2L 10s

2L 10s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 10 small steps, with a period of 1 large step and 5 small steps that repeats every 600.0 ¢, or twice every octave. 2L 10s is a child scale of 2L 8s, expanding it by 2 tones. Generators that produce this scale range from 500 ¢ to 600 ¢, or from 0 ¢ to 100 ¢.

↖ 1L 9s	↑ 2L 9s	3L 9s ↗
← 1L 10s	2L 10s	3L 10s →
↙ 1L 11s	↓ 2L 11s	3L 11s ↘

Scale structure
Step pattern	LsssssLsssss sssssLsssssL
Equave	2/1 (1200.0 ¢)
Period	1\2 (600.0 ¢)
Generator size
Bright	5\12 to 1\2 (500.0 ¢ to 600.0 ¢)
Dark	0\2 to 1\12 (0.0 ¢ to 100.0 ¢)
TAMNAMS information
Related to	2L 8s (jaric)
With tunings	2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent	2L 8s
Sister	10L 2s
Daughters	12L 2s, 2L 12s
Neutralized	4L 8s
2-Flought	14L 10s, 2L 22s
Equal tunings
Equalized (L:s = 1:1)	5\12 (500.0 ¢)
Supersoft (L:s = 4:3)	16\38 (505.3 ¢)
Soft (L:s = 3:2)	11\26 (507.7 ¢)
Semisoft (L:s = 5:3)	17\40 (510.0 ¢)
Basic (L:s = 2:1)	6\14 (514.3 ¢)
Semihard (L:s = 5:2)	13\30 (520.0 ¢)
Hard (L:s = 3:1)	7\16 (525.0 ¢)
Superhard (L:s = 4:1)	8\18 (533.3 ¢)
Collapsed (L:s = 1:0)	1\2 (600.0 ¢)
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2L 10s appears as the chromatic scale of injera and shrutar temperaments, among others. Injera is the harmonic entropy minimum for this pattern, generating 5/4 by moving up four generators from the root. The name for this MOS scale is p-chro jaric.

Modes

Modes of 2L 10s

UDP	Cyclic order	Step pattern
10|0(2)	1	LsssssLsssss
8|2(2)	6	sLsssssLssss
6|4(2)	5	ssLsssssLsss
4|6(2)	4	sssLsssssLss
2|8(2)	3	ssssLsssssLs
0|10(2)	2	sssssLsssssL

Scale tree

Note: the following table uses the dark generator.

Generator ranges:

• Bright generator: 500 cents (5\12) to 600 cents (1\2)
• Dark generator: 0 cents (0\2) to 100 cents (1\12)

Small step (dark generator)						Cents	L	s	L/s	Comments
1\12						100.000	1	1	1.000
					5\62	96.774	6	5	1.200
				4\50		96.000	5	4	1.250
					7\88	95.455	9	7	1.286
			3\38			94.737	4	3	1.333
					8\102	94.118	11	8	1.375
				5\64		93.750	7	5	1.400
					7\90	93.333	10	7	1.429
		2\26				92.308	3	2	1.500	Injera
					7\92	91.304	11	7	1.571
				5\66		90.909	8	5	1.600
					8\106	90.566	13	8	1.625	Unnamed golden tuning (90.6614¢)
			3\40			90.000	5	3	1.667
					7\94	89.362	12	7	1.714
				4\54		88.889	7	4	1.750
					5\68	88.235	9	5	1.800
	1\14					85.714	2	1	2.000	Basic 2L 10s (Generators larger than this are proper)
					4\58	82.759	9	4	2.250
				3\44		81.818	7	3	2.333
					5\74	81.081	12	5	2.400
			2\30			80.000	5	2	2.500
					5\76	78.947	13	5	2.600	Unnamed golden tuning (78.7605¢)
				3\46		78.261	8	3	2.667
					4\62	77.419	11	4	2.750
		1\16				75.000	3	1	3.000
					3\50	72.000	10	3	3.333	Vishnu/vishnean
				2\34		70.588	7	2	3.500
					3\52	69.231	11	3	3.667
			1\18			66.667	4	1	4.000
					2\38	63.158	9	2	4.500
				1\20		60.000	5	1	5.000
					1\22	54.545	6	1	6.000	Shrutar
0\2						0	1	0	→ inf