User:Moremajorthanmajor/10L 3s (19/9-equivalent)

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↖ 9L 2s⟨19/9⟩ ↑ 10L 2s⟨19/9⟩ 11L 2s⟨19/9⟩ ↗
← 9L 3s⟨19/9⟩ 10L 3s<19/9> 11L 3s⟨19/9⟩ →
↙ 9L 4s⟨19/9⟩ ↓ 10L 4s⟨19/9⟩ 11L 4s⟨19/9⟩ ↘ 
┌╥╥╥╥┬╥╥╥┬╥╥╥┬┐
│║║║║│║║║│║║║││
│││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLsLLLsLLLs
sLLLsLLLsLLLL
Equave 19/9 (1293.6¢)
Period 19/9 (1293.6¢)
Generator size(ed19/9)
Bright 9\13 to 7\10 (895.6¢ to 905.5¢)
Dark 3\10 to 4\13 (388.1¢ to 398.0¢)
Related MOS scales
Parent 3L 7s⟨19/9⟩
Sister 3L 10s⟨19/9⟩
Daughters 13L 10s⟨19/9⟩, 10L 13s⟨19/9⟩
Neutralized 7L 6s⟨19/9⟩
2-Flought 23L 3s⟨19/9⟩, 10L 16s⟨19/9⟩
Equal tunings(ed19/9)
Equalized (L:s = 1:1) 9\13 (895.6¢)
Supersoft (L:s = 4:3) 34\49 (897.6¢)
Soft (L:s = 3:2) 25\36 (898.3¢)
Semisoft (L:s = 5:3) 41\59 (898.9¢)
Basic (L:s = 2:1) 16\23 (899.9¢)
Semihard (L:s = 5:2) 39\56 (900.9¢)
Hard (L:s = 3:1) 23\33 (901.6¢)
Superhard (L:s = 4:1) 30\43 (902.5¢)
Collapsed (L:s = 1:0) 7\10 (905.5¢)

10L 3s⟨19/9⟩ is a 19/9-equivalent (non-octave) moment of symmetry scale containing 10 large steps and 3 small steps, repeating every interval of 19/9 (1293.6¢). Generators that produce this scale range from 895.6¢ to 905.5¢, or from 388.1¢ to 398¢.It is the highest just tuning for greater luachoid, a scale pattern that expands on greater sephiroid (3L 7s). A tempered flat chain of 27/16 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 27/16 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
Scale Tree and Tuning Spectrum of 10L 3s⟨19/9⟩
Generator(ed19/9) Cents Step ratio Comments
Bright Dark L:s Hardness
9\13 895.571 398.032 1:1 1.000 Equalized 10L 3s⟨19/9⟩
52\75 896.898 396.705 6:5 1.200
43\62 897.176 396.427 5:4 1.250
77\111 897.364 396.239 9:7 1.286
34\49 897.602 396.001 4:3 1.333 Supersoft 10L 3s⟨19/9⟩
93\134 897.799 395.804 11:8 1.375
59\85 897.913 395.690 7:5 1.400
84\121 898.038 395.565 10:7 1.429
25\36 898.335 395.268 3:2 1.500 Soft 10L 3s⟨19/9⟩
91\131 898.610 394.993 11:7 1.571
66\95 898.714 394.889 8:5 1.600
107\154 898.802 394.801 13:8 1.625
41\59 898.944 394.659 5:3 1.667 Semisoft 10L 3s⟨19/9⟩
98\141 899.100 394.503 12:7 1.714
57\82 899.212 394.391 7:4 1.750
73\105 899.362 394.241 9:5 1.800
16\23 899.898 393.705 2:1 2.000 Basic 10L 3s⟨19/9⟩
Scales with tunings softer than this are proper
71\102 900.449 393.154 9:4 2.250
55\79 900.610 392.993 7:3 2.333
94\135 900.731 392.872 12:5 2.400
39\56 900.902 392.701 5:2 2.500 Semihard 10L 3s⟨19/9⟩
101\145 901.061 392.542 13:5 2.600
62\89 901.162 392.441 8:3 2.667
85\122 901.281 392.322 11:4 2.750
23\33 901.602 392.001 3:1 3.000 Hard 10L 3s⟨19/9⟩
76\109 901.962 391.641 10:3 3.333
53\76 902.118 391.485 7:2 3.500
83\119 902.261 391.342 11:3 3.667
30\43 902.514 391.089 4:1 4.000 Superhard 10L 3s⟨19/9⟩
67\96 902.827 390.776 9:2 4.500
37\53 903.081 390.522 5:1 5.000
44\63 903.469 390.134 6:1 6.000
7\10 905.522 388.081 1:0 → ∞ Collapsed 10L 3s⟨19/9⟩
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