13L 10s

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Todo: confirm
Confirm temperaments that correspond with this mos

↖12L 9s ↑13L 9s 14L 9s↗
←12L 10s13L 10s 14L 10s→
↙12L 11s ↓13L 11s 14L 11s↘
┌╥╥┬╥┬╥┬╥╥┬╥┬╥┬╥╥┬╥┬╥┬╥┬┐
│║║│║│║│║║│║│║│║║│║│║│║││
│││││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLsLsLsLLsLsLsLLsLsLsLs
sLsLsLsLLsLsLsLLsLsLsLL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Step size ranges
Large 1\23 to 1\13 (52.2¢ to 92.3¢)
Small 0\13 to 1\23 (0.0¢ to 52.2¢)
Generator size
Bright 7\23 to 4\13 (365.2¢ to 369.2¢)
Dark 9\13 to 16\23 (830.8¢ to 834.8¢)
TAMNAMS information
Descends from 3L 7s (sephiroid)
Related MOS scales
Parent 10L 3s
Sister 10L 13s
Daughters 23L 13s
13L 23s
Equal tunings
Equalized (L:s = 1:1) 7\23 (365.2¢)
Supersoft (L:s = 4:3) 25\82 (365.9¢)
Soft (L:s = 3:2) 18\59 (366.1¢)
Semisoft (L:s = 5:3) 29\95 (366.3¢)
Basic (L:s = 2:1) 11\36 (366.7¢)
Semihard (L:s = 5:2) 26\85 (367.1¢)
Hard (L:s = 3:1) 15\49 (367.3¢)
Superhard (L:s = 4:1) 19\62 (367.7¢)
Collapsed (L:s = 1:0) 4\13 (369.2¢)

13L 10s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 10 small steps, repeating every octave. 13L 10s is a grandchild scale of 3L 7s, expanding it by 13 tones. Generators that produce this scale range from 365.2¢ to 369.2¢, or from 830.8¢ to 834.8¢.

This scale is the quartertone scale of unidec temperament.

Scale tree

Scale tree and tuning spectrum of 13L 10s
Generator (in steps of edo) Cents Step ratio Comments
Bright Dark L:s Hardness
7\23 365.217 834.783 1:1 1.000 Equalized 13L 10s
39\128 365.625 834.375 6:5 1.200
32\105 365.714 834.286 5:4 1.250
57\187 365.775 834.225 9:7 1.286
25\82 365.854 834.146 4:3 1.333 Supersoft 13L 10s
68\223 365.919 834.081 11:8 1.375
43\141 365.957 834.043 7:5 1.400
61\200 366.000 834.000 10:7 1.429
18\59 366.102 833.898 3:2 1.500 Soft 13L 10s
65\213 366.197 833.803 11:7 1.571
47\154 366.234 833.766 8:5 1.600
76\249 366.265 833.735 13:8 1.625
29\95 366.316 833.684 5:3 1.667 Semisoft 13L 10s
69\226 366.372 833.628 12:7 1.714
40\131 366.412 833.588 7:4 1.750
51\167 366.467 833.533 9:5 1.800
11\36 366.667 833.333 2:1 2.000 Basic 13L 10s
Scales with tunings softer than this are proper
48\157 366.879 833.121 9:4 2.250
37\121 366.942 833.058 7:3 2.333
63\206 366.990 833.010 12:5 2.400
26\85 367.059 832.941 5:2 2.500 Semihard 13L 10s
67\219 367.123 832.877 13:5 2.600
41\134 367.164 832.836 8:3 2.667
56\183 367.213 832.787 11:4 2.750
15\49 367.347 832.653 3:1 3.000 Hard 13L 10s
49\160 367.500 832.500 10:3 3.333
34\111 367.568 832.432 7:2 3.500
53\173 367.630 832.370 11:3 3.667
19\62 367.742 832.258 4:1 4.000 Superhard 13L 10s
42\137 367.883 832.117 9:2 4.500
23\75 368.000 832.000 5:1 5.000
27\88 368.182 831.818 6:1 6.000
4\13 369.231 830.769 1:0 → ∞ Collapsed 13L 10s