2L 5s
| ↖ 1L 4s | ↑ 2L 4s | 3L 4s ↗ |
| ← 1L 5s | 2L 5s | 3L 5s → |
| ↙ 1L 6s | ↓ 2L 6s | 3L 6s ↘ |
┌╥┬┬╥┬┬┬┐ │║││║││││ │││││││││ └┴┴┴┴┴┴┴┘
sssLssL
2L 5s refers to the structure of octave-equivalent MOS scales with generators ranging from 3\7 (3 degrees of 7edo = 514.29¢) to 1\2 (one degree of 2edo = 600¢). In the case of 7edo, L and s are the same size; in the case of 2edo, s becomes so small it disappears (and all that remains are the two equal L's).
While antidiatonic is closely associated with mavila temperament and 7L 2s, not every 2L 5s scale is an instance of "mavila", since some of them extend to 2L 7s scales (like the 2L 5s generated by 11edo's 6\11 = 656.5657¢), not 7L 2s mavila superdiatonic scales. (In particular, between 13\29 and 14\31, and centered on 9\20, is the albitonic scale for the 2.7.11.13 subgroup temperament score, which is not intended to be treated as having any kind of fifth, flat or otherwise.)
In terms of harmonic entropy, the most significant minimum is at Liese/Triton, in which the generator is about 7/5 and three of them make a 3/1.
Names
It is often called antidiatonic, because it has the step pattern of diatonic (5L 2s), but with the large and small steps switched. TAMNAMS uses this name as well.
Notation
We'll use the convention DEFGABCD (D Antidorian, sLsssLs); D = 293.665 Hz, &/@ = raise and lower by one chroma. The chain of mavila fifths becomes … E& B& F C G D A E B F@ C@ … Note that 7 fifths up flattens a note by a chroma, rather than sharpening it as in diatonic (5L 2s).
Intervals
Note: In TAMNAMS, a k-step interval class in antidiatonic may be called a "k-step", "k-mosstep", or "k-pelstep". 1-indexed terms such as "mos(k+1)th" are discouraged for non-diatonic mosses.
Scale tree
| Generator | Cents | L | s | L/s | Comments | |||||
|---|---|---|---|---|---|---|---|---|---|---|
| 3\7 | 514.286 | 1 | 1 | 1.000 | ||||||
| 16\37 | 518.919 | 6 | 5 | 1.200 | ||||||
| 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 | L/s = 3/2, 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 | |||||
| 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 | ||||||
| 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 | |||||
| 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 | L/s = 3/1 | |||||
| 16\35 | 548.571 | 10 | 3 | 3.333 | ||||||
| 11\24 | 550.000 | 7 | 2 | 3.500 | ||||||
| 17\37 | 551.351 | 11 | 3 | 3.667 | ||||||
| 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 | ||||||