6L 2s (3/1-equivalent)

↖ 5L 1s⟨3/1⟩	↑ 6L 1s⟨3/1⟩	7L 1s⟨3/1⟩ ↗
← 5L 2s⟨3/1⟩	6L 2s (3/1-equivalent)	7L 2s⟨3/1⟩ →
↙ 5L 3s⟨3/1⟩	↓ 6L 3s⟨3/1⟩	7L 3s⟨3/1⟩ ↘

Scale structure
Step pattern	LLLsLLLs sLLLsLLL
Equave	3/1 (1902.0 ¢)
Period	1\2 (951.0 ¢)
Generator size(edt)
Bright	1\8 to 1\6 (237.7 ¢ to 317.0 ¢)
Dark	2\6 to 3\8 (634.0 ¢ to 713.2 ¢)
Related MOS scales
Parent	2L 4s⟨3/1⟩
Sister	2L 6s⟨3/1⟩
Daughters	8L 6s⟨3/1⟩, 6L 8s⟨3/1⟩
Neutralized	4L 4s⟨3/1⟩
2-Flought	14L 2s⟨3/1⟩, 6L 10s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1)	1\8 (237.7 ¢)
Supersoft (L:s = 4:3)	4\30 (253.6 ¢)
Soft (L:s = 3:2)	3\22 (259.4 ¢)
Semisoft (L:s = 5:3)	5\36 (264.2 ¢)
Basic (L:s = 2:1)	2\14 (271.7 ¢)
Semihard (L:s = 5:2)	5\34 (279.7 ¢)
Hard (L:s = 3:1)	3\20 (285.3 ¢)
Superhard (L:s = 4:1)	4\26 (292.6 ¢)
Collapsed (L:s = 1:0)	1\6 (317.0 ¢)
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6L 2s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 6 large steps and 2 small steps, with a period of 3 large steps and 1 small step that repeats every 951.0 ¢, or twice every interval of 3/1 (1902.0 ¢). Generators that produce this scale range from 237.7 ¢ to 317 ¢, or from 634 ¢ to 713.2 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.

Theory

Modes

Modes of 6L 2s⟨3/1⟩

UDP	Cyclic order	Step pattern
6|0(2)	1	LLLsLLLs
4|2(2)	2	LLsLLLsL
2|4(2)	3	LsLLLsLL
0|6(2)	4	sLLLsLLL

Temperament interpretations

The temperament that joins 26edt and 32edt produces this MOS. Both 26edt and 32edt are no-twos zeta peaks.

In 26edt it is generated by 4\26 (~292.6¢) and has a hardness of exactly 4.0.

In 32edt it is generated by 5\32 (~297.2¢) and has a hardness of exactly 5.9.

In 26edt this MOS has the intervals (in cents):

• 292.608
• 365.761
• 658.369
• 950.978
• 1243.586
• 1316.738
• 1609.347
• 1901.955

(And rotations thereof.)

That roughly approximates this no-3s 19-limit JI scale:

• 13/11
• 11/9
• 19/13
• 19/11
• 35/17 or 39/19
• 15/7
• 33/13
• 3/1

Or this full 11-limit JI scale:

