8L 13s: 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}}
== Scale tree ==
== Scale tree==
{| class="wikitable"
{{Scale tree}}
! colspan="8" | generator
{{Stub}}
! | L
! | s
! | L/s
! | gen (cents)
! | comment
|-
| | 3\8
| |
| |
| |
| |
| |
| |
|
| | 1
| | 0
| |
| | 450.000
| |
|-
| |
| |
| |
| |
| |
| |
| |
|29\77
| | 8
| | 1
| | 8.000
| | 451.948
| |
|-
| |
| |
| |
| |
| |
| |
| |26\69
|
| | 7
| | 1
| | 7.000
| | 452.174
| |
|-
| |
| |
| |
| |
| |
| |
| |
|49\130
| | 13
| | 2
| | 6.500
| | 452.308
| |
|-
| |
| |
| |
| |
| |
| | 23\61
| |
|
| | 6
| | 1
| | 6.000
| | 452.459
| |
|-
| |
| |
| |
| |
| |
| |
| |43\114
|
| | 11
| | 2
| | 5.500
| | 452.632
| |
|-
| |
| |
| |
| |
| | 20\53
| |
| |
|
| | 5
| | 1
| | 5.000
| | 452.830
| |
|-
| |
| |
| |
| |
| |
| | 37\98
| |
|
| | 9
| | 2
| | 4.500
| | 453.061
| |
|-
| |
| |
| |
| |
| |
| |
| |54\143
|
| | 13
| | 3
| | 4.333
| | 453.147
| |
|-
| |
| |
| |
| | 17\45
| |
| |
| |
|
| | 4
| | 1
| | 4.000
| | 453.333
| |
|-
| |
| |
| |
| |
| |
| | 48\127
| |
|
| | 11
| | 3
| | 3.667
| | 453.543
| |
|-
| |
| |
| |
| |
| | 31\82
| |
| |
|
| | 7
| | 2
| | 3.500
| | 453.659
| |
|-
| |
| |
| |
| |
| |
| | 45\119
| |
|
| | 10
| | 3
| | 3.333
| | 453.782
| |
|-
| |
| |
| | 14\37
| |
| |
| |
| |
|
| | 3
| | 1
| | 3.000
| | 454.054
| |
|-
| |
| |
| |
| |
| |
| | 53\140
| |
|
| | 11
| | 4
| | 2.750
| | 454.286
| |
|-
| |
| |
| |
| |
| | 39\103
| |
| |
|
| | 8
| | 3
| | 2.667
| | 454.369
| |
|-
| |
| |
| |
| | 25\66
| |
| |
| |
|
| | 5
| | 2
| | 2.500
| | 454.545
| |
|-
| |
| |
| |
| |
| | 36\95
| |
| |
|
| | 7
| | 3
| | 2.333
| | 454.737
| |
|-
| |
| |
| |
| |
| |
| | 47\124
| |
|
| | 9
| | 4
| | 2.250
| | 454.839
| |
|-
| |
| | 11\29
| |
| |
| |
| |
| |
|
| | 2
| | 1
| | 2.000
| | 455.172
| |
|-
| |
| |
| |
| |
| |
| | 52\137
| |
|
| | 9
| | 5
| | 1.800
| | 455.474
| |
|-
| |
| |
| |
| |
| | 41\108
| |
| |
|
| | 7
| | 4
| | 1.750
| | 455.556
| |
|-
| |
| |
| |
| | 30\79
| |
| |
| |
|
| | 5
| | 3
| | 1.667
| | 455.696
| |
|-
| |
| |
| |
| |
| | 49\129
| |
| |
|
| | 8
| | 5
| | 1.600
| | 455.814
| |
|-
| |
| |
| | 19\50
| |
| |
| |
| |
|
| | 3
| | 2
| | 1.500
| | 456.000
| |
|-
| |
| |
| |
| |
| | 46\121
| |
| |
|
| | 7
| | 5
| | 1.400
| | 456.198
| |
|-
| |
| |
| |
| | 27\71
| |
| |
| |
|
| | 4
| | 3
| | 1.333
| | 456.338
| |
|-
| |
| |
| |
| |
| | 35\92
| |
| |
|
| | 5
| | 4
| | 1.250
| | 456.522
| |
|-
| |
| |
| |
| |
| |
| | 43\113
| |
|
| | 6
| | 5
| | 1.200
| | 456.637
| |
|-
| |
| |
| |
| |
| |
| |
| |51\134
|
| | 7
| | 6
| | 1.167
| | 456.716
| |
|-
|
|
|
|
|
|
|
|59\155
|8
|7
|1.143
|456.774
|
|-
| | 8\21
| |
| |
| |
| |
| |
| |
|
| | 1
| | 1
| | 1.000
| | 457.143
| |
|}
 
[[category:todo:expand]]
[[category:todo:expand]]

