10L 3s
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| Brightest mode | LLLLsLLLsLLLs | |
| Period | 2/1 | |
| Range for bright generator | 3\10 (360.0¢) to 4\13 (369.2¢) | |
| Range for dark generator | 9\13 (830.8¢) to 7\10 (840.0¢) | |
| 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 |