• 6/5
• 5/4
• 16/11
• 7/4
• 33/16
• 15/7
• 5/2
• 3/1

Intervals

Intervals of 6L 2s⟨3/1⟩

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Diminished 1-mosstep	d1ms	s	0.0 ¢ to 237.7 ¢
	Perfect 1-mosstep	P1ms	L	237.7 ¢ to 317.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	317.0 ¢ to 475.5 ¢
	Major 2-mosstep	M2ms	2L	475.5 ¢ to 634.0 ¢
3-mosstep	Perfect 3-mosstep	P3ms	2L + s	634.0 ¢ to 713.2 ¢
	Augmented 3-mosstep	A3ms	3L	713.2 ¢ to 951.0 ¢
4-mosstep	Perfect 4-mosstep	P4ms	3L + s	951.0 ¢
5-mosstep	Diminished 5-mosstep	d5ms	3L + 2s	951.0 ¢ to 1188.7 ¢
	Perfect 5-mosstep	P5ms	4L + s	1188.7 ¢ to 1268.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	4L + 2s	1268.0 ¢ to 1426.5 ¢
	Major 6-mosstep	M6ms	5L + s	1426.5 ¢ to 1585.0 ¢
7-mosstep	Perfect 7-mosstep	P7ms	5L + 2s	1585.0 ¢ to 1664.2 ¢
	Augmented 7-mosstep	A7ms	6L + s	1664.2 ¢ to 1902.0 ¢
8-mosstep	Perfect 8-mosstep	P8ms	6L + 2s	1902.0 ¢

Scale degrees

Scale degrees of the modes of 6L 2s⟨3/1⟩

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3	4	5	6	7	8
6|0(2)	1	LLLsLLLs	Perf.	Perf.	Maj.	Aug.	Perf.	Perf.	Maj.	Aug.	Perf.
4|2(2)	2	LLsLLLsL	Perf.	Perf.	Maj.	Perf.	Perf.	Perf.	Maj.	Perf.	Perf.
2|4(2)	3	LsLLLsLL	Perf.	Perf.	Min.	Perf.	Perf.	Perf.	Min.	Perf.	Perf.
0|6(2)	4	sLLLsLLL	Perf.	Dim.	Min.	Perf.	Perf.	Dim.	Min.	Perf.	Perf.

Scale tree

Scale tree and tuning spectrum of 6L 2s⟨3/1⟩

Generator(edt)						Cents		Step ratio		Comments(always proper)
						Bright	Dark	L:s	Hardness
1\8						237.744	713.233	1:1	1.000	Equalized 6L 2s⟨3/1⟩
					6\46	248.081	702.896	6:5	1.200
				5\38		250.257	700.720	5:4	1.250
					9\68	251.729	699.248	9:7	1.286
			4\30			253.594	697.384	4:3	1.333	Supersoft 6L 2s⟨3/1⟩
					11\82	255.140	695.837	11:8	1.375
				7\52		256.032	694.945	7:5	1.400
					10\74	257.021	693.957	10:7	1.429
		3\22				259.358	691.620	3:2	1.500	Soft 6L 2s⟨3/1⟩
					11\80	261.519	689.459	11:7	1.571
				8\58		262.339	688.639	8:5	1.600
					13\94	263.036	687.941	13:8	1.625
			5\36			264.160	686.817	5:3	1.667	Semisoft 6L 2s⟨3/1⟩
					12\86	265.389	685.588	12:7	1.714
				7\50		266.274	684.704	7:4	1.750
					9\64	267.462	683.515	9:5	1.800
	2\14					271.708	679.270	2:1	2.000	Basic 6L 2s⟨3/1⟩
					9\62	276.090	674.887	9:4	2.250
				7\48		277.368	673.609	7:3	2.333
					12\82	278.335	672.643	12:5	2.400
			5\34			279.699	671.278	5:2	2.500	Semihard 6L 2s⟨3/1⟩
					13\88	280.971	670.007	13:5	2.600
				8\54		281.771	669.206	8:3	2.667
					11\74	282.723	668.254	11:4	2.750
		3\20				285.293	665.684	3:1	3.000	Hard 6L 2s⟨3/1⟩
					10\66	288.175	662.803	10:3	3.333
				7\46		289.428	661.550	7:2	3.500
					11\72	290.576	660.401	11:3	3.667
			4\26			292.608	658.369	4:1	4.000	Superhard 6L 2s⟨3/1⟩
					9\58	295.131	655.847	9:2	4.500
				5\32		297.180	653.797	5:1	5.000
					6\38	300.309	650.669	6:1	6.000
1\6						316.993	633.985	1:0	→ ∞	Collapsed 6L 2s⟨3/1⟩