12L 7s

12L 7s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 7 small steps, repeating every octave. 12L 7s is a grandchild scale of 5L 2s, expanding it by 12 tones. Generators that produce this scale range from 694.7 ¢ to 700 ¢, or from 500 ¢ to 505.3 ¢.

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

Scale structure
Step pattern	LLsLLsLLsLsLLsLLsLs sLsLLsLLsLsLLsLLsLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	11\19 to 7\12 (694.7 ¢ to 700.0 ¢)
Dark	5\12 to 8\19 (500.0 ¢ to 505.3 ¢)
TAMNAMS information
Related to	5L 2s (diatonic)
With tunings	3:2 to 2:1 (hyposoft)
Related MOS scales
Parent	7L 5s
Sister	7L 12s
Daughters	19L 12s, 12L 19s
Neutralized	5L 14s
2-Flought	31L 7s, 12L 26s
Equal tunings
Equalized (L:s = 1:1)	11\19 (694.7 ¢)
Supersoft (L:s = 4:3)	40\69 (695.7 ¢)
Soft (L:s = 3:2)	29\50 (696.0 ¢)
Semisoft (L:s = 5:3)	47\81 (696.3 ¢)
Basic (L:s = 2:1)	18\31 (696.8 ¢)
Semihard (L:s = 5:2)	43\74 (697.3 ¢)
Hard (L:s = 3:1)	25\43 (697.7 ¢)
Superhard (L:s = 4:1)	32\55 (698.2 ¢)
Collapsed (L:s = 1:0)	7\12 (700.0 ¢)
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Essentially the entire range of this scale is spanned by various tunings of meantone, as the meantone enharmonic scale.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

Intervals

Intervals of 12L 7s

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 100.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	100.0 ¢ to 126.3 ¢
	Major 2-mosstep	M2ms	2L	126.3 ¢ to 200.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	L + 2s	100.0 ¢ to 189.5 ¢
	Major 3-mosstep	M3ms	2L + s	189.5 ¢ to 200.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	2L + 2s	200.0 ¢ to 252.6 ¢
	Major 4-mosstep	M4ms	3L + s	252.6 ¢ to 300.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	3L + 2s	300.0 ¢ to 315.8 ¢
	Major 5-mosstep	M5ms	4L + s	315.8 ¢ to 400.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	3L + 3s	300.0 ¢ to 378.9 ¢
	Major 6-mosstep	M6ms	4L + 2s	378.9 ¢ to 400.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	4L + 3s	400.0 ¢ to 442.1 ¢
	Major 7-mosstep	M7ms	5L + 2s	442.1 ¢ to 500.0 ¢
8-mosstep	Perfect 8-mosstep	P8ms	5L + 3s	500.0 ¢ to 505.3 ¢
	Augmented 8-mosstep	A8ms	6L + 2s	505.3 ¢ to 600.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	5L + 4s	500.0 ¢ to 568.4 ¢
	Major 9-mosstep	M9ms	6L + 3s	568.4 ¢ to 600.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	6L + 4s	600.0 ¢ to 631.6 ¢
	Major 10-mosstep	M10ms	7L + 3s	631.6 ¢ to 700.0 ¢
11-mosstep	Diminished 11-mosstep	d11ms	6L + 5s	600.0 ¢ to 694.7 ¢
	Perfect 11-mosstep	P11ms	7L + 4s	694.7 ¢ to 700.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	7L + 5s	700.0 ¢ to 757.9 ¢
	Major 12-mosstep	M12ms	8L + 4s	757.9 ¢ to 800.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	8L + 5s	800.0 ¢ to 821.1 ¢
	Major 13-mosstep	M13ms	9L + 4s	821.1 ¢ to 900.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	8L + 6s	800.0 ¢ to 884.2 ¢
	Major 14-mosstep	M14ms	9L + 5s	884.2 ¢ to 900.0 ¢
15-mosstep	Minor 15-mosstep	m15ms	9L + 6s	900.0 ¢ to 947.4 ¢
	Major 15-mosstep	M15ms	10L + 5s	947.4 ¢ to 1000.0 ¢
16-mosstep	Minor 16-mosstep	m16ms	10L + 6s	1000.0 ¢ to 1010.5 ¢
	Major 16-mosstep	M16ms	11L + 5s	1010.5 ¢ to 1100.0 ¢
17-mosstep	Minor 17-mosstep	m17ms	10L + 7s	1000.0 ¢ to 1073.7 ¢
	Major 17-mosstep	M17ms	11L + 6s	1073.7 ¢ to 1100.0 ¢
18-mosstep	Minor 18-mosstep	m18ms	11L + 7s	1100.0 ¢ to 1136.8 ¢
	Major 18-mosstep	M18ms	12L + 6s	1136.8 ¢ to 1200.0 ¢
19-mosstep	Perfect 19-mosstep	P19ms	12L + 7s	1200.0 ¢

