7L 13s: Difference between revisions

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{{Todo|review|inline=1|text=Adopt scale tree template, review entries}}{{Infobox MOS}}
{{Infobox MOS}}
{{MOS intro}}
{{MOS intro}}
== Modes ==
== Modes ==
{{MOS modes}}
{{MOS modes}}
== Tuning spectrum ==
== Tuning spectrum ==
Tetracot / enipucrop range.  See also [[7L 6s 7L 13s and 13L 7s]].
Tetracot / enipucrop range.  See also [[7L 6s 7L 13s and 13L 7s]].
 
{{Scale tree}}
{| class="wikitable"
! colspan="8" | generator
! | L
! | s
! | L/s
! | gen (cents)
! | comment
|-
| | 1\7
| |
| |
| |
| |
| |
| |
| |
| | 1
| | 0
| |
| | 171.429
| |
|-
|
|
|
|
|
|
|
|10\69
|8
|1
|8.000
|173.913
|
|-
| |
| |
| |
| |
| |
| |
| | 9\62
| |
| | 7
| | 1
| | 7.000
| | 174.194
| | ^ Enipucrop
|-
| |
| |
| |
| |
| |
| | 8\55
| |
| |
| | 6
| | 1
| | 6.000
| | 174.545
| |
|-
| |
| |
| |
| |
| |
| |
| | 15\103
| |
| | 11
| | 2
| | 5.500
| | 174.757
| |
|-
| |
| |
| |
| |
| | 7\48
| |
| |
| |
| | 5
| | 1
| | 5.000
| | 175.000
| |
|-
| |
| |
| |
| |
| |
| | 13\89
| |
| |
| | 9
| | 2
| | 4.500
| | 175.281
| | Sesquiquartififths
|-
| |
| |
| |
| | 6\41
| |
| |
| |
| |
| | 4
| | 1
| | 4.000
| | 175.610
| | Monkey
|-
| |
| |
| |
| |
| |
| | 17\116
| |
| |
| | 11
| | 3
| | 3.667
| | 175.862
| | Bunya
|-
| |
| |
| |
| |
| | 11\75
| |
| |
| |
| | 7
| | 2
| | 3.500
| | 176.000
| |
|-
| |
| |
| |
| |
| |
| | 16\109
| |
| |
| | 10
| | 3
| | 3.333
| | 176.147
| | Tetracot
|-
| |
| |
| | 5\34
| |
| |
| |
| |
| |
| | 3
| | 1
| | 3.000
| | 176.471
| |
|-
| |
| |
| |
| |
| | 14\95
| |
| |
| |
| | 8
| | 3
| | 2.667
| | 176.842
| | Modus
|-
| |
| |
| |
| | 9\61
| |
| |
| |
| |
| | 5
| | 2
| | 2.500
| | 177.049
| |
|-
| |
| |
| |
| |
| | 13\88
| |
| |
| |
| | 7
| | 3
| | 2.333
| | 177.273
| | Ponens
|-
| |
| |
| |
| |
| |
| | 17\115
| |
| |
| | 9
| | 4
| | 2.250
| | 177.391
| | Wollemia
|-
| |
| | 4\27
| |
| |
| |
| |
| |
| |
| | 2
| | 1
| | 2.000
| | 177.778
| |
|-
| |
| |
| |
| |
| | 15\101
| |
| |
| |
| | 7
| | 4
| | 1.750
| | 178.218
| |
|-
| |
| |
| |
| | 11\74
| |
| |
| |
| |
| | 5
| | 3
| | 1.667
| | 178.378
| |
|-
| |
| |
| | 7\47
| |
| |
| |
| |
| |
| | 3
| | 2
| | 1.500
| | 178.723
| |
|-
| |
| |
| |
| |
| | 17\114
| |
| |
| |
| | 7
| | 5
| | 1.400
| | 178.947
| |
|-
| |
| |
| |
| | 10\67
| |
| |
| |
| |
| | 4
| | 3
| | 1.333
| | 179.104
| |
|-
| |
| |
| |
| |
| | 13\87
| |
| |
| |
| | 5
| | 4
| | 1.250
| | 179.310
| |
|-
| |
| |
| |
| |
| |
| | 16\107
| |
| |
| | 6
| | 5
| | 1.200
| | 179.439
| |
|-
|
|
|
|
|
|
|19\127
|
|7
|6
|1.167
|179.528
|
|-
|
|
|
|
|
|
|
|22\147
|8
|7
|1.143
|179.591
|
|-
| | 3\20
| |
| |
| |
| |
| |
| |
| |
| | 1
| | 1
| | 1.000
| | 180.000
| |
|}

