17L 3s: 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}}{{Stub}}
! colspan="9" | generator
! | L
! | s
! | L/s
! | gen (cents)
! | comment
|-
| | 6\17
| |
| |
| |
| |
| |
| |
|
|
| | 1
| | 0
| |
| | 423.529
| |
|-
| |
| |
| |
| |
| |
| |
| |
|
|55\156
| | 9
| | 1
| | 9.000
| | 423.077
| |
|-
| |
| |
| |
| |
| |
| |
| |
|49\139
|
| | 8
| | 1
| | 8.000
| | 423.022
| |
|-
| |
| |
| |
| |
| |
| |
| |43\122
|
|
| | 7
| | 1
| | 7.000
| | 422.951
| |
|-
| |
| |
| |
| |
| |
| | 37\105
| |
|
|
| | 6
| | 1
| | 6.000
| | 422.857
| |
|-
| |
| |
| |
| |
| | 31\88
| |
| |
|
|
| | 5
| | 1
| | 5.000
| | 422.727
| |
|-
| |
| |
| |
| |
| |
| | 56\159
| |
|
|
| | 9
| | 2
| | 4.500
| | 422.642
| |
|-
| |
| |
| |
| | 25\71
| |
| |
| |
|
|
| | 4
| | 1
| | 4.000
| | 422.535
| |
|-
| |
| |
| |
| |
| | 44\125
| |
| |
|
|
| | 7
| | 2
| | 3.500
| | 422.400
| |
|-
| |
| |
| |
| |
| |
| | 63\179
| |
|
|
| | 10
| | 3
| | 3.333
| | 422.346
| |
|-
| |
| |
| | 19\54
| |
| |
| |
| |
|
|
| | 3
| | 1
| | 3.000
| | 422.222
| |
|-
| |
| |
| |
| |
| | 51\145
| |
| |
|
|
| | 8
| | 3
| | 2.667
| | 422.069
| |
|-
| |
| |
| |
| | 32\91
| |
| |
| |
|
|
| | 5
| | 2
| | 2.500
| | 421.978
| |
|-
| |
| |
| |
| |
| | 45\128
| |
| |
|
|
| | 7
| | 3
| | 2.333
| | 421.875
| |
|-
| |
| |
| |
| |
| |
| | 58\165
| |
|
|
| | 9
| | 4
| | 2.250
| | 421.818
| |
|-
| |
| | 13\37
| |
| |
| |
| |
| |
|
|
| | 2
| | 1
| | 2.000
| | 421.622
| |
|-
| |
| |
| |
| |
| |
| | 59\168
| |
|
|
| | 9
| | 5
| | 1.800
| | 421.429
| |
|-
| |
| |
| |
| |
| | 46\131
| |
| |
|
|
| | 7
| | 4
| | 1.750
| | 421.374
| |
|-
| |
| |
| |
| | 33\94
| |
| |
| |
|
|
| | 5
| | 3
| | 1.667
| | 421.277
| |
|-
| |
| |
| |
| |
| | 53\151
| |
| |
|
|
| | 8
| | 5
| | 1.600
| | 421.192
| |
|-
| |
| |
| | 20\57
| |
| |
| |
| |
|
|
| | 3
| | 2
| | 1.500
| | 421.053
| |
|-
| |
| |
| |
| |
| | 47\134
| |
| |
|
|
| | 7
| | 5
| | 1.400
| | 420.896
| |
|-
| |
| |
| |
| | 27\77
| |
| |
| |
|
|
| | 4
| | 3
| | 1.333
| | 420.779
| |
|-
| |
| |
| |
| |
| |
| | 61\174
| |
|
|
| | 9
| | 7
| | 1.286
| | 420.690
| |
|-
| |
| |
| |
| |
| | 34\97
| |
| |
|
|
| | 5
| | 4
| | 1.250
| | 420.619
| |
|-
| |
| |
| |
| |
| |
| | 41\117
| |
|
|
| | 6
| | 5
| | 1.200
| | 420.513
| |
|-
| |
| |
| |
| |
| |
| |
| |48\137
|
|
| | 7
| | 6
| | 1.167
| | 420.438
| |
|-
| |
| |
| |
| |
| |
| |
| |
|55\157
|
| | 8
| | 7
| | 1.143
| | 420.382
| |
|-
| |
| |
| |
| |
| |
| |
| |
|
|62\177
| | 9
| | 8
| | 1.125
| | 420.339
| |
|-
| | 7\20
| |
| |
| |
| |
| |
| |
|
|
| | 1
| | 1
| | 1.000
| | 420.000
| |
|}  
[[category:todo:expand]]
[[category:todo:expand]]

