2L 10s

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↖ 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
Descends from 2L 8s (jaric)
Ancestor's step ratio range 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 ¢)

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 ¢.

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.

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 diatonic interval categories.

Intervals

The intervals of 2L 10s are named after the number of mossteps (L and s) they subtend. Each interval, apart from the period intervals (perfect 0-mosstep, perfect 6-mosstep, and perfect 12-mosstep), has two varieties, or sizes, each. Interval varieties are named major and minor for the large and small sizes, respectively, and augmented, perfect, and diminished for the scale's generators.

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

A chain of bright generators, each a perfect 5-mosstep, produces the following scale degrees. A chain of 6 bright generators from each period contains the scale degrees of one of the modes of 2L 10s. Expanding each chain to 7 scale degrees produces the modes of either 12L 2s (for soft-of-basic tunings) or 2L 12s (for hard-of-basic tunings).

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
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