5L 7s

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

┌╥┬╥┬╥┬┬╥┬╥┬┬┐ │║│║│║││║│║│││ ││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LsLsLssLsLss ssLsLssLsLsL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	7\12 to 3\5 (700.0 ¢ to 720.0 ¢)
Dark	2\5 to 5\12 (480.0 ¢ to 500.0 ¢)
TAMNAMS information
Related to	5L 2s (diatonic)
With tunings	2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent	5L 2s
Sister	7L 5s
Daughters	12L 5s, 5L 12s
Neutralized	10L 2s
2-Flought	17L 7s, 5L 19s
Equal tunings
Equalized (L:s = 1:1)	7\12 (700.0 ¢)
Supersoft (L:s = 4:3)	24\41 (702.4 ¢)
Soft (L:s = 3:2)	17\29 (703.4 ¢)
Semisoft (L:s = 5:3)	27\46 (704.3 ¢)
Basic (L:s = 2:1)	10\17 (705.9 ¢)
Semihard (L:s = 5:2)	23\39 (707.7 ¢)
Hard (L:s = 3:1)	13\22 (709.1 ¢)
Superhard (L:s = 4:1)	16\27 (711.1 ¢)
Collapsed (L:s = 1:0)	3\5 (720.0 ¢)

5L 7s is the MOS pattern of the Pythagorean/schismic chromatic scale, and also the superpyth chromatic scale. In contrast to the meantone chromatic scale, in which the diatonic semitone is larger than the chromatic semitone, here the reverse is true: the diatonic semitone is smaller than the chromatic semitone, so the diatonic scale subset is actually improper.

The two distinct harmonic entropy minima with this MOS pattern are, on the one hand, scales very close to Pythagorean such that 64/63 is not tempered out, such as the schismatic temperaments known as Helmholtz and Garibaldi, and on the other hand, the much simpler and less accurate scale known as superpyth in which 64/63 is tempered out.

The Pythagorean/schismatic version is proper, but the superpyth version is improper (it does not become proper until you add 5 more notes to form the superpyth enharmonic scale, superpyth[17]).

Modes

• 11|0 LsLsLssLsLss
• 10|1 LsLssLsLsLss
• 9|2 LsLssLsLssLs
• 8|3 LssLsLsLssLs
• 7|4 LssLsLssLsLs
• 6|5 sLsLsLssLsLs
• 5|6 sLsLssLsLsLs
• 4|7 sLsLssLsLssL
• 3|8 sLssLsLsLssL
• 2|9 sLssLsLssLsL
• 1|10 ssLsLsLssLsL
• 0|11 ssLsLssLsLsL

Scales

• Pythagorean12 – Pythagorean tuning
• Garibaldi12 – 94edo tuning
• Cotoneum12 – 217edo tuning
• Pepperoni12 – 271edo tuning
• Supra12 – 56edo tuning
• Archy12 – 472edo tuning
• 12-22a – 22edo tuning

Scale tree

Generator ranges:

• Chroma-positive generator: 700 cents (7\12) to 720 cents (3\5)
• Chroma-negative generator: 480 cents (2\5) to 500 cents (5\12)

Generator						Cents	L	s	L/s	Comments
7\12						700.000	1	1	1.000
					38\65	701.539	6	5	1.200	Photia / pontiac / grackle↑
				31\53		701.887	5	4	1.250	Helmholtz, Pythagorean tuning (701.9550¢)
					55\94	702.128	9	7	1.286	Garibaldi / cassandra
			24\41			702.409	4	3	1.333	Garibaldi / andromeda
					65\111	702.703	11	8	1.375	Kwai
				41\70		702.857	7	5	1.400
					58\99	703.030	10	7	1.428	Undecental
		17\29				703.448	3	2	1.500	Edson
					61\104	703.846	11	7	1.571
				44\75		704.000	8	5	1.600
					71\121	704.132	13	8	1.625	Golden neogothic (704.0956¢)
			27\46			704.348	5	3	1.667	Leapday / polypyth
					64\109	704.587	12	7	1.714	Leapweek
				37\63		704.762	7	4	1.750
					47\80	705.000	9	5	1.800
	10\17					705.882	2	1	2.000	Basic p-chromatic (Generators smaller than this are proper)
					43\73	706.849	9	4	2.250
				33\56		707.143	7	3	2.333	Supra
					56\95	707.368	12	5	2.400
			23\39			707.692	5	2	2.500
					59\100	708.000	13	5	2.600	Golden supra (708.0539¢)
				36\61		708.197	8	3	2.667	Quasisuper / quasisupra
					49\83	708.434	11	4	2.750
		13\22				709.091	3	1	3.000	Suprapyth
					42\71	709.859	10	3	3.333
				29\49		710.204	7	2	3.500	Superpyth
					45\76	710.526	11	3	3.667
			16\27			711.111	4	1	4.000
					35\59	711.864	9	2	4.500
				19\32		712.500	5	1	5.000
					22\37	713.514	6	1	6.000	Oceanfront↓ / ultrapyth↓
3\5						720.000	1	0	→ inf