3L 14s: 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 ==
[[Symbolic]] / [[Sidi]] / [[Smate]] range
[[Symbolic]] / [[Sidi]] / [[Smate]] range
 
{{Scale tree}}
{| class="wikitable"
! colspan="9" | generator
!
! | L
! | s
! | L/s
! | gen (cents)
! | comment
|-
| | 1\3
| |
| |
| |
| |
| |
| |
|
|
|
| | 1
| | 0
| |
| | 400.000
| |
|-
|
|
|
|
|
|
|
|
|
|15\44
|10
|1
|10.000
|409.091
|
|-
| |
| |
| |
| |
| |
| |
| |
|
|14\41
|
| | 9
| | 1
| | 9.000
| | 409.756
| | [[Hocus]]
|-
| |
| |
| |
| |
| |
| |
| |
|
|
|27\79
| | 17
| | 2
| | 8.500
| | 410.127
| |
|-
|-
| |
| |
| |
| |
| |
| |
| |
|13\38
|
|
| | 8
| | 1
| | 8.000
| | 410.526
| |
|-
| |
| |
| |
| |
| |
| |
| |12\35
|
|
|
| | 7
| | 1
| | 7.000
| | 411.429
| |
|-
| |
| |
| |
| |
| |
| |
| |
|23\67
|
|
| | 13
| | 2
| | 6.500
| | 411.940
| |
|-
| |
| |
| |
| |
| |
| | 11\32
| |
|
|
|
| | 6
| | 1
| | 6.000
| | 412.500
| |
|-
| |
| |
| |
| |
| |
| |
| |
|32\93
|
|
| | 17
| | 3
| | 5.667
| | 412.903
| |
|-
| |
| |
| |
| |
| |
| |
| |21\61
|
|
|
| | 11
| | 2
| | 5.500
| | 413.115
| |
|-
| |
| |
| |
| |
| |
| |
| |
|31\90
|
|
| | 16
| | 3
| | 5.333
| | 413.333
| |
|-
| |
| |
| |
| |
| | 10\29
| |
| |
|
|
|
| | 5
| | 1
| | 5.000
| | 413.793
| |
|-
| |
| |
| |
| |
| |
| |
| |
|39\113
|
|
| | 19
| | 4
| | 4.750
| | 414.159
| |
|-
| |
| |
| |
| |
| |
| |
| |29\84
|
|
|
| | 14
| | 3
| | 4.667
| | 414.286
| |
|-
| |
| |
| |
| |
| |
| | 19\55
| |
|
|
|
| | 9
| | 2
| | 4.500
| | 414.545
| | [[Roman]]
|-
| |
| |
| |
| |
| |
| |
| |28\81
|
|
|
| | 13
| | 3
| | 4.333
| | 414.815
| |
|-
| |
| |
| |
| |
| |
| |
| |
|37\107
|
|
| | 17
| | 4
| | 4.250
| | 414.953
| |
|-
| |
| |
| |
| | 9\26
| |
| |
| |
|
|
|
| | 4
| | 1
| | 4.000
| | 415.385
| |
|-
| |
| |
| |
| |
| |
| |
| |35\101
|
|
|
| | 15
| | 4
| | 3.750
| | 415.842
| |
|-
| |
| |
| |
| |
| |
| | 26\75
| |
|
|
|
| | 11
| | 3
| | 3.667
| | 416.000
| |
|-
| |
| |
| |
| |
| | 17\49
| |
| |
|
|
|
| | 7
| | 2
| | 3.500
| | 416.327
| |
|-
| |
| |
| |
| |
| |
| | 25\72
| |
|
|
|
| | 10
| | 3
| | 3.333
| | 416.667
| | [[Sqrtphi]]
|-
| |
| |
| |
| |
| |
| |
| |33\95
|
|
|
| | 13
| | 4
| | 3.250
| | 416.842
| |
