8L 21s: Difference between revisions

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BudjarnLambeth (talk | contribs)
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m {{Infobox MOS}} {{MOS intro}} == Modes == {{MOS modes}} == Tuning spectrum ==
Ganaram inukshuk (talk | contribs)
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Replaced no-entries scale tree; stub
Tag: Replaced
Line 3: Line 3:
== Modes ==
== Modes ==
{{MOS modes}}
{{MOS modes}}
== Tuning spectrum ==
== Scale tree==
{| class="wikitable"
{{Scale tree}}
! colspan="8" | generator
{{Stub}}
! | L
! | s
! | L/s
! | gen (cents)
! | comment
|-
| | 3\8
| |
| |
| |
| |
| |
| |
|
| | 1
| | 0
| |
| | 450.000
| |
|-
| |
| |
| |
| |
| |
| |
| |
|32\85
| | 8
| | 1
| | 8.000
| | 451.765
| |
|-
| |
| |
| |
| |
| |
| |
| |29\77
|
| | 7
| | 1
| | 7.000
| | 451.948
| |
|-
| |
| |
| |
| |
| |
| |
| |
|55\146
| | 13
| | 2
| | 6.500
| | 452.055
| |
|-
| |
| |
| |
| |
| |
| | 26\69
| |
|
| | 6
| | 1
| | 6.000
| | 452.174
| |
|-
| |
| |
| |
| |
| |
| |
| |
|75\199
| | 17
| | 3
| | 5.667
| | 452.261
| |
|-
| |
| |
| |
| |
| |
| |
| |49\130
|
| | 11
| | 2
| | 5.500
| | 452.308
| |
|-
| |
| |
| |
| |
| |
| |
| |
|72\191
| | 16
| | 3
| | 5.333
| | 452.356
| |
|-
| |
| |
| |
| |
| | 23\61
| |
| |
|
| | 5
| | 1
| | 5.000
| | 452.459
| |
|-
| |
| |
| |
| |
| |
| |
| |66\175
|
| | 14
| | 3
| | 4.667
| | 452.571
| |
|-
| |
| |
| |
| |
| |
| | 43\114
| |
|
| | 9
| | 2
| | 4.500
| | 452.632
| |
|-
| |
| |
| |
| |
| |
| |
| |63\167
|
| | 13
| | 3
| | 4.333
| | 452.695
| |
|-
| |
| |
| |
| | 20\53
| |
| |
| |
|
| | 4
| | 1
| | 4.000
| | 452.830
| |
|-
| |
| |
| |
| |
| |
| | 57\151
| |
|
| | 11
| | 3
| | 3.667
| | 452.980
| |
|-
| |
| |
| |
| |
| | 37\98
| |
| |
|
| | 7
| | 2
| | 3.500
| | 453.061
| |
|-
| |
| |
| |
| |
| |
| | 54\143
| |
|
| | 10
| | 3
| | 3.333
| | 453.147
| |
|-
| |
| |
| |
| |
| |
| |
| |71\188
|
| | 13
| | 4
| | 3.250
| | 453.191
| |
|-
| |
| |
| | 17\45
| |
| |
| |
| |
|
| | 3
| | 1
| | 3.000
| | 453.333
| |
|-
| |
| |
| |
| |
| |
| | 65\172
| |
|
| | 11
| | 4
| | 2.750
| | 453.488
| |
|-
| |
| |
| |
| |
| | 48\127
| |
| |
|
| | 8
| | 3
| | 2.667
| | 453.543
| |
|-
| |
| |
| |
| | 31\82
| |
| |
| |
|
| | 5
| | 2
| | 2.500
| | 453.659
| |
|-
| |
| |
| |
| |
| | 45\119
| |
| |
|
| | 7
| | 3
| | 2.333
| | 453.782
| |
|-
| |
| |
| |
| |
| |
| | 59\156
| |
|
| | 9
| | 4
| | 2.250
| | 453.846
| |
|-
| |
| |
| |
| |
| |
| |
| |73\193
|
| | 11
| | 5
| | 2.200
| | 453.886
| |
|-
| |
| | 14\37
| |
| |
| |
| |
| |
|
| | 2
| | 1
| | 2.000
| | 454.054
| |
|-
| |
| |
| |
| |
| |
| | 67\177
| |
|
| | 9
| | 5
| | 1.800
| | 454.237
| |
|-
| |
| |
| |
| |
| | 53\140
| |
| |
|
| | 7
| | 4
| | 1.750
| | 454.286
| |
|-
| |
| |
| |
| | 39\103
| |
| |
| |
|
| | 5
| | 3
| | 1.667
| | 454.369
| |
|-
| |
| |
| |
| |
| | 64\169
| |
| |
|
| | 8
| | 5
| | 1.600
| | 454.438
| |
|-
| |
| |
| | 25\66
| |
| |
| |
| |
|
| | 3
| | 2
| | 1.500
| | 454.545
| |
|-
| |
| |
| |
| |
| | 61\161
| |
| |
|
| | 7
| | 5
| | 1.400
| | 454.658
| |
|-
| |
| |
| |
| | 36\95
| |
| |
| |
|
| | 4
| | 3
| | 1.333
| | 454.737
| |
|-
| |
| |
| |
| |
| | 47\124
| |
| |
|
| | 5
| | 4
| | 1.250
| | 454.839
| |
|-
| |
| |
| |
| |
| |
| | 58\153
| |
|
| | 6
| | 5
| | 1.200
| | 454.902
| |
|-
| |
| |
| |
| |
| |
| |
| |69\182
|
| | 7
| | 6
| | 1.167
| | 454.945
| |
|-
|
|
|
|
|
|
|
|80\211
|8
|7
|1.143
|454.976
|
|-
| | 11\29
| |
| |
| |
| |
| |
| |
|
| | 1
| | 1
| | 1.000
| | 455.172
| |
|}
[[category:todo:expand]]
[[category:todo:expand]]

