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 |
|---|---|---|
| 3/10 | 360.000 | 360.000 |
| 16/53 | 362.264 | 369.231 |
| 29/96 | 362.500 | 370.213 |
| 13/43 | 362.791 | 371.429 |
| 23/76 | 363.158 | 372.973 |
| 33/109 | 363.303 | 373.584 |
| 43/142 | 363.380 | 373.913 |
| 53/175 | 363.429 | 374.118 |
| 363.487 | 374.364 | |
| 10/33 | 363.636 | 375.000 |
| 57/188 | 363.830 | 375.824 |
| 47/155 | 363.871 | 376.000 |
| 37/122 | 363.944 | 376.271 |
| 363.976 | 376.448 | |
| 27/89 | 364.045 | 376.744 |
| 364.112 | 377.033 | |
| 17/56 | 364.286 | 377.778 |
| 24/79 | 364.557 | 378.947 |
| 31/102 | 364.706 | 379.392 |
| 38/125 | 364.800 | 380.000 |
| 7/23 | 365.217 | 381.818 |
| 60/197 | 365.482 | 382.978 |
| 53/174 | 365.517 | 383.132 |
| 46/151 | 365.563 | 383.333 |
| 39/128 | 365.625 | 383.607 |
| 32/105 | 365.714 | 384.000 |
| 25/82 | 365.854 | 384.615 |
| 365.904 | 384.844 | |
| 68/223 | 365.919 | 384.906 |
| 43/141 | 365.957 | 385.075 |
| 61/200 | 366.000 | 385.263 |
| 18/59 | 366.102 | 385.714 |
| 366.256 | 386.402 | |
| 29/95 | 366.316 | 386.667 |
| 40/131 | 366.412 | 387.097 |
| 366.414 | 387.106 | |
| 51/167 | 366.467 | 387.342 |
| 11/36 | 366.667 | 388.235 |
| 37/121 | 366.942 | 389.474 |
| 26/85 | 367.059 | 390.000 |
| 15/49 | 367.347 | 391.304 |
| 34/111 | 367.568 | 392.308 |
| 19/62 | 367.742 | 393.103 |
| 4/13 | 369.231 | 400.000 |
See also
10L 3s (33/16-equivalent) - harmonic subminor ninth tuning
10L 3s (44/21-equivalent) - Neogothic minor ninth tuning
10L 3s (21/10-equivalent) - septimal chromatic minor ninth tuning
10L 3s (19/9-equivalent) - highest tuning