5L 7s: Difference between revisions

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== Scale tree ==
== Scale tree ==
Generator ranges:
{{Scale tree|Comments=6/5: [[Photia]] / [[pontiac]]<br>↑ [[Grackle]] (701.239¢);
* Chroma-positive generator: 700 cents (7\12) to 720 cents (3\5)
5/4: [[Helmholtz]]<br>[[Pythagorean tuning]] (701.9550¢);
* Chroma-negative generator: 480 cents (2\5) to 500 cents (5\12)
9/7: [[Garibaldi]] / [[cassandra]];
 
4/3: Garibaldi / [[andromeda]];
{| class="wikitable center-all"
11/8: [[Kwai]];
! colspan="6" | Generator
10/7: [[Undecental]];
! Cents
3/2: [[Edson]];
! L
13/8: Golden neogothic (704.0956¢);
! s
5/3: [[Leapday]] / [[polypyth]];
! L/s
12/7: [[Leapweek]];
! Comments
7/3: [[Supra]];
|-
13/5: Golden supra (708.0539¢);
| 7\12 || || || || || || 700.000 || 1 || 1 || 1.000 ||
8/3: [[Quasisuper]] / [[quasisupra]];
|-
3/1: [[Suprapyth]];
| || || || || || 38\65 || 701.539 || 6 || 5 || 1.200 || [[Photia]] / [[pontiac]] / [[grackle]]↑
7/2: [[Superpyth]];
|-
6/1: ↓ [[Ultrapyth]] (713.651¢)<br>↓ [[Oceanfront scales|Oceanfront]] (713.910¢)}}
| || || || || 31\53 || || 701.887 || 5 || 4 || 1.250 || [[Helmholtz]], [[Pythagorean tuning]] (701.9550¢)
|-
| || || || || || 55\94 || 702.128 || 9 || 7 || 1.286 || [[Garibaldi]] / [[cassandra]]
|-
| || || || 24\41 || || || 702.409 || 4 || 3 || 1.333 || Garibaldi / [[andromeda]]
|-
| || || || || || 65\111 || 702.703 || 11 || 8 || 1.375 || [[Kwai]]
|-
| || || || || 41\70 || || 702.857 || 7 || 5 || 1.400 ||
|-
| || || || || || 58\99 || 703.030 || 10 || 7 || 1.428 || [[Undecental]]
|-
| || || 17\29 || || || || 703.448 || 3 || 2 || 1.500 || [[Edson]]
|-
| || || || || || 61\104 || 703.846 || 11 || 7 || 1.571 ||
|-
| || || || || 44\75 || || 704.000 || 8 || 5 || 1.600 ||
|-
| || || || || || 71\121 || 704.132 || 13 || 8 || 1.625 || Golden neogothic (704.0956¢)
|-
| || || || 27\46 || || || 704.348 || 5 || 3 || 1.667 || [[Leapday]] / [[polypyth]]
|-
| || || || || || 64\109 || 704.587 || 12 || 7 || 1.714 || [[Leapweek]]
|-
| || || || || 37\63 || || 704.762 || 7 || 4 || 1.750 ||
|-
| || || || || || 47\80 || 705.000 || 9 || 5 || 1.800 ||
|-
| || 10\17 || || || || || 705.882 || 2 || 1 || 2.000 || Basic p-chromatic <br>(Generators smaller than this are proper)
|-
| || || || || || 43\73 || 706.849 || 9 || 4 || 2.250 ||
|-
| || || || || 33\56 || || 707.143 || 7 || 3 || 2.333 || [[Supra]]
|-
| || || || || || 56\95 || 707.368 || 12 || 5 || 2.400 ||
|-
| || || || 23\39 || || || 707.692 || 5 || 2 || 2.500 ||
|-
| || || || || || 59\100 || 708.000 || 13 || 5 || 2.600 || Golden supra (708.0539¢)
|-
| || || || || 36\61 || || 708.197 || 8 || 3 || 2.667 || [[Quasisuper]] / [[quasisupra]]
|-
| || || || || || 49\83 || 708.434 || 11 || 4 || 2.750 ||
|-
| || || 13\22 || || || || 709.091 || 3 || 1 || 3.000 || [[Suprapyth]]
|-
| || || || || || 42\71 || 709.859 || 10 || 3 || 3.333 ||
|-
| || || || || 29\49 || || 710.204 || 7 || 2 || 3.500 || [[Superpyth]]
|-
| || || || || || 45\76 || 710.526 || 11 || 3 || 3.667 ||
|-
| || || || 16\27 || || || 711.111 || 4 || 1 || 4.000 ||
|-
| || || || || || 35\59 || 711.864 || 9 || 2 || 4.500 ||
|-
| || || || || 19\32 || || 712.500 || 5 || 1 || 5.000 ||
|-
| || || || || || 22\37 || 713.514 || 6 || 1 || 6.000 || [[Oceanfront]]↓ / [[ultrapyth]]↓
|-
| 3\5 || || || || || || 720.000 || 1 || 0 || → inf ||
|}
 
[[Category:12-tone scales]]
[[Category:12-tone scales]]
[[Category:P-chromatic| ]] <!-- main article -->
[[Category:P-chromatic| ]]<!-- main article -->
[[Category:Chromatic scales]]
[[Category:Chromatic scales]]

Revision as of 07:33, 19 February 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, 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

Template:Scale tree

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