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

Degrees

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.

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 ¢

Scale tree

Todo: review Review entries from past page revision and enter them into the scale tree.

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details: Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: {{MOS tuning spectrum | 3/2 = Example comment | 4/3 = Another example comment }} The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.

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
			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
				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
				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
1\2						600.000	0.000	1:0	→ ∞	Collapsed 2L 10s