Revision as of 07:49, 1 March 2024

↖ 7L 12s ↑ 8L 12s 9L 12s ↗
← 7L 13s 8L 13s 9L 13s →
↙ 7L 14s ↓ 8L 14s 9L 14s ↘
Scale structure
Step pattern LsLssLsLssLssLsLssLss
ssLssLsLssLssLsLssLsL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 13\21 to 5\8 (742.9 ¢ to 750.0 ¢)
Dark 3\8 to 8\21 (450.0 ¢ to 457.1 ¢)
TAMNAMS information
Related to 5L 3s (oneirotonic)
With tunings 1:1 to 3:2 (soft)
Related MOS scales
Parent 8L 5s
Sister 13L 8s
Daughters 21L 8s, 8L 21s
Neutralized 16L 5s
2-Flought 29L 13s, 8L 34s
Equal tunings
Equalized (L:s = 1:1) 13\21 (742.9 ¢)
Supersoft (L:s = 4:3) 44\71 (743.7 ¢)
Soft (L:s = 3:2) 31\50 (744.0 ¢)
Semisoft (L:s = 5:3) 49\79 (744.3 ¢)
Basic (L:s = 2:1) 18\29 (744.8 ¢)
Semihard (L:s = 5:2) 41\66 (745.5 ¢)
Hard (L:s = 3:1) 23\37 (745.9 ¢)
Superhard (L:s = 4:1) 28\45 (746.7 ¢)
Collapsed (L:s = 1:0) 5\8 (750.0 ¢)
View • Talk • Edit

8L 13s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 8 large steps and 13 small steps, repeating every octave. 8L 13s is a grandchild scale of 5L 3s, expanding it by 13 tones. Generators that produce this scale range from 742.9 ¢ to 750 ¢, or from 450 ¢ to 457.1 ¢.

Modes

Modes of 8L 13s
UDP Cyclic
order		 Step
pattern
20|0 1 LsLssLsLssLssLsLssLss
19|1 14 LsLssLssLsLssLsLssLss
18|2 6 LsLssLssLsLssLssLsLss
17|3 19 LssLsLssLsLssLssLsLss
16|4 11 LssLsLssLssLsLssLsLss
15|5 3 LssLsLssLssLsLssLssLs
14|6 16 LssLssLsLssLsLssLssLs
13|7 8 LssLssLsLssLssLsLssLs
12|8 21 sLsLssLsLssLssLsLssLs
11|9 13 sLsLssLssLsLssLsLssLs
10|10 5 sLsLssLssLsLssLssLsLs
9|11 18 sLssLsLssLsLssLssLsLs
8|12 10 sLssLsLssLssLsLssLsLs
7|13 2 sLssLsLssLssLsLssLssL
6|14 15 sLssLssLsLssLsLssLssL
5|15 7 sLssLssLsLssLssLsLssL
4|16 20 ssLsLssLsLssLssLsLssL
3|17 12 ssLsLssLssLsLssLsLssL
2|18 4 ssLsLssLssLsLssLssLsL
1|19 17 ssLssLsLssLsLssLssLsL
0|20 9 ssLssLsLssLssLsLssLsL

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 13s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
13\21 742.857 457.143 1:1 1.000 Equalized 8L 13s
70\113 743.363 456.637 6:5 1.200
57\92 743.478 456.522 5:4 1.250
101\163 743.558 456.442 9:7 1.286
44\71 743.662 456.338 4:3 1.333 Supersoft 8L 13s
119\192 743.750 456.250 11:8 1.375
75\121 743.802 456.198 7:5 1.400
106\171 743.860 456.140 10:7 1.429
31\50 744.000 456.000 3:2 1.500 Soft 8L 13s
111\179 744.134 455.866 11:7 1.571
80\129 744.186 455.814 8:5 1.600
129\208 744.231 455.769 13:8 1.625
49\79 744.304 455.696 5:3 1.667 Semisoft 8L 13s
116\187 744.385 455.615 12:7 1.714
67\108 744.444 455.556 7:4 1.750
85\137 744.526 455.474 9:5 1.800
18\29 744.828 455.172 2:1 2.000 Basic 8L 13s
Scales with tunings softer than this are proper
77\124 745.161 454.839 9:4 2.250
59\95 745.263 454.737 7:3 2.333
100\161 745.342 454.658 12:5 2.400
41\66 745.455 454.545 5:2 2.500 Semihard 8L 13s
105\169 745.562 454.438 13:5 2.600
64\103 745.631 454.369 8:3 2.667
87\140 745.714 454.286 11:4 2.750
23\37 745.946 454.054 3:1 3.000 Hard 8L 13s
74\119 746.218 453.782 10:3 3.333
51\82 746.341 453.659 7:2 3.500
79\127 746.457 453.543 11:3 3.667
28\45 746.667 453.333 4:1 4.000 Superhard 8L 13s
61\98 746.939 453.061 9:2 4.500
33\53 747.170 452.830 5:1 5.000
38\61 747.541 452.459 6:1 6.000
5\8 750.000 450.000 1:0 → ∞ Collapsed 8L 13s
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