5L 7s

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↖ 4L 6s ↑5L 6s 6L 6s ↗
← 4L 7s5L 7s 6L 7s →
↙ 4L 8s ↓5L 8s 6L 8s ↘
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│║│║│║││║│║│││
││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┘
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
Descends from 5L 2s (diatonic)
Required step ratio range 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, also called p-chromatic, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 7 small steps, repeating every octave. 5L 7s is a child scale of 5L 2s, expanding it by 5 tones. Generators that produce this scale range from 700¢ to 720¢, or from 480¢ to 500¢. 5L 7s represents the chromatic scales of Pythagorean/schismic and superpyth, the former being proper but the latter improper until expanded by 5 more notes, producing superpyth[17]. Such scales are characterized by having a small step (diatonic semitone) that is smaller than the chroma (chromatic semitone), the reverse of 7L 5s.

The two distinct harmonic entropy minima 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.

Modes

The modes are named by Eliora after Chinese zodiac animals. 5L 7s is the opposite mos to 7L 5s, named after a Western concept, Gregorian months, therefore this mos scale has Eastern nomenclature.

  • 11|0 LsLsLssLsLss - Rat
  • 10|1 LsLssLsLsLss - Ox
  • 9|2 LsLssLsLssLs - Tiger
  • 8|3 LssLsLsLssLs - Rabbit
  • 7|4 LssLsLssLsLs - Dragon
  • 6|5 sLsLsLssLsLs - Snake
  • 5|6 sLsLssLsLsLs - Horse
  • 4|7 sLsLssLsLssL - Goat
  • 3|8 sLssLsLsLssL - Monkey
  • 2|9 sLssLsLssLsL - Rooster
  • 1|10 ssLsLsLssLsL - Dog
  • 0|11 ssLsLssLsLsL - Pig

Scales

Scale tree

Scale Tree and Tuning Spectrum of 5L 7s
Generator(edo) Cents Step Ratio Comments
Bright Dark L:s Hardness
7\12 700.000 500.000 1:1 1.000 Equalized 5L 7s
38\65 701.538 498.462 6:5 1.200 Photia / pontiac / grackle
31\53 701.887 498.113 5:4 1.250 Helmholtz, Pythagorean tuning (701.9550¢)
55\94 702.128 497.872 9:7 1.286 Garibaldi / cassandra
24\41 702.439 497.561 4:3 1.333 Supersoft 5L 7s
Garibaldi / andromeda
65\111 702.703 497.297 11:8 1.375 Kwai
41\70 702.857 497.143 7:5 1.400
58\99 703.030 496.970 10:7 1.429 Undecental
17\29 703.448 496.552 3:2 1.500 Soft 5L 7s
Edson
61\104 703.846 496.154 11:7 1.571
44\75 704.000 496.000 8:5 1.600
71\121 704.132 495.868 13:8 1.625 Golden neogothic (704.0956¢)
27\46 704.348 495.652 5:3 1.667 Semisoft 5L 7s
Leapday / polypyth
64\109 704.587 495.413 12:7 1.714 Leapweek
37\63 704.762 495.238 7:4 1.750
47\80 705.000 495.000 9:5 1.800
10\17 705.882 494.118 2:1 2.000 Basic 5L 7s
Scales with tunings softer than this are proper
43\73 706.849 493.151 9:4 2.250
33\56 707.143 492.857 7:3 2.333 Supra
56\95 707.368 492.632 12:5 2.400
23\39 707.692 492.308 5:2 2.500 Semihard 5L 7s
59\100 708.000 492.000 13:5 2.600 Golden supra (708.0539¢)
36\61 708.197 491.803 8:3 2.667 Quasisuper / quasisupra
49\83 708.434 491.566 11:4 2.750
13\22 709.091 490.909 3:1 3.000 Hard 5L 7s
Suprapyth
42\71 709.859 490.141 10:3 3.333
29\49 710.204 489.796 7:2 3.500 Superpyth
45\76 710.526 489.474 11:3 3.667
16\27 711.111 488.889 4:1 4.000 Superhard 5L 7s
35\59 711.864 488.136 9:2 4.500
19\32 712.500 487.500 5:1 5.000
22\37 713.514 486.486 6:1 6.000 Ultrapyth / Oceanfront
3\5 720.000 480.000 1:0 → ∞ Collapsed 5L 7s