Generator chain

Generator chain of 12L 7s

Bright gens	Scale degree	Abbrev.
30	Augmented 7-mosdegree	A7md
29	Augmented 15-mosdegree	A15md
28	Augmented 4-mosdegree	A4md
27	Augmented 12-mosdegree	A12md
26	Augmented 1-mosdegree	A1md
25	Augmented 9-mosdegree	A9md
24	Augmented 17-mosdegree	A17md
23	Augmented 6-mosdegree	A6md
22	Augmented 14-mosdegree	A14md
21	Augmented 3-mosdegree	A3md
20	Augmented 11-mosdegree	A11md
19	Augmented 0-mosdegree	A0md
18	Augmented 8-mosdegree	A8md
17	Major 16-mosdegree	M16md
16	Major 5-mosdegree	M5md
15	Major 13-mosdegree	M13md
14	Major 2-mosdegree	M2md
13	Major 10-mosdegree	M10md
12	Major 18-mosdegree	M18md
11	Major 7-mosdegree	M7md
10	Major 15-mosdegree	M15md
9	Major 4-mosdegree	M4md
8	Major 12-mosdegree	M12md
7	Major 1-mosdegree	M1md
6	Major 9-mosdegree	M9md
5	Major 17-mosdegree	M17md
4	Major 6-mosdegree	M6md
3	Major 14-mosdegree	M14md
2	Major 3-mosdegree	M3md
1	Perfect 11-mosdegree	P11md
0	Perfect 0-mosdegree Perfect 19-mosdegree	P0md P19md
−1	Perfect 8-mosdegree	P8md
−2	Minor 16-mosdegree	m16md
−3	Minor 5-mosdegree	m5md
−4	Minor 13-mosdegree	m13md
−5	Minor 2-mosdegree	m2md
−6	Minor 10-mosdegree	m10md
−7	Minor 18-mosdegree	m18md
−8	Minor 7-mosdegree	m7md
−9	Minor 15-mosdegree	m15md
−10	Minor 4-mosdegree	m4md
−11	Minor 12-mosdegree	m12md
−12	Minor 1-mosdegree	m1md
−13	Minor 9-mosdegree	m9md
−14	Minor 17-mosdegree	m17md
−15	Minor 6-mosdegree	m6md
−16	Minor 14-mosdegree	m14md
−17	Minor 3-mosdegree	m3md
−18	Diminished 11-mosdegree	d11md
−19	Diminished 19-mosdegree	d19md
−20	Diminished 8-mosdegree	d8md
−21	Diminished 16-mosdegree	d16md
−22	Diminished 5-mosdegree	d5md
−23	Diminished 13-mosdegree	d13md
−24	Diminished 2-mosdegree	d2md
−25	Diminished 10-mosdegree	d10md
−26	Diminished 18-mosdegree	d18md
−27	Diminished 7-mosdegree	d7md
−28	Diminished 15-mosdegree	d15md
−29	Diminished 4-mosdegree	d4md
−30	Diminished 12-mosdegree	d12md

