10L 3s

From Xenharmonic Wiki
Jump to navigation Jump to search
↖9L 2s↑10L 2s 11L 2s↗
←9L 3s10L 3s11L 3s→
↙9L 4s↓10L 4s 11L 4s↘
Brightest mode LLLLsLLLsLLLs
Period 2/1
Range for bright generator 9\13 (830.8¢) to 7\10 (840¢)
Range for dark generator 3\10 (360¢) to 4\13 (369.2¢)
Parent MOS 3L 7s
Sister MOS 3L 10s
Daughter MOSes 13L 10s, 10L 13s
Equal tunings
Supersoft (L:s = 4:3) 34\49 (832.7¢)
Soft (L:s = 3:2) 25\36 (833.3¢)
Semisoft (L:s = 5:3) 41\59 (833.9¢)
Basic (L:s = 2:1) 16\23 (834.8¢)
Semihard (L:s = 5:2) 39\56 (835.7¢)
Hard (L:s = 3:1) 23\33 (836.4¢)
Superhard (L:s = 4:1) 30\43 (837.2¢)
Brightest-mode tunings on xenpaper
Supersoft Soft Semisoft Basic Semihard Hard Superhard

10L 3s is an octave-equivalent moment of symmetry scale containing 10 large steps and 3 small steps, repeating every octave. 10L 3s is a child scale of 3L 7s, expanding it by 3 tones. Generators that produce this scale range from 830.8¢ to 840¢, or from 360¢ to 369.2¢.

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" (Hebrew calendar) modes the degrees are to be taken as numbered in 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.

Luachoid is a proposed name for this scale.

Modes

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

Scale tree and tuning spectrum of 10L 3s
Generator (in steps of edo) Cents Step ratio Comments
Bright Dark L:s Hardness
9\13 830.769 369.231 1:1 1.000 Equalized 10L 3s
52\75 832.000 368.000 6:5 1.200
43\62 832.258 367.742 5:4 1.250
77\111 832.432 367.568 9:7 1.286
34\49 832.653 367.347 4:3 1.333 Supersoft 10L 3s
93\134 832.836 367.164 11:8 1.375
59\85 832.941 367.059 7:5 1.400
84\121 833.058 366.942 10:7 1.429
25\36 833.333 366.667 3:2 1.500 Soft 10L 3s
91\131 833.588 366.412 11:7 1.571
66\95 833.684 366.316 8:5 1.600
107\154 833.766 366.234 13:8 1.625
41\59 833.898 366.102 5:3 1.667 Semisoft 10L 3s
98\141 834.043 365.957 12:7 1.714
57\82 834.146 365.854 7:4 1.750
73\105 834.286 365.714 9:5 1.800
16\23 834.783 365.217 2:1 2.000 Basic 10L 3s
Bright generators smaller than this are proper
71\102 835.294 364.706 9:4 2.250
55\79 835.443 364.557 7:3 2.333
94\135 835.556 364.444 12:5 2.400
39\56 835.714 364.286 5:2 2.500 Semihard 10L 3s
101\145 835.862 364.138 13:5 2.600
62\89 835.955 364.045 8:3 2.667
85\122 836.066 363.934 11:4 2.750
23\33 836.364 363.636 3:1 3.000 Hard 10L 3s
76\109 836.697 363.303 10:3 3.333
53\76 836.842 363.158 7:2 3.500
83\119 836.975 363.025 11:3 3.667
30\43 837.209 362.791 4:1 4.000 Superhard 10L 3s
67\96 837.500 362.500 9:2 4.500
37\53 837.736 362.264 5:1 5.000
44\63 838.095 361.905 6:1 6.000
7\10 840.000 360.000 1:0 → ∞ Collapsed 10L 3s