1L 3s
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| ↑ 1L 2s | 2L 2s ↗ | |
| 1L 3s | 2L 3s → | |
| ↓ 1L 4s | 2L 4s ↘ |
┌╥┬┬┬┐ │║││││ ││││││ └┴┴┴┴┘
Scale structure
sssL
Generator size
Related MOS scales
Equal tunings
1L 3s, also called antetric, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 3 small steps, repeating every octave. Generators that produce this scale range from 900 ¢ to 1200 ¢, or from 0 ¢ to 300 ¢.
In South Africa, the San use a tetratonic scale which can be approximated by basic 1L 3s.[1]
Scale properties
- This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.
Intervals
| Intervals | Steps subtended |
Range in cents | ||
|---|---|---|---|---|
| Generic | Specific | Abbrev. | ||
| 0-mosstep | Perfect 0-mosstep | P0ms | 0 | 0.0 ¢ |
| 1-mosstep | Perfect 1-mosstep | P1ms | s | 0.0 ¢ to 300.0 ¢ |
| Augmented 1-mosstep | A1ms | L | 300.0 ¢ to 1200.0 ¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | 2s | 0.0 ¢ to 600.0 ¢ |
| Major 2-mosstep | M2ms | L + s | 600.0 ¢ to 1200.0 ¢ | |
| 3-mosstep | Diminished 3-mosstep | d3ms | 3s | 0.0 ¢ to 900.0 ¢ |
| Perfect 3-mosstep | P3ms | L + 2s | 900.0 ¢ to 1200.0 ¢ | |
| 4-mosstep | Perfect 4-mosstep | P4ms | L + 3s | 1200.0 ¢ |
Generator chain
| Bright gens | Scale degree | Abbrev. |
|---|---|---|
| 4 | Augmented 0-mosdegree | A0md |
| 3 | Augmented 1-mosdegree | A1md |
| 2 | Major 2-mosdegree | M2md |
| 1 | Perfect 3-mosdegree | P3md |
| 0 | Perfect 0-mosdegree Perfect 4-mosdegree |
P0md P4md |
| −1 | Perfect 1-mosdegree | P1md |
| −2 | Minor 2-mosdegree | m2md |
| −3 | Diminished 3-mosdegree | d3md |
| −4 | Diminished 4-mosdegree | d4md |
Modes
| UDP | Cyclic order |
Step pattern |
Scale degree (mosdegree) | ||||
|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | |||
| 3|0 | 1 | Lsss | Perf. | Aug. | Maj. | Perf. | Perf. |
| 2|1 | 4 | sLss | Perf. | Perf. | Maj. | Perf. | Perf. |
| 1|2 | 3 | ssLs | Perf. | Perf. | Min. | Perf. | Perf. |
| 0|3 | 2 | sssL | Perf. | Perf. | Min. | Dim. | Perf. |
Scale tree
Generator ranges:
- Chroma-positive generator: 900 ¢ (3\4) to 1200 ¢ (1\1)
- Chroma-negative generator: 0 ¢ (0\1) to 300 ¢ (1\4)
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 3\4 | 900.000 | 300.000 | 1:1 | 1.000 | Equalized 1L 3s | |||||
| 16\21 | 914.286 | 285.714 | 6:5 | 1.200 | ||||||
| 13\17 | 917.647 | 282.353 | 5:4 | 1.250 | ||||||
| 23\30 | 920.000 | 280.000 | 9:7 | 1.286 | ||||||
| 10\13 | 923.077 | 276.923 | 4:3 | 1.333 | Supersoft 1L 3s | |||||
| 27\35 | 925.714 | 274.286 | 11:8 | 1.375 | ||||||
| 17\22 | 927.273 | 272.727 | 7:5 | 1.400 | ||||||
| 24\31 | 929.032 | 270.968 | 10:7 | 1.429 | Orson/Orwell | |||||
| 7\9 | 933.333 | 266.667 | 3:2 | 1.500 | Soft 1L 3s | |||||
| 25\32 | 937.500 | 262.500 | 11:7 | 1.571 | ||||||
| 18\23 | 939.130 | 260.870 | 8:5 | 1.600 | ||||||
| 29\37 | 940.541 | 259.459 | 13:8 | 1.625 | ||||||
| 11\14 | 942.857 | 257.143 | 5:3 | 1.667 | Semisoft 1L 3s | |||||
| 26\33 | 945.455 | 254.545 | 12:7 | 1.714 | ||||||
| 15\19 | 947.368 | 252.632 | 7:4 | 1.750 | ||||||
| 19\24 | 950.000 | 250.000 | 9:5 | 1.800 | Godzilla | |||||
| 4\5 | 960.000 | 240.000 | 2:1 | 2.000 | Basic 1L 3s Scales with tunings softer than this are proper | |||||
| 17\21 | 971.429 | 228.571 | 9:4 | 2.250 | Laconic/gorgo | |||||
| 13\16 | 975.000 | 225.000 | 7:3 | 2.333 | ||||||
| 22\27 | 977.778 | 222.222 | 12:5 | 2.400 | ||||||
| 9\11 | 981.818 | 218.182 | 5:2 | 2.500 | Semihard 1L 3s | |||||
| 23\28 | 985.714 | 214.286 | 13:5 | 2.600 | Unnamed golden tuning (213.5979 ¢) | |||||
| 14\17 | 988.235 | 211.765 | 8:3 | 2.667 | ||||||
| 19\23 | 991.304 | 208.696 | 11:4 | 2.750 | ||||||
| 5\6 | 1000.000 | 200.000 | 3:1 | 3.000 | Hard 1L 3s | |||||
| 16\19 | 1010.526 | 189.474 | 10:3 | 3.333 | Isra/deutone | |||||
| 11\13 | 1015.385 | 184.615 | 7:2 | 3.500 | ||||||
| 17\20 | 1020.000 | 180.000 | 11:3 | 3.667 | ||||||
| 6\7 | 1028.571 | 171.429 | 4:1 | 4.000 | Superhard 1L 3s | |||||
| 13\15 | 1040.000 | 160.000 | 9:2 | 4.500 | Porcupine | |||||
| 7\8 | 1050.000 | 150.000 | 5:1 | 5.000 | ||||||
| 8\9 | 1066.667 | 133.333 | 6:1 | 6.000 | ||||||
| 1\1 | 1200.000 | 0.000 | 1:0 | → ∞ | Collapsed 1L 3s | |||||
Sources
- ↑ Wikipedia contributors. (2022, November 21). Tetratonic scale. In Wikipedia, The Free Encyclopedia. Retrieved 09:40, August 13, 2024, from https://en.wikipedia.org/w/index.php?title=Tetratonic_scale&oldid=1123114247
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Todo: expand |