15L 4s: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Ganaram inukshuk (talk | contribs)
autopatrolled, emailconfirmed
6,211 edits
m Order of templates
Ganaram inukshuk (talk | contribs)
autopatrolled, emailconfirmed
6,211 edits
→Scale tree: Replaced and populated scale tree
Line 11: Line 11:


== Scale tree ==
== Scale tree ==
{| class="wikitable"
{{Scale tree|Comments=11/8: [[Catakleismic]]}}
! colspan="6" |Generator
!Bright gen.
!Dark gen.
!L
!s
!L/s
!Comments
|-
|5\19
|
|
|
|
|
|315.789
|884.211
|1
|1
|1.000
|Equalized 15L 4s (Degenerate case)
|-
|
|
|
|
|
|29\110
|316.364
|883.636
|6
|5
|1.200
|
|-
|
|
|
|
|24\91
|
|316.484
|883.516
|5
|4
|1.250
|
|-
|
|
|
|
|
|43\163
|316.564
|883.436
|9
|7
|1.286
|
|-
|
|
|
|19\72
|
|
|316.667
|883.333
|4
|3
|1.333
|Supersoft 15L 4s
|-
|
|
|
|
|
|52\197
|316.751
|883.249
|11
|8
|1.375
|
|-
|
|
|
|
|33\125
|
|316.800
|883.200
|7
|5
|1.400
|
|-
|
|
|
|
|
|47\178
|316.854
|883.146
|10
|7
|1.429
|
|-
|
|
|14\53
|
|
|
|316.981
|883.019
|3
|2
|1.500
|Monosoft 15L 4s
|-
|
|
|
|
|
|51\193
|317.098
|882.902
|11
|7
|1.571
|
|-
|
|
|
|
|37\140
|
|317.143
|882.857
|8
|5
|1.600
|
|-
|
|
|
|
|
|60\227
|317.181
|882.819
|13
|8
|1.625
|Golden 15L 4s sequence can be found here
|-
|
|
|
|23\87
|
|
|317.241
|882.759
|5
|3
|1.667
|Semisoft 15L 4s
|-
|
|
|
|
|
|55\208
|317.308
|882.692
|12
|7
|1.714
|
|-
|
|
|
|
|32\121
|
|317.355
|882.645
|7
|4
|1.750
|
|-
|
|
|
|
|
|41\155
|317.419
|882.581
|9
|5
|1.800
|
|-
|
|9\34
|
|
|
|
|317.647
|882.353
|2
|1
|2.000
|Basic 15L 4s (Generators smaller than this are proper)
|-
|
|
|
|
|
|40\151
|317.881
|882.119
|9
|4
|2.250
|
|-
|
|
|
|
|31\117
|
|317.949
|882.051
|7
|3
|2.333
|
|-
|
|
|
|
|
|53\200
|318.000
|882.000
|12
|5
|2.400
|
|-
|
|
|
|22\83
|
|
|318.072
|881.928
|5
|2
|2.500
|Semihard 15L 4s
|-
|
|
|
|
|
|57\215
|318.140
|881.860
|13
|5
|2.600
|
|-
|
|
|
|
|35\132
|
|318.182
|881.818
|8
|3
|2.667
|
|-
|
|
|
|
|
|48\181
|318.232
|881.768
|11
|4
|2.750
|
|-
|
|
|13\49
|
|
|
|318.367
|881.633
|3
|1
|3.000
|Monohard 15L 4s
|-
|
|
|
|
|
|43\162
|318.519
|881.481
|10
|3
|3.333
|
|-
|
|
|
|
|30\113
|
|318.584
|881.416
|7
|2
|3.500
|
|-
|
|
|
|
|
|47\177
|318.644
|881.356
|11
|3
|3.667
|
|-
|
|
|
|17\64
|
|
|318.750
|881.250
|4
|1
|4.000
|Superhard 15L 4s
|-
|
|
|
|
|
|38\143
|318.881
|881.119
|9
|2
|4.500
|
|-
|
|
|
|
|21\79
|
|318.987
|881.013
|5
|1
|5.000
|
|-
|
|
|
|
|
|25\94
|319.149
|880.851
|6
|1
|6.000
|
|-
|4\15
|
|
|
|
|
|320.000
|880.000
|1
|0
|→ inf
|Collapsed 15L 4s (Degenerate case)
|}