|-
| |
| |
| |
| |
| |
| |
| |
|41\118
|
|
| | 16
| | 5
| | 3.200
| | 416.949
| |
|-
| |
| |
| | 8\23
| |
| |
| |
| |
|
|
|
| | 3
| | 1
| | 3.000
| | 417.391
| |
|-
| |
| |
| |
| |
| |
| |
| |39\112
|
|
|
| | 14
| | 5
| | 2.800
| | 417.857
| |
|-
| |
| |
| |
| |
| |
| | 31\89
| |
|
|
|
| | 11
| | 4
| | 2.750
| | 417.978
| |
|-
| |
| |
| |
| |
| | 23\66
| |
| |
|
|
|
| | 8
| | 3
| | 2.667
| | 418.182
| |
|-
| |
| |
| |
| |
| |
| | 38\109
| |
|
|
|
| | 13
| | 5
| | 2.600
| | 418.349
| |
|-
| |
| |
| |
| | 15\43
| |
| |
| |
|
|
|
| | 5
| | 2
| | 2.500
| | 418.605
| |
|-
| |
| |
| |
| |
| |
| | 37\106
| |
|
|
|
| | 12
| | 5
| | 2.400
| | 418.868
| |
|-
| |
| |
| |
| |
| | 22\63
| |
| |
|
|
|
| | 7
| | 3
| | 2.333
| | 419.048
| |
|-
| |
| |
| |
| |
| |
| | 29\83
| |
|
|
|
| | 9
| | 4
| | 2.250
| | 419.277
| |
|-
| |
| |
| |
| |
| |
| |
| |36\103
|
|
|
| | 11
| | 5
| | 2.200
| | 419.417
| |
|-
| |
| | 7\20
| |
| |
| |
| |
| |
|
|
|
| | 2
| | 1
| | 2.000
| | 420.000
| |
|-
| |
| |
| |
| |
| |
| |
| |41\117
|
|
|
| | 11
| | 6
| | 1.833
| | 420.513
| |
|-
| |
| |
| |
| |
| |
| | 34\97
| |
|
|
|
| | 9
| | 5
| | 1.800
| | 420.619
| |
|-
| |
| |
| |
| |
| | 27\77
| |
| |
|
|
|
| | 7
| | 4
| | 1.750
| | 420.779
| |
|-
| |
| |
| |
| | 20\57
| |
| |
| |
|
|
|
| | 5
| | 3
| | 1.667
| | 421.053
| |
|-
| |
| |
| |
| |
| | 33\94
| |
| |
|
|
|
| | 8
| | 5
| | 1.600
| | 421.277
| | [[Bossier]]
|-
| |
| |
| | 13\37
| |
| |
| |
| |
|
|
|
| | 3
| | 2
| | 1.500
| | 421.622
| |
|-
| |
| |
| |
| |
| | 32\91
| |
| |
|
|
|
| | 7
| | 5
| | 1.400
| | 421.978
| |
|-
| |
| |
| |
| | 19\54
| |
| |
| |
|
|
|
| | 4
| | 3
| | 1.333
| | 422.222
| |
|-
| |
| |
| |
| |
| | 25\71
| |
| |
|
|
|
| | 5
| | 4
| | 1.250
| | 422.535
| |
|-
| |
| |
| |
| |
| |
| | 31\88
| |
|
|
|
| | 6
| | 5
| | 1.200
| | 422.727
| |
|-
| |
| |
| |
| |
| |
| |
| |37\105
|
|
|
| | 7
| | 6
| | 1.167
| | 422.857
| |
|-
|
|
|
|
|
|
|
|43\122
|
|
|8
|7
|1.143
|422.951
|
|-
|
|
|
|
|
|
|
|
|49\139
|
|9
|8
|1.125
|423.022
|
|-
|
|
|
|
|
|
|
|
|
|55\156
|10
|9
|1.111
|423.077
|
|-
| | 6\17
| |
| |
| |
| |
| |
| |
|
|
|
| | 1
| | 1
| | 1.000
| | 423.529
| |
|}

