1L 10s

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↑ 1L 9s 2L 9s ↗
1L 10s 2L 10s →
↓ 1L 11s 2L 11s ↘ 
┌╥┬┬┬┬┬┬┬┬┬┬┐
│║│││││││││││
│││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern Lssssssssss
ssssssssssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 10\11 to 1\1 (1090.9 ¢ to 1200.0 ¢)
Dark 0\1 to 1\11 (0.0 ¢ to 109.1 ¢)
TAMNAMS information
Descends from 1L 9s (antisinatonic)
Ancestor's step ratio range 2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent 1L 9s
Sister 10L 1s
Daughters 11L 1s, 1L 11s
Neutralized 2L 9s
2-Flought 12L 10s, 1L 21s
Equal tunings
Equalized (L:s = 1:1) 10\11 (1090.9 ¢)
Supersoft (L:s = 4:3) 31\34 (1094.1 ¢)
Soft (L:s = 3:2) 21\23 (1095.7 ¢)
Semisoft (L:s = 5:3) 32\35 (1097.1 ¢)
Basic (L:s = 2:1) 11\12 (1100.0 ¢)
Semihard (L:s = 5:2) 23\25 (1104.0 ¢)
Hard (L:s = 3:1) 12\13 (1107.7 ¢)
Superhard (L:s = 4:1) 13\14 (1114.3 ¢)
Collapsed (L:s = 1:0) 1\1 (1200.0 ¢)

1L 10s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 10 small steps, repeating every octave. 1L 10s is a child scale of 1L 9s, expanding it by 1 tones. Generators that produce this scale range from 1090.9 ¢ to 1200 ¢, or from 0 ¢ to 109.1 ¢.

This MOS achieves its simplest harmonic entropy minimum where two generators equal 9/8. The temperament which occupies this harmonic entropy minimum is called Ripple, but there are several lower (and more complex) harmonic entropy minima of note including (in descending order of generator height): Passion (6/5 = +3 generators), Octacot (3/2 = +8 generators), Nautilus (3/2 = -6 generators) and Valentine (7/4 = -3 generators).

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

Intervals of 1L 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 109.1 ¢
Augmented 1-mosstep A1ms L 109.1 ¢ to 1200.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 218.2 ¢
Major 2-mosstep M2ms L + s 218.2 ¢ to 1200.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 327.3 ¢
Major 3-mosstep M3ms L + 2s 327.3 ¢ to 1200.0 ¢
4-mosstep Minor 4-mosstep m4ms 4s 0.0 ¢ to 436.4 ¢
Major 4-mosstep M4ms L + 3s 436.4 ¢ to 1200.0 ¢
5-mosstep Minor 5-mosstep m5ms 5s 0.0 ¢ to 545.5 ¢
Major 5-mosstep M5ms L + 4s 545.5 ¢ to 1200.0 ¢
6-mosstep Minor 6-mosstep m6ms 6s 0.0 ¢ to 654.5 ¢
Major 6-mosstep M6ms L + 5s 654.5 ¢ to 1200.0 ¢
7-mosstep Minor 7-mosstep m7ms 7s 0.0 ¢ to 763.6 ¢
Major 7-mosstep M7ms L + 6s 763.6 ¢ to 1200.0 ¢
8-mosstep Minor 8-mosstep m8ms 8s 0.0 ¢ to 872.7 ¢
Major 8-mosstep M8ms L + 7s 872.7 ¢ to 1200.0 ¢
9-mosstep Minor 9-mosstep m9ms 9s 0.0 ¢ to 981.8 ¢
Major 9-mosstep M9ms L + 8s 981.8 ¢ to 1200.0 ¢
10-mosstep Diminished 10-mosstep d10ms 10s 0.0 ¢ to 1090.9 ¢
Perfect 10-mosstep P10ms L + 9s 1090.9 ¢ to 1200.0 ¢
11-mosstep Perfect 11-mosstep P11ms L + 10s 1200.0 ¢

