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.

Scales

• Meantone12
• Flattone12

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