6L 2s
| ↖ 5L 1s | ↑6L 1s | 7L 1s ↗ |
| ← 5L 2s | 6L 2s | 7L 2s → |
| ↙ 5L 3s | ↓6L 3s | 7L 3s ↘ |
┌╥╥╥┬╥╥╥┬┐ │║║║│║║║││ ││││││││││ └┴┴┴┴┴┴┴┴┘
sLLLsLLL
6L 2s, named ekic in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 6 large steps and 2 small steps, with a period of 3 large steps and 1 small step that repeats every 600.0¢, or twice every octave. Generators that produce this scale range from 150¢ to 200¢, or from 400¢ to 450¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period. There is only one significant (though small) harmonic entropy minimum with this MOS pattern: hedgehog, in which two generators are 6/5 and three are 4/3, same as porcupine.
6L 2s can be seen as a warped diatonic scale, where one additional large step is added to diatonic (5L 2s).
In addition to the true MOS pattern, there is a near-mos pattern, LLLLsLLs, in which the period is the only interval with more than two varieties. This near-MOS pattern is only proper if the generator is smaller than 2\14. Hedgehog is among these tunings.
Intervals
| Intervals | Steps subtended | Range in cents | Average of HE (from HE Calc) |
Min of HE | ||
|---|---|---|---|---|---|---|
| Generic[1] | Specific[2] | Abbrev.[3] | ||||
| 0-ekstep | Perfect 0-ekstep | P0ms | 0 | 0.0¢ | ~2.4654 nats | ~2.4654 nats |
| 1-ekstep | Diminished 1-ekstep | d1ms | s | 0.0¢ to 150.0¢ | ~4.7185 nats | ~4.6521 nats |
| Perfect 1-ekstep | P1ms | L | 150.0¢ to 200.0¢ | ~4.6038 nats | ~4.5938 nats | |
| 2-ekstep | Minor 2-ekstep | m2ms | L + s | 200.0¢ to 300.0¢ | ~4.5760 nats | ~4.5636 nats |
| Major 2-ekstep | M2ms | 2L | 300.0¢ to 400.0¢ | ~4.5837 nats | ~4.5422 nats | |
| 3-ekstep | Perfect 3-ekstep | P3ms | 2L + s | 400.0¢ to 450.0¢ | ~4.6017 nats | ~4.5972 nats |
| Augmented 3-ekstep | A3ms | 3L | 450.0¢ to 600.0¢ | ~4.5165 nats | ~4.3665 nats | |
| 4-ekstep | Perfect 4-ekstep | P4ms | 3L + s | 600.0¢ | ~4.5799 nats | ~4.5799 nats |
| 5-ekstep | Diminished 5-ekstep | d5ms | 3L + 2s | 600.0¢ to 750.0¢ | ~4.4208 nats | ~4.1319 nats |
| Perfect 5-ekstep | P5ms | 4L + s | 750.0¢ to 800.0¢ | ~4.6148 nats | ~4.6034 nats | |
| 6-ekstep | Minor 6-ekstep | m6ms | 4L + 2s | 800.0¢ to 900.0¢ | ~4.5515 nats | ~4.4330 nats |
| Major 6-ekstep | M6ms | 5L + s | 900.0¢ to 1000.0¢ | ~4.5862 nats | ~4.5308 nats | |
| 7-ekstep | Perfect 7-ekstep | P7ms | 5L + 2s | 1000.0¢ to 1050.0¢ | ~4.5884 nats | ~4.5784 nats |
| Augmented 7-ekstep | A7ms | 6L + s | 1050.0¢ to 1200.0¢ | ~4.6525 nats | ~4.6089 nats | |
| 8-ekstep | Perfect 8-ekstep | P8ms | 6L + 2s | 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 (ekdegree) | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |||
| 6|0(2) | 1 | LLLsLLLs | Perf. | Perf. | Maj. | Aug. | Perf. | Perf. | Maj. | Aug. | Perf. |
| 4|2(2) | 2 | LLsLLLsL | Perf. | Perf. | Maj. | Perf. | Perf. | Perf. | Maj. | Perf. | Perf. |
| 2|4(2) | 3 | LsLLLsLL | Perf. | Perf. | Min. | Perf. | Perf. | Perf. | Min. | Perf. | Perf. |
| 0|6(2) | 4 | sLLLsLLL | Perf. | Dim. | Min. | Perf. | Perf. | Dim. | Min. | Perf. | Perf. |
Proposed Names
The following mode names are advocated by Frostburn for their dreamy, yet oppressing sound especially in 20edo.
