12L 29s

12L 29s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 29 small steps, repeating every octave. 12L 29s is related to 5L 2s, expanding it by 34 tones. Generators that produce this scale range from 497.6 ¢ to 500 ¢, or from 700 ¢ to 702.4 ¢. Its chroma-positive generator is an almost-perfect fourth, where large step is identified with the 29-comma and the small step is identified with the pythagorean comma. Pythagorean tuning generates this scale, with a hardness of 1.8459. This mos is often associated with schismic temperaments and other accurate fifth-based temperaments. It is known as pythamystonic in TAMNAMS Extension.

↖ 11L 28s	↑ 12L 28s	13L 28s ↗
← 11L 29s	12L 29s	13L 29s →
↙ 11L 30s	↓ 12L 30s	13L 30s ↘

Scale structure
Step pattern	...41 steps...
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	17\41 to 5\12 (497.6 ¢ to 500.0 ¢)
Dark	7\12 to 24\41 (700.0 ¢ to 702.4 ¢)
TAMNAMS information
Related to	5L 2s (diatonic)
With tunings	2:1 to 7:3
Related MOS scales
Parent	12L 17s
Sister	29L 12s
Daughters	41L 12s, 12L 41s
Neutralized	24L 17s
2-Flought	53L 29s, 12L 70s
Equal tunings
Equalized (L:s = 1:1)	17\41 (497.6 ¢)
Supersoft (L:s = 4:3)	56\135 (497.8 ¢)
Soft (L:s = 3:2)	39\94 (497.9 ¢)
Semisoft (L:s = 5:3)	61\147 (498.0 ¢)
Basic (L:s = 2:1)	22\53 (498.1 ¢)
Semihard (L:s = 5:2)	49\118 (498.3 ¢)
Hard (L:s = 3:1)	27\65 (498.5 ¢)
Superhard (L:s = 4:1)	32\77 (498.7 ¢)
Collapsed (L:s = 1:0)	5\12 (500.0 ¢)
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Intervals

