3L 5s (5/2-equivalent)

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↖2L 4s⟨5/2⟩ ↑3L 4s⟨5/2⟩ 4L 4s⟨5/2⟩↗
←2L 5s⟨5/2⟩3L 5s (5/2-equivalent) 4L 5s⟨5/2⟩→
↙2L 6s⟨5/2⟩ ↓3L 6s⟨5/2⟩ 4L 6s⟨5/2⟩↘
 
┌╥┬╥┬┬╥┬┬┐
│║│║││║│││
││││││││││
└┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsLssLss
ssLssLsL
Equave 5/2 (1586.3¢)
Period 5/2 (1586.3¢)
Generator size(ed5/2)
Bright 5\8 to 2\3 (991.4¢ to 1057.5¢)
Dark 1\3 to 3\8 (528.8¢ to 594.9¢)
Related MOS scales
Parent 3L 2s⟨5/2⟩
Sister 5L 3s⟨5/2⟩
Daughters 8L 3s⟨5/2⟩
3L 8s⟨5/2⟩
Equal tunings(ed5/2)
Equalized (L:s = 1:1) 5\8 (991.4¢)
Supersoft (L:s = 4:3) 17\27 (998.8¢)
Soft (L:s = 3:2) 12\19 (1001.9¢)
Semisoft (L:s = 5:3) 19\30 (1004.7¢)
Basic (L:s = 2:1) 7\11 (1009.5¢)
Semihard (L:s = 5:2) 16\25 (1015.2¢)
Hard (L:s = 3:1) 9\14 (1019.8¢)
Superhard (L:s = 4:1) 11\17 (1026.4¢)
Collapsed (L:s = 1:0) 2\3 (1057.5¢)

3L 5s⟨5/2⟩ is a 5/2-equivalent (non-octave) moment of symmetry scale containing 3 large steps and 5 small steps, repeating every interval of 5/2 (1586.3¢). Generators that produce this scale range from 991.4¢ to 1057.5¢, or from 528.8¢ to 594.9¢.

Modes

Modes of 3L 5s⟨5/2⟩
UDP Rotational order Step pattern
7|0 1 LsLssLss
6|1 6 LssLsLss
5|2 3 LssLssLs
4|3 8 sLsLssLs
3|4 5 sLssLsLs
2|5 2 sLssLssL
1|6 7 ssLsLssL
0|7 4 ssLssLsL

Scale tree

Scale Tree and Tuning Spectrum of 3L 5s⟨5/2⟩
Generator(ed5/2) Cents Step Ratio Comments
Bright Dark L:s Hardness
5\8 991.446 594.868 1:1 1.000 Equalized 3L 5s⟨5/2⟩
27\43 996.057 590.256 6:5 1.200
22\35 997.111 589.202 5:4 1.250
39\62 997.842 588.471 9:7 1.286
17\27 998.790 587.524 4:3 1.333 Supersoft 3L 5s⟨5/2⟩
46\73 999.595 586.719 11:8 1.375
29\46 1000.067 586.246 7:5 1.400
41\65 1000.598 585.716 10:7 1.429
12\19 1001.882 584.431 3:2 1.500 Soft 3L 5s⟨5/2⟩
43\68 1003.110 583.204 11:7 1.571
31\49 1003.586 582.727 8:5 1.600
50\79 1003.996 582.318 13:8 1.625
19\30 1004.665 581.648 5:3 1.667 Semisoft 3L 5s⟨5/2⟩
45\71 1005.410 580.904 12:7 1.714
26\41 1005.955 580.359 7:4 1.750
33\52 1006.699 579.615 9:5 1.800
7\11 1009.472 576.841 2:1 2.000 Basic 3L 5s⟨5/2⟩
Scales with tunings softer than this are proper
30\47 1012.541 573.773 9:4 2.250
23\36 1013.478 572.836 7:3 2.333
39\61 1014.201 572.113 12:5 2.400
16\25 1015.241 571.073 5:2 2.500 Semihard 3L 5s⟨5/2⟩
41\64 1016.232 570.081 13:5 2.600
25\39 1016.868 569.446 8:3 2.667
34\53 1017.635 568.679 11:4 2.750
9\14 1019.773 566.541 3:1 3.000 Hard 3L 5s⟨5/2⟩
29\45 1022.291 564.023 10:3 3.333
20\31 1023.428 562.886 7:2 3.500
31\48 1024.494 561.819 11:3 3.667
11\17 1026.438 559.875 4:1 4.000 Superhard 3L 5s⟨5/2⟩
24\37 1028.960 557.353 9:2 4.500
13\20 1031.104 555.210 5:1 5.000
15\23 1034.552 551.761 6:1 6.000
2\3 1057.542 528.771 1:0 → ∞ Collapsed 3L 5s⟨5/2⟩
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