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/Helmholtz/Garibaldi chromatic scale, and also the superpyth chromatic scale. In contrast to the meantone chromatic scale, in which diatonic semitones are larger than chromatic semitones, here the reverse is true: diatonic semitones are smaller than chromatic semitones, 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 doesn't 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
• Garibaldi12
• Supra12
• Archy12

Scale tree

Generator						Cents	L	s	L/s	Comments
7\12						700.000	1	1	1.000
					38\65	701.539	6	5	1.200	Photia
				31\53		701.887	5	4	1.250	Helmholtz
					55\94	702.128	9	7	1.286	Garibaldi
			24\41			702.409	4	3	1.333	Garibaldi/andromeda
					65\111	702.703	11	8	1.375
				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	L/s = 3/2 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
			27\46			704.348	5	3	1.667	Leapday
					64\109	704.587	12	7	1.714
				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
				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	L/s = 3/1 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
3\5						720.000	1	0	→ inf