2L 3s (3/2-equivalent)

↖ 1L 2s⟨3/2⟩	↑ 2L 2s⟨3/2⟩	3L 2s⟨3/2⟩ ↗
← 1L 3s⟨3/2⟩	2L 3s (3/2-equivalent)	3L 3s⟨3/2⟩ →
↙ 1L 4s⟨3/2⟩	↓ 2L 4s⟨3/2⟩	3L 4s⟨3/2⟩ ↘

┌╥┬╥┬┬┐ │║│║│││ │││││││ └┴┴┴┴┴┘
Scale structure
Step pattern	LsLss ssLsL
Equave	3/2 (702.0 ¢)
Period	3/2 (702.0 ¢)
Generator size(edf)
Bright	2\5 to 1\2 (280.8 ¢ to 351.0 ¢)
Dark	1\2 to 3\5 (351.0 ¢ to 421.2 ¢)
Related MOS scales
Parent	2L 1s⟨3/2⟩
Sister	3L 2s⟨3/2⟩
Daughters	5L 2s⟨3/2⟩, 2L 5s⟨3/2⟩
Neutralized	4L 1s⟨3/2⟩
2-Flought	7L 3s⟨3/2⟩, 2L 8s⟨3/2⟩
Equal tunings(edf)
Equalized (L:s = 1:1)	2\5 (280.8 ¢)
Supersoft (L:s = 4:3)	7\17 (289.0 ¢)
Soft (L:s = 3:2)	5\12 (292.5 ¢)
Semisoft (L:s = 5:3)	8\19 (295.6 ¢)
Basic (L:s = 2:1)	3\7 (300.8 ¢)
Semihard (L:s = 5:2)	7\16 (307.1 ¢)
Hard (L:s = 3:1)	4\9 (312.0 ¢)
Superhard (L:s = 4:1)	5\11 (319.1 ¢)
Collapsed (L:s = 1:0)	1\2 (351.0 ¢)

2L 3s⟨3/2⟩, also called saturnian, is a 3/2-equivalent (fifth-equivalent) moment of symmetry scale containing 2 large steps and 3 small steps, repeating every interval of 3/2 (702.0 ¢). Generators that produce this scale range from 280.8 ¢ to 351 ¢, or from 351 ¢ to 421.2 ¢. Due to its minor third generator, this scale has a wealth of diminished triads. Basic saturnian is in 7edf, an approximation of 12edo, which allows for playing regular music and saturnian music at the same time.

Notation

The main way of notating the saturnian scale is using a 3/2-repeating notation consisting of 5 naturals (e.g. ABCDE for the 2|2 mode).

Intervals

MOS degrees is deprecated. Please use Template:MOS tunings instead.

Scale degree of 2L 3s⟨3/2⟩

Scale degree	On A	7edf (Basic, L:s = 2:1)		9edf (Hard, L:s = 3:1)		12edf (Soft, L:s = 3:2)		Approx. JI Ratios
		Steps	Cents	Steps	Cents	Steps	Cents
Perfect 0-mosdegree (unison)	A	0	0	0	0	0	0	1/1 (exact)
Minor 1-mosdegree	B	1	100.3	1	78	2	117
Major 1-mosdegree	B#	2	200.6	3	234	3	175.5
Diminished 2-mosdegree	Cb	2	200.6	2	156	4	234
Perfect 2-mosdegree	C	3	300.8	4	312	5	292.5
Perfect 3-mosdegree	D	4	401.1	5	390	7	409.5
Augmented 3-mosdegree	D#	5	501.4	7	546	8	468
Minor 4-mosdegree	Eb	5	501.4	6	468	9	526.5
Major 4-mosdegree	E	6	601.7	8	624	10	585
Perfect 5-mosdegree (equave)	A	7	702	9	702	12	702	3/2 (exact)

Genchain

-4	-3	-2	-1	0	1	2	3	4
d2ms	m4ms	m1ms	P3ms	P0ms	P2ms	M4ms	M1ms	A3ms

Theory

2L 3s⟨3/2⟩ can be interpreted as the nonoctave regular temperament named pythium by User:CompactStar, tempering out 81/80 in the 3/2.4.5 subgroup. This is the simplest 3/2-equivalent temperament not containing octaves. Because the 3/2-reduced 5th harmonic of 40/27 is conflated with the just perfect fifth, the CTE generator of this temperament is exactly the 32/27 Pythagorean minor third. Although the most accurate tunings use near-32/27 generators, pythium can be tuned with minor thirds as high as that of 11edf's (319 cents).

Modes

The mode names are based on the 5 largest satellites of Saturn.

Modes of 2L 3s⟨3/2⟩

UDP	Cyclic order	Step pattern
4|0	1	LsLss
3|1	3	LssLs
2|2	5	sLsLs
1|3	2	sLssL
0|4	4	ssLsL