7L 5s

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

┌╥╥┬╥┬╥╥┬╥┬╥┬┐ │║║│║│║║│║│║││ ││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLsLsLLsLsLs sLsLsLLsLsLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	5\12 to 3\7 (500.0 ¢ to 514.3 ¢)
Dark	4\7 to 7\12 (685.7 ¢ to 700.0 ¢)
TAMNAMS information
Related to	5L 2s (diatonic)
With tunings	1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent	5L 2s
Sister	5L 7s
Daughters	12L 7s, 7L 12s
Neutralized	2L 10s
2-Flought	19L 5s, 7L 17s
Equal tunings
Equalized (L:s = 1:1)	5\12 (500.0 ¢)
Supersoft (L:s = 4:3)	18\43 (502.3 ¢)
Soft (L:s = 3:2)	13\31 (503.2 ¢)
Semisoft (L:s = 5:3)	21\50 (504.0 ¢)
Basic (L:s = 2:1)	8\19 (505.3 ¢)
Semihard (L:s = 5:2)	19\45 (506.7 ¢)
Hard (L:s = 3:1)	11\26 (507.7 ¢)
Superhard (L:s = 4:1)	14\33 (509.1 ¢)
Collapsed (L:s = 1:0)	3\7 (514.3 ¢)

7L 5s is the MOS pattern of the meantone chromatic scale, which is the only notable harmonic entropy minimum in this range of possible scales. In meantone, "diatonic" semitones (~16/15), such as appear in the diatonic scale, for example B-C, are larger than "chromatic" semitones (~25/24), the intervals by which flats and sharps alter pitches.

The meantone chromatic scale is proper.

Scale tree

Generator						in cents	Comments
3\7						514.286
					20\47	510.638
				17\40		510
					31\73	509.589
			14\33			509.091
					39\92	508.696
				25\59		508.475
					36\85	508.235
						507.934	L/s = pi
		11\26				507.692	Flattone
					41\97	507.216	Flattone
						507.151	L/s = e
				30\71		507.042	Flattone
						506.9365	L/s = phi+1
					49\116	506.897	Flattone
			19\45			506.667	Flattone
					46\109	506.422	Flattone
				27\64		506.25	Flattone
					35\83	506.024
	8\19					505.263	Boundary of propriety: generators smaller than this are proper. Meanenneadecal; L/s = 2
					37\88	504.5455
						504.507	Lucy Tuning
				29\69		504.348
						504.275	L/s = sqrt(3)
					50\119	504.202
			21\50			504	Meantone / Meanpop
					55\131	503.817	Golden meantone
						503.7855	L/s = phi
				34\81		503.704	Optimal meantone is around here
					47\112	503.571	Meantone / Meanpop
						503.5685	L/s = pi/2
		13\31				503.226	Optimal rank range (L/s = 3/2)
					44\105	502.857	Meantone / Huygens
				31\74		502.703	Meantone / Huygens
					49\117	502.564
			18\43			502.326	Meantone / Meridetone
					41\98	502.041
				23\55		501.818
					28\67	501.493
5\12						500