2L 5s
| ↖ 1L 4s | ↑ 2L 4s | 3L 4s ↗ |
| ← 1L 5s | 2L 5s | 3L 5s → |
| ↙ 1L 6s | ↓ 2L 6s | 3L 6s ↘ |
┌╥┬┬╥┬┬┬┐ │║││║││││ │││││││││ └┴┴┴┴┴┴┴┘
sssLssL
2L 5s, named antidiatonic in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 5 small steps, repeating every octave. Generators that produce this scale range from 514.3 ¢ to 600 ¢, or from 600 ¢ to 685.7 ¢.
Name
TAMNAMS suggests the temperament-agnostic name antidiatonic for this scale, adopted from the common use of the term to refer to diatonic (5L 2s) but with the large and small steps switched.
Notation
- This article assumes TAMNAMS for naming step ratios, intervals, and scale degrees, and diamond-MOS notation for note names.
Intervals and degrees
Names for this scale's intervals (mossteps) and scale degrees (mosdegrees) are based on the number of large and small steps from the root, starting at 0 (0-mosstep and 0-mosdegree) for the unison, per TAMNAMS. Ordinal names, such as mos-1st for the unison, are discouraged for non-diatonic MOS scales.
Being a moment-of-symmetry scale, every interval class of 2L 5s, except for the unison and octave, has two varieties – large and small – whose relative qualities are denoted as major or minor, or augmented, perfect, and diminished for the generators.
| Intervals | Steps subtended |
Range in cents | ||
|---|---|---|---|---|
| Generic | Specific | Abbrev. | ||
| 0-pelstep | Perfect 0-pelstep | P0pels | 0 | 0.0 ¢ |
| 1-pelstep | Minor 1-pelstep | m1pels | s | 0.0 ¢ to 171.4 ¢ |
| Major 1-pelstep | M1pels | L | 171.4 ¢ to 600.0 ¢ | |
| 2-pelstep | Minor 2-pelstep | m2pels | 2s | 0.0 ¢ to 342.9 ¢ |
| Major 2-pelstep | M2pels | L + s | 342.9 ¢ to 600.0 ¢ | |
| 3-pelstep | Diminished 3-pelstep | d3pels | 3s | 0.0 ¢ to 514.3 ¢ |
| Perfect 3-pelstep | P3pels | L + 2s | 514.3 ¢ to 600.0 ¢ | |
| 4-pelstep | Perfect 4-pelstep | P4pels | L + 3s | 600.0 ¢ to 685.7 ¢ |
| Augmented 4-pelstep | A4pels | 2L + 2s | 685.7 ¢ to 1200.0 ¢ | |
| 5-pelstep | Minor 5-pelstep | m5pels | L + 4s | 600.0 ¢ to 857.1 ¢ |
| Major 5-pelstep | M5pels | 2L + 3s | 857.1 ¢ to 1200.0 ¢ | |
| 6-pelstep | Minor 6-pelstep | m6pels | L + 5s | 600.0 ¢ to 1028.6 ¢ |
| Major 6-pelstep | M6pels | 2L + 4s | 1028.6 ¢ to 1200.0 ¢ | |
| 7-pelstep | Perfect 7-pelstep | P7pels | 2L + 5s | 1200.0 ¢ |
Note names
For this article, note names are based on diamond-MOS notation, where the naturals JKLMNOP are applied to the step pattern sLsssLs and the accidentals & (pronounced "am" or "amp") and @ (pronounced "at") are used to represent sharps and flats respectively. Thus, the basic gamut for 2L 5s is the following:
J, K, K&/L@, L, M, N, O, O&/P@, P, J
Theory
Antidiatonic is similar to diatonic (5L 2s) except interval classes are flipped. For example, there are natural, harmonic, and melodic major scales instead of minor scales, and its locrian scale, called "antilocrian", has an augmented "fifth" instead of a diminished fifth. The flatter the "fifth" (or 4-mosstep) gets, the less the scale resembles diatonic. Additionally, there are temperaments associated with this MOS, such as score, that do not have intervals that resemble a diatonic 5th, flattened or otherwise.
