11L 5s

↖ 10L 4s	↑ 11L 4s	12L 4s ↗
← 10L 5s	11L 5s	12L 5s →
↙ 10L 6s	↓ 11L 6s	12L 6s ↘

Scale structure
Step pattern	LLLsLLsLLsLLsLLs sLLsLLsLLsLLsLLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	13\16 to 9\11 (975.0 ¢ to 981.8 ¢)
Dark	2\11 to 3\16 (218.2 ¢ to 225.0 ¢)
TAMNAMS information
Related to	5L 1s (machinoid)
With tunings	2:1 to 3:1 (hypohard)
Related MOS scales
Parent	5L 6s
Sister	5L 11s
Daughters	16L 11s, 11L 16s
Neutralized	6L 10s
2-Flought	27L 5s, 11L 21s
Equal tunings
Equalized (L:s = 1:1)	13\16 (975.0 ¢)
Supersoft (L:s = 4:3)	48\59 (976.3 ¢)
Soft (L:s = 3:2)	35\43 (976.7 ¢)
Semisoft (L:s = 5:3)	57\70 (977.1 ¢)
Basic (L:s = 2:1)	22\27 (977.8 ¢)
Semihard (L:s = 5:2)	53\65 (978.5 ¢)
Hard (L:s = 3:1)	31\38 (978.9 ¢)
Superhard (L:s = 4:1)	40\49 (979.6 ¢)
Collapsed (L:s = 1:0)	9\11 (981.8 ¢)
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11L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 11 large steps and 5 small steps, repeating every octave. 11L 5s is a grandchild scale of 5L 1s, expanding it by 10 tones. Generators that produce this scale range from 975 ¢ to 981.8 ¢, or from 218.2 ¢ to 225 ¢.

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 5s

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 75.0 ¢
	Major 1-mosstep	M1ms	L	75.0 ¢ to 109.1 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	109.1 ¢ to 150.0 ¢
	Major 2-mosstep	M2ms	2L	150.0 ¢ to 218.2 ¢
3-mosstep	Perfect 3-mosstep	P3ms	2L + s	218.2 ¢ to 225.0 ¢
	Augmented 3-mosstep	A3ms	3L	225.0 ¢ to 327.3 ¢
4-mosstep	Minor 4-mosstep	m4ms	2L + 2s	218.2 ¢ to 300.0 ¢
	Major 4-mosstep	M4ms	3L + s	300.0 ¢ to 327.3 ¢
5-mosstep	Minor 5-mosstep	m5ms	3L + 2s	327.3 ¢ to 375.0 ¢
	Major 5-mosstep	M5ms	4L + s	375.0 ¢ to 436.4 ¢
6-mosstep	Minor 6-mosstep	m6ms	4L + 2s	436.4 ¢ to 450.0 ¢
	Major 6-mosstep	M6ms	5L + s	450.0 ¢ to 545.5 ¢
7-mosstep	Minor 7-mosstep	m7ms	4L + 3s	436.4 ¢ to 525.0 ¢
	Major 7-mosstep	M7ms	5L + 2s	525.0 ¢ to 545.5 ¢
8-mosstep	Minor 8-mosstep	m8ms	5L + 3s	545.5 ¢ to 600.0 ¢
	Major 8-mosstep	M8ms	6L + 2s	600.0 ¢ to 654.5 ¢
9-mosstep	Minor 9-mosstep	m9ms	6L + 3s	654.5 ¢ to 675.0 ¢
	Major 9-mosstep	M9ms	7L + 2s	675.0 ¢ to 763.6 ¢
10-mosstep	Minor 10-mosstep	m10ms	6L + 4s	654.5 ¢ to 750.0 ¢
	Major 10-mosstep	M10ms	7L + 3s	750.0 ¢ to 763.6 ¢
11-mosstep	Minor 11-mosstep	m11ms	7L + 4s	763.6 ¢ to 825.0 ¢
	Major 11-mosstep	M11ms	8L + 3s	825.0 ¢ to 872.7 ¢
12-mosstep	Minor 12-mosstep	m12ms	8L + 4s	872.7 ¢ to 900.0 ¢
	Major 12-mosstep	M12ms	9L + 3s	900.0 ¢ to 981.8 ¢
13-mosstep	Diminished 13-mosstep	d13ms	8L + 5s	872.7 ¢ to 975.0 ¢
	Perfect 13-mosstep	P13ms	9L + 4s	975.0 ¢ to 981.8 ¢
14-mosstep	Minor 14-mosstep	m14ms	9L + 5s	981.8 ¢ to 1050.0 ¢
	Major 14-mosstep	M14ms	10L + 4s	1050.0 ¢ to 1090.9 ¢
15-mosstep	Minor 15-mosstep	m15ms	10L + 5s	1090.9 ¢ to 1125.0 ¢
	Major 15-mosstep	M15ms	11L + 4s	1125.0 ¢ to 1200.0 ¢
16-mosstep	Perfect 16-mosstep	P16ms	11L + 5s	1200.0 ¢

