1L 3s (3/2-equivalent)

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

┌╥┬┬┬┐
│║││││
││││││
└┴┴┴┴┘

Scale structure

Step pattern

Lsss
sssL

Equave

3/2 (702.0¢)

Period

3/2 (702.0¢)

Generator size^(edf)

Bright

3\4 to 1\1 (526.5¢ to 702.0¢)

Dark

0\1 to 1\4 (0.0¢ to 175.5¢)

Related MOS scales

4L 1s⟨3/2⟩
1L 4s⟨3/2⟩

Equal tunings^(edf)

Equalized (L:s = 1:1)

3\4 (526.5¢)

Supersoft (L:s = 4:3)

10\13 (540.0¢)

Soft (L:s = 3:2)

7\9 (546.0¢)

Semisoft (L:s = 5:3)

11\14 (551.5¢)

Basic (L:s = 2:1)

4\5 (561.6¢)

Semihard (L:s = 5:2)

9\11 (574.3¢)

Hard (L:s = 3:1)

5\6 (585.0¢)

Superhard (L:s = 4:1)

6\7 (601.7¢)

Collapsed (L:s = 1:0)

1\1 (702.0¢)

1L 3s<3/2> (or neptunian), is a fifth-repeating MOS scale with 1 large step and 3 small steps. The name "neptunian" was given by CompactStar in analogy to "uranian" name for 3L 2s<3/2>.

Notation

Due to being a tetratonic scale, neptunian interval classes often line up with diatonic interval classes (at least for L/s < 2/1) so similar note names can be used. Although, one difference is that the "perfect fourth" can go up to a subfifth in the most extreme case.

Modes

3|0 Lsss "tritonian"
2|1 sLss "protean"
1|2 ssLs "nereidian"
0|3 sssL "larissan"

Scale tree

Scale tree and tuning spectrum of 1L 3s⟨3/2⟩
Generator^(edf)						Cents		Step ratio		Comments
Generator^(edf)						Bright	Dark	L:s	Hardness	Comments
3\4						526.466	175.489	1:1	1.000	Equalized 1L 3s⟨3/2⟩
					16\21	534.823	167.132	6:5	1.200
				13\17		536.789	165.166	5:4	1.250
					23\30	538.166	163.790	9:7	1.286
			10\13			539.965	161.990	4:3	1.333	Supersoft 1L 3s⟨3/2⟩
					27\35	541.508	160.447	11:8	1.375
				17\22		542.420	159.535	7:5	1.400
					24\31	543.449	158.506	10:7	1.429
		7\9				545.965	155.990	3:2	1.500	Soft 1L 3s⟨3/2⟩ Poseidon and Auk are around here
					25\32	548.402	153.553	11:7	1.571
				18\23		549.356	152.599	8:5	1.600
					29\37	550.181	151.774	13:8	1.625
			11\14			551.536	150.419	5:3	1.667	Semisoft 1L 3s⟨3/2⟩
					26\33	553.055	148.900	12:7	1.714
				15\19		554.175	147.780	7:4	1.750
					19\24	555.714	146.241	9:5	1.800
	4\5					561.564	140.391	2:1	2.000	Basic 1L 3s⟨3/2⟩ Scales with tunings softer than this are proper
					17\21	568.249	133.706	9:4	2.250
				13\16		570.338	131.617	7:3	2.333
					22\27	571.963	129.992	12:5	2.400
			9\11			574.327	127.628	5:2	2.500	Semihard 1L 3s⟨3/2⟩ Halftone (incomplete)
					23\28	576.606	125.349	13:5	2.600
				14\17		578.081	123.874	8:3	2.667
					19\23	579.876	122.079	11:4	2.750
		5\6				584.963	116.993	3:1	3.000	Hard 1L 3s⟨3/2⟩
					16\19	591.120	110.835	10:3	3.333
				11\13		593.962	107.993	7:2	3.500
					17\20	596.662	105.293	11:3	3.667
			6\7			601.676	100.279	4:1	4.000	Superhard 1L 3s⟨3/2⟩
					13\15	608.361	93.594	9:2	4.500
				7\8		614.211	87.744	5:1	5.000
					8\9	623.960	77.995	6:1	6.000
1\1						701.955	0.000	1:0	→ ∞	Collapsed 1L 3s⟨3/2⟩

Temperaments

Poseidon

This temperament equates 2 11/8 with 5/4. It contains an 8:10:11 triad, which sounds quite similar to a major triad although with increased tension. 9edf (and thus Carlos Alpha) is a good tuning for this temperament with its accurate 5/4 and 11/8.

Subgroup: 3/2.5/4.11/8

Comma list: 121/120

Gencom: [3/2 12/11; 121/120]

POTE generator: ~12/11 = 158.29

Mapping: [⟨1 1 1], ⟨0 2 -1]]

Supporting EDFs: 9, 5, 13, 22, 14, 31, 17, 6[+5/4], 23, 40, 35, 21[-5/4], 19[+5/4], 49

Auk

Main article: Auk

Subgroup: 3/2.7.13

Comma list: 87808/85293

CTE generator: ~28/9 = 1950.859

Mapping: [⟨1 2 -2], ⟨0 1 3]]

Supporting ETs: 5, 9, 13, 14, 6[+13], 17[-7, -13], 7[-7, -13], 22[-7], 19[+13], 23[+13], 11[+13], 21[-7, -13], 31[-7], 25[-7, -13]

Halftone

Main article: Halftone

Subgroup: 3/2.5/2.7/2

Comma list: 9604/9375

Sval mapping: [⟨1 3 4], ⟨0 -4 -5]]

sval mapping generators: ~3/2, ~15/14

Optimal tuning (subgroup CTE): ~3/2 = 1\1edf, ~15/14 = 128.783

Supporting ETs: *5, *6, *7[+5/2, +7/2], *9[-5/2, --7/2], *11, *16, *17[+5/2], *23[+5/2, +7/2], *21[-7/2], *27, *28[+5/2], *38, *43[-7/2], *49

* wart for 3/2