Revision as of 07:49, 1 March 2024

↖ 7L 20s ↑ 8L 20s 9L 20s ↗
← 7L 21s 8L 21s 9L 21s →
↙ 7L 22s ↓ 8L 22s 9L 22s ↘
Scale structure
Step pattern LssLsssLssLsssLsssLssLsssLsss
sssLsssLssLsssLsssLssLsssLssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 18\29 to 5\8 (744.8 ¢ to 750.0 ¢)
Dark 3\8 to 11\29 (450.0 ¢ to 455.2 ¢)
TAMNAMS information
Related to 5L 3s (oneirotonic)
With tunings 1:1 to 4:3 (ultrasoft)
Related MOS scales
Parent 8L 13s
Sister 21L 8s
Daughters 29L 8s, 8L 29s
Neutralized 16L 13s
2-Flought 37L 21s, 8L 50s
Equal tunings
Equalized (L:s = 1:1) 18\29 (744.8 ¢)
Supersoft (L:s = 4:3) 59\95 (745.3 ¢)
Soft (L:s = 3:2) 41\66 (745.5 ¢)
Semisoft (L:s = 5:3) 64\103 (745.6 ¢)
Basic (L:s = 2:1) 23\37 (745.9 ¢)
Semihard (L:s = 5:2) 51\82 (746.3 ¢)
Hard (L:s = 3:1) 28\45 (746.7 ¢)
Superhard (L:s = 4:1) 33\53 (747.2 ¢)
Collapsed (L:s = 1:0) 5\8 (750.0 ¢)
View • Talk • Edit

8L 21s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 8 large steps and 21 small steps, repeating every octave. 8L 21s is a great-grandchild scale of 5L 3s, expanding it by 21 tones. Generators that produce this scale range from 744.8 ¢ to 750 ¢, or from 450 ¢ to 455.2 ¢.