Low harmonic entropy scales
There is one notable harmonic entropy minimum: Liese/triton, in which the generator is 7/5 (582.5¢) and three of them make a 3/1 (1902¢).
Temperament interpretations
2L 5s has several rank-2 temperament interpretations, such as:
Modes
Modes of the antidiatonic scale are usually named as "anti-" combined with the opposite mode of the diatonic scale, e.g. 4|2 being called "antiaeolian". CompactStar also gave original names based on regions of France to mirror how modes of the diatonic scale are named on regions of Greece and Turkey.
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 6|0 | 1 | LssLsss |
| 5|1 | 4 | LsssLss |
| 4|2 | 7 | sLssLss |
| 3|3 | 3 | sLsssLs |
| 2|4 | 6 | ssLssLs |
| 1|5 | 2 | ssLsssL |
| 0|6 | 5 | sssLssL |
Scale tree
Generator ranges:
- Chroma-positive generator: 514.2857 cents (3\7) to 600 cents (1\2)
- Chroma-negative generator: 600 cents (1\2) to 685.7143 cents (4\7)
| Generator | Cents | L | s | L/s | Comments | |||||
|---|---|---|---|---|---|---|---|---|---|---|
| 3\7 | 514.286 | 1 | 1 | 1.000 | ||||||
| 16\37 | 518.919 | 6 | 5 | 1.200 | Gravity↑ | |||||
| 13\30 | 520.000 | 5 | 4 | 1.250 | ||||||
| 23\53 | 520.755 | 9 | 7 | 1.286 | ||||||
| 10\23 | 521.739 | 4 | 3 | 1.333 | ||||||
| 27\62 | 522.581 | 11 | 8 | 1.375 | ||||||
| 17\39 | 523.077 | 7 | 5 | 1.400 | ||||||
| 24\55 | 523.636 | 10 | 7 | 1.428 | ||||||
| 7\16 | 525.000 | 3 | 2 | 1.500 | Mavila is in this region | |||||
| 25\57 | 526.316 | 11 | 7 | 1.571 | ||||||
| 18\41 | 526.829 | 8 | 5 | 1.600 | ||||||
| 29\66 | 527.273 | 13 | 8 | 1.625 | Golden mavila (527.1497¢) | |||||
| 11\25 | 528.000 | 5 | 3 | 1.667 | ||||||
| 26\59 | 528.814 | 12 | 7 | 1.714 | ||||||
| 15\34 | 529.412 | 7 | 4 | 1.750 | ||||||
| 19\43 | 530.233 | 9 | 5 | 1.800 | Mabila / Amavil | |||||
| 4\9 | 533.333 | 2 | 1 | 2.000 | Basic antidiatonic (Generators smaller than this are proper) | |||||
| 17\38 | 536.842 | 9 | 4 | 2.250 | ||||||
| 13\29 | 537.931 | 7 | 3 | 2.333 | ||||||
| 22\49 | 538.776 | 12 | 5 | 2.400 | ||||||
| 9\20 | 540.000 | 5 | 2 | 2.500 | Score | |||||
| 23\51 | 541.176 | 13 | 5 | 2.600 | Unnamed golden tuning (541.3837¢) | |||||
| 14\31 | 541.935 | 8 | 3 | 2.667 | Casablanca is around here | |||||
| 19\42 | 542.857 | 11 | 4 | 2.750 | ||||||
| 5\11 | 545.455 | 3 | 1 | 3.000 | ||||||
| 16\35 | 548.571 | 10 | 3 | 3.333 | ||||||
| 11\24 | 550.000 | 7 | 2 | 3.500 | ||||||
| 17\37 | 551.351 | 11 | 3 | 3.667 | Freivald / emka | |||||
| 6\13 | 553.846 | 4 | 1 | 4.000 | ||||||
| 13\28 | 557.143 | 9 | 2 | 4.500 | ||||||
| 7\15 | 560.000 | 5 | 1 | 5.000 | Thuja is around here | |||||
| 8\17 | 564.706 | 6 | 1 | 6.000 | Liese↓, triton↓ | |||||
| 1\2 | 600.000 | 1 | 0 | → inf | ||||||