7L 3s (4/1-equivalent)

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↖6L 2s⟨4/1⟩↑7L 2s⟨4/1⟩ 8L 2s⟨4/1⟩↗
←6L 3s⟨4/1⟩7L 3s⟨4/1⟩8L 3s⟨4/1⟩→
↙6L 4s⟨4/1⟩↓7L 4s⟨4/1⟩ 8L 4s⟨4/1⟩↘
Brightest mode LLLsLLsLLs
Period 4/1
Range for bright generator 7\10ed4 (1680¢) to 5\7ed4 (1714.3¢)
Range for dark generator 2\7ed4 (685.7¢) to 3\10ed4 (720¢)
Parent MOS 3L 4s⟨4/1⟩
Sister MOS 3L 7s⟨4/1⟩
Daughter MOSes 10L 7s⟨4/1⟩, 7L 10s⟨4/1⟩
Equal tunings
Supersoft (L:s = 4:3) 26\37ed4 (1686.5¢)
Soft (L:s = 3:2) 19\27ed4 (1688.9¢)
Semisoft (L:s = 5:3) 31\44ed4 (1690.9¢)
Basic (L:s = 2:1) 12\17ed4 (1694.1¢)
Semihard (L:s = 5:2) 29\41ed4 (1697.6¢)
Hard (L:s = 3:1) 17\24ed4 (1700¢)
Superhard (L:s = 4:1) 22\31ed4 (1703.2¢)
Brightest-mode tunings on xenpaper
Supersoft Soft Semisoft Basic Semihard Hard Superhard

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.

Intervals

Dark generators Notation 17ed4 cents Bright generators Notation 17ed4 cents
0 C perfect 0-step 0.00 0 C perfect 10-step 0.00
1 F perfect 3-step 705.90 1 K perfect 7-step 1694.16
2 Jb minor 6-step 1411.80 2 E major 4-step 988.26
3 Bb minor 9-step 2117.70 3 D major 1-step 282.36
4 Eb minor 2-step 423.54 4 A major 8-step 1976.52
5 Hb minor 5-step 1129.44 5 H major 5-step 1270.62
6 Ab minor 8-step 1835.34 6 E major 2-step 564.72
7 Db minor 1-step 141.18 7 B major 9-step 2258.88
8 Gb minor 4-step 847.08 8 J major 6-step 1552.98

Modes

The darker modes contain both major triads and augmented triads on the root, and the brighter modes contain both minor and diminished triads on the root.

  • 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

Scale tree and tuning spectrum of 7L 3s⟨4/1⟩
Generator (in steps of ed4/1) Cents Step ratio Comments
Bright Dark L:s Hardness
7\10 1680.000 720.000 1:1 1.000 Equalized 7L 3s⟨4/1⟩
40\57 1684.211 715.789 6:5 1.200
33\47 1685.106 714.894 5:4 1.250
59\84 1685.714 714.286 9:7 1.286
26\37 1686.486 713.514 4:3 1.333 Supersoft 7L 3s⟨4/1⟩
71\101 1687.129 712.871 11:8 1.375
45\64 1687.500 712.500 7:5 1.400
64\91 1687.912 712.088 10:7 1.429
19\27 1688.889 711.111 3:2 1.500 Soft 7L 3s⟨4/1⟩
69\98 1689.796 710.204 11:7 1.571
50\71 1690.141 709.859 8:5 1.600
81\115 1690.435 709.565 13:8 1.625
31\44 1690.909 709.091 5:3 1.667 Semisoft 7L 3s⟨4/1⟩
Quarchy is around here
74\105 1691.429 708.571 12:7 1.714
43\61 1691.803 708.197 7:4 1.750
55\78 1692.308 707.692 9:5 1.800
12\17 1694.118 705.882 2:1 2.000 Basic 7L 3s⟨4/1⟩
Scales with tunings softer than this are proper
53\75 1696.000 704.000 9:4 2.250
41\58 1696.552 703.448 7:3 2.333
70\99 1696.970 703.030 12:5 2.400
29\41 1697.561 702.439 5:2 2.500 Semihard 7L 3s⟨4/1⟩
75\106 1698.113 701.887 13:5 2.600
46\65 1698.462 701.538 8:3 2.667
63\89 1698.876 701.124 11:4 2.750
17\24 1700.000 700.000 3:1 3.000 Hard 7L 3s⟨4/1⟩
Tetrominant is around here
56\79 1701.266 698.734 10:3 3.333
39\55 1701.818 698.182 7:2 3.500
61\86 1702.326 697.674 11:3 3.667
22\31 1703.226 696.774 4:1 4.000 Superhard 7L 3s⟨4/1⟩
Meanquad is around here
49\69 1704.348 695.652 9:2 4.500
27\38 1705.263 694.737 5:1 5.000
32\45 1706.667 693.333 6:1 6.000
5\7 1714.286 685.714 1:0 → ∞ Collapsed 7L 3s⟨4/1⟩

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