Revision as of 07:34, 1 March 2024

↖ 14L 3s ↑ 15L 3s 16L 3s ↗
← 14L 4s 15L 4s 16L 4s →
↙ 14L 5s ↓ 15L 5s 16L 5s ↘
Scale structure
Step pattern LLLLsLLLLsLLLLsLLLs
sLLLsLLLLsLLLLsLLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 5\19 to 4\15 (315.8 ¢ to 320.0 ¢)
Dark 11\15 to 14\19 (880.0 ¢ to 884.2 ¢)
TAMNAMS information
Related to 4L 3s (smitonic)
With tunings 3:1 to 4:1 (parahard)
Related MOS scales
Parent 4L 11s
Sister 4L 15s
Daughters 19L 15s, 15L 19s
Neutralized 11L 8s
2-Flought 34L 4s, 15L 23s
Equal tunings
Equalized (L:s = 1:1) 5\19 (315.8 ¢)
Supersoft (L:s = 4:3) 19\72 (316.7 ¢)
Soft (L:s = 3:2) 14\53 (317.0 ¢)
Semisoft (L:s = 5:3) 23\87 (317.2 ¢)
Basic (L:s = 2:1) 9\34 (317.6 ¢)
Semihard (L:s = 5:2) 22\83 (318.1 ¢)
Hard (L:s = 3:1) 13\49 (318.4 ¢)
Superhard (L:s = 4:1) 17\64 (318.8 ¢)
Collapsed (L:s = 1:0) 4\15 (320.0 ¢)
View • Talk • Edit

15L 4s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 15 large steps and 4 small steps, repeating every octave. 15L 4s is a great-grandchild scale of 4L 3s, expanding it by 12 tones. Generators that produce this scale range from 315.8 ¢ to 320 ¢, or from 880 ¢ to 884.2 ¢. It is notable as the MOS scale of Catakleismic[19].

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 15L 4s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
5\19 315.789 884.211 1:1 1.000 Equalized 15L 4s
29\110 316.364 883.636 6:5 1.200
24\91 316.484 883.516 5:4 1.250
43\163 316.564 883.436 9:7 1.286
19\72 316.667 883.333 4:3 1.333 Supersoft 15L 4s
52\197 316.751 883.249 11:8 1.375 Catakleismic
33\125 316.800 883.200 7:5 1.400
47\178 316.854 883.146 10:7 1.429
14\53 316.981 883.019 3:2 1.500 Soft 15L 4s
51\193 317.098 882.902 11:7 1.571
37\140 317.143 882.857 8:5 1.600
60\227 317.181 882.819 13:8 1.625
23\87 317.241 882.759 5:3 1.667 Semisoft 15L 4s
55\208 317.308 882.692 12:7 1.714
32\121 317.355 882.645 7:4 1.750
41\155 317.419 882.581 9:5 1.800
9\34 317.647 882.353 2:1 2.000 Basic 15L 4s
Scales with tunings softer than this are proper
40\151 317.881 882.119 9:4 2.250
31\117 317.949 882.051 7:3 2.333
53\200 318.000 882.000 12:5 2.400
22\83 318.072 881.928 5:2 2.500 Semihard 15L 4s
57\215 318.140 881.860 13:5 2.600
35\132 318.182 881.818 8:3 2.667
48\181 318.232 881.768 11:4 2.750
13\49 318.367 881.633 3:1 3.000 Hard 15L 4s
43\162 318.519 881.481 10:3 3.333
30\113 318.584 881.416 7:2 3.500
47\177 318.644 881.356 11:3 3.667
17\64 318.750 881.250 4:1 4.000 Superhard 15L 4s
38\143 318.881 881.119 9:2 4.500
21\79 318.987 881.013 5:1 5.000
25\94 319.149 880.851 6:1 6.000
4\15 320.000 880.000 1:0 → ∞ Collapsed 15L 4s
Retrieved from "https://en.xen.wiki/index.php?title=15L_4s&oldid=137707"