7L 4s

7L 4s has a generator of an augmented minor or diminished neutral third of 327.273 (3/11edo) to 342.857 (2/7edo) cents. Its harmonic entropy minimum, insofar as it may be said to have one, is improper (Amity/Hitchcock/Sixix) and also tonally awkward because its large and steps are extremely unequal (L>=4, s=1). However, it is still notable for representing 17:14 with tolerable accuracy for as much as that's worth.

↖ 6L 3s	↑ 7L 3s	8L 3s ↗
← 6L 4s	7L 4s	8L 4s →
↙ 6L 5s	↓ 7L 5s	8L 5s ↘

Scale structure
Step pattern	LLsLLsLLsLs sLsLLsLLsLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	3\11 to 2\7 (327.3 ¢ to 342.9 ¢)
Dark	5\7 to 8\11 (857.1 ¢ to 872.7 ¢)
TAMNAMS information
Related to	4L 3s (smitonic)
With tunings	1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent	4L 3s
Sister	4L 7s
Daughters	11L 7s, 7L 11s
Neutralized	3L 8s
2-Flought	18L 4s, 7L 15s
Equal tunings
Equalized (L:s = 1:1)	3\11 (327.3 ¢)
Supersoft (L:s = 4:3)	11\40 (330.0 ¢)
Soft (L:s = 3:2)	8\29 (331.0 ¢)
Semisoft (L:s = 5:3)	13\47 (331.9 ¢)
Basic (L:s = 2:1)	5\18 (333.3 ¢)
Semihard (L:s = 5:2)	12\43 (334.9 ¢)
Hard (L:s = 3:1)	7\25 (336.0 ¢)
Superhard (L:s = 4:1)	9\32 (337.5 ¢)
Collapsed (L:s = 1:0)	2\7 (342.9 ¢)
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Scale tree

Generator						Cents	L	s	L/s	Comments
3\11						327.273	1	1	1.000
					17\62	329.032	6	5	1.200	Is used as a calendar leap cycle
				14\51		329.412	5	4	1.250
					25\91	329.670	9	7	1.286
			11\40			330.000	4	3	1.333
					30\109	330.275	11	8	1.375
				19\69		330.435	7	5	1.400
					27\98	330.612	10	7	1.428
		8\29				331.034	3	2	1.500	L/s = 3/2
					29\105	331.429	11	7	1.571
				21\76		331.579	8	5	1.600
					34\123	331.707	13	8	1.625	Unnamed golden tuning
			13\47			331.915	5	3	1.667
					31\112	332.143	12	7	1.714
				18\65		332.308	7	4	1.750
					23\83	332.530	9	5	1.800
	5\18					333.333	2	1	2.000	Basic suprasmitonic (Generators smaller than this are proper)
					22\79	334.177	9	4	2.250
				17\61		334.426	7	3	2.333
					29\104	334.615	12	5	2.400
			12\43			334.884	5	2	2.500
					31\111	335.135	13	5	2.600	17-limit Cohemimabila
				19\68		335.294	8	3	2.667
					26\93	335.484	11	4	2.750
		7\25				336.000	3	1	3.000	L/s = 3/1
					23\82	336.585	10	3	3.333
				16\57		336.842	7	2	3.500
					25\89	337.079	11	3	3.667
			9\32			337.500	4	1	4.000	Sixix
					20\71	338.028	9	2	4.500
				11\39		338.462	5	1	5.000
					13\46	339.130	6	1	6.000	Amity/hitchcock↓
2\7						342.857	1	0	→ inf