11L 9s

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← 10L 9s	11L 9s	12L 9s →
↙ 10L 10s	↓ 11L 10s	12L 10s ↘

Scale structure
Step pattern	LLsLsLsLsLLsLsLsLsLs sLsLsLsLsLLsLsLsLsLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	9\20 to 5\11 (540.0 ¢ to 545.5 ¢)
Dark	6\11 to 11\20 (654.5 ¢ to 660.0 ¢)
TAMNAMS information
Related to	2L 7s (balzano)
With tunings	3:2 to 2:1 (hyposoft)
Related MOS scales
Parent	9L 2s
Sister	9L 11s
Daughters	20L 11s, 11L 20s
Neutralized	2L 18s
2-Flought	31L 9s, 11L 29s
Equal tunings
Equalized (L:s = 1:1)	9\20 (540.0 ¢)
Supersoft (L:s = 4:3)	32\71 (540.8 ¢)
Soft (L:s = 3:2)	23\51 (541.2 ¢)
Semisoft (L:s = 5:3)	37\82 (541.5 ¢)
Basic (L:s = 2:1)	14\31 (541.9 ¢)
Semihard (L:s = 5:2)	33\73 (542.5 ¢)
Hard (L:s = 3:1)	19\42 (542.9 ¢)
Superhard (L:s = 4:1)	24\53 (543.4 ¢)
Collapsed (L:s = 1:0)	5\11 (545.5 ¢)
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11L 9s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 11 large steps and 9 small steps, repeating every octave. 11L 9s is a grandchild scale of 2L 7s, expanding it by 11 tones. Generators that produce this scale range from 540 ¢ to 545.5 ¢, or from 654.5 ¢ to 660 ¢.

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 11L 9s

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 60.0 ¢
	Major 1-mosstep	M1ms	L	60.0 ¢ to 109.1 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	109.1 ¢ to 120.0 ¢
	Major 2-mosstep	M2ms	2L	120.0 ¢ to 218.2 ¢
3-mosstep	Minor 3-mosstep	m3ms	L + 2s	109.1 ¢ to 180.0 ¢
	Major 3-mosstep	M3ms	2L + s	180.0 ¢ to 218.2 ¢
4-mosstep	Minor 4-mosstep	m4ms	2L + 2s	218.2 ¢ to 240.0 ¢
	Major 4-mosstep	M4ms	3L + s	240.0 ¢ to 327.3 ¢
5-mosstep	Minor 5-mosstep	m5ms	2L + 3s	218.2 ¢ to 300.0 ¢
	Major 5-mosstep	M5ms	3L + 2s	300.0 ¢ to 327.3 ¢
6-mosstep	Minor 6-mosstep	m6ms	3L + 3s	327.3 ¢ to 360.0 ¢
	Major 6-mosstep	M6ms	4L + 2s	360.0 ¢ to 436.4 ¢
7-mosstep	Minor 7-mosstep	m7ms	3L + 4s	327.3 ¢ to 420.0 ¢
	Major 7-mosstep	M7ms	4L + 3s	420.0 ¢ to 436.4 ¢
8-mosstep	Minor 8-mosstep	m8ms	4L + 4s	436.4 ¢ to 480.0 ¢
	Major 8-mosstep	M8ms	5L + 3s	480.0 ¢ to 545.5 ¢
9-mosstep	Diminished 9-mosstep	d9ms	4L + 5s	436.4 ¢ to 540.0 ¢
	Perfect 9-mosstep	P9ms	5L + 4s	540.0 ¢ to 545.5 ¢
10-mosstep	Minor 10-mosstep	m10ms	5L + 5s	545.5 ¢ to 600.0 ¢
	Major 10-mosstep	M10ms	6L + 4s	600.0 ¢ to 654.5 ¢
11-mosstep	Perfect 11-mosstep	P11ms	6L + 5s	654.5 ¢ to 660.0 ¢
	Augmented 11-mosstep	A11ms	7L + 4s	660.0 ¢ to 763.6 ¢
12-mosstep	Minor 12-mosstep	m12ms	6L + 6s	654.5 ¢ to 720.0 ¢
	Major 12-mosstep	M12ms	7L + 5s	720.0 ¢ to 763.6 ¢
13-mosstep	Minor 13-mosstep	m13ms	7L + 6s	763.6 ¢ to 780.0 ¢
	Major 13-mosstep	M13ms	8L + 5s	780.0 ¢ to 872.7 ¢
14-mosstep	Minor 14-mosstep	m14ms	7L + 7s	763.6 ¢ to 840.0 ¢
	Major 14-mosstep	M14ms	8L + 6s	840.0 ¢ to 872.7 ¢
15-mosstep	Minor 15-mosstep	m15ms	8L + 7s	872.7 ¢ to 900.0 ¢
	Major 15-mosstep	M15ms	9L + 6s	900.0 ¢ to 981.8 ¢
16-mosstep	Minor 16-mosstep	m16ms	8L + 8s	872.7 ¢ to 960.0 ¢
	Major 16-mosstep	M16ms	9L + 7s	960.0 ¢ to 981.8 ¢
17-mosstep	Minor 17-mosstep	m17ms	9L + 8s	981.8 ¢ to 1020.0 ¢
	Major 17-mosstep	M17ms	10L + 7s	1020.0 ¢ to 1090.9 ¢
18-mosstep	Minor 18-mosstep	m18ms	9L + 9s	981.8 ¢ to 1080.0 ¢
	Major 18-mosstep	M18ms	10L + 8s	1080.0 ¢ to 1090.9 ¢
19-mosstep	Minor 19-mosstep	m19ms	10L + 9s	1090.9 ¢ to 1140.0 ¢
	Major 19-mosstep	M19ms	11L + 8s	1140.0 ¢ to 1200.0 ¢
20-mosstep	Perfect 20-mosstep	P20ms	11L + 9s	1200.0 ¢

