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.

Intervals

Intervals of 7L 5s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Minor 1-mosstep	m1ms	s	0.0 ¢ to 100.0 ¢
	Major 1-mosstep	M1ms	L	100.0 ¢ to 171.4 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	171.4 ¢ to 200.0 ¢
	Major 2-mosstep	M2ms	2L	200.0 ¢ to 342.9 ¢
3-mosstep	Minor 3-mosstep	m3ms	L + 2s	171.4 ¢ to 300.0 ¢
	Major 3-mosstep	M3ms	2L + s	300.0 ¢ to 342.9 ¢
4-mosstep	Minor 4-mosstep	m4ms	2L + 2s	342.9 ¢ to 400.0 ¢
	Major 4-mosstep	M4ms	3L + s	400.0 ¢ to 514.3 ¢
5-mosstep	Diminished 5-mosstep	d5ms	2L + 3s	342.9 ¢ to 500.0 ¢
	Perfect 5-mosstep	P5ms	3L + 2s	500.0 ¢ to 514.3 ¢
6-mosstep	Minor 6-mosstep	m6ms	3L + 3s	514.3 ¢ to 600.0 ¢
	Major 6-mosstep	M6ms	4L + 2s	600.0 ¢ to 685.7 ¢
7-mosstep	Perfect 7-mosstep	P7ms	4L + 3s	685.7 ¢ to 700.0 ¢
	Augmented 7-mosstep	A7ms	5L + 2s	700.0 ¢ to 857.1 ¢
8-mosstep	Minor 8-mosstep	m8ms	4L + 4s	685.7 ¢ to 800.0 ¢
	Major 8-mosstep	M8ms	5L + 3s	800.0 ¢ to 857.1 ¢
9-mosstep	Minor 9-mosstep	m9ms	5L + 4s	857.1 ¢ to 900.0 ¢
	Major 9-mosstep	M9ms	6L + 3s	900.0 ¢ to 1028.6 ¢
10-mosstep	Minor 10-mosstep	m10ms	5L + 5s	857.1 ¢ to 1000.0 ¢
	Major 10-mosstep	M10ms	6L + 4s	1000.0 ¢ to 1028.6 ¢
11-mosstep	Minor 11-mosstep	m11ms	6L + 5s	1028.6 ¢ to 1100.0 ¢
	Major 11-mosstep	M11ms	7L + 4s	1100.0 ¢ to 1200.0 ¢
12-mosstep	Perfect 12-mosstep	P12ms	7L + 5s	1200.0 ¢

Modes

Scale degrees of the modes of 7L 5s

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3	4	5	6	7	8	9	10	11	12
11|0	1	LLsLsLLsLsLs	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Aug.	Maj.	Maj.	Maj.	Maj.	Perf.
10|1	6	LLsLsLsLLsLs	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.
9|2	11	LsLLsLsLLsLs	Perf.	Maj.	Min.	Maj.	Maj.	Perf.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.
8|3	4	LsLLsLsLsLLs	Perf.	Maj.	Min.	Maj.	Maj.	Perf.	Maj.	Perf.	Maj.	Min.	Maj.	Maj.	Perf.
7|4	9	LsLsLLsLsLLs	Perf.	Maj.	Min.	Maj.	Min.	Perf.	Maj.	Perf.	Maj.	Min.	Maj.	Maj.	Perf.
6|5	2	LsLsLLsLsLsL	Perf.	Maj.	Min.	Maj.	Min.	Perf.	Maj.	Perf.	Maj.	Min.	Maj.	Min.	Perf.
5|6	7	LsLsLsLLsLsL	Perf.	Maj.	Min.	Maj.	Min.	Perf.	Min.	Perf.	Maj.	Min.	Maj.	Min.	Perf.
4|7	12	sLLsLsLLsLsL	Perf.	Min.	Min.	Maj.	Min.	Perf.	Min.	Perf.	Maj.	Min.	Maj.	Min.	Perf.
3|8	5	sLLsLsLsLLsL	Perf.	Min.	Min.	Maj.	Min.	Perf.	Min.	Perf.	Min.	Min.	Maj.	Min.	Perf.
2|9	10	sLsLLsLsLLsL	Perf.	Min.	Min.	Min.	Min.	Perf.	Min.	Perf.	Min.	Min.	Maj.	Min.	Perf.
1|10	3	sLsLLsLsLsLL	Perf.	Min.	Min.	Min.	Min.	Perf.	Min.	Perf.	Min.	Min.	Min.	Min.	Perf.
0|11	8	sLsLsLLsLsLL	Perf.	Min.	Min.	Min.	Min.	Dim.	Min.	Perf.	Min.	Min.	Min.	Min.	Perf.

Proposed Names

Both Eliora and Ganaram have independently proposed mode names based on names of the months. The former scheme uses mode names from the Gregorian calendar using cyclic order, starting with January assigned to the step pattern LsLsLsLLsLsL due to positioning of 31-day and 30-day months, 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

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