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 systematic name for this MOS scale is p-chro jaric, although Lériendil has proposed the bespoke name thalassic, being an antonym to telluric as used for 10L 2s.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

Intervals

Intervals of 2L 10s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Perfect 1-mosstep	P1ms	s	0.0 ¢ to 100.0 ¢
	Augmented 1-mosstep	A1ms	L	100.0 ¢ to 600.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 200.0 ¢
	Major 2-mosstep	M2ms	L + s	200.0 ¢ to 600.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0 ¢ to 300.0 ¢
	Major 3-mosstep	M3ms	L + 2s	300.0 ¢ to 600.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	4s	0.0 ¢ to 400.0 ¢
	Major 4-mosstep	M4ms	L + 3s	400.0 ¢ to 600.0 ¢
5-mosstep	Diminished 5-mosstep	d5ms	5s	0.0 ¢ to 500.0 ¢
	Perfect 5-mosstep	P5ms	L + 4s	500.0 ¢ to 600.0 ¢
6-mosstep	Perfect 6-mosstep	P6ms	L + 5s	600.0 ¢
7-mosstep	Perfect 7-mosstep	P7ms	L + 6s	600.0 ¢ to 700.0 ¢
	Augmented 7-mosstep	A7ms	2L + 5s	700.0 ¢ to 1200.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	L + 7s	600.0 ¢ to 800.0 ¢
	Major 8-mosstep	M8ms	2L + 6s	800.0 ¢ to 1200.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	L + 8s	600.0 ¢ to 900.0 ¢
	Major 9-mosstep	M9ms	2L + 7s	900.0 ¢ to 1200.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	L + 9s	600.0 ¢ to 1000.0 ¢
	Major 10-mosstep	M10ms	2L + 8s	1000.0 ¢ to 1200.0 ¢
11-mosstep	Diminished 11-mosstep	d11ms	L + 10s	600.0 ¢ to 1100.0 ¢
	Perfect 11-mosstep	P11ms	2L + 9s	1100.0 ¢ to 1200.0 ¢
12-mosstep	Perfect 12-mosstep	P12ms	2L + 10s	1200.0 ¢

Generator chain

Generator chain of 2L 10s

Bright gens	Scale degree	Abbrev.	Scale degree	Abbrev.
6	Augmented 0-mosdegree	A0md	Augmented 6-mosdegree	A6md
5	Augmented 1-mosdegree	A1md	Augmented 7-mosdegree	A7md
4	Major 2-mosdegree	M2md	Major 8-mosdegree	M8md
3	Major 3-mosdegree	M3md	Major 9-mosdegree	M9md
2	Major 4-mosdegree	M4md	Major 10-mosdegree	M10md
1	Perfect 5-mosdegree	P5md	Perfect 11-mosdegree	P11md
0	Perfect 0-mosdegree Perfect 6-mosdegree	P0md P6md	Perfect 6-mosdegree Perfect 12-mosdegree	P6md P12md
−1	Perfect 1-mosdegree	P1md	Perfect 7-mosdegree	P7md
−2	Minor 2-mosdegree	m2md	Minor 8-mosdegree	m8md
−3	Minor 3-mosdegree	m3md	Minor 9-mosdegree	m9md
−4	Minor 4-mosdegree	m4md	Minor 10-mosdegree	m10md
−5	Diminished 5-mosdegree	d5md	Diminished 11-mosdegree	d11md
−6	Diminished 6-mosdegree	d6md	Diminished 12-mosdegree	d12md

Modes

Scale degrees of the modes of 2L 10s

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3	4	5	6	7	8	9	10	11	12
10|0(2)	1	LsssssLsssss	Perf.	Aug.	Maj.	Maj.	Maj.	Perf.	Perf.	Aug.	Maj.	Maj.	Maj.	Perf.	Perf.
8|2(2)	6	sLsssssLssss	Perf.	Perf.	Maj.	Maj.	Maj.	Perf.	Perf.	Perf.	Maj.	Maj.	Maj.	Perf.	Perf.
6|4(2)	5	ssLsssssLsss	Perf.	Perf.	Min.	Maj.	Maj.	Perf.	Perf.	Perf.	Min.	Maj.	Maj.	Perf.	Perf.
4|6(2)	4	sssLsssssLss	Perf.	Perf.	Min.	Min.	Maj.	Perf.	Perf.	Perf.	Min.	Min.	Maj.	Perf.	Perf.
2|8(2)	3	ssssLsssssLs	Perf.	Perf.	Min.	Min.	Min.	Perf.	Perf.	Perf.	Min.	Min.	Min.	Perf.	Perf.
0|10(2)	2	sssssLsssssL	Perf.	Perf.	Min.	Min.	Min.	Dim.	Perf.	Perf.	Min.	Min.	Min.	Dim.	Perf.

Scale tree

Scale tree and tuning spectrum of 2L 10s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
5\12						500.000	100.000	1:1	1.000	Equalized 2L 10s
					26\62	503.226	96.774	6:5	1.200
				21\50		504.000	96.000	5:4	1.250
					37\88	504.545	95.455	9:7	1.286
			16\38			505.263	94.737	4:3	1.333	Supersoft 2L 10s
					43\102	505.882	94.118	11:8	1.375
				27\64		506.250	93.750	7:5	1.400
					38\90	506.667	93.333	10:7	1.429
		11\26				507.692	92.308	3:2	1.500	Soft 2L 10s
					39\92	508.696	91.304	11:7	1.571
				28\66		509.091	90.909	8:5	1.600
					45\106	509.434	90.566	13:8	1.625	Unnamed golden tuning (90.6614 ¢)
			17\40			510.000	90.000	5:3	1.667	Semisoft 2L 10s
					40\94	510.638	89.362	12:7	1.714
				23\54		511.111	88.889	7:4	1.750
					29\68	511.765	88.235	9:5	1.800
	6\14					514.286	85.714	2:1	2.000	Basic 2L 10s Scales with tunings softer than this are proper
					25\58	517.241	82.759	9:4	2.250
				19\44		518.182	81.818	7:3	2.333
					32\74	518.919	81.081	12:5	2.400
			13\30			520.000	80.000	5:2	2.500	Semihard 2L 10s
					33\76	521.053	78.947	13:5	2.600	Unnamed golden tuning (78.7605 ¢)
				20\46		521.739	78.261	8:3	2.667
					27\62	522.581	77.419	11:4	2.750
		7\16				525.000	75.000	3:1	3.000	Hard 2L 10s
					22\50	528.000	72.000	10:3	3.333	Vishnu/vishnean
				15\34		529.412	70.588	7:2	3.500
					23\52	530.769	69.231	11:3	3.667
			8\18			533.333	66.667	4:1	4.000	Superhard 2L 10s
					17\38	536.842	63.158	9:2	4.500
				9\20		540.000	60.000	5:1	5.000
					10\22	545.455	54.545	6:1	6.000	Shrutar ↓
1\2						600.000	0.000	1:0	→ ∞	Collapsed 2L 10s