5L 7s

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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
Related to 5L 2s (diatonic)
With tunings 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 tuning or the schismatic temperament, and on the other hand, the simpler and less accurate temperament known as superpyth in which 64/63 is tempered out.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

Intervals

Intervals of 5L 7s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Minor 1-mosstep m1ms s 0.0 ¢ to 100.0 ¢
Major 1-mosstep M1ms L 100.0 ¢ to 240.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 200.0 ¢
Major 2-mosstep M2ms L + s 200.0 ¢ to 240.0 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 240.0 ¢ to 300.0 ¢
Major 3-mosstep M3ms 2L + s 300.0 ¢ to 480.0 ¢
4-mosstep Minor 4-mosstep m4ms L + 3s 240.0 ¢ to 400.0 ¢
Major 4-mosstep M4ms 2L + 2s 400.0 ¢ to 480.0 ¢
5-mosstep Perfect 5-mosstep P5ms 2L + 3s 480.0 ¢ to 500.0 ¢
Augmented 5-mosstep A5ms 3L + 2s 500.0 ¢ to 720.0 ¢
6-mosstep Minor 6-mosstep m6ms 2L + 4s 480.0 ¢ to 600.0 ¢
Major 6-mosstep M6ms 3L + 3s 600.0 ¢ to 720.0 ¢
7-mosstep Diminished 7-mosstep d7ms 2L + 5s 480.0 ¢ to 700.0 ¢
Perfect 7-mosstep P7ms 3L + 4s 700.0 ¢ to 720.0 ¢
8-mosstep Minor 8-mosstep m8ms 3L + 5s 720.0 ¢ to 800.0 ¢
Major 8-mosstep M8ms 4L + 4s 800.0 ¢ to 960.0 ¢
9-mosstep Minor 9-mosstep m9ms 3L + 6s 720.0 ¢ to 900.0 ¢
Major 9-mosstep M9ms 4L + 5s 900.0 ¢ to 960.0 ¢
10-mosstep Minor 10-mosstep m10ms 4L + 6s 960.0 ¢ to 1000.0 ¢
Major 10-mosstep M10ms 5L + 5s 1000.0 ¢ to 1200.0 ¢
11-mosstep Minor 11-mosstep m11ms 4L + 7s 960.0 ¢ to 1100.0 ¢
Major 11-mosstep M11ms 5L + 6s 1100.0 ¢ to 1200.0 ¢
12-mosstep Perfect 12-mosstep P12ms 5L + 7s 1200.0 ¢

Generator chain

Generator chain of 5L 7s
Bright gens Scale degree Abbrev.
16 Augmented 4-mosdegree A4md
15 Augmented 9-mosdegree A9md
14 Augmented 2-mosdegree A2md
13 Augmented 7-mosdegree A7md
12 Augmented 0-mosdegree A0md
11 Augmented 5-mosdegree A5md
10 Major 10-mosdegree M10md
9 Major 3-mosdegree M3md
8 Major 8-mosdegree M8md
7 Major 1-mosdegree M1md
6 Major 6-mosdegree M6md
5 Major 11-mosdegree M11md
4 Major 4-mosdegree M4md
3 Major 9-mosdegree M9md
2 Major 2-mosdegree M2md
1 Perfect 7-mosdegree P7md
0 Perfect 0-mosdegree
Perfect 12-mosdegree		 P0md
P12md
−1 Perfect 5-mosdegree P5md
−2 Minor 10-mosdegree m10md
−3 Minor 3-mosdegree m3md
−4 Minor 8-mosdegree m8md
−5 Minor 1-mosdegree m1md
−6 Minor 6-mosdegree m6md
−7 Minor 11-mosdegree m11md
−8 Minor 4-mosdegree m4md
−9 Minor 9-mosdegree m9md
−10 Minor 2-mosdegree m2md
−11 Diminished 7-mosdegree d7md
−12 Diminished 12-mosdegree d12md
−13 Diminished 5-mosdegree d5md
−14 Diminished 10-mosdegree d10md
−15 Diminished 3-mosdegree d3md
−16 Diminished 8-mosdegree d8md

Modes

Scale degrees of the modes of 5L 7s
UDP Cyclic
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. Furthermore, 12edo (equalized tuning of this MOS) was independently discovered in China.


Modes of 5L 7s
UDP Cyclic
order		 Step
pattern		 Mode names
11|0 1 LsLsLssLsLss Rat
10|1 8 LsLssLsLsLss Ox
9|2 3 LsLssLsLssLs Tiger
8|3 10 LssLsLsLssLs Rabbit
7|4 5 LssLsLssLsLs Dragon
6|5 12 sLsLsLssLsLs Snake
5|6 7 sLsLssLsLsLs Horse
4|7 2 sLsLssLsLssL Goat
3|8 9 sLssLsLsLssL Monkey
2|9 4 sLssLsLssLsL Rooster
1|10 11 ssLsLsLssLsL Dog
0|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, ↑ grackle
31\53 701.887 498.113 5:4 1.250 Helmholtz, Pythagorean tuning (701.955 ¢)
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, argent tuning (702.944 ¢)
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 Polypyth, golden neogothic (704.096 ¢)
27\46 704.348 495.652 5:3 1.667 Semisoft 5L 7s
Leapday
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 (708.054 ¢)
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 ↓ Oceanfront / ultrapyth
3\5 720.000 480.000 1:0 → ∞ Collapsed 5L 7s
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