Revision as of 20:50, 22 September 2024

↖ 2L 13s ↑ 3L 13s 4L 13s ↗
← 2L 14s 3L 14s 4L 14s →
↙ 2L 15s ↓ 3L 15s 4L 15s ↘
Scale structure
Step pattern LssssLsssssLsssss
sssssLsssssLssssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 11\17 to 2\3 (776.5 ¢ to 800.0 ¢)
Dark 1\3 to 6\17 (400.0 ¢ to 423.5 ¢)
TAMNAMS information
Related to 3L 5s (checkertonic)
With tunings 4:1 to 1:0 (ultrahard)
Related MOS scales
Parent 3L 11s
Sister 14L 3s
Daughters 17L 3s, 3L 17s
Neutralized 6L 11s
2-Flought 20L 14s, 3L 31s
Equal tunings
Equalized (L:s = 1:1) 11\17 (776.5 ¢)
Supersoft (L:s = 4:3) 35\54 (777.8 ¢)
Soft (L:s = 3:2) 24\37 (778.4 ¢)
Semisoft (L:s = 5:3) 37\57 (778.9 ¢)
Basic (L:s = 2:1) 13\20 (780.0 ¢)
Semihard (L:s = 5:2) 28\43 (781.4 ¢)
Hard (L:s = 3:1) 15\23 (782.6 ¢)
Superhard (L:s = 4:1) 17\26 (784.6 ¢)
Collapsed (L:s = 1:0) 2\3 (800.0 ¢)
View • Talk • Edit

3L 14s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 14 small steps, repeating every octave. 3L 14s is a great-grandchild scale of 3L 5s, expanding it by 9 tones. Generators that produce this scale range from 776.5 ¢ to 800 ¢, or from 400 ¢ to 423.5 ¢.

Modes

Modes of 3L 14s
UDP Cyclic
order		 Step
pattern
16|0 1 LssssLsssssLsssss
15|1 12 LsssssLssssLsssss
14|2 6 LsssssLsssssLssss
13|3 17 sLssssLsssssLssss
12|4 11 sLsssssLssssLssss
11|5 5 sLsssssLsssssLsss
10|6 16 ssLssssLsssssLsss
9|7 10 ssLsssssLssssLsss
8|8 4 ssLsssssLsssssLss
7|9 15 sssLssssLsssssLss
6|10 9 sssLsssssLssssLss
5|11 3 sssLsssssLsssssLs
4|12 14 ssssLssssLsssssLs
3|13 8 ssssLsssssLssssLs
2|14 2 ssssLsssssLsssssL
1|15 13 sssssLssssLsssssL
0|16 7 sssssLsssssLssssL

Tuning spectrum

Symbolic / Sidi / Smate range

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 3L 14s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
11\17 776.471 423.529 1:1 1.000 Equalized 3L 14s
57\88 777.273 422.727 6:5 1.200
46\71 777.465 422.535 5:4 1.250
81\125 777.600 422.400 9:7 1.286
35\54 777.778 422.222 4:3 1.333 Supersoft 3L 14s
94\145 777.931 422.069 11:8 1.375
59\91 778.022 421.978 7:5 1.400
83\128 778.125 421.875 10:7 1.429
24\37 778.378 421.622 3:2 1.500 Soft 3L 14s
85\131 778.626 421.374 11:7 1.571
61\94 778.723 421.277 8:5 1.600
98\151 778.808 421.192 13:8 1.625
37\57 778.947 421.053 5:3 1.667 Semisoft 3L 14s
87\134 779.104 420.896 12:7 1.714
50\77 779.221 420.779 7:4 1.750
63\97 779.381 420.619 9:5 1.800
13\20 780.000 420.000 2:1 2.000 Basic 3L 14s
Scales with tunings softer than this are proper
54\83 780.723 419.277 9:4 2.250
41\63 780.952 419.048 7:3 2.333
69\106 781.132 418.868 12:5 2.400
28\43 781.395 418.605 5:2 2.500 Semihard 3L 14s
71\109 781.651 418.349 13:5 2.600
43\66 781.818 418.182 8:3 2.667
58\89 782.022 417.978 11:4 2.750
15\23 782.609 417.391 3:1 3.000 Hard 3L 14s
47\72 783.333 416.667 10:3 3.333
32\49 783.673 416.327 7:2 3.500
49\75 784.000 416.000 11:3 3.667
17\26 784.615 415.385 4:1 4.000 Superhard 3L 14s
36\55 785.455 414.545 9:2 4.500
19\29 786.207 413.793 5:1 5.000
21\32 787.500 412.500 6:1 6.000
2\3 800.000 400.000 1:0 → ∞ Collapsed 3L 14s
Retrieved from "https://en.xen.wiki/index.php?title=3L_14s&oldid=156152"