4L 4s
| ↖ 3L 3s | ↑ 4L 3s | 5L 3s ↗ |
| ← 3L 4s | 4L 4s | 5L 4s → |
| ↙ 3L 5s | ↓ 4L 5s | 5L 5s ↘ |
┌╥┬╥┬╥┬╥┬┐ │║│║│║│║││ ││││││││││ └┴┴┴┴┴┴┴┴┘
sLsLsLsL
4L 4s, named tetrawood in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 4 small steps, with a period of 1 large step and 1 small step that repeats every 300.0¢, or 4 times every octave. Generators that produce this scale range from 150¢ to 300¢, or from 0¢ to 150¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period. The minimum harmonic entropy scale with this MOS pattern is diminished[8], the familiar octatonic scale of 12edo.
In addition to the true MOS form, LsLsLsLs, there are four near-MOS forms – LLsLsLss, LLsLssLs, LLssLLss, and LLssLsLs – in which the period and its multiples are the only intervals with more than two varieties. The near-MOS forms are only proper if the dark generator is larger than 1\12 (100¢).
Intervals
| Intervals | Steps subtended |
Range in cents | ||
|---|---|---|---|---|
| Generic | Specific | Abbrev. | ||
| 0-tetrawdstep | Perfect 0-tetrawdstep | P0ttws | 0 | 0.0¢ |
| 1-tetrawdstep | Minor 1-tetrawdstep | m1ttws | s | 0.0¢ to 150.0¢ |
| Major 1-tetrawdstep | M1ttws | L | 150.0¢ to 300.0¢ | |
| 2-tetrawdstep | Perfect 2-tetrawdstep | P2ttws | L + s | 300.0¢ |
| 3-tetrawdstep | Minor 3-tetrawdstep | m3ttws | L + 2s | 300.0¢ to 450.0¢ |
| Major 3-tetrawdstep | M3ttws | 2L + s | 450.0¢ to 600.0¢ | |
| 4-tetrawdstep | Perfect 4-tetrawdstep | P4ttws | 2L + 2s | 600.0¢ |
| 5-tetrawdstep | Minor 5-tetrawdstep | m5ttws | 2L + 3s | 600.0¢ to 750.0¢ |
| Major 5-tetrawdstep | M5ttws | 3L + 2s | 750.0¢ to 900.0¢ | |
| 6-tetrawdstep | Perfect 6-tetrawdstep | P6ttws | 3L + 3s | 900.0¢ |
| 7-tetrawdstep | Minor 7-tetrawdstep | m7ttws | 3L + 4s | 900.0¢ to 1050.0¢ |
| Major 7-tetrawdstep | M7ttws | 4L + 3s | 1050.0¢ to 1200.0¢ | |
| 8-tetrawdstep | Perfect 8-tetrawdstep | P8ttws | 4L + 4s | 1200.0¢ |
Modes
| UDP | Cyclic order |
Step pattern |
Scale degree (tetrawddegree) | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |||
| 4|0(4) | 1 | LsLsLsLs | Perf. | Maj. | Perf. | Maj. | Perf. | Maj. | Perf. | Maj. | Perf. |
| 0|4(4) | 2 | sLsLsLsL | Perf. | Min. | Perf. | Min. | Perf. | Min. | Perf. | Min. | Perf. |
Scale tree
| Generator | Cents | L | s | L/s | Comments | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Chroma-positive | Chroma-negative | ||||||||||
| 1\8 | 150.000 | 150.000 | 1 | 1 | 1.000 | ||||||
| 6\44 | 163.636 | 136.364 | 6 | 5 | 1.200 | Fourfives↑ | |||||
| 5\36 | 166.667 | 133.333 | 5 | 4 | 1.250 | ||||||
| 9\64 | 168.750 | 105.000 | 9 | 7 | 1.286 | ||||||
| 4\28 | 171.429 | 128.571 | 4 | 3 | 1.333 | ||||||
| 11\76 | 173.684 | 126.316 | 11 | 8 | 1.375 | ||||||
| 7\48 | 175.000 | 125.000 | 7 | 5 | 1.400 | ||||||
| 10\68 | 176.471 | 123.529 | 10 | 7 | 1.428 | ||||||
| 3\20 | 180.000 | 60.000 | 3 | 2 | 1.500 | L/s = 3/2 | |||||
| 11\72 | 183.333 | 116.667 | 11 | 7 | 1.571 | ||||||
| 8\52 | 184.615 | 115.385 | 8 | 5 | 1.600 | ||||||
| 13\84 | 185.714 | 114.286 | 13 | 8 | 1.625 | Golden diminished | |||||
| 5\32 | 187.500 | 112.500 | 5 | 3 | 1.667 | ||||||
| 12\76 | 189.474 | 110.526 | 12 | 7 | 1.714 | ||||||
| 7\44 | 190.909 | 109.091 | 7 | 4 | 1.750 | ||||||
| 9\56 | 192.857 | 107.143 | 9 | 5 | 1.800 | ||||||
| 2\12 | 200.000 | 100.000 | 2 | 1 | 2.000 | Basic tetrawood Diminished is optimal around here | |||||
| 9\52 | 207.692 | 92.308 | 9 | 4 | 2.250 | ||||||
| 7\40 | 210.000 | 90.000 | 7 | 3 | 2.333 | ||||||
| 12\68 | 211.765 | 88.235 | 12 | 5 | 2.400 | ||||||
| 5\28 | 214.286 | 85.714 | 5 | 2 | 2.500 | ||||||
| 13\72 | 216.667 | 83.333 | 13 | 5 | 2.600 | Unnamed golden tuning | |||||
| 8\44 | 218.182 | 81.818 | 8 | 3 | 2.667 | ||||||
| 11\60 | 220.000 | 80.000 | 11 | 4 | 2.750 | ||||||
| 3\16 | 225.000 | 75.000 | 3 | 1 | 3.000 | L/s = 3/1 | |||||
| 10\52 | 230.769 | 69.231 | 10 | 3 | 3.333 | ||||||
| 7\36 | 233.333 | 66.667 | 7 | 2 | 3.500 | ||||||
| 11\56 | 235.714 | 64.286 | 11 | 3 | 3.667 | ||||||
| 4\20 | 240.000 | 60.000 | 4 | 1 | 4.000 | ||||||
| 9\44 | 245.455 | 54.545 | 9 | 2 | 4.500 | ||||||
| 5\24 | 250.000 | 50.000 | 5 | 1 | 5.000 | ||||||
| 6\28 | 257.143 | 42.857 | 6 | 1 | 6.000 | Quadritikleismic↓ | |||||
| 1\4 | 300.000 | 0.000 | 1 | 0 | → inf | ||||||