2L 5s

↖ 1L 4s	↑ 2L 4s	3L 4s ↗
← 1L 5s	2L 5s	3L 5s →
↙ 1L 6s	↓ 2L 6s	3L 6s ↘

┌╥┬┬╥┬┬┬┐ │║││║││││ │││││││││ └┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LssLsss sssLssL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	3\7 to 1\2 (514.3 ¢ to 600.0 ¢)
Dark	1\2 to 4\7 (600.0 ¢ to 685.7 ¢)
TAMNAMS information
Name	antidiatonic
Prefix	pel-
Abbrev.	pel
Related MOS scales
Parent	2L 3s
Sister	5L 2s
Daughters	7L 2s, 2L 7s
Neutralized	4L 3s
2-Flought	9L 5s, 2L 12s
Equal tunings
Equalized (L:s = 1:1)	3\7 (514.3 ¢)
Supersoft (L:s = 4:3)	10\23 (521.7 ¢)
Soft (L:s = 3:2)	7\16 (525.0 ¢)
Semisoft (L:s = 5:3)	11\25 (528.0 ¢)
Basic (L:s = 2:1)	4\9 (533.3 ¢)
Semihard (L:s = 5:2)	9\20 (540.0 ¢)
Hard (L:s = 3:1)	5\11 (545.5 ¢)
Superhard (L:s = 4:1)	6\13 (553.8 ¢)
Collapsed (L:s = 1:0)	1\2 (600.0 ¢)

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).

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