Revision as of 07:27, 1 March 2024

↖ 16L 2s ↑ 17L 2s 18L 2s ↗
← 16L 3s 17L 3s 18L 3s →
↙ 16L 4s ↓ 17L 4s 18L 4s ↘
Scale structure
Step pattern LLLLLLsLLLLLLsLLLLLs
sLLLLLsLLLLLLsLLLLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 7\20 to 6\17 (420.0 ¢ to 423.5 ¢)
Dark 11\17 to 13\20 (776.5 ¢ to 780.0 ¢)
TAMNAMS information
Related to 3L 5s (checkertonic)
With tunings 4:1 to 5:1
Related MOS scales
Parent 3L 14s
Sister 3L 17s
Daughters 20L 17s, 17L 20s
Neutralized 14L 6s
2-Flought 37L 3s, 17L 23s
Equal tunings
Equalized (L:s = 1:1) 7\20 (420.0 ¢)
Supersoft (L:s = 4:3) 27\77 (420.8 ¢)
Soft (L:s = 3:2) 20\57 (421.1 ¢)
Semisoft (L:s = 5:3) 33\94 (421.3 ¢)
Basic (L:s = 2:1) 13\37 (421.6 ¢)
Semihard (L:s = 5:2) 32\91 (422.0 ¢)
Hard (L:s = 3:1) 19\54 (422.2 ¢)
Superhard (L:s = 4:1) 25\71 (422.5 ¢)
Collapsed (L:s = 1:0) 6\17 (423.5 ¢)
View • Talk • Edit

17L 3s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 17 large steps and 3 small steps, repeating every octave. 17L 3s is related to 3L 5s, expanding it by 12 tones. Generators that produce this scale range from 420 ¢ to 423.5 ¢, or from 776.5 ¢ to 780 ¢.

Modes

Modes of 17L 3s
UDP Cyclic
order		 Step
pattern
19|0 1 LLLLLLsLLLLLLsLLLLLs
18|1 8 LLLLLLsLLLLLsLLLLLLs
17|2 15 LLLLLsLLLLLLsLLLLLLs
16|3 2 LLLLLsLLLLLLsLLLLLsL
15|4 9 LLLLLsLLLLLsLLLLLLsL
14|5 16 LLLLsLLLLLLsLLLLLLsL
13|6 3 LLLLsLLLLLLsLLLLLsLL
12|7 10 LLLLsLLLLLsLLLLLLsLL
11|8 17 LLLsLLLLLLsLLLLLLsLL
10|9 4 LLLsLLLLLLsLLLLLsLLL
9|10 11 LLLsLLLLLsLLLLLLsLLL
8|11 18 LLsLLLLLLsLLLLLLsLLL
7|12 5 LLsLLLLLLsLLLLLsLLLL
6|13 12 LLsLLLLLsLLLLLLsLLLL
5|14 19 LsLLLLLLsLLLLLLsLLLL
4|15 6 LsLLLLLLsLLLLLsLLLLL
3|16 13 LsLLLLLsLLLLLLsLLLLL
2|17 20 sLLLLLLsLLLLLLsLLLLL
1|18 7 sLLLLLLsLLLLLsLLLLLL
0|19 14 sLLLLLsLLLLLLsLLLLLL

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 17L 3s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
7\20 420.000 780.000 1:1 1.000 Equalized 17L 3s
41\117 420.513 779.487 6:5 1.200
34\97 420.619 779.381 5:4 1.250
61\174 420.690 779.310 9:7 1.286
27\77 420.779 779.221 4:3 1.333 Supersoft 17L 3s
74\211 420.853 779.147 11:8 1.375
47\134 420.896 779.104 7:5 1.400
67\191 420.942 779.058 10:7 1.429
20\57 421.053 778.947 3:2 1.500 Soft 17L 3s
73\208 421.154 778.846 11:7 1.571
53\151 421.192 778.808 8:5 1.600
86\245 421.224 778.776 13:8 1.625
33\94 421.277 778.723 5:3 1.667 Semisoft 17L 3s
79\225 421.333 778.667 12:7 1.714
46\131 421.374 778.626 7:4 1.750
59\168 421.429 778.571 9:5 1.800
13\37 421.622 778.378 2:1 2.000 Basic 17L 3s
Scales with tunings softer than this are proper
58\165 421.818 778.182 9:4 2.250
45\128 421.875 778.125 7:3 2.333
77\219 421.918 778.082 12:5 2.400
32\91 421.978 778.022 5:2 2.500 Semihard 17L 3s
83\236 422.034 777.966 13:5 2.600
51\145 422.069 777.931 8:3 2.667
70\199 422.111 777.889 11:4 2.750
19\54 422.222 777.778 3:1 3.000 Hard 17L 3s
63\179 422.346 777.654 10:3 3.333
44\125 422.400 777.600 7:2 3.500
69\196 422.449 777.551 11:3 3.667
25\71 422.535 777.465 4:1 4.000 Superhard 17L 3s
56\159 422.642 777.358 9:2 4.500
31\88 422.727 777.273 5:1 5.000
37\105 422.857 777.143 6:1 6.000
6\17 423.529 776.471 1:0 → ∞ Collapsed 17L 3s
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