User:Moremajorthanmajor/Greater Luachoid: Difference between revisions

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== See also ==
== See also ==
[[10L 3s (33/16-equivalent)]] - harmonic subminor ninth tuning
[[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 (21/10-equivalent)]] - septimal chromatic minor ninth tuning


[[10L 3s (19/9-equivalent)]] - highest tuning
[[10L 3s (19/9-equivalent)]] - highest tuning

Revision as of 16:17, 19 July 2023

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

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