Modes

Modes of 8L 21s
UDP Cyclic
order		 Step
pattern
28|0 1 LssLsssLssLsssLsssLssLsssLsss
27|1 19 LssLsssLsssLssLsssLssLsssLsss
26|2 8 LssLsssLsssLssLsssLsssLssLsss
25|3 26 LsssLssLsssLssLsssLsssLssLsss
24|4 15 LsssLssLsssLsssLssLsssLssLsss
23|5 4 LsssLssLsssLsssLssLsssLsssLss
22|6 22 LsssLsssLssLsssLssLsssLsssLss
21|7 11 LsssLsssLssLsssLsssLssLsssLss
20|8 29 sLssLsssLssLsssLsssLssLsssLss
19|9 18 sLssLsssLsssLssLsssLssLsssLss
18|10 7 sLssLsssLsssLssLsssLsssLssLss
17|11 25 sLsssLssLsssLssLsssLsssLssLss
16|12 14 sLsssLssLsssLsssLssLsssLssLss
15|13 3 sLsssLssLsssLsssLssLsssLsssLs
14|14 21 sLsssLsssLssLsssLssLsssLsssLs
13|15 10 sLsssLsssLssLsssLsssLssLsssLs
12|16 28 ssLssLsssLssLsssLsssLssLsssLs
11|17 17 ssLssLsssLsssLssLsssLssLsssLs
10|18 6 ssLssLsssLsssLssLsssLsssLssLs
9|19 24 ssLsssLssLsssLssLsssLsssLssLs
8|20 13 ssLsssLssLsssLsssLssLsssLssLs
7|21 2 ssLsssLssLsssLsssLssLsssLsssL
6|22 20 ssLsssLsssLssLsssLssLsssLsssL
5|23 9 ssLsssLsssLssLsssLsssLssLsssL
4|24 27 sssLssLsssLssLsssLsssLssLsssL
3|25 16 sssLssLsssLsssLssLsssLssLsssL
2|26 5 sssLssLsssLsssLssLsssLsssLssL
1|27 23 sssLsssLssLsssLssLsssLsssLssL
0|28 12 sssLsssLssLsssLsssLssLsssLssL

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 8L 21s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
18\29 744.828 455.172 1:1 1.000 Equalized 8L 21s
95\153 745.098 454.902 6:5 1.200
77\124 745.161 454.839 5:4 1.250
136\219 745.205 454.795 9:7 1.286
59\95 745.263 454.737 4:3 1.333 Supersoft 8L 21s
159\256 745.312 454.688 11:8 1.375
100\161 745.342 454.658 7:5 1.400
141\227 745.374 454.626 10:7 1.429
41\66 745.455 454.545 3:2 1.500 Soft 8L 21s
146\235 745.532 454.468 11:7 1.571
105\169 745.562 454.438 8:5 1.600
169\272 745.588 454.412 13:8 1.625
64\103 745.631 454.369 5:3 1.667 Semisoft 8L 21s
151\243 745.679 454.321 12:7 1.714
87\140 745.714 454.286 7:4 1.750
110\177 745.763 454.237 9:5 1.800
23\37 745.946 454.054 2:1 2.000 Basic 8L 21s
Scales with tunings softer than this are proper
97\156 746.154 453.846 9:4 2.250
74\119 746.218 453.782 7:3 2.333
125\201 746.269 453.731 12:5 2.400
51\82 746.341 453.659 5:2 2.500 Semihard 8L 21s
130\209 746.411 453.589 13:5 2.600
79\127 746.457 453.543 8:3 2.667
107\172 746.512 453.488 11:4 2.750
28\45 746.667 453.333 3:1 3.000 Hard 8L 21s
89\143 746.853 453.147 10:3 3.333
61\98 746.939 453.061 7:2 3.500
94\151 747.020 452.980 11:3 3.667
33\53 747.170 452.830 4:1 4.000 Superhard 8L 21s
71\114 747.368 452.632 9:2 4.500
38\61 747.541 452.459 5:1 5.000
43\69 747.826 452.174 6:1 6.000
5\8 750.000 450.000 1:0 → ∞ Collapsed 8L 21s
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