7L 5s

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.

↖ 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 ¢)
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The meantone chromatic scale with generator between 5\12 (500 cents) and 8\19 (505.263 cents) is proper.

Modes

• 11|0 LLsLsLLsLsLs
• 10|1 LLsLsLsLLsLs
• 9|2 LsLLsLsLLsLs
• 8|3 LsLLsLsLsLLs
• 7|4 LsLsLLsLsLLs
• 6|5 LsLsLLsLsLsL
• 5|6 LsLsLsLLsLsL
• 4|7 sLLsLsLLsLsL
• 3|8 sLLsLsLsLLsL
• 2|9 sLsLLsLsLLsL
• 1|10 sLsLLsLsLsLL
• 0|11 sLsLsLLsLsLL

Scales

• Meantone12 – 31edo tuning
• Meaneb471a – equal beating tuning of meantone
• Flattone12 – 13-limit POTE tuning of flattone

Scale tree

Generator ranges:

• Chroma-positive generator: 500 cents (5\12) to 514.2857 cents (3\7)
• Chroma-negative generator: 685.7143 cents (4\7) to 700 cents (7\12)

Generator						Cents	L	s	L/s	Comments
5\12						500.000	1	1	1.000
					28\67	501.493	6	5	1.200
				23\55		501.818	5	4	1.250
					41\98	502.041	9	7	1.286
			18\43			502.326	4	3	1.333	Meantone / meridetone
					49\117	502.564	11	8	1.375
				31\74		502.703	7	5	1.400	Meantone / huygens / grosstone
					44\105	502.857	10	7	1.428
		13\31				503.226	3	2	1.500
					47\112	503.571	11	7	1.571
				34\81		503.704	8	5	1.600	Meantone
					55\131	503.817	13	8	1.625	Golden meantone (503.7855¢)
			21\50			504.000	5	3	1.667	Meantone / meanpop
					50\119	504.202	12	7	1.714
				29\69		504.348	7	4	1.750
					37\88	504.545	9	5	1.800
	8\19					505.263	2	1	2.000	Basic m-chromatic (Generators smaller than this are proper)
					35\83	506.024	9	4	2.250
				27\64		506.250	7	3	2.333
					46\109	506.422	12	5	2.400
			19\45			506.667	5	2	2.500	Flattone
					49\116	506.897	13	5	2.600	Golden flattone (506.9365¢)
				30\71		507.042	8	3	2.667
					41\97	507.216	11	4	2.750
		11\26				507.692	3	1	3.000
					36\85	508.235	10	3	3.333
				25\59		508.475	7	2	3.500
					39\92	508.696	11	3	3.667
			14\33			509.091	4	1	4.000
					31\73	509.589	9	2	4.500
				17\40		510.000	5	1	5.000
					20\47	510.638	6	1	6.000
3\7						514.286	1	0	→ inf