Revision as of 20:43, 22 September 2024

↖ 6L 12s ↑ 7L 12s 8L 12s ↗
← 6L 13s 7L 13s 8L 13s →
↙ 6L 14s ↓ 7L 14s 8L 14s ↘
Scale structure
Step pattern LsLssLssLssLssLssLss
ssLssLssLssLssLssLsL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 17\20 to 6\7 (1020.0 ¢ to 1028.6 ¢)
Dark 1\7 to 3\20 (171.4 ¢ to 180.0 ¢)
TAMNAMS information
Related to 6L 1s (archaeotonic)
With tunings 1:1 to 3:2 (soft)
Related MOS scales
Parent 7L 6s
Sister 13L 7s
Daughters 20L 7s, 7L 20s
Neutralized 14L 6s
2-Flought 27L 13s, 7L 33s
Equal tunings
Equalized (L:s = 1:1) 17\20 (1020.0 ¢)
Supersoft (L:s = 4:3) 57\67 (1020.9 ¢)
Soft (L:s = 3:2) 40\47 (1021.3 ¢)
Semisoft (L:s = 5:3) 63\74 (1021.6 ¢)
Basic (L:s = 2:1) 23\27 (1022.2 ¢)
Semihard (L:s = 5:2) 52\61 (1023.0 ¢)
Hard (L:s = 3:1) 29\34 (1023.5 ¢)
Superhard (L:s = 4:1) 35\41 (1024.4 ¢)
Collapsed (L:s = 1:0) 6\7 (1028.6 ¢)
View • Talk • Edit

7L 13s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 13 small steps, repeating every octave. 7L 13s is a grandchild scale of 6L 1s, expanding it by 13 tones. Generators that produce this scale range from 1020 ¢ to 1028.6 ¢, or from 171.4 ¢ to 180 ¢.

Modes

Modes of 7L 13s
UDP Cyclic
order		 Step
pattern
19|0 1 LsLssLssLssLssLssLss
18|1 18 LssLsLssLssLssLssLss
17|2 15 LssLssLsLssLssLssLss
16|3 12 LssLssLssLsLssLssLss
15|4 9 LssLssLssLssLsLssLss
14|5 6 LssLssLssLssLssLsLss
13|6 3 LssLssLssLssLssLssLs
12|7 20 sLsLssLssLssLssLssLs
11|8 17 sLssLsLssLssLssLssLs
10|9 14 sLssLssLsLssLssLssLs
9|10 11 sLssLssLssLsLssLssLs
8|11 8 sLssLssLssLssLsLssLs
7|12 5 sLssLssLssLssLssLsLs
6|13 2 sLssLssLssLssLssLssL
5|14 19 ssLsLssLssLssLssLssL
4|15 16 ssLssLsLssLssLssLssL
3|16 13 ssLssLssLsLssLssLssL
2|17 10 ssLssLssLssLsLssLssL
1|18 7 ssLssLssLssLssLsLssL
0|19 4 ssLssLssLssLssLssLsL

Tuning spectrum

Tetracot / enipucrop range. See also 7L 6s 7L 13s and 13L 7s.

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 7L 13s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
17\20 1020.000 180.000 1:1 1.000 Equalized 7L 13s
91\107 1020.561 179.439 6:5 1.200
74\87 1020.690 179.310 5:4 1.250
131\154 1020.779 179.221 9:7 1.286
57\67 1020.896 179.104 4:3 1.333 Supersoft 7L 13s
154\181 1020.994 179.006 11:8 1.375
97\114 1021.053 178.947 7:5 1.400
137\161 1021.118 178.882 10:7 1.429
40\47 1021.277 178.723 3:2 1.500 Soft 7L 13s
143\168 1021.429 178.571 11:7 1.571
103\121 1021.488 178.512 8:5 1.600
166\195 1021.538 178.462 13:8 1.625
63\74 1021.622 178.378 5:3 1.667 Semisoft 7L 13s
149\175 1021.714 178.286 12:7 1.714
86\101 1021.782 178.218 7:4 1.750
109\128 1021.875 178.125 9:5 1.800
23\27 1022.222 177.778 2:1 2.000 Basic 7L 13s
Scales with tunings softer than this are proper
98\115 1022.609 177.391 9:4 2.250
75\88 1022.727 177.273 7:3 2.333
127\149 1022.819 177.181 12:5 2.400
52\61 1022.951 177.049 5:2 2.500 Semihard 7L 13s
133\156 1023.077 176.923 13:5 2.600
81\95 1023.158 176.842 8:3 2.667
110\129 1023.256 176.744 11:4 2.750
29\34 1023.529 176.471 3:1 3.000 Hard 7L 13s
93\109 1023.853 176.147 10:3 3.333
64\75 1024.000 176.000 7:2 3.500
99\116 1024.138 175.862 11:3 3.667
35\41 1024.390 175.610 4:1 4.000 Superhard 7L 13s
76\89 1024.719 175.281 9:2 4.500
41\48 1025.000 175.000 5:1 5.000
47\55 1025.455 174.545 6:1 6.000
6\7 1028.571 171.429 1:0 → ∞ Collapsed 7L 13s
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