7L 12s

7L 12s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 12 small steps, repeating every octave. 7L 12s is a grandchild scale of 5L 2s, expanding it by 12 tones. Generators that produce this scale range from 505.3 ¢ to 514.3 ¢, or from 685.7 ¢ to 694.7 ¢.

↖ 6L 11s	↑ 7L 11s	8L 11s ↗
← 6L 12s	7L 12s	8L 12s →
↙ 6L 13s	↓ 7L 13s	8L 13s ↘

Scale structure
Step pattern	LsLssLssLsLssLssLss ssLssLssLsLssLssLsL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	8\19 to 3\7 (505.3 ¢ to 514.3 ¢)
Dark	4\7 to 11\19 (685.7 ¢ to 694.7 ¢)
TAMNAMS information
Related to	5L 2s (diatonic)
With tunings	1:1 to 3:2 (soft)
Related MOS scales
Parent	7L 5s
Sister	12L 7s
Daughters	19L 7s, 7L 19s
Neutralized	14L 5s
2-Flought	26L 12s, 7L 31s
Equal tunings
Equalized (L:s = 1:1)	8\19 (505.3 ¢)
Supersoft (L:s = 4:3)	27\64 (506.2 ¢)
Soft (L:s = 3:2)	19\45 (506.7 ¢)
Semisoft (L:s = 5:3)	30\71 (507.0 ¢)
Basic (L:s = 2:1)	11\26 (507.7 ¢)
Semihard (L:s = 5:2)	25\59 (508.5 ¢)
Hard (L:s = 3:1)	14\33 (509.1 ¢)
Superhard (L:s = 4:1)	17\40 (510.0 ¢)
Collapsed (L:s = 1:0)	3\7 (514.3 ¢)
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Temperaments associated with this scale include flattone, as the flattone enharmonic scale.

Modes

Modes of 7L 12s

UDP	Cyclic order	Step pattern
18|0	1	LsLssLssLsLssLssLss
17|1	9	LsLssLssLssLsLssLss
16|2	17	LssLsLssLssLsLssLss
15|3	6	LssLsLssLssLssLsLss
14|4	14	LssLssLsLssLssLsLss
13|5	3	LssLssLsLssLssLssLs
12|6	11	LssLssLssLsLssLssLs
11|7	19	sLsLssLssLsLssLssLs
10|8	8	sLsLssLssLssLsLssLs
9|9	16	sLssLsLssLssLsLssLs
8|10	5	sLssLsLssLssLssLsLs
7|11	13	sLssLssLsLssLssLsLs
6|12	2	sLssLssLsLssLssLssL
5|13	10	sLssLssLssLsLssLssL
4|14	18	ssLsLssLssLsLssLssL
3|15	7	ssLsLssLssLssLsLssL
2|16	15	ssLssLsLssLssLsLssL
1|17	4	ssLssLsLssLssLssLsL
0|18	12	ssLssLssLsLssLssLsL

