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 contains 2 diminished triads. Basic saturnian is in 7edf, an approximation of 12edo, which allows for playing regular music and saturnian music at the same time. It is also a parent of the 3/2-repeating microdiatonic scale, 5L 2s⟨3/2⟩.

Notation

The main way of notating the saturnian scale is using a 3/2-repeating notation consisting of 5 naturals (e.g. A-E 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