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

Equal tunings

Equalized (L:s = 1:1)

3\7 (514.3 ¢)

Supersoft (L:s = 4:3)

10\23 (521.7 ¢)

7\16 (525.0 ¢)

11\25 (528.0 ¢)

4\9 (533.3 ¢)

9\20 (540.0 ¢)

5\11 (545.5 ¢)

Superhard (L:s = 4:1)

6\13 (553.8 ¢)

Collapsed (L:s = 1:0)

1\2 (600.0 ¢)

2L 5s or antidiatonic 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, 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 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.

Notation

Diamond MOS notation, &/@ = raise and lower by one chroma. We'll write this using CDEFGABC is C Antiionian (ssLsssL); C = 261.6256 Hz. 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 in degrees of an edo							generator in cents	tetrachord	L in cents	s in cents	L to s ratio	comments
3\7							514.3	1 1 1	171.4	171.4	1.00
						19\44	518.2	6 6 7	190.9	163.6	1.17
					16\37		518.9	5 5 6	194.6	162.2	1.20
				13\30			520.0	4 4 5	200.0	160.0	1.25	Mavila extends from here...
			10\23				521.7	3 3 4	208.7	156.5	1.33
				17\39			523.1	5 5 7	215.4	153.8	1.40
		7\16					525.0	2 2 3	225.0	150.0	1.50	Mavila in Armodue Optimum rank range (L/s=3/2)
							526.3	2 2 pi	231.5	147.4	pi/2
				18\41			526.8	5 5 8	234.1	146.3	1.60
							1200*5/(13-phi)	1 1 phi	235.7	145.7	phi	Golden mavila
					29\66		527.3	8 8 13	236.4	145.5	1.625
			11\25				528.0	3 3 5	240.0	144.0	1.67
							529.1	1 1 √3	245.6	141.8	√3
				15\34			529.4	4 4 7	247.1	141.2	1.75	...to somewhere around here
	4\9						533.3	1 1 2	266.7	133.3	2.00	Boundary of propriety (generators smaller than this are proper)
				13\29			537.9	3 3 7	289.7	124.1	2.33
			9\20				540.0	2 2 5	300.0	120.0	2.50
							541.4	1 1 phi+1	306.9	117.2	1 1 phi+1
				14\31			541.9	3 3 8	309.7	116.1	2.66
							542.5	1 1 e	321.55	115.0	e	L/s = e
		5\11					545.5	1 1 3	327.3	109.1	3.00	L/s = 3
							546.8	1 1 pi	334.1	106.35	pi	L/s = pi
				11\24			550.0	2 2 7	350.0	100.0	3.50
			6\13				553.8	1 1 4	369.2	92.3	4.00	Thuja is optimal around here L/s = 4
				7\15			560.0	1 1 5	400.0	80.0	5.00	ie. (11/8)^5 = 5/1
					8\17		564.7	1 1 6	423.5	70.6	6.00
						9\19	568.4	1 1 7	442.1	63.2	7.00	Liese/Triton is around here
1\2							600.0	0 0 1	600.0	0	—

Musical Examples

Mike Battaglia has "translated" several common practice pieces into mavila antidiatonic by using Graham Breed's Lilypond code to tune the generators flat. Musical examples are provided in 9-EDO, 16-EDO, 23-EDO, and 25-EDO, for comparison. Note that the melodic and/or intonational properties differ slightly for each tuning.

9-EDO: Provided ID could not be validated.

16-EDO: Provided ID could not be validated.

23-EDO: Provided ID could not be validated.

25-EDO: Provided ID could not be validated.