Intervals

Intervals of 7L 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 63.2 ¢
	Major 1-mosstep	M1ms	L	63.2 ¢ to 171.4 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 126.3 ¢
	Major 2-mosstep	M2ms	L + s	126.3 ¢ to 171.4 ¢
3-mosstep	Minor 3-mosstep	m3ms	L + 2s	171.4 ¢ to 189.5 ¢
	Major 3-mosstep	M3ms	2L + s	189.5 ¢ to 342.9 ¢
4-mosstep	Minor 4-mosstep	m4ms	L + 3s	171.4 ¢ to 252.6 ¢
	Major 4-mosstep	M4ms	2L + 2s	252.6 ¢ to 342.9 ¢
5-mosstep	Minor 5-mosstep	m5ms	L + 4s	171.4 ¢ to 315.8 ¢
	Major 5-mosstep	M5ms	2L + 3s	315.8 ¢ to 342.9 ¢
6-mosstep	Minor 6-mosstep	m6ms	2L + 4s	342.9 ¢ to 378.9 ¢
	Major 6-mosstep	M6ms	3L + 3s	378.9 ¢ to 514.3 ¢
7-mosstep	Minor 7-mosstep	m7ms	2L + 5s	342.9 ¢ to 442.1 ¢
	Major 7-mosstep	M7ms	3L + 4s	442.1 ¢ to 514.3 ¢
8-mosstep	Diminished 8-mosstep	d8ms	2L + 6s	342.9 ¢ to 505.3 ¢
	Perfect 8-mosstep	P8ms	3L + 5s	505.3 ¢ to 514.3 ¢
9-mosstep	Minor 9-mosstep	m9ms	3L + 6s	514.3 ¢ to 568.4 ¢
	Major 9-mosstep	M9ms	4L + 5s	568.4 ¢ to 685.7 ¢
10-mosstep	Minor 10-mosstep	m10ms	3L + 7s	514.3 ¢ to 631.6 ¢
	Major 10-mosstep	M10ms	4L + 6s	631.6 ¢ to 685.7 ¢
11-mosstep	Perfect 11-mosstep	P11ms	4L + 7s	685.7 ¢ to 694.7 ¢
	Augmented 11-mosstep	A11ms	5L + 6s	694.7 ¢ to 857.1 ¢
12-mosstep	Minor 12-mosstep	m12ms	4L + 8s	685.7 ¢ to 757.9 ¢
	Major 12-mosstep	M12ms	5L + 7s	757.9 ¢ to 857.1 ¢
13-mosstep	Minor 13-mosstep	m13ms	4L + 9s	685.7 ¢ to 821.1 ¢
	Major 13-mosstep	M13ms	5L + 8s	821.1 ¢ to 857.1 ¢
14-mosstep	Minor 14-mosstep	m14ms	5L + 9s	857.1 ¢ to 884.2 ¢
	Major 14-mosstep	M14ms	6L + 8s	884.2 ¢ to 1028.6 ¢
15-mosstep	Minor 15-mosstep	m15ms	5L + 10s	857.1 ¢ to 947.4 ¢
	Major 15-mosstep	M15ms	6L + 9s	947.4 ¢ to 1028.6 ¢
16-mosstep	Minor 16-mosstep	m16ms	5L + 11s	857.1 ¢ to 1010.5 ¢
	Major 16-mosstep	M16ms	6L + 10s	1010.5 ¢ to 1028.6 ¢
17-mosstep	Minor 17-mosstep	m17ms	6L + 11s	1028.6 ¢ to 1073.7 ¢
	Major 17-mosstep	M17ms	7L + 10s	1073.7 ¢ to 1200.0 ¢
18-mosstep	Minor 18-mosstep	m18ms	6L + 12s	1028.6 ¢ to 1136.8 ¢
	Major 18-mosstep	M18ms	7L + 11s	1136.8 ¢ to 1200.0 ¢
19-mosstep	Perfect 19-mosstep	P19ms	7L + 12s	1200.0 ¢

Scale tree

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details: Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: {{MOS tuning spectrum | 3/2 = Example comment | 4/3 = Another example comment }} The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.

Scale tree and tuning spectrum of 7L 12s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
8\19						505.263	694.737	1:1	1.000	Equalized 7L 12s
					43\102	505.882	694.118	6:5	1.200
				35\83		506.024	693.976	5:4	1.250
					62\147	506.122	693.878	9:7	1.286
			27\64			506.250	693.750	4:3	1.333	Supersoft 7L 12s
					73\173	506.358	693.642	11:8	1.375
				46\109		506.422	693.578	7:5	1.400
					65\154	506.494	693.506	10:7	1.429
		19\45				506.667	693.333	3:2	1.500	Soft 7L 12s
					68\161	506.832	693.168	11:7	1.571
				49\116		506.897	693.103	8:5	1.600
					79\187	506.952	693.048	13:8	1.625
			30\71			507.042	692.958	5:3	1.667	Semisoft 7L 12s
					71\168	507.143	692.857	12:7	1.714
				41\97		507.216	692.784	7:4	1.750
					52\123	507.317	692.683	9:5	1.800
	11\26					507.692	692.308	2:1	2.000	Basic 7L 12s Scales with tunings softer than this are proper
					47\111	508.108	691.892	9:4	2.250
				36\85		508.235	691.765	7:3	2.333
					61\144	508.333	691.667	12:5	2.400
			25\59			508.475	691.525	5:2	2.500	Semihard 7L 12s
					64\151	508.609	691.391	13:5	2.600
				39\92		508.696	691.304	8:3	2.667
					53\125	508.800	691.200	11:4	2.750
		14\33				509.091	690.909	3:1	3.000	Hard 7L 12s
					45\106	509.434	690.566	10:3	3.333
				31\73		509.589	690.411	7:2	3.500
					48\113	509.735	690.265	11:3	3.667
			17\40			510.000	690.000	4:1	4.000	Superhard 7L 12s
					37\87	510.345	689.655	9:2	4.500
				20\47		510.638	689.362	5:1	5.000
					23\54	511.111	688.889	6:1	6.000
3\7						514.286	685.714	1:0	→ ∞	Collapsed 7L 12s