6L 3s
↖ 5L 2s | ↑ 6L 2s | 7L 2s ↗ |
← 5L 3s | 6L 3s | 7L 3s → |
↙ 5L 4s | ↓ 6L 4s | 7L 4s ↘ |
┌╥╥┬╥╥┬╥╥┬┐ │║║│║║│║║││ │││││││││││ └┴┴┴┴┴┴┴┴┴┘
sLLsLLsLL
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
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 |