6L 3s

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↖ 5L 2s↑ 6L 2s 7L 2s ↗
← 5L 3s6L 3s7L 3s →
↙ 5L 4s↓ 6L 4s 7L 4s ↘
┌╥╥┬╥╥┬╥╥┬┐
│║║│║║│║║││
│││││││││││
└┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLsLLsLLs
sLLsLLsLL
Equave 2/1 (1200.0¢)
Period 1\3 (400.0¢)
Generator size
Bright 1\9 to 1\6 (133.3¢ to 200.0¢)
Dark 1\6 to 2\9 (200.0¢ to 266.7¢)
TAMNAMS information
Name hyrulic
Prefix hyru-
Abbrev. hy
Related MOS scales
Parent 3L 3s
Sister 3L 6s
Daughters 9L 6s, 6L 9s
Neutralized 3L 6s
2-Flought 15L 3s, 6L 12s
Equal tunings
Equalized (L:s = 1:1) 1\9 (133.3¢)
Supersoft (L:s = 4:3) 4\33 (145.5¢)
Soft (L:s = 3:2) 3\24 (150.0¢)
Semisoft (L:s = 5:3) 5\39 (153.8¢)
Basic (L:s = 2:1) 2\15 (160.0¢)
Semihard (L:s = 5:2) 5\36 (166.7¢)
Hard (L:s = 3:1) 3\21 (171.4¢)
Superhard (L:s = 4:1) 4\27 (177.8¢)
Collapsed (L:s = 1:0) 1\6 (200.0¢)

6L 3s, named hyrulic in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 6 large steps and 3 small steps, with a period of 2 large steps and 1 small step that repeats every 400.0¢, or 3 times every octave. Generators that produce this scale range from 133.3¢ to 200¢, or from 200¢ to 266.7¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period. The tiny region between 26\171 and 281\1848 is the terrain region, giving the albitonic scale for the remarkable terrain temperament chromatic pair. If you feel that is too small a region to allocate or prefer EDOs of a more usual size, you can call it the region between 5\33 and 6\39, but that misses the extreme accuracy of this temperament.

For a more down-to-earth temperament, try triforce.

Modes

Scale degrees of the modes of 6L 3s 
UDP Cyclic
order
Step
pattern
Scale degree (hyrudegree)
0 1 2 3 4 5 6 7 8 9
6|0(3) 1 LLsLLsLLs Perf. Perf. Aug. Perf. Perf. Aug. Perf. Perf. Aug. Perf.
3|3(3) 2 LsLLsLLsL Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf.
0|6(3) 3 sLLsLLsLL Perf. Dim. Perf. Perf. Dim. Perf. Perf. Dim. Perf. Perf.

Scales

Scale tree

Generator ranges:

  • Chroma-positive generator: 133.3333 cents (1\9) to 200 cents (1\6)
  • Chroma-negative generator: 200 cents (1\6) to 266.6667 cents (2\9)
Generator Cents L s L/s Comments
1\9 133.333 1 1 1.000
6\51 141.176 6 5 1.200
5\42 142.857 5 4 1.250
9\75 144.000 9 7 1.286
4\33 145.455 4 3 1.333
11\90 146.667 11 8 1.375
7\57 147.368 7 5 1.400
10\81 148.148 10 7 1.429
3\24 150.000 3 2 1.500
11\87 151.724 11 7 1.571 Hemimist
8\63 152.381 8 5 1.600
13\102 152.911 13 8 1.625 Golden triforce (152.7864¢)
5\39 153.846 5 3 1.667
12\93 154.839 12 7 1.714
7\54 155.556 7 4 1.750
9\69 156.522 9 5 1.800
2\15 160.000 2 1 2.000 Basic hyrulic
9\66 163.636 9 4 2.250
7\51 164.706 7 3 2.333
12\87 165.517 12 5 2.400
5\36 166.667 5 2 2.500
13\93 167.742 13 5 2.600 Unnamed golden tuning (167.9285¢)
8\57 168.421 8 3 2.667
11\78 169.231 11 4 2.750
3\21 171.439 3 1 3.000
10\69 173.913 10 3 3.333
7\48 175.000 7 2 3.500
11\75 176.000 11 3 3.667 Oodako
4\27 177.778 4 1 4.000
9\60 180.000 9 2 4.500
5\33 181.818 5 1 5.000
6\39 184.615 6 1 6.000 Mirkat
1\6 200.000 1 0 → inf