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 ¢)
View • Talk • Edit

5L 7s 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 is deprecated. Please use Template: MOS tuning spectrum instead. Details:
Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: 
{{MOS tuning spectrum
| 3/2 = Example comment
| 4/3 = Another example comment
}}


The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.


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
31\53 701.887 498.113 5:4 1.250
55\94 702.128 497.872 9:7 1.286
24\41 702.439 497.561 4:3 1.333 Supersoft 5L 7s
65\111 702.703 497.297 11:8 1.375
41\70 702.857 497.143 7:5 1.400
58\99 703.030 496.970 10:7 1.429
17\29 703.448 496.552 3:2 1.500 Soft 5L 7s
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
27\46 704.348 495.652 5:3 1.667 Semisoft 5L 7s
64\109 704.587 495.413 12:7 1.714
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
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
36\61 708.197 491.803 8:3 2.667
49\83 708.434 491.566 11:4 2.750
13\22 709.091 490.909 3:1 3.000 Hard 5L 7s
42\71 709.859 490.141 10:3 3.333
29\49 710.204 489.796 7:2 3.500
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
3\5 720.000 480.000 1:0 → ∞ Collapsed 5L 7s
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