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¢)
Step size ranges
Large	1\9 to 1\6 (133.3¢ to 200.0¢)
Small	0\6 to 1\9 (0.0¢ to 133.3¢)
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.	hyru
Related MOS scales
Parent	3L 3s
Sister	3L 6s
Daughters	9L 6s 6L 9s
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 abitonic 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 down-to-earth temperament, try triforce.

Modes

Modes of 6L 3s

UDP	Rotational order	Step pattern
6|0(3)	1	LLsLLsLLs
3|3(3)	2	LsLLsLLsL
0|6(3)	3	sLLsLLsLL

Scales

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

Scale tree

Generator ranges:

• Chroma-positive generator: 133.3333 cents (1\9) to 200 cents (1\6)
• Chroma-negative generator: 200 cents (1\6) to 266.6667 cents (2\9)

Generator						Cents	L	s	L/s	Comments
1\9						133.333	1	1	1.000
					6\51	141.176	6	5	1.200
				5\42		142.857	5	4	1.250
					9\75	144.000	9	7	1.286
			4\33			145.455	4	3	1.333
					11\90	146.667	11	8	1.375
				7\57		147.368	7	5	1.400
					10\81	148.148	10	7	1.429
		3\24				150.000	3	2	1.500
					11\87	151.724	11	7	1.571	Hemimist
				8\63		152.381	8	5	1.600
					13\102	152.911	13	8	1.625	Golden triforce (152.7864¢)
			5\39			153.846	5	3	1.667
					12\93	154.839	12	7	1.714
				7\54		155.556	7	4	1.750
					9\69	156.522	9	5	1.800
	2\15					160.000	2	1	2.000	Basic hyrulic
					9\66	163.636	9	4	2.250
				7\51		164.706	7	3	2.333
					12\87	165.517	12	5	2.400
			5\36			166.667	5	2	2.500
					13\93	167.742	13	5	2.600	Unnamed golden tuning (167.9285¢)
				8\57		168.421	8	3	2.667
					11\78	169.231	11	4	2.750
		3\21				171.439	3	1	3.000
					10\69	173.913	10	3	3.333
				7\48		175.000	7	2	3.500
					11\75	176.000	11	3	3.667	Oodako
			4\27			177.778	4	1	4.000
					9\60	180.000	9	2	4.500
				5\33		181.818	5	1	5.000
					6\39	184.615	6	1	6.000	Mirkat
1\6						200.000	1	0	→ inf