Lua error in Module:MOS at line 28: attempt to index local 'equave' (a nil value).
Lua error in Module:MOS at line 28: attempt to index local 'equave' (a nil value).
10L 3s(<19/9>) 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
|
|
|
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
|
| 7/23
|
|
|
365.217
|
381.818
|
700.000
|
700.000
|
|
|
|
|
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
|
|
|
|