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7L 3s (4/1-equivalent)

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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.

↖ 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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Intervals

Dark generators Notation (J = 1/1) Bright generators Notation (J = 1/1)
0 J perfect 0-step 0 J perfect 10-step
1 M perfect 3-step 1 Q perfect 7-step
2 Pb minor 6-step 2 N major 4-step
3 Sb minor 9-step 3 K major 1-step
4 Lb minor 2-step 4 R major 8-step
5 Ob minor 5-step 5 O major 5-step
6 Rb minor 8-step 6 L major 2-step
7 Kb minor 1-step 7 S major 9-step
8 Nb minor 4-step 8 P major 6-step

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


Scale tree

Dark generator Cents L s L/s Comments
3\10ed4 720.000 1 1 1.000
14\47ed4 714.894 5 4 1.250
11\37ed4 713.514 4 3 1.333
8\27ed4 711.111 3 2 1.500
13\44ed4 709.091 5 3 1.667 Quarchy is around here
5\17ed4 705.882 2 1 2.000 Basic diaquadic
12\41ed4 702.439 5 2 2.500
7\24ed4 700.000 3 1 3.000 Tetrominant is around here
9\31ed4 696.774 4 1 4.000 Meanquad is around here
11\38ed4 694.737 5 1 5.000
2\7ed4 685.714 1 0 -> ∞

Temperaments

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

Meanquad

Main article: Meanquad

Tetrominant

Quarchy

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