User:Moremajorthanmajor/Greater Luachoid

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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

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