9s	790.2 ¢ to 815.1 ¢
	Major 36-mosstep	M36ms	28L + 8s	815.1 ¢ to 819.5 ¢
37-mosstep	Minor 37-mosstep	m37ms	28L + 9s	819.5 ¢ to 837.7 ¢
	Major 37-mosstep	M37ms	29L + 8s	837.7 ¢ to 848.8 ¢
38-mosstep	Minor 38-mosstep	m38ms	29L + 9s	848.8 ¢ to 860.4 ¢
	Major 38-mosstep	M38ms	30L + 8s	860.4 ¢ to 878.0 ¢
39-mosstep	Minor 39-mosstep	m39ms	30L + 9s	878.0 ¢ to 883.0 ¢
	Major 39-mosstep	M39ms	31L + 8s	883.0 ¢ to 907.3 ¢
40-mosstep	Minor 40-mosstep	m40ms	30L + 10s	878.0 ¢ to 905.7 ¢
	Major 40-mosstep	M40ms	31L + 9s	905.7 ¢ to 907.3 ¢
41-mosstep	Minor 41-mosstep	m41ms	31L + 10s	907.3 ¢ to 928.3 ¢
	Major 41-mosstep	M41ms	32L + 9s	928.3 ¢ to 936.6 ¢
42-mosstep	Minor 42-mosstep	m42ms	32L + 10s	936.6 ¢ to 950.9 ¢
	Major 42-mosstep	M42ms	33L + 9s	950.9 ¢ to 965.9 ¢
43-mosstep	Minor 43-mosstep	m43ms	33L + 10s	965.9 ¢ to 973.6 ¢
	Major 43-mosstep	M43ms	34L + 9s	973.6 ¢ to 995.1 ¢
44-mosstep	Minor 44-mosstep	m44ms	34L + 10s	995.1 ¢ to 996.2 ¢
	Major 44-mosstep	M44ms	35L + 9s	996.2 ¢ to 1024.4 ¢
45-mosstep	Minor 45-mosstep	m45ms	34L + 11s	995.1 ¢ to 1018.9 ¢
	Major 45-mosstep	M45ms	35L + 10s	1018.9 ¢ to 1024.4 ¢
46-mosstep	Minor 46-mosstep	m46ms	35L + 11s	1024.4 ¢ to 1041.5 ¢
	Major 46-mosstep	M46ms	36L + 10s	1041.5 ¢ to 1053.7 ¢
47-mosstep	Minor 47-mosstep	m47ms	36L + 11s	1053.7 ¢ to 1064.2 ¢
	Major 47-mosstep	M47ms	37L + 10s	1064.2 ¢ to 1082.9 ¢
48-mosstep	Minor 48-mosstep	m48ms	37L + 11s	1082.9 ¢ to 1086.8 ¢
	Major 48-mosstep	M48ms	38L + 10s	1086.8 ¢ to 1112.2 ¢
49-mosstep	Minor 49-mosstep	m49ms	37L + 12s	1082.9 ¢ to 1109.4 ¢
	Major 49-mosstep	M49ms	38L + 11s	1109.4 ¢ to 1112.2 ¢
50-mosstep	Minor 50-mosstep	m50ms	38L + 12s	1112.2 ¢ to 1132.1 ¢
	Major 50-mosstep	M50ms	39L + 11s	1132.1 ¢ to 1141.5 ¢
51-mosstep	Minor 51-mosstep	m51ms	39L + 12s	1141.5 ¢ to 1154.7 ¢
	Major 51-mosstep	M51ms	40L + 11s	1154.7 ¢ to 1170.7 ¢
52-mosstep	Minor 52-mosstep	m52ms	40L + 12s	1170.7 ¢ to 1177.4 ¢
	Major 52-mosstep	M52ms	41L + 11s	1177.4 ¢ to 1200.0 ¢
53-mosstep	Perfect 53-mosstep	P53ms	41L + 12s	1200.0 ¢

Scales

• Pythagorean53

Scale tree

Scale tree and tuning spectrum of 41L 12s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
31\53						701.887	498.113	1:1	1.000	Equalized 41L 12s
					179\306	701.961	498.039	6:5	1.200	Pythagorean tuning (701.955c)
				148\253		701.976	498.024	5:4	1.250
					265\453	701.987	498.013	9:7	1.286
			117\200			702.000	498.000	4:3	1.333	Supersoft 41L 12s
					320\547	702.011	497.989	11:8	1.375
				203\347		702.017	497.983	7:5	1.400
					289\494	702.024	497.976	10:7	1.429
		86\147				702.041	497.959	3:2	1.500	Soft 41L 12s
					313\535	702.056	497.944	11:7	1.571
				227\388		702.062	497.938	8:5	1.600
					368\629	702.067	497.933	13:8	1.625
			141\241			702.075	497.925	5:3	1.667	Semisoft 41L 12s
					337\576	702.083	497.917	12:7	1.714
				196\335		702.090	497.910	7:4	1.750
					251\429	702.098	497.902	9:5	1.800
	55\94					702.128	497.872	2:1	2.000	Basic 41L 12s Scales with tunings softer than this are proper Garibaldi / cassandra
					244\417	702.158	497.842	9:4	2.250
				189\323		702.167	497.833	7:3	2.333
					323\552	702.174	497.826	12:5	2.400
			134\229			702.183	497.817	5:2	2.500	Semihard 41L 12s
					347\593	702.192	497.808	13:5	2.600
				213\364		702.198	497.802	8:3	2.667
					292\499	702.204	497.796	11:4	2.750
		79\135				702.222	497.778	3:1	3.000	Hard 41L 12s
					261\446	702.242	497.758	10:3	3.333
				182\311		702.251	497.749	7:2	3.500
					285\487	702.259	497.741	11:3	3.667
			103\176			702.273	497.727	4:1	4.000	Superhard 41L 12s
					230\393	702.290	497.710	9:2	4.500
				127\217		702.304	497.696	5:1	5.000
					151\258	702.326	497.674	6:1	6.000
24\41						702.439	497.561	1:0	→ ∞	Collapsed 41L 12s