7L 3s (4/1-equivalent)

↖ 6L 2s⟨4/1⟩	↑ 7L 2s⟨4/1⟩	8L 2s⟨4/1⟩ ↗
← 6L 3s⟨4/1⟩	7L 3s (4/1-equivalent)	8L 3s⟨4/1⟩ →
↙ 6L 4s⟨4/1⟩	↓ 7L 4s⟨4/1⟩	8L 4s⟨4/1⟩ ↘

Scale structure
Step pattern	LLLsLLsLLs sLLsLLsLLL
Equave	4/1 (2400.0 ¢)
Period	4/1 (2400.0 ¢)
Generator size(ed4/1)
Bright	7\10 to 5\7 (1680.0 ¢ to 1714.3 ¢)
Dark	2\7 to 3\10 (685.7 ¢ to 720.0 ¢)
Related MOS scales
Parent	3L 4s⟨4/1⟩
Sister	3L 7s⟨4/1⟩
Daughters	10L 7s⟨4/1⟩, 7L 10s⟨4/1⟩
Neutralized	4L 6s⟨4/1⟩
2-Flought	17L 3s⟨4/1⟩, 7L 13s⟨4/1⟩
Equal tunings(ed4/1)
Equalized (L:s = 1:1)	7\10 (1680.0 ¢)
Supersoft (L:s = 4:3)	26\37 (1686.5 ¢)
Soft (L:s = 3:2)	19\27 (1688.9 ¢)
Semisoft (L:s = 5:3)	31\44 (1690.9 ¢)
Basic (L:s = 2:1)	12\17 (1694.1 ¢)
Semihard (L:s = 5:2)	29\41 (1697.6 ¢)
Hard (L:s = 3:1)	17\24 (1700.0 ¢)
Superhard (L:s = 4:1)	22\31 (1703.2 ¢)
Collapsed (L:s = 1:0)	5\7 (1714.3 ¢)
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7L 3s<4/1> (sometimes called diaquadic) refers to a non-octave MOS scale family with a period of a 4/1 and which has 7 large and 3 small steps. These scales are in some ways a double octave clone of diatonic scales because they are generated from perfect fifths and have the 7edo/7ed4 685-cent flat fifth and 5edo/10ed4's 720-cent sharp fifth at the ends of the tuning spectrum. However, ~3/2 is now the chroma-negative rather than chroma-positive generator, equalized and collapsed tunings are now swapped (equalized is 720-cent fifth and collapsed is 685-cent fifth), and the basic tuning is now the 705-cent gentle fifth from 17edo/17ed4 instead of 12edo's fifth. Diaquadic scales are also more widely spaced than diatonic scales, closer melodically to an octave-period pentatonic scale.

Modes

• LLLsLLsLLs 9|0
• LLsLLLsLLs 8|1
• LLsLLsLLLs 7|2
• LLsLLsLLsL 6|3
• LsLLLsLLsL 5|4
• LsLLsLLLsL 4|5
• LsLLsLLsLL 3|6
• sLLLsLLsLL 2|7
• sLLsLLLsLL 1|8
• sLLsLLsLLL 0|9

Temperaments

There are two major rank-2 temperament interpretations of diaquadic, corresponding to double octave clones of meantone and archy.

Meanquad

• Subgroup: 4.5.6
• Comma list: 81/80
• Vals: 7, 31, 38, 24, 17, 10, 69, 45, 55, 11[-5], 52, 41, 13[+5], 27[+5]
• CTE tuning: ~3/2 = 697.214