5L 7s

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↖ 4L 6s ↑5L 6s 6L 6s ↗
← 4L 7s5L 7s 6L 7s →
↙ 4L 8s ↓5L 8s 6L 8s ↘
 
┌╥┬╥┬╥┬┬╥┬╥┬┬┐
│║│║│║││║│║│││
││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsLsLssLsLss
ssLsLssLsLsL
Equave 2/1 (1200.0¢)
Period 1\12 (100.0¢)
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)
Ancestor's 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.

Intervals

Intervals of 5L 7s
Intervals Steps subtended Range in cents Average of HE
(from HE Calc) 		Min of HE
Generic[1] Specific[2] Abbrev.[3]
0-mosstep Perfect 0-mosstep P0ms 0 0.0¢ ~2.4654 nats ~2.4654 nats
1-mosstep Minor 1-mosstep m1ms s 0.0¢ to 100.0¢ ~4.7510 nats ~4.7000 nats
Major 1-mosstep M1ms L 100.0¢ to 240.0¢ ~4.6291 nats ~4.5989 nats
2-mosstep Minor 2-mosstep m2ms 2s 0.0¢ to 200.0¢ ~4.6383 nats ~4.6005 nats
Major 2-mosstep M2ms L + s 200.0¢ to 240.0¢ ~4.5843 nats ~4.5840 nats
3-mosstep Minor 3-mosstep m3ms L + 2s 240.0¢ to 300.0¢ ~4.5737 nats ~4.5636 nats
Major 3-mosstep M3ms 2L + s 300.0¢ to 480.0¢ ~4.5608 nats ~4.4947 nats
4-mosstep Minor 4-mosstep m4ms L + 3s 240.0¢ to 400.0¢ ~4.5641 nats ~4.4998 nats
Major 4-mosstep M4ms 2L + 2s 400.0¢ to 480.0¢ ~4.5978 nats ~4.5784 nats
5-mosstep Perfect 5-mosstep P5ms 2L + 3s 480.0¢ to 500.0¢ ~4.3855 nats ~4.3672 nats
Augmented 5-mosstep A5ms 3L + 2s 500.0¢ to 720.0¢ ~4.5983 nats ~4.5596 nats
6-mosstep Minor 6-mosstep m6ms 2L + 4s 480.0¢ to 600.0¢ ~4.5945 nats ~4.5597 nats
Major 6-mosstep M6ms 3L + 3s 600.0¢ to 720.0¢ ~4.6195 nats ~4.5971 nats
7-mosstep Diminished 7-mosstep d7ms 2L + 5s 480.0¢ to 700.0¢ ~4.6065 nats ~4.5653 nats
Perfect 7-mosstep P7ms 3L + 4s 700.0¢ to 720.0¢ ~4.1430 nats ~4.1224 nats
8-mosstep Minor 8-mosstep m8ms 3L + 5s 720.0¢ to 800.0¢ ~4.6131 nats ~4.5987 nats
Major 8-mosstep M8ms 4L + 4s 800.0¢ to 960.0¢ ~4.5507 nats ~4.4255 nats
9-mosstep Minor 9-mosstep m9ms 3L + 6s 720.0¢ to 900.0¢ ~4.5569 nats ~4.4434 nats
Major 9-mosstep M9ms 4L + 5s 900.0¢ to 960.0¢ ~4.5972 nats ~4.5568 nats
10-mosstep Minor 10-mosstep m10ms 4L + 6s 960.0¢ to 1000.0¢ ~4.5657 nats ~4.5392 nats
Major 10-mosstep M10ms 5L + 5s 1000.0¢ to 1200.0¢ ~4.6058 nats ~4.5819 nats
11-mosstep Minor 11-mosstep m11ms 4L + 7s 960.0¢ to 1100.0¢ ~4.6025 nats ~4.5800 nats
Major 11-mosstep M11ms 5L + 6s 1100.0¢ to 1200.0¢ ~4.6744 nats ~4.6313 nats
12-mosstep Perfect 12-mosstep P12ms 5L + 7s 1200.0¢ ~3.3273 nats ~3.3273 nats

  1. Generic intervals are denoted solely by the number of steps they subtend.
  2. Specific intervals denote whether an interval is major, minor, augmented, perfect, or diminished.
  3. Abbreviations can be further shortened to 'ms' if context allows.

Modes

Scale degree qualities of 5L 7s modes
UDP Rotational Order Step pattern Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12
11|0 1 LsLsLssLsLss Perf. Maj. Maj. Maj. Maj. Aug. Maj. Perf. Maj. Maj. Maj. Maj. Perf.
10|1 8 LsLssLsLsLss Perf. Maj. Maj. Maj. Maj. Perf. Maj. Perf. Maj. Maj. Maj. Maj. Perf.
9|2 3 LsLssLsLssLs Perf. Maj. Maj. Maj. Maj. Perf. Maj. Perf. Maj. Maj. Min. Maj. Perf.
8|3 10 LssLsLsLssLs Perf. Maj. Maj. Min. Maj. Perf. Maj. Perf. Maj. Maj. Min. Maj. Perf.
7|4 5 LssLsLssLsLs Perf. Maj. Maj. Min. Maj. Perf. Maj. Perf. Min. Maj. Min. Maj. Perf.
6|5 12 sLsLsLssLsLs Perf. Min. Maj. Min. Maj. Perf. Maj. Perf. Min. Maj. Min. Maj. Perf.
5|6 7 sLsLssLsLsLs Perf. Min. Maj. Min. Maj. Perf. Min. Perf. Min. Maj. Min. Maj. Perf.
4|7 2 sLsLssLsLssL Perf. Min. Maj. Min. Maj. Perf. Min. Perf. Min. Maj. Min. Min. Perf.
3|8 9 sLssLsLsLssL Perf. Min. Maj. Min. Min. Perf. Min. Perf. Min. Maj. Min. Min. Perf.
2|9 4 sLssLsLssLsL Perf. Min. Maj. Min. Min. Perf. Min. Perf. Min. Min. Min. Min. Perf.
1|10 11 ssLsLsLssLsL Perf. Min. Min. Min. Min. Perf. Min. Perf. Min. Min. Min. Min. Perf.
0|11 6 ssLsLssLsLsL Perf. Min. Min. Min. Min. Perf. Min. Dim. Min. Min. Min. Min. Perf.

Proposed Names

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.

Modes of 5L 7s
UDP Rotational order Step pattern Mode names
10|0 1 LsLsLssLsLss Rat
9|1 8 LsLssLsLsLss Ox
8|2 3 LsLssLsLssLs Tiger
7|3 10 LssLsLsLssLs Rabbit
6|4 5 LssLsLssLsLs Dragon
5|5 12 sLsLsLssLsLs Snake
4|6 7 sLsLssLsLsLs Horse
3|7 2 sLsLssLsLssL Goat
2|8 9 sLssLsLsLssL Monkey
1|9 4 sLssLsLssLsL Rooster
0|10 11 ssLsLsLssLsL Dog
-1|11 6 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
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