This is the chromatic scale of the Sephiroth temperament explicated on the page for 3L 7s. However, a tempered-flat chain of the 13th harmonic 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 is descending order so that the the tempered 13th harmonic 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)
|
|
| 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
|
Mode 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
|
| 3/10
|
|
360
|
| 16/53
|
|
362.264
|
| 13/43
|
|
362.791
|
|
|
|
363.487
|
| 10/33
|
|
363.818
|
|
|
|
363.976
|
|
|
27/89
|
364.045
|
|
|
|
364.112
|
|
|
17/56
|
364.286
|
| 7/23
|
|
365.217
|
|
|
|
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
|