5L 12s: Difference between revisions

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== Scale tree ==
== Scale tree ==
Generator ranges:
{{Scale tree|Comments=
* Chroma-positive generator: 705.8824 cents (10\17) to 720 cents (3\5)
4/3: [[Supra]];
* Chroma-negative generator: 480 cents (2\5) to 494.1176 cents (7\17)
13/8: Golden supra (708.0539¢);
 
5/3: [[Quasisuper]] / [[quasisupra]];
{| class="wikitable center-all"
5/2: [[Superpyth]];
! colspan="6" | Generator
13/5: Golden superpyth (710.4345¢);
! Cents
5/1: [[Oceanfront]] / [[ultrapyth]];
! L
6/1: [[Hemiseven]]↓
! s
}}
! L/s
! Comments
|-
| 10\17 || || || || || || 705.882 || 1 || 1 || 1.000 ||
|-
| || || || || || 53\90 || 706.667 || 6 || 5 || 1.200 ||
|-
| || || || || 43\73 || || 706.849 || 5 || 4 || 1.250 ||
|-
| || || || || || 76\129 || 706.977 || 9 || 7 || 1.286 ||
|-
| || || || 33\56 || || || 707.143 || 4 || 3 || 1.333 || [[Supra]]
|-
| || || || || || 89\151 || 707.285 || 11 || 8 || 1.375 ||
|-
| || || || || 56\95 || || 707.368 || 7 || 5 || 1.400 ||
|-
| || || || || || 79\134 || 707.463 || 10 || 7 || 1.428 ||
|-
| || || 23\39 || || || || 707.692 || 3 || 2 || 1.500 ||
|-
| || || || || || 82\139 || 707.914 || 11 || 7 || 1.571 ||
|-
| || || || || 59\100 || || 708.000 || 8 || 5 || 1.600 ||
|-
| || || || || || 95\161 || 708.075 || 13 || 8 || 1.625 || Golden supra (708.0539¢)
|-
| || || || 36\61 || || || 708.197 || 5 || 3 || 1.667 || [[Quasisuper]] / [[quasisupra]]
|-
| || || || || || 85\144 || 708.333 || 12 || 7 || 1.714 ||
|-
| || || || || 49\83 || || 708.434 || 7 || 4 || 1.750 ||
|-
| || || || || || 62\105 || 708.571 || 9 || 5 || 1.800 ||
|-
| || 13\22 || || || || || 709.091 || 2 || 1 || 2.000 || Basic 5L 12s <br>(Generators smaller than this are proper)
|-
| || || || || || 55\93 || 709.677 || 9 || 4 || 2.250 ||
|-
| || || || || 42\71 || || 709.859 || 7 || 3 || 2.333 ||
|-
| || || || || || 71\120 || 710.000 || 12 || 5 || 2.400 ||
|-
| || || || 29\49 || || || 710.204 || 5 || 2 || 2.500 || [[Superpyth]]
|-
| || || || || || 74\125 || 710.400 || 13 || 5 || 2.600 || Golden superpyth (710.4345¢)
|-
| || || || || 45\76 || || 710.526 || 8 || 3 || 2.667 ||
|-
| || || || || || 61\103 || 710.680 || 11 || 4 || 2.750 ||
|-
| || || 16\27 || || || || 711.111 || 3 || 1 || 3.000 ||
|-
| || || || || || 51\86 || 711.628 || 10 || 3 || 3.333 ||
|-
| || || || || 35\59 || || 711.864 || 7 || 2 || 3.500 ||
|-
| || || || || || 54\91 || 712.088 || 11 || 3 || 3.667 ||
|-
| || || || 19\32 || || || 712.500 || 4 || 1 || 4.000 ||
|-
| || || || || || 41\69 || 713.043 || 9 || 2 || 4.500 ||
|-
| || || || || 22\37 || || 713.514 || 5 || 1 || 5.000 || [[Oceanfront]] / [[Ultrapyth]]
|-
| || || || || || 25\42 || 714.286 || 6 || 1 || 6.000 || [[Hemiseven]]↓
|-
| 3\5 || || || || || || 720.000 || 1 || 0 || → inf ||
|}


[[Category:17-tone scales]]
[[Category:17-tone scales]]
[[Category:Mega chromatic scales]]
[[Category:Mega chromatic scales]]

Revision as of 08:44, 7 August 2024

Todo: review

Adopt scale tree template, review entries

↖ 4L 11s ↑ 5L 11s 6L 11s ↗
← 4L 12s 5L 12s 6L 12s →
↙ 4L 13s ↓ 5L 13s 6L 13s ↘ 
┌╥┬┬╥┬┬╥┬┬┬╥┬┬╥┬┬┬┐
│║││║││║│││║││║││││
│││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LssLssLsssLssLsss
sssLssLsssLssLssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 10\17 to 3\5 (705.9 ¢ to 720.0 ¢)
Dark 2\5 to 7\17 (480.0 ¢ to 494.1 ¢)
TAMNAMS information
Related to 5L 2s (diatonic)
With tunings 3:1 to 1:0 (hard)
Related MOS scales
Parent 5L 7s
Sister 12L 5s
Daughters 17L 5s, 5L 17s
Neutralized 10L 7s
2-Flought 22L 12s, 5L 29s
Equal tunings
Equalized (L:s = 1:1) 10\17 (705.9 ¢)
Supersoft (L:s = 4:3) 33\56 (707.1 ¢)
Soft (L:s = 3:2) 23\39 (707.7 ¢)
Semisoft (L:s = 5:3) 36\61 (708.2 ¢)
Basic (L:s = 2:1) 13\22 (709.1 ¢)
Semihard (L:s = 5:2) 29\49 (710.2 ¢)
Hard (L:s = 3:1) 16\27 (711.1 ¢)
Superhard (L:s = 4:1) 19\32 (712.5 ¢)
Collapsed (L:s = 1:0) 3\5 (720.0 ¢)

5L 12s, also called s-enharmonic, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 12 small steps, repeating every octave. 5L 12s is a grandchild scale of 5L 2s, expanding it by 10 tones. Generators that produce this scale range from 705.9 ¢ to 720 ¢, or from 480 ¢ to 494.1 ¢. This scale is characterized by having a diesis (the difference between a large step and two small steps) that is larger than the chroma.

The supra/quasisuper version is proper, but the superpyth/ultrapyth version is improper (it does not become proper until you add 5 more notes to form the superpyth 22-note scale).

Modes

Modes of 5L 12s
UDP Cyclic
order		 Step
pattern
16|0 1 LssLssLsssLssLsss
15|1 11 LssLsssLssLssLsss
14|2 4 LssLsssLssLsssLss
13|3 14 LsssLssLssLsssLss
12|4 7 LsssLssLsssLssLss
11|5 17 sLssLssLsssLssLss
10|6 10 sLssLsssLssLssLss
9|7 3 sLssLsssLssLsssLs
8|8 13 sLsssLssLssLsssLs
7|9 6 sLsssLssLsssLssLs
6|10 16 ssLssLssLsssLssLs
5|11 9 ssLssLsssLssLssLs
4|12 2 ssLssLsssLssLsssL
3|13 12 ssLsssLssLssLsssL
2|14 5 ssLsssLssLsssLssL
1|15 15 sssLssLssLsssLssL
0|16 8 sssLssLsssLssLssL

Scale tree

Template:Scale tree

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