| UDP | Rotational order | Step pattern | Mode names |
|---|---|---|---|
| 4|0(2) | 1 | LLLsLLLs | Paralysis |
| 2|2(2) | 2 | LLsLLLsL | Nightmare |
| 0|4(2) | 3 | LsLLLsLL | Succubus |
| -2|6(2) | 4 | sLLLsLLL | Incubus |
Scale tree
| Generator(edo) | Cents | Step Ratio | Comments(always proper) | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 1\8 | 150.000 | 450.000 | 1:1 | 1.000 | Equalized 6L 2s | |||||
| 6\46 | 156.522 | 443.478 | 6:5 | 1.200 | Bison | |||||
| 5\38 | 157.895 | 442.105 | 5:4 | 1.250 | ||||||
| 9\68 | 158.824 | 441.176 | 9:7 | 1.286 | ||||||
| 4\30 | 160.000 | 440.000 | 4:3 | 1.333 | Supersoft 6L 2s | |||||
| 11\82 | 160.976 | 439.024 | 11:8 | 1.375 | ||||||
| 7\52 | 161.538 | 438.462 | 7:5 | 1.400 | ||||||
| 10\74 | 162.162 | 437.838 | 10:7 | 1.429 | ||||||
| 3\22 | 163.636 | 436.364 | 3:2 | 1.500 | Soft 6L 2s Hedgehog is around here | |||||
| 11\80 | 165.000 | 435.000 | 11:7 | 1.571 | Echidna | |||||
| 8\58 | 165.517 | 434.483 | 8:5 | 1.600 | ||||||
| 13\94 | 165.957 | 434.043 | 13:8 | 1.625 | Supers, pogo | |||||
| 5\36 | 166.667 | 433.333 | 5:3 | 1.667 | Semisoft 6L 2s | |||||
| 12\86 | 167.442 | 432.558 | 12:7 | 1.714 | ||||||
| 7\50 | 168.000 | 432.000 | 7:4 | 1.750 | ||||||
| 9\64 | 168.750 | 431.250 | 9:5 | 1.800 | ||||||
| 2\14 | 171.429 | 428.571 | 2:1 | 2.000 | Basic 6L 2s | |||||
| 9\62 | 174.194 | 425.806 | 9:4 | 2.250 | ||||||
| 7\48 | 175.000 | 425.000 | 7:3 | 2.333 | ||||||
| 12\82 | 175.610 | 424.390 | 12:5 | 2.400 | ||||||
| 5\34 | 176.471 | 423.529 | 5:2 | 2.500 | Semihard 6L 2s | |||||
| 13\88 | 177.273 | 422.727 | 13:5 | 2.600 | Golden ekic | |||||
| 8\54 | 177.778 | 422.222 | 8:3 | 2.667 | ||||||
| 11\74 | 178.378 | 421.622 | 11:4 | 2.750 | ||||||
| 3\20 | 180.000 | 420.000 | 3:1 | 3.000 | Hard 6L 2s | |||||
| 10\66 | 181.818 | 418.182 | 10:3 | 3.333 | ||||||
| 7\46 | 182.609 | 417.391 | 7:2 | 3.500 | ||||||
| 11\72 | 183.333 | 416.667 | 11:3 | 3.667 | Unidec | |||||
| 4\26 | 184.615 | 415.385 | 4:1 | 4.000 | Superhard 6L 2s | |||||
| 9\58 | 186.207 | 413.793 | 9:2 | 4.500 | Secant | |||||
| 5\32 | 187.500 | 412.500 | 5:1 | 5.000 | ||||||
| 6\38 | 189.474 | 410.526 | 6:1 | 6.000 | ||||||
| 1\6 | 200.000 | 400.000 | 1:0 | → ∞ | Collapsed 6L 2s | |||||