Generator chain

Generator chain of 11L 9s

Bright gens	Scale degree	Abbrev.
30	Augmented 10-mosdegree	A10md
29	Augmented 1-mosdegree	A1md
28	Augmented 12-mosdegree	A12md
27	Augmented 3-mosdegree	A3md
26	Augmented 14-mosdegree	A14md
25	Augmented 5-mosdegree	A5md
24	Augmented 16-mosdegree	A16md
23	Augmented 7-mosdegree	A7md
22	Augmented 18-mosdegree	A18md
21	Augmented 9-mosdegree	A9md
20	Augmented 0-mosdegree	A0md
19	Augmented 11-mosdegree	A11md
18	Major 2-mosdegree	M2md
17	Major 13-mosdegree	M13md
16	Major 4-mosdegree	M4md
15	Major 15-mosdegree	M15md
14	Major 6-mosdegree	M6md
13	Major 17-mosdegree	M17md
12	Major 8-mosdegree	M8md
11	Major 19-mosdegree	M19md
10	Major 10-mosdegree	M10md
9	Major 1-mosdegree	M1md
8	Major 12-mosdegree	M12md
7	Major 3-mosdegree	M3md
6	Major 14-mosdegree	M14md
5	Major 5-mosdegree	M5md
4	Major 16-mosdegree	M16md
3	Major 7-mosdegree	M7md
2	Major 18-mosdegree	M18md
1	Perfect 9-mosdegree	P9md
0	Perfect 0-mosdegree Perfect 20-mosdegree	P0md P20md
−1	Perfect 11-mosdegree	P11md
−2	Minor 2-mosdegree	m2md
−3	Minor 13-mosdegree	m13md
−4	Minor 4-mosdegree	m4md
−5	Minor 15-mosdegree	m15md
−6	Minor 6-mosdegree	m6md
−7	Minor 17-mosdegree	m17md
−8	Minor 8-mosdegree	m8md
−9	Minor 19-mosdegree	m19md
−10	Minor 10-mosdegree	m10md
−11	Minor 1-mosdegree	m1md
−12	Minor 12-mosdegree	m12md
−13	Minor 3-mosdegree	m3md
−14	Minor 14-mosdegree	m14md
−15	Minor 5-mosdegree	m5md
−16	Minor 16-mosdegree	m16md
−17	Minor 7-mosdegree	m7md
−18	Minor 18-mosdegree	m18md
−19	Diminished 9-mosdegree	d9md
−20	Diminished 20-mosdegree	d20md
−21	Diminished 11-mosdegree	d11md
−22	Diminished 2-mosdegree	d2md
−23	Diminished 13-mosdegree	d13md
−24	Diminished 4-mosdegree	d4md
−25	Diminished 15-mosdegree	d15md
−26	Diminished 6-mosdegree	d6md
−27	Diminished 17-mosdegree	d17md
−28	Diminished 8-mosdegree	d8md
−29	Diminished 19-mosdegree	d19md
−30	Diminished 10-mosdegree	d10md

