3L 16s: Difference between revisions

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== Modes ==
== Modes ==
* 18|0 LsssssLsssssLssssss
{{MOS modes}}
* 17|1 LsssssLssssssLsssss
* 16|2 LssssssLsssssLsssss
* 15|3 sLsssssLsssssLsssss
* 14|4 sLsssssLssssssLssss
* 13|5 sLssssssLsssssLssss
* 12|6 ssLsssssLsssssLssss
* 11|7 ssLsssssLssssssLsss
* 10|8 ssLssssssLsssssLsss
* 9|9 sssLsssssLsssssLsss
* 8|10 sssLsssssLssssssLss
* 7|11 sssLssssssLsssssLss
* 6|12 ssssLsssssLsssssLss
* 5|13 ssssLsssssLssssssLs
* 4|14 ssssLssssssLsssssLs
* 3|15 sssssLsssssLsssssLs
* 2|16 sssssLsssssLssssssL
* 1|17 sssssLssssssLsssssL
* 0|18 ssssssLsssssLsssssL


== Scales tree ==
== Scales tree ==
Generator ranges:
{{Scale tree|depth=5|Comments=11/8:[[Witchcraft]]; 3/2:[[Magic]] is around here; 13/8:[[Necromancy]]<br>Golden magic (380.8191¢); 12/5:[[Marveltri]] is around here; 13/5:Unnamed golden tuning (383.2314¢); 9/2:[[Sulis]]; 5/1:[[Grendel]]/[[Würschmidt]]}}
* Bright generator: 378.9474 cents (6\19) to 400 cents (1\3)
* Dark generator: 800 cents (2\3) to 821.0526 cents (13\19)
 
{| class="wikitable center-all"
! colspan="6" | Bright generator
! Cents
! L
! s
! L/s
! Comments
|-
| 6\19 || || || || || || 378.947 || 1 || 1 || 1.000 ||
|-
| || || || || || 31\98 || 379.592 || 6 || 5 || 1.200 ||
|-
| || || || || 25\79 || || 379.747 || 5 || 4 || 1.250 ||
|-
| || || || || || 44\139 || 379.856 || 9 || 7 || 1.286 ||
|-
| || || || 19\60 || || || 380.000 || 4 || 3 || 1.333 ||
|-
| || || || || || 51\161 || 380.124 || 11 || 8 || 1.375 || [[Witchcraft]]
|-
| || || || || 32\101 || || 380.198 || 7 || 5 || 1.400 ||
|-
| || || || || || 45\142 || 380.282 || 10 || 7 || 1.429 ||
|-
| || || 13\41 || || || || 380.488 || 3 || 2 || 1.500 || [[Magic]] is around here
|-
| || || || || || 46\145 || 380.690 || 11 || 7 || 1.571 ||
|-
| || || || || 33\104 || || 380.769 || 8 || 5 || 1.600 ||
|-
| || || || || || 53\167 || 380.838 || 13 || 8 || 1.625 || [[Necromancy]] <br>Golden magic (380.8191¢)
|-
| || || || 20\63 || || || 380.952 || 5 || 3 || 1.667 ||
|-
| || || || || || 47\148 || 381.081 || 12 || 7 || 1.714 ||
|-
| || || || || 27\85 || || 381.176 || 7 || 4 || 1.750 ||
|-
| || || || || || 34\107 || 381.308 || 9 || 5 || 1.800 ||
|-
| || 7\22 || || || || || 381.818 || 2 || 1 || 2.000 || Basic 3L 16s <br>(Generators smaller than this are proper)
|-
| || || || || || 29\91 || 382.418 || 9 || 4 || 2.250 ||
|-
| || || || || 22\69 || || 382.609 || 7 || 3 || 2.333 || [[Marveltri]]
|-
| || || || || || 37\116 || 382.759 || 12 || 5 || 2.400 || Marveltri
|-
| || || || 15\47 || || || 382.979 || 5 || 2 || 2.500 || Marveltri
|-
| || || || || || 38\119 || 383.193 || 13 || 5 || 2.600 || Unnamed golden tuning (383.2314¢)
|-
| || || || || 23\72 || || 383.333 || 8 || 3 || 2.667 ||
|-
| || || || || || 31\97 || 383.505 || 11 || 4 || 2.750 ||
|-
| || || 8\25 || || || || 384.000 || 3 || 1 || 3.000 ||
|-
| || || || || || 25\78 || 384.615 || 10 || 3 || 3.333 ||
|-
| || || || || 17\53 || || 384.906 || 7 || 2 || 3.500 ||
|-
| || || || || || 26\81 || 385.185 || 11 || 3 || 3.667 ||
|-
| || || || 9\28 || || || 385.714 || 4 || 1 || 4.000 ||
|-
| || || || || || 19\59 || 386.441 || 9 || 2 || 4.500 || [[Sulis]]
|-
| || || || || 10\31 || || 387.097 || 5 || 1 || 5.000 || [[Grendel]]/[[Würschmidt]]
|-
| || || || || || 11\34 || 388.235 || 6 || 1 || 6.000 ||
|-
| 1\3 || || || || || || 400.000 || 1 || 0 || → inf ||
|}


