6L 3s

↖ 5L 2s	↑ 6L 2s	7L 2s ↗
← 5L 3s	6L 3s	7L 3s →
↙ 5L 4s	↓ 6L 4s	7L 4s ↘

┌╥╥┬╥╥┬╥╥┬┐ │║║│║║│║║││ │││││││││││ └┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLsLLsLLs sLLsLLsLL
Equave	2/1 (1200.0 ¢)
Period	1\3 (400.0 ¢)
Generator size
Bright	1\9 to 1\6 (133.3 ¢ to 200.0 ¢)
Dark	1\6 to 2\9 (200.0 ¢ to 266.7 ¢)
TAMNAMS information
Name	hyrulic
Prefix	hyru-
Abbrev.	hy
Related MOS scales
Parent	3L 3s
Sister	3L 6s
Daughters	9L 6s, 6L 9s
Neutralized	3L 6s
2-Flought	15L 3s, 6L 12s
Equal tunings
Equalized (L:s = 1:1)	1\9 (133.3 ¢)
Supersoft (L:s = 4:3)	4\33 (145.5 ¢)
Soft (L:s = 3:2)	3\24 (150.0 ¢)
Semisoft (L:s = 5:3)	5\39 (153.8 ¢)
Basic (L:s = 2:1)	2\15 (160.0 ¢)
Semihard (L:s = 5:2)	5\36 (166.7 ¢)
Hard (L:s = 3:1)	3\21 (171.4 ¢)
Superhard (L:s = 4:1)	4\27 (177.8 ¢)
Collapsed (L:s = 1:0)	1\6 (200.0 ¢)

6L 3s, named hyrulic in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 6 large steps and 3 small steps, with a period of 2 large steps and 1 small step that repeats every 400.0 ¢, or 3 times every octave. Generators that produce this scale range from 133.3 ¢ to 200 ¢, or from 200 ¢ to 266.7 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.

The tiny region between 26\171 and 281\1848 is the terrain region, giving the albitonic scale for the remarkable terrain temperament chromatic pair. If you feel that is too small a region to allocate or prefer EDOs of a more usual size, you can call it the region between 5\33 and 6\39, but that misses the extreme accuracy of this temperament.

For a more approachable temperament, try triforce.

Intervals

Intervals of 6L 3s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-hyrustep	Perfect 0-hyrustep	P0hys	0	0.0 ¢
1-hyrustep	Diminished 1-hyrustep	d1hys	s	0.0 ¢ to 133.3 ¢
	Perfect 1-hyrustep	P1hys	L	133.3 ¢ to 200.0 ¢
2-hyrustep	Perfect 2-hyrustep	P2hys	L + s	200.0 ¢ to 266.7 ¢
	Augmented 2-hyrustep	A2hys	2L	266.7 ¢ to 400.0 ¢
3-hyrustep	Perfect 3-hyrustep	P3hys	2L + s	400.0 ¢
4-hyrustep	Diminished 4-hyrustep	d4hys	2L + 2s	400.0 ¢ to 533.3 ¢
	Perfect 4-hyrustep	P4hys	3L + s	533.3 ¢ to 600.0 ¢
5-hyrustep	Perfect 5-hyrustep	P5hys	3L + 2s	600.0 ¢ to 666.7 ¢
	Augmented 5-hyrustep	A5hys	4L + s	666.7 ¢ to 800.0 ¢
6-hyrustep	Perfect 6-hyrustep	P6hys	4L + 2s	800.0 ¢
7-hyrustep	Diminished 7-hyrustep	d7hys	4L + 3s	800.0 ¢ to 933.3 ¢
	Perfect 7-hyrustep	P7hys	5L + 2s	933.3 ¢ to 1000.0 ¢
8-hyrustep	Perfect 8-hyrustep	P8hys	5L + 3s	1000.0 ¢ to 1066.7 ¢
	Augmented 8-hyrustep	A8hys	6L + 2s	1066.7 ¢ to 1200.0 ¢
9-hyrustep	Perfect 9-hyrustep	P9hys	6L + 3s	1200.0 ¢

Modes

Scale degrees of the modes of 6L 3s

UDP	Cyclic order	Step pattern	Scale degree (hyrudegree)
			0	1	2	3	4	5	6	7	8	9
6|0(3)	1	LLsLLsLLs	Perf.	Perf.	Aug.	Perf.	Perf.	Aug.	Perf.	Perf.	Aug.	Perf.
3|3(3)	2	LsLLsLLsL	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.
0|6(3)	3	sLLsLLsLL	Perf.	Dim.	Perf.	Perf.	Dim.	Perf.	Perf.	Dim.	Perf.	Perf.

Scales

• Triphi – L:s = φ tuning
• Terrain9 – 3558edo tuning

Scale tree

Scale tree and tuning spectrum of 6L 3s

Generator(edo)						Cents		Step ratio		Comments(always proper)
						Bright	Dark	L:s	Hardness
1\9						133.333	266.667	1:1	1.000	Equalized 6L 3s
					6\51	141.176	258.824	6:5	1.200
				5\42		142.857	257.143	5:4	1.250
					9\75	144.000	256.000	9:7	1.286
			4\33			145.455	254.545	4:3	1.333	Supersoft 6L 3s
					11\90	146.667	253.333	11:8	1.375
				7\57		147.368	252.632	7:5	1.400
					10\81	148.148	251.852	10:7	1.429
		3\24				150.000	250.000	3:2	1.500	Soft 6L 3s
					11\87	151.724	248.276	11:7	1.571	Hemimist
				8\63		152.381	247.619	8:5	1.600
					13\102	152.941	247.059	13:8	1.625	Golden triforce (152.7864 ¢)
			5\39			153.846	246.154	5:3	1.667	Semisoft 6L 3s Triforce
					12\93	154.839	245.161	12:7	1.714
				7\54		155.556	244.444	7:4	1.750
					9\69	156.522	243.478	9:5	1.800
	2\15					160.000	240.000	2:1	2.000	Basic 6L 3s
					9\66	163.636	236.364	9:4	2.250
				7\51		164.706	235.294	7:3	2.333
					12\87	165.517	234.483	12:5	2.400
			5\36			166.667	233.333	5:2	2.500	Semihard 6L 3s
					13\93	167.742	232.258	13:5	2.600	Unnamed golden tuning (167.9285¢)
				8\57		168.421	231.579	8:3	2.667
					11\78	169.231	230.769	11:4	2.750
		3\21				171.429	228.571	3:1	3.000	Hard 6L 3s
					10\69	173.913	226.087	10:3	3.333
				7\48		175.000	225.000	7:2	3.500
					11\75	176.000	224.000	11:3	3.667
			4\27			177.778	222.222	4:1	4.000	Superhard 6L 3s Oodako
					9\60	180.000	220.000	9:2	4.500
				5\33		181.818	218.182	5:1	5.000
					6\39	184.615	215.385	6:1	6.000	Mirkat
1\6						200.000	200.000	1:0	→ ∞	Collapsed 6L 3s