Intervals of 12L 29s

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 100.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 58.5 ¢
	Major 2-mosstep	M2ms	L + s	58.5 ¢ to 100.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0 ¢ to 87.8 ¢
	Major 3-mosstep	M3ms	L + 2s	87.8 ¢ to 100.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	L + 3s	100.0 ¢ to 117.1 ¢
	Major 4-mosstep	M4ms	2L + 2s	117.1 ¢ to 200.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	L + 4s	100.0 ¢ to 146.3 ¢
	Major 5-mosstep	M5ms	2L + 3s	146.3 ¢ to 200.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	L + 5s	100.0 ¢ to 175.6 ¢
	Major 6-mosstep	M6ms	2L + 4s	175.6 ¢ to 200.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	2L + 5s	200.0 ¢ to 204.9 ¢
	Major 7-mosstep	M7ms	3L + 4s	204.9 ¢ to 300.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	2L + 6s	200.0 ¢ to 234.1 ¢
	Major 8-mosstep	M8ms	3L + 5s	234.1 ¢ to 300.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	2L + 7s	200.0 ¢ to 263.4 ¢
	Major 9-mosstep	M9ms	3L + 6s	263.4 ¢ to 300.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	2L + 8s	200.0 ¢ to 292.7 ¢
	Major 10-mosstep	M10ms	3L + 7s	292.7 ¢ to 300.0 ¢
11-mosstep	Minor 11-mosstep	m11ms	3L + 8s	300.0 ¢ to 322.0 ¢
	Major 11-mosstep	M11ms	4L + 7s	322.0 ¢ to 400.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	3L + 9s	300.0 ¢ to 351.2 ¢
	Major 12-mosstep	M12ms	4L + 8s	351.2 ¢ to 400.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	3L + 10s	300.0 ¢ to 380.5 ¢
	Major 13-mosstep	M13ms	4L + 9s	380.5 ¢ to 400.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	4L + 10s	400.0 ¢ to 409.8 ¢
	Major 14-mosstep	M14ms	5L + 9s	409.8 ¢ to 500.0 ¢
15-mosstep	Minor 15-mosstep	m15ms	4L + 11s	400.0 ¢ to 439.0 ¢
	Major 15-mosstep	M15ms	5L + 10s	439.0 ¢ to 500.0 ¢
16-mosstep	Minor 16-mosstep	m16ms	4L + 12s	400.0 ¢ to 468.3 ¢
	Major 16-mosstep	M16ms	5L + 11s	468.3 ¢ to 500.0 ¢
17-mosstep	Diminished 17-mosstep	d17ms	4L + 13s	400.0 ¢ to 497.6 ¢
	Perfect 17-mosstep	P17ms	5L + 12s	497.6 ¢ to 500.0 ¢
18-mosstep	Minor 18-mosstep	m18ms	5L + 13s	500.0 ¢ to 526.8 ¢
	Major 18-mosstep	M18ms	6L + 12s	526.8 ¢ to 600.0 ¢
19-mosstep	Minor 19-mosstep	m19ms	5L + 14s	500.0 ¢ to 556.1 ¢
	Major 19-mosstep	M19ms	6L + 13s	556.1 ¢ to 600.0 ¢
20-mosstep	Minor 20-mosstep	m20ms	5L + 15s	500.0 ¢ to 585.4 ¢
	Major 20-mosstep	M20ms	6L + 14s	585.4 ¢ to 600.0 ¢
21-mosstep	Minor 21-mosstep	m21ms	6L + 15s	600.0 ¢ to 614.6 ¢
	Major 21-mosstep	M21ms	7L + 14s	614.6 ¢ to 700.0 ¢
22-mosstep	Minor 22-mosstep	m22ms	6L + 16s	600.0 ¢ to 643.9 ¢
	Major 22-mosstep	M22ms	7L + 15s	643.9 ¢ to 700.0 ¢
23-mosstep	Minor 23-mosstep	m23ms	6L + 17s	600.0 ¢ to 673.2 ¢
	Major 23-mosstep	M23ms	7L + 16s	673.2 ¢ to 700.0 ¢
24-mosstep	Perfect 24-mosstep	P24ms	7L + 17s	700.0 ¢ to 702.4 ¢
	Augmented 24-mosstep	A24ms	8L + 16s	702.4 ¢ to 800.0 ¢
25-mosstep	Minor 25-mosstep	m25ms	7L + 18s	700.0 ¢ to 731.7 ¢
	Major 25-mosstep	M25ms	8L + 17s	731.7 ¢ to 800.0 ¢
26-mosstep	Minor 26-mosstep	m26ms	7L + 19s	700.0 ¢ to 761.0 ¢
	Major 26-mosstep	M26ms	8L + 18s	761.0 ¢ to 800.0 ¢
27-mosstep	Minor 27-mosstep	m27ms	7L + 20s	700.0 ¢ to 790.2 ¢
	Major 27-mosstep	M27ms	8L + 19s	790.2 ¢ to 800.0 ¢
28-mosstep	Minor 28-mosstep	m28ms	8L + 20s	800.0 ¢ to 819.5 ¢
	Major 28-mosstep	M28ms	9L + 19s	819.5 ¢ to 900.0 ¢
29-mosstep	Minor 29-mosstep	m29ms	8L + 21s	800.0 ¢ to 848.8 ¢
	Major 29-mosstep	M29ms	9L + 20s	848.8 ¢ to 900.0 ¢
30-mosstep	Minor 30-mosstep	m30ms	8L + 22s	800.0 ¢ to 878.0 ¢
	Major 30-mosstep	M30ms	9L + 21s	878.0 ¢ to 900.0 ¢
31-mosstep	Minor 31-mosstep	m31ms	9L + 22s	900.0 ¢ to 907.3 ¢
	Major 31-mosstep	M31ms	10L + 21s	907.3 ¢ to 1000.0 ¢
32-mosstep	Minor 32-mosstep	m32ms	9L + 23s	900.0 ¢ to 936.6 ¢
	Major 32-mosstep	M32ms	10L + 22s	936.6 ¢ to 1000.0 ¢
33-mosstep	Minor 33-mosstep	m33ms	9L + 24s	900.0 ¢ to 965.9 ¢
	Major 33-mosstep	M33ms	10L + 23s	965.9 ¢ to 1000.0 ¢
34-mosstep	Minor 34-mosstep	m34ms	9L + 25s	900.0 ¢ to 995.1 ¢
	Major 34-mosstep	M34ms	10L + 24s	995.1 ¢ to 1000.0 ¢
35-mosstep	Minor 35-mosstep	m35ms	10L + 25s	1000.0 ¢ to 1024.4 ¢
	Major 35-mosstep	M35ms	11L + 24s	1024.4 ¢ to 1100.0 ¢
36-mosstep	Minor 36-mosstep	m36ms	10L + 26s	1000.0 ¢ to 1053.7 ¢
	Major 36-mosstep	M36ms	11L + 25s	1053.7 ¢ to 1100.0 ¢
37-mosstep	Minor 37-mosstep	m37ms	10L + 27s	1000.0 ¢ to 1082.9 ¢
	Major 37-mosstep	M37ms	11L + 26s	1082.9 ¢ to 1100.0 ¢
38-mosstep	Minor 38-mosstep	m38ms	11L + 27s	1100.0 ¢ to 1112.2 ¢
	Major 38-mosstep	M38ms	12L + 26s	1112.2 ¢ to 1200.0 ¢
39-mosstep	Minor 39-mosstep	m39ms	11L + 28s	1100.0 ¢ to 1141.5 ¢
	Major 39-mosstep	M39ms	12L + 27s	1141.5 ¢ to 1200.0 ¢
40-mosstep	Minor 40-mosstep	m40ms	11L + 29s	1100.0 ¢ to 1170.7 ¢
	Major 40-mosstep	M40ms	12L + 28s	1170.7 ¢ to 1200.0 ¢
41-mosstep	Perfect 41-mosstep	P41ms	12L + 29s	1200.0 ¢

