User:Moremajorthanmajor/5L 1s (11/6-equivalent)

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←4L 1s⟨11/6⟩5L 1s<11/6> 6L 1s⟨11/6⟩→
↙4L 2s⟨11/6⟩ ↓5L 2s⟨11/6⟩ 6L 2s⟨11/6⟩↘
 
┌╥╥╥╥╥┬┐
│║║║║║││
││││││││
└┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLLs
sLLLLL
Equave 11/6 (1049.4¢)
Period 11/6 (1049.4¢)
Generator size(ed11/6)
Bright 1\6 to 1\5 (174.9¢ to 209.9¢)
Dark 4\5 to 5\6 (839.5¢ to 874.5¢)
Related MOS scales
Parent 1L 4s⟨11/6⟩
Sister 1L 5s⟨11/6⟩
Daughters 6L 5s⟨11/6⟩
5L 6s⟨11/6⟩
Equal tunings(ed11/6)
Equalized (L:s = 1:1) 1\6 (174.9¢)
Supersoft (L:s = 4:3) 4\23 (182.5¢)
Soft (L:s = 3:2) 3\17 (185.2¢)
Semisoft (L:s = 5:3) 5\28 (187.4¢)
Basic (L:s = 2:1) 2\11 (190.8¢)
Semihard (L:s = 5:2) 5\27 (194.3¢)
Hard (L:s = 3:1) 3\16 (196.8¢)
Superhard (L:s = 4:1) 4\21 (199.9¢)
Collapsed (L:s = 1:0) 1\5 (209.9¢)

5L 1s⟨11/6⟩ is a 11/6-equivalent (non-octave) moment of symmetry scale containing 5 large steps and 1 small step, repeating every interval of 11/6 (1049.4¢). Generators that produce this scale range from 174.9¢ to 209.9¢, or from 839.5¢ to 874.5¢. Scales of this form are always proper because there is only one small step.

It is the rare simplest tuning of the greater whole tone scale with a major seventh.

The only notable low-harmonic-entropy scale with this MOS pattern is tetracot, in which the large step is 10/9 and four of them make a 3/2 since the seventh (septave) 11/6 is 1049.323¢.

Scales with this pattern are always proper, because there is only one small step.

Scale tree

Scale Tree and Tuning Spectrum of 5L 1s⟨11/6⟩
Generator(ed11/6) Cents Step Ratio Comments(always proper)
Bright Dark L:s Hardness
1\6 174.894 874.469 1:1 1.000 Equalized 5L 1s⟨11/6⟩
6\35 179.891 869.472 6:5 1.200
5\29 180.925 868.438 5:4 1.250
9\52 181.621 867.742 9:7 1.286
4\23 182.498 866.865 4:3 1.333 Supersoft 5L 1s⟨11/6⟩
11\63 183.222 866.141 11:8 1.375
7\40 183.639 865.724 7:5 1.400
10\57 184.099 865.264 10:7 1.429
3\17 185.182 864.181 3:2 1.500 Soft 5L 1s⟨11/6⟩
11\62 186.177 863.186 11:7 1.571
8\45 186.553 862.810 8:5 1.600
13\73 186.873 862.490 13:8 1.625
5\28 187.386 861.977 5:3 1.667 Semisoft 5L 1s⟨11/6⟩
12\67 187.946 861.417 12:7 1.714
7\39 188.347 861.016 7:4 1.750
9\50 188.885 860.478 9:5 1.800
2\11 190.793 858.570 2:1 2.000 Basic 5L 1s⟨11/6⟩
9\49 192.740 856.623 9:4 2.250
7\38 193.304 856.059 7:3 2.333
12\65 193.729 855.634 12:5 2.400
5\27 194.326 855.036 5:2 2.500 Semihard 5L 1s⟨11/6⟩
13\70 194.882 854.481 13:5 2.600
8\43 195.230 854.133 8:3 2.667
11\59 195.644 853.719 11:4 2.750
3\16 196.756 852.607 3:1 3.000 Hard 5L 1s⟨11/6⟩
10\53 197.993 851.370 10:3 3.333
7\37 198.528 850.835 7:2 3.500
11\58 199.017 850.346 11:3 3.667
4\21 199.879 849.484 4:1 4.000 Superhard 5L 1s⟨11/6⟩
9\47 200.942 848.421 9:2 4.500
5\26 201.801 847.562 5:1 5.000
6\31 203.103 846.260 6:1 6.000
1\5 209.873 839.490 1:0 → ∞ Collapsed 5L 1s⟨11/6⟩
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