3L 16s: Difference between revisions

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This MOS divides its small steps 5-5-6 between its large steps. Its generator is a small major third no less than 6/19edo (378.947 cents). Around +5g = 3, magic appears. Going higher, würschmidt appears where the generator is exactly 5/4.
{{Infobox MOS
| Periods = 1
| nLargeSteps = 3
| nSmallSteps = 16
| Equalized = 6
| Paucitonic = 1
| Pattern = LsssssLsssssLssssss
}}


{| class="wikitable"
'''3L 16s''' occupies the spectrum from [[19edo]] (L = s) to [[3edo]] (s = 0).
 
This MOS divides its small steps 5-5-6 between its large steps. Its generator is a small major third no less than 6/19 octave (378.947 cents). Around +5g = 3, [[magic]] appears. Going higher, würschmidt appears where the generator is exactly 5/4.
 
== Modes ==
* 18|0 LsssssLsssssLssssss
* 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 ==
Generator ranges:
* 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 ||
|-
|-
| | 1/3
| || || || || || 45\142 || 380.282 || 10 || 7 || 1.429 ||  
| |  
| |  
| |  
| |  
| |  
| | 400
|-
|-
|
| || || 13\41 || || || || 380.488 || 3 || 2 || 1.500 || [[Magic]] is around here
|
|
|
|
|11/34
|388.235
|-
|-
| |  
| || || || || || 46\145 || 380.690 || 11 || 7 || 1.571 ||
| |  
| |  
| |  
| | 10/31
| |  
| | 387.091
|-
|-
| |  
| || || || || 33\104 || || 380.769 || 8 || 5 || 1.600 ||
| |  
| |  
| |  
| |  
| | 19/59
| | 386.441
|-
|-
| |  
| || || || || || 53\167 || 380.838 || 13 || 8 || 1.625 || [[Necromancy]] <br>Golden magic (380.8191¢)
| |  
| |  
| | 9/28
| |  
| |  
| | 385.857
|-
|-
| |  
| || || || 20\63 || || || 380.952 || 5 || 3 || 1.667 ||
| |  
| |  
| |  
| | 17/53
| |  
| | 384.906
|-
|-
| |  
| || || || || || 47\148 || 381.081 || 12 || 7 || 1.714 ||
| |  
| |  
| |  
| |  
| |  
| | 384.053
|-
|-
| |  
| || || || || 27\85 || || 381.176 || 7 || 4 || 1.750 ||  
| |  
| | 8/25
| |  
| |  
| |  
| | 384
|-
|-
| |  
| || || || || || 34\107 || 381.308 || 9 || 5 || 1.800 ||
| |  
| |  
| |  
| |  
| |  
| | 383.947
|-
|-
| |  
| || 7\22 || || || || || 381.818 || 2 || 1 || 2.000 || Basic 3L 16s <br>(Generators smaller than this are proper)
| |  
| |  
| |  
| | 23/72
| |  
| | 383.333
|-
|-
| |  
| || || || || || 29\91 || 382.418 || 9 || 4 || 2.250 ||
| |  
| |  
| |  
| |  
| |  
| | 383.231
|-
|-
| |  
| || || || || 22\69 || || 382.609 || 7 || 3 || 2.333 || [[Marveltri]]
| |  
| |  
| | 15/47
| |  
| |  
| | 382.979
|-
|-
| |  
| || || || || || 37\116 || 382.759 || 12 || 5 || 2.400 ||
| |  
| |  
| |  
| | 22/69
| |  
| | 382.609
|-
|-
| |  
| || || || 15\47 || || || 382.979 || 5 || 2 || 2.500 ||
| | 7/22
| |  
| |  
| |  
| |  
| | 381.818
|-
|-
| |  
| || || || || || 38\119 || 383.193 || 13 || 5 || 2.600 || Unnamed golden tuning (383.2314¢)
| |  
| |  
| |  
| | 27/85
| |  
| | 381.1765
|-
|-
| |  
| || || || || 23\72 || || 383.333 || 8 || 3 || 2.667 ||
| |  
| |  
| |  
| |  
| |  
| | 381.138
|-
|-
| |  
| || || || || || 31\97 || 383.505 || 11 || 4 || 2.750 ||
| |  
| |  
| | 20/63
| |  
| |  
| | 380.952
|-
|-
| |  
| || || 8\25 || || || || 384.000 || 3 || 1 || 3.000 ||
| |  
| |  
| |  
| |  
| |  
| | 380.819
|-
|-
| |  
| || || || || || 25\78 || 384.615 || 10 || 3 || 3.333 ||
| |  
| |  
| |  
| | 33/104
| |  
| | 380.769
|-
|-
| |  
| || || || || 17\53 || || 384.906 || 7 || 2 || 3.500 ||
| |  
| |  
| |  
| |  
| |  
| | 380.688
|-
|-
| |  
| || || || || || 26\81 || 385.185 || 11 || 3 || 3.667 ||
| |  
| | 13/41
| |  
| |  
| |  
| | 380.488
|-
|-
| |  
| || || || 9\28 || || || 385.714 || 4 || 1 || 4.000 ||
| |  
| |  
| |  
| | 32/101
| |  
| | 380.198
|-
|-
| |  
| || || || || || 19\59 || 386.441 || 9 || 2 || 4.500 || [[Sulis]]
| |  
| |  
| | 19/60
| |  
| |  
| | 380
|-
|-
| |  
| || || || || 10\31 || || 387.097 || 5 || 1 || 5.000 || [[Grendel]]/[[Würschmidt]]
| |  
| |  
| |  
| | 25/79
| |  
| | 379.747
|-
|-
|
| || || || || || 11\34 || 388.235 || 6 || 1 || 6.000 ||
|
|
|
|
|31/98
|379.592
|-
|-
| | 6/19
| 1\3 || || || || || || 400.000 || 1 || 0 || → inf ||  
| |  
| |  
| |  
| |  
| |  
| | 378.947
|}
|}

Revision as of 10:18, 14 April 2023

↖ 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 occupies the spectrum from 19edo (L = s) to 3edo (s = 0).

This MOS divides its small steps 5-5-6 between its large steps. Its generator is a small major third no less than 6/19 octave (378.947 cents). Around +5g = 3, magic appears. Going higher, würschmidt appears where the generator is exactly 5/4.

Modes

  • 18|0 LsssssLsssssLssssss
  • 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

Generator ranges:

  • Bright generator: 378.9474 cents (6\19) to 400 cents (1\3)
  • Dark generator: 800 cents (2\3) to 821.0526 cents (13\19)
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
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
(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
15\47 382.979 5 2 2.500
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
Retrieved from "https://en.xen.wiki/index.php?title=3L_16s&oldid=107676"