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, also called m-chromatic, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 5 small steps, repeating every octave. 7L 5s is a child scale of 5L 2s, expanding it by 5 tones. Generators that produce this scale range from 500 ¢ to 514.3 ¢, or from 685.7 ¢ to 700 ¢. 7L 5s represents the chromatic scale of meantone, or meantone chromatic scale. Such scales are characterized by having a small step (diatonic semitone) that is larger than the chroma (chromatic semitone), the reverse of 5L 7s.

Meantone is the only notable harmonic entropy minimum.

Modes

Both Eliora and Ganaram have independently proposed mode names based on names of the months. The latter scheme uses mode names from the Gregorian calendar, starting with January assigned to the step pattern LsLsLsLLsLsL, with successive rotations assigned to successive months. The latter scheme is based on month names from the Roman calendar, starting with Mensis Martius as the brightest mode, with successive month names for each mode by descending brightness.

Modes of 7L 5s

UDP	Cyclic order	Step pattern
11|0	1	LLsLsLLsLsLs
10|1	6	LLsLsLsLLsLs
9|2	11	LsLLsLsLLsLs
8|3	4	LsLLsLsLsLLs
7|4	9	LsLsLLsLsLLs
6|5	2	LsLsLLsLsLsL
5|6	7	LsLsLsLLsLsL
4|7	12	sLLsLsLLsLsL
3|8	5	sLLsLsLsLLsL
2|9	10	sLsLLsLsLLsL
1|10	3	sLsLLsLsLsLL
0|11	8	sLsLsLLsLsLL

Modes of 7L 5s

UDP	Cyclic order	Step pattern
11|0	1	LLsLsLLsLsLs
10|1	6	LLsLsLsLLsLs
9|2	11	LsLLsLsLLsLs
8|3	4	LsLLsLsLsLLs
7|4	9	LsLsLLsLsLLs
6|5	2	LsLsLLsLsLsL
5|6	7	LsLsLsLLsLsL
4|7	12	sLLsLsLLsLsL
3|8	5	sLLsLsLsLLsL
2|9	10	sLsLLsLsLLsL
1|10	3	sLsLLsLsLsLL
0|11	8	sLsLsLLsLsLL

Scales

• Meaneb471a – an equal beating tuning of meantone
• Meantone12 – 31edo tuning
• Ratwolf – 20/13 wolf fifth tuning of meantone
• Meaneb471 – the other 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