Generator chain

Generator chain of 11L 5s

Bright gens	Scale degree	Abbrev.
26	Augmented 2-mosdegree	A2md
25	Augmented 5-mosdegree	A5md
24	Augmented 8-mosdegree	A8md
23	Augmented 11-mosdegree	A11md
22	Augmented 14-mosdegree	A14md
21	Augmented 1-mosdegree	A1md
20	Augmented 4-mosdegree	A4md
19	Augmented 7-mosdegree	A7md
18	Augmented 10-mosdegree	A10md
17	Augmented 13-mosdegree	A13md
16	Augmented 0-mosdegree	A0md
15	Augmented 3-mosdegree	A3md
14	Major 6-mosdegree	M6md
13	Major 9-mosdegree	M9md
12	Major 12-mosdegree	M12md
11	Major 15-mosdegree	M15md
10	Major 2-mosdegree	M2md
9	Major 5-mosdegree	M5md
8	Major 8-mosdegree	M8md
7	Major 11-mosdegree	M11md
6	Major 14-mosdegree	M14md
5	Major 1-mosdegree	M1md
4	Major 4-mosdegree	M4md
3	Major 7-mosdegree	M7md
2	Major 10-mosdegree	M10md
1	Perfect 13-mosdegree	P13md
0	Perfect 0-mosdegree Perfect 16-mosdegree	P0md P16md
−1	Perfect 3-mosdegree	P3md
−2	Minor 6-mosdegree	m6md
−3	Minor 9-mosdegree	m9md
−4	Minor 12-mosdegree	m12md
−5	Minor 15-mosdegree	m15md
−6	Minor 2-mosdegree	m2md
−7	Minor 5-mosdegree	m5md
−8	Minor 8-mosdegree	m8md
−9	Minor 11-mosdegree	m11md
−10	Minor 14-mosdegree	m14md
−11	Minor 1-mosdegree	m1md
−12	Minor 4-mosdegree	m4md
−13	Minor 7-mosdegree	m7md
−14	Minor 10-mosdegree	m10md
−15	Diminished 13-mosdegree	d13md
−16	Diminished 16-mosdegree	d16md
−17	Diminished 3-mosdegree	d3md
−18	Diminished 6-mosdegree	d6md
−19	Diminished 9-mosdegree	d9md
−20	Diminished 12-mosdegree	d12md
−21	Diminished 15-mosdegree	d15md
−22	Diminished 2-mosdegree	d2md
−23	Diminished 5-mosdegree	d5md
−24	Diminished 8-mosdegree	d8md
−25	Diminished 11-mosdegree	d11md
−26	Diminished 14-mosdegree	d14md