Modes

Scale degrees of the modes of 11L 9s

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	20
19|0	1	LLsLsLsLsLLsLsLsLsLs	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Aug.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.
18|1	10	LLsLsLsLsLsLLsLsLsLs	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.
17|2	19	LsLLsLsLsLsLLsLsLsLs	Perf.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.
16|3	8	LsLLsLsLsLsLsLLsLsLs	Perf.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Perf.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.
15|4	17	LsLsLLsLsLsLsLLsLsLs	Perf.	Maj.	Min.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Perf.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.
14|5	6	LsLsLLsLsLsLsLsLLsLs	Perf.	Maj.	Min.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Perf.	Maj.	Min.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Perf.
13|6	15	LsLsLsLLsLsLsLsLLsLs	Perf.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Maj.	Perf.	Maj.	Perf.	Maj.	Min.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Perf.
12|7	4	LsLsLsLLsLsLsLsLsLLs	Perf.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Maj.	Perf.	Maj.	Perf.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Maj.	Perf.
11|8	13	LsLsLsLsLLsLsLsLsLLs	Perf.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Perf.	Maj.	Perf.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Maj.	Perf.
10|9	2	LsLsLsLsLLsLsLsLsLsL	Perf.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Perf.	Maj.	Perf.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Perf.
9|10	11	LsLsLsLsLsLLsLsLsLsL	Perf.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Perf.	Min.	Perf.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Perf.
8|11	20	sLLsLsLsLsLLsLsLsLsL	Perf.	Min.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Perf.	Min.	Perf.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Perf.
7|12	9	sLLsLsLsLsLsLLsLsLsL	Perf.	Min.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Perf.	Min.	Perf.	Min.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Perf.
6|13	18	sLsLLsLsLsLsLLsLsLsL	Perf.	Min.	Min.	Min.	Min.	Maj.	Min.	Maj.	Min.	Perf.	Min.	Perf.	Min.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Perf.
5|14	7	sLsLLsLsLsLsLsLLsLsL	Perf.	Min.	Min.	Min.	Min.	Maj.	Min.	Maj.	Min.	Perf.	Min.	Perf.	Min.	Min.	Min.	Min.	Maj.	Min.	Maj.	Min.	Perf.
4|15	16	sLsLsLLsLsLsLsLLsLsL	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Maj.	Min.	Perf.	Min.	Perf.	Min.	Min.	Min.	Min.	Maj.	Min.	Maj.	Min.	Perf.
3|16	5	sLsLsLLsLsLsLsLsLLsL	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Maj.	Min.	Perf.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Maj.	Min.	Perf.
2|17	14	sLsLsLsLLsLsLsLsLLsL	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Maj.	Min.	Perf.
1|18	3	sLsLsLsLLsLsLsLsLsLL	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.
0|19	12	sLsLsLsLsLLsLsLsLsLL	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Dim.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.

Scale tree

Scale tree and tuning spectrum of 11L 9s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
9\20						540.000	660.000	1:1	1.000	Equalized 11L 9s
					50\111	540.541	659.459	6:5	1.200
				41\91		540.659	659.341	5:4	1.250
					73\162	540.741	659.259	9:7	1.286
			32\71			540.845	659.155	4:3	1.333	Supersoft 11L 9s
					87\193	540.933	659.067	11:8	1.375
				55\122		540.984	659.016	7:5	1.400
					78\173	541.040	658.960	10:7	1.429
		23\51				541.176	658.824	3:2	1.500	Soft 11L 9s
					83\184	541.304	658.696	11:7	1.571
				60\133		541.353	658.647	8:5	1.600
					97\215	541.395	658.605	13:8	1.625
			37\82			541.463	658.537	5:3	1.667	Semisoft 11L 9s
					88\195	541.538	658.462	12:7	1.714
				51\113		541.593	658.407	7:4	1.750
					65\144	541.667	658.333	9:5	1.800
	14\31					541.935	658.065	2:1	2.000	Basic 11L 9s Scales with tunings softer than this are proper
					61\135	542.222	657.778	9:4	2.250
				47\104		542.308	657.692	7:3	2.333
					80\177	542.373	657.627	12:5	2.400
			33\73			542.466	657.534	5:2	2.500	Semihard 11L 9s
					85\188	542.553	657.447	13:5	2.600
				52\115		542.609	657.391	8:3	2.667
					71\157	542.675	657.325	11:4	2.750
		19\42				542.857	657.143	3:1	3.000	Hard 11L 9s
					62\137	543.066	656.934	10:3	3.333
				43\95		543.158	656.842	7:2	3.500
					67\148	543.243	656.757	11:3	3.667
			24\53			543.396	656.604	4:1	4.000	Superhard 11L 9s
					53\117	543.590	656.410	9:2	4.500
				29\64		543.750	656.250	5:1	5.000
					34\75	544.000	656.000	6:1	6.000
5\11						545.455	654.545	1:0	→ ∞	Collapsed 11L 9s

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