4L 4s
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Scale structure
Step pattern
LsLsLsLs
sLsLsLsL
Equave
2/1 (1200.0¢)
Period
1\2 (600.0¢)
Generator size
Bright
1\8 to 1\4 (150.0¢ to 300.0¢)
Dark
0\4 to 1\8 (0.0¢ to 150.0¢)
TAMNAMS information
Name
tetrawood
Prefix
tetrawd-
Abbrev.
ttw
Related MOS scales
Parent
4L 0s
Sister
4L 4s
Daughters
8L 4s, 4L 8s
Neutralized
8L 0s
2-Flought
12L 4s, 4L 12s
Equal tunings
Equalized (L:s = 1:1)
1\8 (150.0¢)
Supersoft (L:s = 4:3)
4\28 (171.4¢)
Soft (L:s = 3:2)
3\20 (180.0¢)
Semisoft (L:s = 5:3)
5\32 (187.5¢)
Basic (L:s = 2:1)
2\12 (200.0¢)
Semihard (L:s = 5:2)
5\28 (214.3¢)
Hard (L:s = 3:1)
3\16 (225.0¢)
Superhard (L:s = 4:1)
4\20 (240.0¢)
Collapsed (L:s = 1:0)
1\4 (300.0¢)
| ↖ 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 | Average of HE (from HE Calc) |
Min of HE | ||
|---|---|---|---|---|---|---|
| Generic[1] | Specific[2] | Abbrev.[3] | ||||
| 0-tetrawdstep | Perfect 0-tetrawdstep | P0ms | 0 | 0.0¢ | ~2.4654 nats | ~2.4654 nats |
| 1-tetrawdstep | Minor 1-tetrawdstep | m1ms | s | 0.0¢ to 150.0¢ | ~4.6945 nats | ~4.6426 nats |
| Major 1-tetrawdstep | M1ms | L | 150.0¢ to 300.0¢ | ~4.5904 nats | ~4.5841 nats | |
| 2-tetrawdstep | Perfect 2-tetrawdstep | P2ms | L + s | 300.0¢ | ~4.5654 nats | ~4.5654 nats |
| 3-tetrawdstep | Minor 3-tetrawdstep | m3ms | L + 2s | 300.0¢ to 450.0¢ | ~4.5631 nats | ~4.4856 nats |
| Major 3-tetrawdstep | M3ms | 2L + s | 450.0¢ to 600.0¢ | ~4.5125 nats | ~4.3665 nats | |
| 4-tetrawdstep | Perfect 4-tetrawdstep | P4ms | 2L + 2s | 600.0¢ | ~4.5799 nats | ~4.5799 nats |
| 5-tetrawdstep | Minor 5-tetrawdstep | m5ms | 2L + 3s | 600.0¢ to 750.0¢ | ~4.4080 nats | ~4.1319 nats |
| Major 5-tetrawdstep | M5ms | 3L + 2s | 750.0¢ to 900.0¢ | ~4.5955 nats | ~4.5709 nats | |
| 6-tetrawdstep | Perfect 6-tetrawdstep | P6ms | 3L + 3s | 900.0¢ | ~4.4980 nats | ~4.4980 nats |
| 7-tetrawdstep | Minor 7-tetrawdstep | m7ms | 3L + 4s | 900.0¢ to 1050.0¢ | ~4.5684 nats | ~4.5338 nats |
| Major 7-tetrawdstep | M7ms | 4L + 3s | 1050.0¢ to 1200.0¢ | ~4.6332 nats | ~4.6079 nats | |
| 8-tetrawdstep | Perfect 8-tetrawdstep | P8ms | 4L + 4s | 1200.0¢ | ~3.3273 nats | ~3.3273 nats |
- Generic intervals are denoted solely by the number of steps they subtend.
- Specific intervals denote whether an interval is major, minor, augmented, perfect, or diminished.
- Abbreviations can be further shortened to 'ms' if context allows.
Modes
| UDP | Rotational 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 | ||||||