Modes

Scale degrees of the modes of 11L 5s

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
15|0	1	LLLsLLsLLsLLsLLs	Perf.	Maj.	Maj.	Aug.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Perf.
14|1	14	LLsLLLsLLsLLsLLs	Perf.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Perf.
13|2	11	LLsLLsLLLsLLsLLs	Perf.	Maj.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Perf.
12|3	8	LLsLLsLLsLLLsLLs	Perf.	Maj.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Perf.
11|4	5	LLsLLsLLsLLsLLLs	Perf.	Maj.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Perf.
10|5	2	LLsLLsLLsLLsLLsL	Perf.	Maj.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Perf.	Maj.	Min.	Perf.
9|6	15	LsLLLsLLsLLsLLsL	Perf.	Maj.	Min.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Perf.	Maj.	Min.	Perf.
8|7	12	LsLLsLLLsLLsLLsL	Perf.	Maj.	Min.	Perf.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Perf.	Maj.	Min.	Perf.
7|8	9	LsLLsLLsLLLsLLsL	Perf.	Maj.	Min.	Perf.	Maj.	Min.	Min.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Perf.	Maj.	Min.	Perf.
6|9	6	LsLLsLLsLLsLLLsL	Perf.	Maj.	Min.	Perf.	Maj.	Min.	Min.	Maj.	Min.	Min.	Maj.	Min.	Min.	Perf.	Maj.	Min.	Perf.
5|10	3	LsLLsLLsLLsLLsLL	Perf.	Maj.	Min.	Perf.	Maj.	Min.	Min.	Maj.	Min.	Min.	Maj.	Min.	Min.	Perf.	Min.	Min.	Perf.
4|11	16	sLLLsLLsLLsLLsLL	Perf.	Min.	Min.	Perf.	Maj.	Min.	Min.	Maj.	Min.	Min.	Maj.	Min.	Min.	Perf.	Min.	Min.	Perf.
3|12	13	sLLsLLLsLLsLLsLL	Perf.	Min.	Min.	Perf.	Min.	Min.	Min.	Maj.	Min.	Min.	Maj.	Min.	Min.	Perf.	Min.	Min.	Perf.
2|13	10	sLLsLLsLLLsLLsLL	Perf.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Maj.	Min.	Min.	Perf.	Min.	Min.	Perf.
1|14	7	sLLsLLsLLsLLLsLL	Perf.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Perf.
0|15	4	sLLsLLsLLsLLsLLL	Perf.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Dim.	Min.	Min.	Perf.

Scale tree

Scale tree and tuning spectrum of 11L 5s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
13\16						975.000	225.000	1:1	1.000	Equalized 11L 5s
					74\91	975.824	224.176	6:5	1.200
				61\75		976.000	224.000	5:4	1.250
					109\134	976.119	223.881	9:7	1.286
			48\59			976.271	223.729	4:3	1.333	Supersoft 11L 5s
					131\161	976.398	223.602	11:8	1.375
				83\102		976.471	223.529	7:5	1.400
					118\145	976.552	223.448	10:7	1.429
		35\43				976.744	223.256	3:2	1.500	Soft 11L 5s
					127\156	976.923	223.077	11:7	1.571
				92\113		976.991	223.009	8:5	1.600
					149\183	977.049	222.951	13:8	1.625
			57\70			977.143	222.857	5:3	1.667	Semisoft 11L 5s Kumonga
					136\167	977.246	222.754	12:7	1.714
				79\97		977.320	222.680	7:4	1.750
					101\124	977.419	222.581	9:5	1.800
	22\27					977.778	222.222	2:1	2.000	Basic 11L 5s Scales with tunings softer than this are proper
					97\119	978.151	221.849	9:4	2.250
				75\92		978.261	221.739	7:3	2.333
					128\157	978.344	221.656	12:5	2.400
			53\65			978.462	221.538	5:2	2.500	Semihard 11L 5s Fortune
					137\168	978.571	221.429	13:5	2.600
				84\103		978.641	221.359	8:3	2.667
					115\141	978.723	221.277	11:4	2.750
		31\38				978.947	221.053	3:1	3.000	Hard 11L 5s
					102\125	979.200	220.800	10:3	3.333
				71\87		979.310	220.690	7:2	3.500
					111\136	979.412	220.588	11:3	3.667
			40\49			979.592	220.408	4:1	4.000	Superhard 11L 5s
					89\109	979.817	220.183	9:2	4.500
				49\60		980.000	220.000	5:1	5.000
					58\71	980.282	219.718	6:1	6.000
9\11						981.818	218.182	1:0	→ ∞	Collapsed 11L 5s

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