5L 6s

↖ 4L 5s	↑5L 5s	6L 5s ↗
← 4L 6s	5L 6s	6L 6s →
↙ 4L 7s	↓5L 7s	6L 7s ↘

┌╥┬╥┬╥┬╥┬╥┬┬┐ │║│║│║│║│║│││ │││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LsLsLsLsLss ssLsLsLsLsL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	2\11 to 1\5 (218.2¢ to 240.0¢)
Dark	4\5 to 9\11 (960.0¢ to 981.8¢)
TAMNAMS information
Descends from	5L 1s (machinoid)
Required step ratio range	2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent	5L 1s
Sister	6L 5s
Daughters	11L 5s, 5L 11s
Neutralized	10L 1s
Equal tunings
Equalized (L:s = 1:1)	2\11 (218.2¢)
Supersoft (L:s = 4:3)	7\38 (221.1¢)
Soft (L:s = 3:2)	5\27 (222.2¢)
Semisoft (L:s = 5:3)	8\43 (223.3¢)
Basic (L:s = 2:1)	3\16 (225.0¢)
Semihard (L:s = 5:2)	7\37 (227.0¢)
Hard (L:s = 3:1)	4\21 (228.6¢)
Superhard (L:s = 4:1)	5\26 (230.8¢)
Collapsed (L:s = 1:0)	1\5 (240.0¢)

5L 6s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 6 small steps, repeating every octave. 5L 6s is a child scale of 5L 1s, expanding it by 5 tones. Generators that produce this scale range from 218.2¢ to 240¢, or from 960¢ to 981.8¢. This pattern has multiple significant harmonic entropy minima, but they are all improper. The only saving grace for it is that is has harmonic entropy minima where the ratio between the large and small steps is optimal for melody, and that the generator for these scales is less than 6 cents flat of 8/7. The saving grace of the more lopsided scales is that a syntonic fifth is three generators up from the root. The name for this MOS pattern is p-chro machinoid.

Intervals of 5L 6s

Intervals		Size		Abbrev.
Generic	Specific	Steps	Range in cents
0-diastep (root)	Perfect 0-diastep	0	0.0¢	P0ms
1-diastep	Minor 1-diastep	s	0.0¢ to 109.1¢	m1ms
	Major 1-diastep	L	109.1¢ to 240.0¢	M1ms
2-diastep	Diminished 2-diastep	2s	0.0¢ to 218.2¢	d2ms
	Perfect 2-diastep	L + s	218.2¢ to 240.0¢	P2ms
3-diastep	Minor 3-diastep	L + 2s	240.0¢ to 327.3¢	m3ms
	Major 3-diastep	2L + s	327.3¢ to 480.0¢	M3ms
4-diastep	Minor 4-diastep	L + 3s	240.0¢ to 436.4¢	m4ms
	Major 4-diastep	2L + 2s	436.4¢ to 480.0¢	M4ms
5-diastep	Minor 5-diastep	2L + 3s	480.0¢ to 545.5¢	m5ms
	Major 5-diastep	3L + 2s	545.5¢ to 720.0¢	M5ms
6-diastep	Minor 6-diastep	2L + 4s	480.0¢ to 654.5¢	m6ms
	Major 6-diastep	3L + 3s	654.5¢ to 720.0¢	M6ms
7-diastep	Minor 7-diastep	3L + 4s	720.0¢ to 763.6¢	m7ms
	Major 7-diastep	4L + 3s	763.6¢ to 960.0¢	M7ms
8-diastep	Minor 8-diastep	3L + 5s	720.0¢ to 872.7¢	m8ms
	Major 8-diastep	4L + 4s	872.7¢ to 960.0¢	M8ms
9-diastep	Perfect 9-diastep	4L + 5s	960.0¢ to 981.8¢	P9ms
	Augmented 9-diastep	5L + 4s	981.8¢ to 1200.0¢	A9ms
10-diastep	Minor 10-diastep	4L + 6s	960.0¢ to 1090.9¢	m10ms
	Major 10-diastep	5L + 5s	1090.9¢ to 1200.0¢	M10ms
11-diastep (octave)	Perfect 11-diastep	5L + 6s	1200.0¢	P11ms

Modes

Modes of 5L 6s

UDP	Rotational order	Step pattern
10|0	1	LsLsLsLsLss
9|1	3	LsLsLsLssLs
8|2	5	LsLsLssLsLs
7|3	7	LsLssLsLsLs
6|4	9	LssLsLsLsLs
5|5	11	sLsLsLsLsLs
4|6	2	sLsLsLsLssL
3|7	4	sLsLsLssLsL
2|8	6	sLsLssLsLsL
1|9	8	sLssLsLsLsL
0|10	10	ssLsLsLsLsL

Scale tree

Scale Tree and Tuning Spectrum of 5L 6s

Generator(edo)						Cents		Step Ratio		Comments
						Bright	Dark	L:s	Hardness
2\11						218.182	981.818	1:1	1.000	Equalized 5L 6s
					11\60	220.000	980.000	6:5	1.200
				9\49		220.408	979.592	5:4	1.250
					16\87	220.690	979.310	9:7	1.286
			7\38			221.053	978.947	4:3	1.333	Supersoft 5L 6s
					19\103	221.359	978.641	11:8	1.375
				12\65		221.538	978.462	7:5	1.400
					17\92	221.739	978.261	10:7	1.429
		5\27				222.222	977.778	3:2	1.500	Soft 5L 6s
					18\97	222.680	977.320	11:7	1.571
				13\70		222.857	977.143	8:5	1.600
					21\113	223.009	976.991	13:8	1.625
			8\43			223.256	976.744	5:3	1.667	Semisoft 5L 6s
					19\102	223.529	976.471	12:7	1.714
				11\59		223.729	976.271	7:4	1.750
					14\75	224.000	976.000	9:5	1.800
	3\16					225.000	975.000	2:1	2.000	Basic 5L 6s Scales with tunings softer than this are proper
					13\69	226.087	973.913	9:4	2.250
				10\53		226.415	973.585	7:3	2.333
					17\90	226.667	973.333	12:5	2.400
			7\37			227.027	972.973	5:2	2.500	Semihard 5L 6s
					18\95	227.368	972.632	13:5	2.600
				11\58		227.586	972.414	8:3	2.667
					15\79	227.848	972.152	11:4	2.750
		4\21				228.571	971.429	3:1	3.000	Hard 5L 6s
					13\68	229.412	970.588	10:3	3.333
				9\47		229.787	970.213	7:2	3.500
					14\73	230.137	969.863	11:3	3.667
			5\26			230.769	969.231	4:1	4.000	Superhard 5L 6s
					11\57	231.579	968.421	9:2	4.500	Cynder
				6\31		232.258	967.742	5:1	5.000	Mothra
					7\36	233.333	966.667	6:1	6.000	Slendric, ↓ Rodan
1\5						240.000	960.000	1:0	→ ∞	Collapsed 5L 6s