Generator chain

Generator chain of 1L 10s
Bright gens Scale degree Abbrev.
11 Augmented 0-mosdegree A0md
10 Augmented 1-mosdegree A1md
9 Major 2-mosdegree M2md
8 Major 3-mosdegree M3md
7 Major 4-mosdegree M4md
6 Major 5-mosdegree M5md
5 Major 6-mosdegree M6md
4 Major 7-mosdegree M7md
3 Major 8-mosdegree M8md
2 Major 9-mosdegree M9md
1 Perfect 10-mosdegree P10md
0 Perfect 0-mosdegree
Perfect 11-mosdegree		 P0md
P11md
−1 Perfect 1-mosdegree P1md
−2 Minor 2-mosdegree m2md
−3 Minor 3-mosdegree m3md
−4 Minor 4-mosdegree m4md
−5 Minor 5-mosdegree m5md
−6 Minor 6-mosdegree m6md
−7 Minor 7-mosdegree m7md
−8 Minor 8-mosdegree m8md
−9 Minor 9-mosdegree m9md
−10 Diminished 10-mosdegree d10md
−11 Diminished 11-mosdegree d11md

Modes

Scale degrees of the modes of 1L 10s
UDP Cyclic
order		 Step
pattern		 Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11
10|0 1 Lssssssssss Perf. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
9|1 11 sLsssssssss Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
8|2 10 ssLssssssss Perf. Perf. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
7|3 9 sssLsssssss Perf. Perf. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
6|4 8 ssssLssssss Perf. Perf. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
5|5 7 sssssLsssss Perf. Perf. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Perf. Perf.
4|6 6 ssssssLssss Perf. Perf. Min. Min. Min. Min. Min. Maj. Maj. Maj. Perf. Perf.
3|7 5 sssssssLsss Perf. Perf. Min. Min. Min. Min. Min. Min. Maj. Maj. Perf. Perf.
2|8 4 ssssssssLss Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Maj. Perf. Perf.
1|9 3 sssssssssLs Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Perf.
0|10 2 ssssssssssL Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Dim. Perf.

Scale tree

Scale tree and tuning spectrum of 1L 10s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
10\11 1090.909 109.091 1:1 1.000 Equalized 1L 10s
51\56 1092.857 107.143 6:5 1.200
41\45 1093.333 106.667 5:4 1.250
72\79 1093.671 106.329 9:7 1.286
31\34 1094.118 105.882 4:3 1.333 Supersoft 1L 10s
83\91 1094.505 105.495 11:8 1.375
52\57 1094.737 105.263 7:5 1.400
73\80 1095.000 105.000 10:7 1.429 Septendesemi
21\23 1095.652 104.348 3:2 1.500 Soft 1L 10s
74\81 1096.296 103.704 11:7 1.571
53\58 1096.552 103.448 8:5 1.600
85\93 1096.774 103.226 13:8 1.625 Golden ripple (103.288 ¢)
32\35 1097.143 102.857 5:3 1.667 Semisoft 1L 10s
75\82 1097.561 102.439 12:7 1.714
43\47 1097.872 102.128 7:4 1.750
54\59 1098.305 101.695 9:5 1.800
11\12 1100.000 100.000 2:1 2.000 Basic 1L 10s
Scales with tunings softer than this are proper
45\49 1102.041 97.959 9:4 2.250 Passion
34\37 1102.703 97.297 7:3 2.333
57\62 1103.226 96.774 12:5 2.400
23\25 1104.000 96.000 5:2 2.500 Semihard 1L 10s
58\63 1104.762 95.238 13:5 2.600 Unnamed golden tuning
35\38 1105.263 94.737 8:3 2.667
47\51 1105.882 94.118 11:4 2.750
12\13 1107.692 92.308 3:1 3.000 Hard 1L 10s
37\40 1110.000 90.000 10:3 3.333
25\27 1111.111 88.889 7:2 3.500
38\41 1112.195 87.805 11:3 3.667 Octacot
13\14 1114.286 85.714 4:1 4.000 Superhard 1L 10s
Nuke
27\29 1117.241 82.759 9:2 4.500 Nautilus
14\15 1120.000 80.000 5:1 5.000 Valentine
15\16 1125.000 75.000 6:1 6.000 ↓ Slurpee
1\1 1200.000 0.000 1:0 → ∞ Collapsed 1L 10s
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