User:Moremajorthanmajor/Greater Luachoid
10L 3s(<19/9>), also known as greater luachoid is a scale pattern that expands on greater sephiroid (3L 7s). A tempered (flat) chain of the 13th harmonic or 5/3 really comes into its own as a distinct scale when extended to 13 tones. In these "Luach" modes the degrees are to be taken as numbered in descending order so that the the tempered 13th harmonic or 5/3 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.
| 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 |
| Generator | Cents | Normalized Cents | Centishrutis | ed23\22 | ||
|---|---|---|---|---|---|---|
| 3/10 | 360 | 360 | 660 | 690 | ||
| 16/53 | 362.264 | 369.231 | 676.923 | 694.340 | ||
| 45/149 | 362.416 | 369.863 | 678.082 | 694.631 | ||
| 29/96 | 362.500 | 370.213 | 678.723 | 694.792 | ||
| 42/139 | 362.590 | 370.588 | 679.412 | 694.964 | ||
| 13/43 | 362.791 | 371.429 | 680.952 | 695.349 | ||
| 36/119 | 363.025 | 372.414 | 682.757 | 695.798 | ||
| 23/76 | 363.158 | 372.973 | 683.784 | 696.052 | ||
| 33/109 | 363.303 | 373.584 | 684.906 | 696.330 | ||
| 363.487 | 374.364 | 686.335 | 696.683 | |||
| 10/33 | 363.636 | 375.000 | 687.500 | 696.970 | ||
| 47/155 | 363.871 | 376.000 | 689.333 | 697.419 | ||
| 37/122 | 363.944 | 376.271 | 689.8305 | 697.540 | ||
| 363.976 | 376.448 | 690.155 | 697.620 | |||
| 27/89 | 364.045 | 376.744 | 690.698 | 697.753 | ||
| 364.112 | 377.033 | 691.227 | 697.882 | |||
| 17/56 | 364.286 | 377.778 | 692.593 | 698.214 | ||
| 41/135 | 364.444 | 378.4615 | 693.846 | 698.5185 | ||
| 24/79 | 364.557 | 378.947 | 694.737 | 698.734 | ||
| 31/102 | 364.706 | 379.392 | 695.918 | 699.020 | ||
| 38/125 | 364.800 | 380.000 | 696.667 | 699.200 | ||
| 7/23 | 365.217 | 381.818 | 700.000 | 700.000 | ||
| 39/128 | 365.625 | 383.607 | 703.279 | 700.781 | ||
| 32/105 | 365.714 | 384.000 | 704.000 | 700.952 | ||
| 25/82 | 365.854 | 384.615 | 705.182 | 701.2195 | ||
| 365.904 | 384.844 | 705.5475 | 701.319 | |||
| 43/141 | 365.9575 | 385.075 | 705.970 | 701.418 | ||
| 61/200 | 366 | 385.263 | 706.316 | 701.500 | ||
| 18/59 | 366.102 | 385.714 | 707.143 | 701.694 | ||
| 366.256 | 386.402 | 708.404 | 701.991 | |||
| 29/95 | 366.316 | 386.667 | 708.889 | 702.105 | ||
| 40/131 | 366.412 | 387.097 | 709.677 | 702.290 | ||
| 366.414 | 387.1065 | 709.695 | 702.294 | |||
| 51/167 | 366.467 | 387.342 | 710.127 | 702.395 | ||
| 11/36 | 366.667 | 388.235 | 711.765 | 702.778 | ||
| 37/121 | 366.942 | 389.474 | 713.196 | 703.306 | ||
| 63/206 | 366.990 | 389.691 | 714.433 | 703.398 | ||
| 26/85 | 367.059 | 390.000 | 715.000 | 703.529 | ||
| 15/49 | 367.347 | 391.304 | 717.391 | 704.082 | ||
| 49/160 | 367.500 | 392.000 | 718.667 | 704.375 | ||
| 34/111 | 367.568 | 392.308 | 719.231 | 704.5045 | ||
| 19/62 | 367.742 | 393.103 | 720.690 | 704.838 | ||
| 4/13 | 369.231 | 400.000 | 733.333 | 707.692 | ||
See also
10L 3s (33/16-equivalent) - harmonic subminor ninth tuning
10L 3s (21/10-equivalent) - septimal chromatic minor ninth tuning
10L 3s (19/9-equivalent) - highest tuning