3L 8s: Difference between revisions

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== Scale tree ==
== Scale tree ==
{| class="wikitable"
{{Scale tree|Comments=1/0: [[Ditonic]] (for generators approaching this tuning);
! colspan="2" |Gen
7/1: [[Roman]];
!Cents
5/2: [[Squares]];
!L:s
7/2: [[Bossier]];
!Comments
11/2: [[Sqrtphi]] (416.667¢)|depth=6}}
|-
| | 1\3
| |
| | 400
|∞
| | Paucitonic, 3edo
|-
| | 18\53
| |
| | 407.547
|
| | Ditonic
|-
| | 17\50
| |
| | 408.000
|
| |
|-
| | 16\47
| |
| | 408.511
|
| |
|-
| | 15\44
| |
| | 409.091
|
| |
|-
| | 14\41
| |
| | 409.756
|
| |
|-
| | 13\38
| |
| | 410.526
|
| |
|-
| | 12\35
| |
| | 411.429
|
| |
|-
| | 11\32
| |
| | 412.500
|
| |
|-
| | 10\29
| |
| | 413.793
|
| | Roman
|-
| | 9\26
| |
| | 415.385
|
| |
|-
| |
| | 17\49
| | 416.3265
|
| |
|-
| |
| | 25\72
| | 416.667
|
| | Sqrtphi
|-
| | 8\23
| |
| | 417.391
|
| |
|-
| | 7\20
| |
| | 420
|4:1
| |
|-
| |
| | 13\37
| | 421.621
|
| | Bossier
|-
| |
| |
| | 422.956
|
| |
|-
| | 6\17
| |
| | 423.529
|3:1
| |
|-
| |
| |
| | 424.76
|
| |
|-
| |
| | 17\48
| | 425
|
| |
|-
| |
| |
| | 425.23
|
| |
|-
| |
| | 11\31
| | 425.806
|5:2
| | Squares
|-
| |
| | 16\45
| | 426.667
|
| |
|-
| | 5\14
| |
| | 428.521
|2:1
| |
|-
| |
| | 19\53
| | 430.187
|
| |
|-
| |
| |
| | 430.312
|
| |
|-
| |
| | 14\39
| | 430.769
|
| |
|-
| |
| |
| | 431.1185
|
| |
|-
| |
| | 23\64
| | 431.25
|
| |
|-
| |
| |
| | 431.465
|
| |
|-
| | 9\25
| |
| | 432
|3:2
| |
|-
| |
| | 22\61
| | 432.787
|
| |
|-
| | 13\36
| |
| | 433.333
|
| |
|-
| | 17\47
| |
| | 434.043
|
| |
|-
| | 21\58
| |
| | 434.483
|
| |
|-
| | 25\69
| |
| | 434.783
|7:6
| |
|-
|29\80
|
|435
|8:7
|
|-
|33\91
|
|435.164
|9:8
|
|-
| | 4\11
| |
| | 436.364
|1:1
| | Equalized, 11edo
|}
 
[[Category:11-tone scales]]
[[Category:11-tone scales]]

Revision as of 00:51, 19 February 2024

↖ 2L 7s ↑ 3L 7s 4L 7s ↗
← 2L 8s 3L 8s 4L 8s →
↙ 2L 9s ↓ 3L 9s 4L 9s ↘
Scale structure
Step pattern LssLsssLsss
sssLsssLssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 7\11 to 2\3 (763.6 ¢ to 800.0 ¢)
Dark 1\3 to 4\11 (400.0 ¢ to 436.4 ¢)
TAMNAMS information
Related to 3L 5s (checkertonic)
With tunings 2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent 3L 5s
Sister 8L 3s
Daughters 11L 3s, 3L 11s
Neutralized 6L 5s
2-Flought 14L 8s, 3L 19s
Equal tunings
Equalized (L:s = 1:1) 7\11 (763.6 ¢)
Supersoft (L:s = 4:3) 23\36 (766.7 ¢)
Soft (L:s = 3:2) 16\25 (768.0 ¢)
Semisoft (L:s = 5:3) 25\39 (769.2 ¢)
Basic (L:s = 2:1) 9\14 (771.4 ¢)
Semihard (L:s = 5:2) 20\31 (774.2 ¢)
Hard (L:s = 3:1) 11\17 (776.5 ¢)
Superhard (L:s = 4:1) 13\20 (780.0 ¢)
Collapsed (L:s = 1:0) 2\3 (800.0 ¢)
View • Talk • Edit

3L 8s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 8 small steps, repeating every octave. 3L 8s is a child scale of 3L 5s, expanding it by 3 tones. Generators that produce this scale range from 763.6 ¢ to 800 ¢, or from 400 ¢ to 436.4 ¢. This scale has versions relating to ditonic/coditone, roman, bossier, sqrtphi and squares.