[[Category:19-tone scales]]
[[Category:19-tone scales]]
[[Category:Magic]]
[[Category:Magic]]

Revision as of 09:53, 14 July 2024

Todo: review

Adopt scale tree template, review entries

↖ 2L 15s ↑ 3L 15s 4L 15s ↗
← 2L 16s 3L 16s 4L 16s →
↙ 2L 17s ↓ 3L 17s 4L 17s ↘ 
┌╥┬┬┬┬┬╥┬┬┬┬┬╥┬┬┬┬┬┬┐
│║│││││║│││││║│││││││
│││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsssssLsssssLssssss
ssssssLsssssLsssssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 6\19 to 1\3 (378.9 ¢ to 400.0 ¢)
Dark 2\3 to 13\19 (800.0 ¢ to 821.1 ¢)
TAMNAMS information
Related to 3L 7s (sephiroid)
With tunings 4:1 to 1:0 (ultrahard)
Related MOS scales
Parent 3L 13s
Sister 16L 3s
Daughters 19L 3s, 3L 19s
Neutralized 6L 13s
2-Flought 22L 16s, 3L 35s
Equal tunings
Equalized (L:s = 1:1) 6\19 (378.9 ¢)
Supersoft (L:s = 4:3) 19\60 (380.0 ¢)
Soft (L:s = 3:2) 13\41 (380.5 ¢)
Semisoft (L:s = 5:3) 20\63 (381.0 ¢)
Basic (L:s = 2:1) 7\22 (381.8 ¢)
Semihard (L:s = 5:2) 15\47 (383.0 ¢)
Hard (L:s = 3:1) 8\25 (384.0 ¢)
Superhard (L:s = 4:1) 9\28 (385.7 ¢)
Collapsed (L:s = 1:0) 1\3 (400.0 ¢)

3L 16s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 16 small steps, repeating every octave. 3L 16s is a great-grandchild scale of 3L 7s, expanding it by 9 tones. Generators that produce this scale range from 378.9 ¢ to 400 ¢, or from 800 ¢ to 821.1 ¢. This scale is associated with magic temperament, where 5 bright generators maps to 3/1, and würschmidt temperament, where the generator is 5/4.

Modes

Modes of 3L 16s
UDP Cyclic
order		 Step
pattern
18|0 1 LsssssLsssssLssssss
17|1 7 LsssssLssssssLsssss
16|2 13 LssssssLsssssLsssss
15|3 19 sLsssssLsssssLsssss
14|4 6 sLsssssLssssssLssss
13|5 12 sLssssssLsssssLssss
12|6 18 ssLsssssLsssssLssss
11|7 5 ssLsssssLssssssLsss
10|8 11 ssLssssssLsssssLsss
9|9 17 sssLsssssLsssssLsss
8|10 4 sssLsssssLssssssLss
7|11 10 sssLssssssLsssssLss
6|12 16 ssssLsssssLsssssLss
5|13 3 ssssLsssssLssssssLs
4|14 9 ssssLssssssLsssssLs
3|15 15 sssssLsssssLsssssLs
2|16 2 sssssLsssssLssssssL
1|17 8 sssssLssssssLsssssL
0|18 14 ssssssLsssssLsssssL

Scales tree

Template:Scale tree

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