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
Related to	5L 1s (machinoid)
With tunings	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
2-Flought	16L 6s, 5L 17s
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 ¢ 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, although the alternative name mothroid was given by CompactStar as part of their temperament-centric MOS naming system (TCMNAMS). It has also been named slentonic by Inthar, after slendric temperament.

Scale properties

Intervals

Intervals of 5L 6s

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 109.1 ¢
	Major 1-mosstep	M1ms	L	109.1 ¢ to 240.0 ¢
2-mosstep	Diminished 2-mosstep	d2ms	2s	0.0 ¢ to 218.2 ¢
	Perfect 2-mosstep	P2ms	L + s	218.2 ¢ to 240.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	L + 2s	240.0 ¢ to 327.3 ¢
	Major 3-mosstep	M3ms	2L + s	327.3 ¢ to 480.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	L + 3s	240.0 ¢ to 436.4 ¢
	Major 4-mosstep	M4ms	2L + 2s	436.4 ¢ to 480.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	2L + 3s	480.0 ¢ to 545.5 ¢
	Major 5-mosstep	M5ms	3L + 2s	545.5 ¢ to 720.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	2L + 4s	480.0 ¢ to 654.5 ¢
	Major 6-mosstep	M6ms	3L + 3s	654.5 ¢ to 720.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	3L + 4s	720.0 ¢ to 763.6 ¢
	Major 7-mosstep	M7ms	4L + 3s	763.6 ¢ to 960.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	3L + 5s	720.0 ¢ to 872.7 ¢
	Major 8-mosstep	M8ms	4L + 4s	872.7 ¢ to 960.0 ¢
9-mosstep	Perfect 9-mosstep	P9ms	4L + 5s	960.0 ¢ to 981.8 ¢
	Augmented 9-mosstep	A9ms	5L + 4s	981.8 ¢ to 1200.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	4L + 6s	960.0 ¢ to 1090.9 ¢
	Major 10-mosstep	M10ms	5L + 5s	1090.9 ¢ to 1200.0 ¢
11-mosstep	Perfect 11-mosstep	P11ms	5L + 6s	1200.0 ¢

Generator chain

Generator chain of 5L 6s

Bright gens	Scale degree	Abbrev.
15	Augmented 8-mosdegree	A8md
14	Augmented 6-mosdegree	A6md
13	Augmented 4-mosdegree	A4md
12	Augmented 2-mosdegree	A2md
11	Augmented 0-mosdegree	A0md
10	Augmented 9-mosdegree	A9md
9	Major 7-mosdegree	M7md
8	Major 5-mosdegree	M5md
7	Major 3-mosdegree	M3md
6	Major 1-mosdegree	M1md
5	Major 10-mosdegree	M10md
4	Major 8-mosdegree	M8md
3	Major 6-mosdegree	M6md
2	Major 4-mosdegree	M4md
1	Perfect 2-mosdegree	P2md
0	Perfect 0-mosdegree Perfect 11-mosdegree	P0md P11md
−1	Perfect 9-mosdegree	P9md
−2	Minor 7-mosdegree	m7md
−3	Minor 5-mosdegree	m5md
−4	Minor 3-mosdegree	m3md
−5	Minor 1-mosdegree	m1md
−6	Minor 10-mosdegree	m10md
−7	Minor 8-mosdegree	m8md
−8	Minor 6-mosdegree	m6md
−9	Minor 4-mosdegree	m4md
−10	Diminished 2-mosdegree	d2md
−11	Diminished 11-mosdegree	d11md
−12	Diminished 9-mosdegree	d9md
−13	Diminished 7-mosdegree	d7md
−14	Diminished 5-mosdegree	d5md
−15	Diminished 3-mosdegree	d3md

Modes

Scale degrees of the modes of 5L 6s

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3	4	5	6	7	8	9	10	11
10|0	1	LsLsLsLsLss	Perf.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Aug.	Maj.	Perf.
9|1	3	LsLsLsLssLs	Perf.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Perf.
8|2	5	LsLsLssLsLs	Perf.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Min.	Maj.	Perf.	Maj.	Perf.
7|3	7	LsLssLsLsLs	Perf.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Min.	Maj.	Perf.	Maj.	Perf.
6|4	9	LssLsLsLsLs	Perf.	Maj.	Perf.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Perf.	Maj.	Perf.
5|5	11	sLsLsLsLsLs	Perf.	Min.	Perf.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Perf.	Maj.	Perf.
4|6	2	sLsLsLsLssL	Perf.	Min.	Perf.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Perf.	Min.	Perf.
3|7	4	sLsLsLssLsL	Perf.	Min.	Perf.	Min.	Maj.	Min.	Maj.	Min.	Min.	Perf.	Min.	Perf.
2|8	6	sLsLssLsLsL	Perf.	Min.	Perf.	Min.	Maj.	Min.	Min.	Min.	Min.	Perf.	Min.	Perf.
1|9	8	sLssLsLsLsL	Perf.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Perf.
0|10	10	ssLsLsLsLsL	Perf.	Min.	Dim.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Perf.

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	Kumonga
					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 Shoe
					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	Mothra
				6\31		232.258	967.742	5:1	5.000	Mosura
					7\36	233.333	966.667	6:1	6.000	Slendric, Rodan ↓
1\5						240.000	960.000	1:0	→ ∞	Collapsed 5L 6s