Modes

Scale degrees of the modes of 12L 7s

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19
18|0	1	LLsLLsLLsLsLLsLLsLs	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Aug.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.
17|1	12	LLsLLsLsLLsLLsLLsLs	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.
16|2	4	LLsLLsLsLLsLLsLsLLs	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Perf.
15|3	15	LLsLsLLsLLsLLsLsLLs	Perf.	Maj.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Perf.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Perf.
14|4	7	LLsLsLLsLLsLsLLsLLs	Perf.	Maj.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Perf.	Maj.	Maj.	Perf.	Maj.	Min.	Maj.	Maj.	Min.	Maj.	Maj.	Perf.
13|5	18	LsLLsLLsLLsLsLLsLLs	Perf.	Maj.	Min.	Maj.	Maj.	Min.	Maj.	Maj.	Perf.	Maj.	Maj.	Perf.	Maj.	Min.	Maj.	Maj.	Min.	Maj.	Maj.	Perf.
12|6	10	LsLLsLLsLsLLsLLsLLs	Perf.	Maj.	Min.	Maj.	Maj.	Min.	Maj.	Maj.	Perf.	Maj.	Min.	Perf.	Maj.	Min.	Maj.	Maj.	Min.	Maj.	Maj.	Perf.
11|7	2	LsLLsLLsLsLLsLLsLsL	Perf.	Maj.	Min.	Maj.	Maj.	Min.	Maj.	Maj.	Perf.	Maj.	Min.	Perf.	Maj.	Min.	Maj.	Maj.	Min.	Maj.	Min.	Perf.
10|8	13	LsLLsLsLLsLLsLLsLsL	Perf.	Maj.	Min.	Maj.	Maj.	Min.	Maj.	Min.	Perf.	Maj.	Min.	Perf.	Maj.	Min.	Maj.	Maj.	Min.	Maj.	Min.	Perf.
9|9	5	LsLLsLsLLsLLsLsLLsL	Perf.	Maj.	Min.	Maj.	Maj.	Min.	Maj.	Min.	Perf.	Maj.	Min.	Perf.	Maj.	Min.	Maj.	Min.	Min.	Maj.	Min.	Perf.
8|10	16	LsLsLLsLLsLLsLsLLsL	Perf.	Maj.	Min.	Maj.	Min.	Min.	Maj.	Min.	Perf.	Maj.	Min.	Perf.	Maj.	Min.	Maj.	Min.	Min.	Maj.	Min.	Perf.
7|11	8	LsLsLLsLLsLsLLsLLsL	Perf.	Maj.	Min.	Maj.	Min.	Min.	Maj.	Min.	Perf.	Maj.	Min.	Perf.	Min.	Min.	Maj.	Min.	Min.	Maj.	Min.	Perf.
6|12	19	sLLsLLsLLsLsLLsLLsL	Perf.	Min.	Min.	Maj.	Min.	Min.	Maj.	Min.	Perf.	Maj.	Min.	Perf.	Min.	Min.	Maj.	Min.	Min.	Maj.	Min.	Perf.
5|13	11	sLLsLLsLsLLsLLsLLsL	Perf.	Min.	Min.	Maj.	Min.	Min.	Maj.	Min.	Perf.	Min.	Min.	Perf.	Min.	Min.	Maj.	Min.	Min.	Maj.	Min.	Perf.
4|14	3	sLLsLLsLsLLsLLsLsLL	Perf.	Min.	Min.	Maj.	Min.	Min.	Maj.	Min.	Perf.	Min.	Min.	Perf.	Min.	Min.	Maj.	Min.	Min.	Min.	Min.	Perf.
3|15	14	sLLsLsLLsLLsLLsLsLL	Perf.	Min.	Min.	Maj.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Perf.	Min.	Min.	Maj.	Min.	Min.	Min.	Min.	Perf.
2|16	6	sLLsLsLLsLLsLsLLsLL	Perf.	Min.	Min.	Maj.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.
1|17	17	sLsLLsLLsLLsLsLLsLL	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.
0|18	9	sLsLLsLLsLsLLsLLsLL	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Dim.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.

Scale tree

Scale tree and tuning spectrum of 12L 7s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
11\19						694.737	505.263	1:1	1.000	Equalized 12L 7s
					62\107	695.327	504.673	6:5	1.200
				51\88		695.455	504.545	5:4	1.250
					91\157	695.541	504.459	9:7	1.286
			40\69			695.652	504.348	4:3	1.333	Supersoft 12L 7s
					109\188	695.745	504.255	11:8	1.375
				69\119		695.798	504.202	7:5	1.400
					98\169	695.858	504.142	10:7	1.429
		29\50				696.000	504.000	3:2	1.500	Soft 12L 7s
					105\181	696.133	503.867	11:7	1.571
				76\131		696.183	503.817	8:5	1.600
					123\212	696.226	503.774	13:8	1.625	Golden meantone (696.2145¢);
			47\81			696.296	503.704	5:3	1.667	Semisoft 12L 7s Meantone / meanpop;
					112\193	696.373	503.627	12:7	1.714
				65\112		696.429	503.571	7:4	1.750
					83\143	696.503	503.497	9:5	1.800
	18\31					696.774	503.226	2:1	2.000	Basic 12L 7s Scales with tunings softer than this are proper
					79\136	697.059	502.941	9:4	2.250
				61\105		697.143	502.857	7:3	2.333	Meantone / huygens;
					104\179	697.207	502.793	12:5	2.400
			43\74			697.297	502.703	5:2	2.500	Semihard 12L 7s Meantone / huygens / grosstone;
					111\191	697.382	502.618	13:5	2.600	Golden grosstone (697.3969¢);
				68\117		697.436	502.564	8:3	2.667
					93\160	697.500	502.500	11:4	2.750
		25\43				697.674	502.326	3:1	3.000	Hard 12L 7s Meantone / meridetone
					82\141	697.872	502.128	10:3	3.333
				57\98		697.959	502.041	7:2	3.500
					89\153	698.039	501.961	11:3	3.667
			32\55			698.182	501.818	4:1	4.000	Superhard 12L 7s
					71\122	698.361	501.639	9:2	4.500
				39\67		698.507	501.493	5:1	5.000
					46\79	698.734	501.266	6:1	6.000
7\12						700.000	500.000	1:0	→ ∞	Collapsed 12L 7s