Modes

Modes of 3L 8s
UDP Cyclic
order		 Step
pattern
10|0 1 LssLsssLsss
9|1 8 LsssLssLsss
8|2 4 LsssLsssLss
7|3 11 sLssLsssLss
6|4 7 sLsssLssLss
5|5 3 sLsssLsssLs
4|6 10 ssLssLsssLs
3|7 6 ssLsssLssLs
2|8 2 ssLsssLsssL
1|9 9 sssLssLsssL
0|10 5 sssLsssLssL

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 3L 8s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
7\11 763.636 436.364 1:1 1.000 Equalized 3L 8s
44\69 765.217 434.783 7:6 1.167
37\58 765.517 434.483 6:5 1.200
67\105 765.714 434.286 11:9 1.222
30\47 765.957 434.043 5:4 1.250
83\130 766.154 433.846 14:11 1.273
53\83 766.265 433.735 9:7 1.286
76\119 766.387 433.613 13:10 1.300
23\36 766.667 433.333 4:3 1.333 Supersoft 3L 8s
85\133 766.917 433.083 15:11 1.364
62\97 767.010 432.990 11:8 1.375
101\158 767.089 432.911 18:13 1.385
39\61 767.213 432.787 7:5 1.400
94\147 767.347 432.653 17:12 1.417
55\86 767.442 432.558 10:7 1.429
71\111 767.568 432.432 13:9 1.444
16\25 768.000 432.000 3:2 1.500 Soft 3L 8s
73\114 768.421 431.579 14:9 1.556
57\89 768.539 431.461 11:7 1.571
98\153 768.627 431.373 19:12 1.583
41\64 768.750 431.250 8:5 1.600
107\167 768.862 431.138 21:13 1.615
66\103 768.932 431.068 13:8 1.625
91\142 769.014 430.986 18:11 1.636
25\39 769.231 430.769 5:3 1.667 Semisoft 3L 8s
84\131 769.466 430.534 17:10 1.700
59\92 769.565 430.435 12:7 1.714
93\145 769.655 430.345 19:11 1.727
34\53 769.811 430.189 7:4 1.750
77\120 770.000 430.000 16:9 1.778
43\67 770.149 429.851 9:5 1.800
52\81 770.370 429.630 11:6 1.833
9\14 771.429 428.571 2:1 2.000 Basic 3L 8s
Scales with tunings softer than this are proper
47\73 772.603 427.397 11:5 2.200
38\59 772.881 427.119 9:4 2.250
67\104 773.077 426.923 16:7 2.286
29\45 773.333 426.667 7:3 2.333
78\121 773.554 426.446 19:8 2.375
49\76 773.684 426.316 12:5 2.400
69\107 773.832 426.168 17:7 2.429
20\31 774.194 425.806 5:2 2.500 Semihard 3L 8s
71\110 774.545 425.455 18:7 2.571
51\79 774.684 425.316 13:5 2.600
82\127 774.803 425.197 21:8 2.625
31\48 775.000 425.000 8:3 2.667
73\113 775.221 424.779 19:7 2.714
42\65 775.385 424.615 11:4 2.750
53\82 775.610 424.390 14:5 2.800
11\17 776.471 423.529 3:1 3.000 Hard 3L 8s
46\71 777.465 422.535 13:4 3.250
35\54 777.778 422.222 10:3 3.333
59\91 778.022 421.978 17:5 3.400
24\37 778.378 421.622 7:2 3.500
61\94 778.723 421.277 18:5 3.600
37\57 778.947 421.053 11:3 3.667
50\77 779.221 420.779 15:4 3.750
13\20 780.000 420.000 4:1 4.000 Superhard 3L 8s
41\63 780.952 419.048 13:3 4.333
28\43 781.395 418.605 9:2 4.500
43\66 781.818 418.182 14:3 4.667
15\23 782.609 417.391 5:1 5.000
32\49 783.673 416.327 11:2 5.500
17\26 784.615 415.385 6:1 6.000
19\29 786.207 413.793 7:1 7.000
2\3 800.000 400.000 1:0 → ∞ Collapsed 3L 8s
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