Scales

• Pythagorean41

Scale tree

Scale tree and tuning spectrum of 12L 29s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
17\41						497.561	702.439	1:1	1.000	Equalized 12L 29s
					90\217	497.696	702.304	6:5	1.200	Cotoneum
				73\176		497.727	702.273	5:4	1.250
					129\311	497.749	702.251	9:7	1.286
			56\135			497.778	702.222	4:3	1.333	Supersoft 12L 29s Gary
					151\364	497.802	702.198	11:8	1.375
				95\229		497.817	702.183	7:5	1.400
					134\323	497.833	702.167	10:7	1.429
		39\94				497.872	702.128	3:2	1.500	Soft 12L 29s Garibaldi / cassandra
					139\335	497.910	702.090	11:7	1.571
				100\241		497.925	702.075	8:5	1.600
					161\388	497.938	702.062	13:8	1.625
			61\147			497.959	702.041	5:3	1.667	Semisoft 12L 29s
					144\347	497.983	702.017	12:7	1.714
				83\200		498.000	702.000	7:4	1.750
					105\253	498.024	701.976	9:5	1.800	Pythagorean tuning (701.955 ¢)
	22\53					498.113	701.887	2:1	2.000	Basic 12L 29s Scales with tunings softer than this are proper
					93\224	498.214	701.786	9:4	2.250	Ponta
				71\171		498.246	701.754	7:3	2.333	Pontiac
					120\289	498.270	701.730	12:5	2.400	Helmholtz
			49\118			498.305	701.695	5:2	2.500	Semihard 12L 29s
					125\301	498.339	701.661	13:5	2.600
				76\183		498.361	701.639	8:3	2.667
					103\248	498.387	701.613	11:4	2.750
		27\65				498.462	701.538	3:1	3.000	Hard 12L 29s
					86\207	498.551	701.449	10:3	3.333
				59\142		498.592	701.408	7:2	3.500
					91\219	498.630	701.370	11:3	3.667
			32\77			498.701	701.299	4:1	4.000	Superhard 12L 29s Grackle
					69\166	498.795	701.205	9:2	4.500
				37\89		498.876	701.124	5:1	5.000
					42\101	499.010	700.990	6:1	6.000	↓ Gracecordial
5\12						500.000	700.000	1:0	→ ∞	Collapsed 12L 29s