6L 10s

↖5L 9s	↑6L 9s	7L 9s↗
←5L 10s	6L 10s	7L 10s→
↙5L 11s	↓6L 11s	7L 11s↘

┌╥┬╥┬┬╥┬┬╥┬╥┬┬╥┬┬┐ │║│║││║││║│║││║│││ ││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LsLssLssLsLssLss ssLssLsLssLssLsL
Equave	2/1 (1200.0¢)
Period	1\2 (600.0¢)
Step size
Large	1\16 to 1\6 (75.0¢ to 200.0¢)
Small	0\6 to 1\16 (0.0¢ to 75.0¢)
Generator size
Bright	5\16 to 2\6 (375.0¢ to 400.0¢)
Dark	1\6 to 3\16 (200.0¢ to 225.0¢)
TAMNAMS information
Descends from	6L 4s (lemon)
Related MOS scales
Parent	6L 4s
Sister	10L 6s
Daughters	16L 6s 6L 16s
Equal tunings
Equalized (L:s = 1:1)	5\16 (375.0¢)
Supersoft (L:s = 4:3)	17\54 (377.8¢)
Soft (L:s = 3:2)	12\38 (378.9¢)
Semisoft (L:s = 5:3)	19\60 (380.0¢)
Basic (L:s = 2:1)	7\22 (381.8¢)
Semihard (L:s = 5:2)	16\50 (384.0¢)
Hard (L:s = 3:1)	9\28 (385.7¢)
Superhard (L:s = 4:1)	11\34 (388.2¢)
Collapsed (L:s = 1:0)	2\6 (400.0¢)

6L 10s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 6 large steps and 10 small steps, with a period of 3 large steps and 5 small steps that repeats every 600.0¢, or twice every octave. 6L 10s is a child scale of 6L 4s, expanding it by 6 tones. Generators that produce this scale range from 375¢ to 400¢, or from 200¢ to 225¢.

Being a small major third scale with a half octave period, this makes it the same scale as Magic/Würschmidt[16] enforcing the half octaves as diatonic notes to the scale. With a half octave period, the generator inverts to 1/6edo (200) to 3/16edo (225 cents).

Modes

Modes of 6L 10s

UDP	Rotational order	Step pattern
14|0(2)	1	LsLssLssLsLssLss
12|2(2)	6	LssLsLssLssLsLss
10|4(2)	3	LssLssLsLssLssLs
8|6(2)	8	sLsLssLssLsLssLs
6|8(2)	5	sLssLsLssLssLsLs
4|10(2)	2	sLssLssLsLssLssL
2|12(2)	7	ssLsLssLssLsLssL
0|14(2)	4	ssLssLsLssLssLsL

Scale tree

Scale tree and tuning spectrum of 6L 10s

Generator (in steps of edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
5\16						375.000	225.000	1:1	1.000	Equalized 6L 10s
					27\86	376.744	223.256	6:5	1.200
				22\70		377.143	222.857	5:4	1.250
					39\124	377.419	222.581	9:7	1.286
			17\54			377.778	222.222	4:3	1.333	Supersoft 6L 10s
					46\146	378.082	221.918	11:8	1.375
				29\92		378.261	221.739	7:5	1.400
					41\130	378.462	221.538	10:7	1.429
		12\38				378.947	221.053	3:2	1.500	Soft 6L 10s
					43\136	379.412	220.588	11:7	1.571
				31\98		379.592	220.408	8:5	1.600
					50\158	379.747	220.253	13:8	1.625
			19\60			380.000	220.000	5:3	1.667	Semisoft 6L 10s
					45\142	380.282	219.718	12:7	1.714
				26\82		380.488	219.512	7:4	1.750
					33\104	380.769	219.231	9:5	1.800
	7\22					381.818	218.182	2:1	2.000	Basic 6L 10s Scales with tunings softer than this are proper
					30\94	382.979	217.021	9:4	2.250
				23\72		383.333	216.667	7:3	2.333
					39\122	383.607	216.393	12:5	2.400
			16\50			384.000	216.000	5:2	2.500	Semihard 6L 10s
					41\128	384.375	215.625	13:5	2.600
				25\78		384.615	215.385	8:3	2.667
					34\106	384.906	215.094	11:4	2.750
		9\28				385.714	214.286	3:1	3.000	Hard 6L 10s
					29\90	386.667	213.333	10:3	3.333
				20\62		387.097	212.903	7:2	3.500
					31\96	387.500	212.500	11:3	3.667
			11\34			388.235	211.765	4:1	4.000	Superhard 6L 10s
					24\74	389.189	210.811	9:2	4.500
				13\40		390.000	210.000	5:1	5.000
					15\46	391.304	208.696	6:1	6.000
2\6						400.000	200.000	1:0	→ ∞	Collapsed 6L 10s