10L 3s

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10L 3s
Pattern LLLLsLLLsLLLs
Period 2/1
Generator range 3\10 (360.0¢) to 4\13 (369.2¢)
Parent MOS 3L 7s
Daughter MOSes 13L 10s, 10L 13s
Sister MOS 3L 10s
Equal tunings
Supersoft (L:s = 4:3) 15\49 (367.3¢)
Soft (L:s = 3:2) 11\36 (366.7¢)
Semisoft (L:s = 5:3) 18\59 (366.1¢)
Basic (L:s = 2:1) 7\23 (365.2¢)
Semihard (L:s = 5:2) 17\56 (364.3¢)
Hard (L:s = 3:1) 10\33 (363.6¢)
Superhard (L:s = 4:1) 13\43 (362.8¢)

10L 3s is a scale pattern that expands on sephiroid (3L 7s). A tempered-flat chain of the 13th harmonic really comes into its own as a distinct scale when extended to 13 tones. In these "Luach" (Hebrew calendar) modes the degrees are to be taken as numbered in descending order so that the the tempered 13th harmonic is fifth rather than tenth in the scale. This inverts the meaning of major and minor so that the Ionian-like mode reaches its degrees almost exclusively by backtracking.

10L 3s does not have a TAMNAMS name, but other proposed names include "luachoid".

Circle of fifths Ascending scale Mode
I-V-IX-XIII-IV-VIII-XII-III-VII-XI-II-VI-X L L L L s L L L s L L L s Tishrei
x-I-V-IX-XIII-IV-VIII-XII-III-VII-XI-II-VI L L L s L L L s L L L s L Cheshvan
vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII-XI-II L L s L L L s L L L s L L Kislev
ii-vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII-XI L s L L L s L L L s L L L Tevet
xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII s L L L s L L L s L L L L Shvat
vii-xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII-III L L L s L L L s L L L L s Adar minor
iii-vii-xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII L L s L L L s L L L L s L Adar major
xii-iii-vii-xi-ii-vi-x-I-V-IX-XIII-IV-VIII L s L L L s L L L L s L L Nisan
viii-xii-iii-vii-xi-ii-vi-x-I-V-IX-XIII-IV s L L L s L L L L s L L L Iyar
iv-viii-xii-iii-vii-xi-ii-vi-x-I-V-IX-XIII L L L s L L L L s L L L s Sivan
xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I-V-IX L L s L L L L s L L L s L Tammuz
ix-xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I-V L s L L L L s L L L s L L Av
v-ix-xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I s L L L L s L L L s L L L Elul
3/10 360
16/53 362.264
13/43 362.791
363.487
10/33 363.818
363.976
27/89 364.045
364.112
17/56 364.286
7/23 365.217
365.904
18/59 366.102
366.256
29/95 366.316
366.414
11/36 366.667
15/49 367.347
19/62 367.742
4/13 369.231