5L 11s

5L 11s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 11 small steps, repeating every octave. 5L 11s is a grandchild scale of 5L 1s, expanding it by 10 tones. Generators that produce this scale range from 225 ¢ to 240 ¢, or from 960 ¢ to 975 ¢.

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

Scale structure
Step pattern	LssLssLssLssLsss sssLssLssLssLssL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	3\16 to 1\5 (225.0 ¢ to 240.0 ¢)
Dark	4\5 to 13\16 (960.0 ¢ to 975.0 ¢)
TAMNAMS information
Related to	5L 1s (machinoid)
With tunings	3:1 to 1:0 (hard)
Related MOS scales
Parent	5L 6s
Sister	11L 5s
Daughters	16L 5s, 5L 16s
Neutralized	10L 6s
2-Flought	21L 11s, 5L 27s
Equal tunings
Equalized (L:s = 1:1)	3\16 (225.0 ¢)
Supersoft (L:s = 4:3)	10\53 (226.4 ¢)
Soft (L:s = 3:2)	7\37 (227.0 ¢)
Semisoft (L:s = 5:3)	11\58 (227.6 ¢)
Basic (L:s = 2:1)	4\21 (228.6 ¢)
Semihard (L:s = 5:2)	9\47 (229.8 ¢)
Hard (L:s = 3:1)	5\26 (230.8 ¢)
Superhard (L:s = 4:1)	6\31 (232.3 ¢)
Collapsed (L:s = 1:0)	1\5 (240.0 ¢)
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This mos has a large "diatonic" whole tone of 3\16edo (225 cents) to 1\5edo (240 cents) as a generator. Converging to 5edo as it becomes ever more improper, it moves from gorgo into slendric (the 2.3.7-subgroup temperament which tempers out the gamelisma of 1029/1024).

Modes

Modes of 5L 11s

UDP	Cyclic order	Step pattern
15|0	1	LssLssLssLssLsss
14|1	4	LssLssLssLsssLss
13|2	7	LssLssLsssLssLss
12|3	10	LssLsssLssLssLss
11|4	13	LsssLssLssLssLss
10|5	16	sLssLssLssLssLss
9|6	3	sLssLssLssLsssLs
8|7	6	sLssLssLsssLssLs
7|8	9	sLssLsssLssLssLs
6|9	12	sLsssLssLssLssLs
5|10	15	ssLssLssLssLssLs
4|11	2	ssLssLssLssLsssL
3|12	5	ssLssLssLsssLssL
2|13	8	ssLssLsssLssLssL
1|14	11	ssLsssLssLssLssL
0|15	14	sssLssLssLssLssL

Intervals

Intervals of 5L 11s

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 240.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 150.0 ¢
	Major 2-mosstep	M2ms	L + s	150.0 ¢ to 240.0 ¢
3-mosstep	Diminished 3-mosstep	d3ms	3s	0.0 ¢ to 225.0 ¢
	Perfect 3-mosstep	P3ms	L + 2s	225.0 ¢ to 240.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	L + 3s	240.0 ¢ to 300.0 ¢
	Major 4-mosstep	M4ms	2L + 2s	300.0 ¢ to 480.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	L + 4s	240.0 ¢ to 375.0 ¢
	Major 5-mosstep	M5ms	2L + 3s	375.0 ¢ to 480.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	L + 5s	240.0 ¢ to 450.0 ¢
	Major 6-mosstep	M6ms	2L + 4s	450.0 ¢ to 480.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	2L + 5s	480.0 ¢ to 525.0 ¢
	Major 7-mosstep	M7ms	3L + 4s	525.0 ¢ to 720.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	2L + 6s	480.0 ¢ to 600.0 ¢
	Major 8-mosstep	M8ms	3L + 5s	600.0 ¢ to 720.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	2L + 7s	480.0 ¢ to 675.0 ¢
	Major 9-mosstep	M9ms	3L + 6s	675.0 ¢ to 720.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	3L + 7s	720.0 ¢ to 750.0 ¢
	Major 10-mosstep	M10ms	4L + 6s	750.0 ¢ to 960.0 ¢
11-mosstep	Minor 11-mosstep	m11ms	3L + 8s	720.0 ¢ to 825.0 ¢
	Major 11-mosstep	M11ms	4L + 7s	825.0 ¢ to 960.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	3L + 9s	720.0 ¢ to 900.0 ¢
	Major 12-mosstep	M12ms	4L + 8s	900.0 ¢ to 960.0 ¢
13-mosstep	Perfect 13-mosstep	P13ms	4L + 9s	960.0 ¢ to 975.0 ¢
	Augmented 13-mosstep	A13ms	5L + 8s	975.0 ¢ to 1200.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	4L + 10s	960.0 ¢ to 1050.0 ¢
	Major 14-mosstep	M14ms	5L + 9s	1050.0 ¢ to 1200.0 ¢
15-mosstep	Minor 15-mosstep	m15ms	4L + 11s	960.0 ¢ to 1125.0 ¢
	Major 15-mosstep	M15ms	5L + 10s	1125.0 ¢ to 1200.0 ¢
16-mosstep	Perfect 16-mosstep	P16ms	5L + 11s	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 5L 11s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
3\16						225.000	975.000	1:1	1.000	Equalized 5L 11s
					16\85	225.882	974.118	6:5	1.200
				13\69		226.087	973.913	5:4	1.250
					23\122	226.230	973.770	9:7	1.286
			10\53			226.415	973.585	4:3	1.333	Supersoft 5L 11s
					27\143	226.573	973.427	11:8	1.375
				17\90		226.667	973.333	7:5	1.400
					24\127	226.772	973.228	10:7	1.429
		7\37				227.027	972.973	3:2	1.500	Soft 5L 11s
					25\132	227.273	972.727	11:7	1.571
				18\95		227.368	972.632	8:5	1.600
					29\153	227.451	972.549	13:8	1.625
			11\58			227.586	972.414	5:3	1.667	Semisoft 5L 11s
					26\137	227.737	972.263	12:7	1.714
				15\79		227.848	972.152	7:4	1.750
					19\100	228.000	972.000	9:5	1.800
	4\21					228.571	971.429	2:1	2.000	Basic 5L 11s Scales with tunings softer than this are proper
					17\89	229.213	970.787	9:4	2.250
				13\68		229.412	970.588	7:3	2.333
					22\115	229.565	970.435	12:5	2.400
			9\47			229.787	970.213	5:2	2.500	Semihard 5L 11s
					23\120	230.000	970.000	13:5	2.600
				14\73		230.137	969.863	8:3	2.667
					19\99	230.303	969.697	11:4	2.750
		5\26				230.769	969.231	3:1	3.000	Hard 5L 11s
					16\83	231.325	968.675	10:3	3.333
				11\57		231.579	968.421	7:2	3.500
					17\88	231.818	968.182	11:3	3.667
			6\31			232.258	967.742	4:1	4.000	Superhard 5L 11s
					13\67	232.836	967.164	9:2	4.500
				7\36		233.333	966.667	5:1	5.000
					8\41	234.146	965.854	6:1	6.000
1\5						240.000	960.000	1:0	→ ∞	Collapsed 5L 11s