5L 7s: Difference between revisions

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5L 7s represents the chromatic scales of [[Pythagorean tuning|Pythagorean]]/[[Schismatic family|schismic]] and [[superpyth]], the former being [[Rothenberg propriety|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]].
5L 7s represents the chromatic scales of [[Pythagorean tuning|Pythagorean]]/[[Schismatic family|schismic]] and [[superpyth]], the former being [[Rothenberg propriety|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.
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, th simpler and less accurate temperament known as [[archy]] in which 64/63 is tempered out.
==Intervals==
==Intervals==
{{MOS intervals}}
{{MOS intervals}}

Revision as of 01:51, 29 July 2024

↖ 4L 6s ↑ 5L 6s 6L 6s ↗
← 4L 7s 5L 7s 6L 7s →
↙ 4L 8s ↓ 5L 8s 6L 8s ↘ 
┌╥┬╥┬╥┬┬╥┬╥┬┬┐
│║│║│║││║│║│││
││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┘
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 such that 64/63 is not tempered out, such as the schismatic temperaments known as Helmholtz and Garibaldi, and on the other hand, th simpler and less accurate temperament known as archy in which 64/63 is tempered out.

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 ¢

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.

Modes of 5L 7s
UDP Cyclic
order		 Step
pattern
11|0 1 LsLsLssLsLss
10|1 8 LsLssLsLsLss
9|2 3 LsLssLsLssLs
8|3 10 LssLsLsLssLs
7|4 5 LssLsLssLsLs
6|5 12 sLsLsLssLsLs
5|6 7 sLsLssLsLsLs
4|7 2 sLsLssLsLssL
3|8 9 sLssLsLsLssL
2|9 4 sLssLsLssLsL
1|10 11 ssLsLsLssLsL
0|11 6 ssLsLssLsLsL

Scales

Scale tree

Template:Scale tree

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