4L 8s: Difference between revisions

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Modes & intro
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→Scale tree: Replaced scale tree
Line 13: Line 13:
{{MOS modes}}
{{MOS modes}}


==Scale tree==
== Scale tree ==
{| class="wikitable"
{{Scale tree}}
|-
| | 0/4
| |
| |
| | 0
|-
| | 1/28
| |
| |
| | 42.857
|-
| |
| | 6/164
| |
| | 43.902
|-
| |
| | 5/136
| |
| | 44.118
|-
| |
| | 4/108
| |
| | 44.449
|-
| |
| | 3/80
| |
| | 45
|-
| |
| | 2/52
| |
| | 46.154
|-
| |
| | 3/76
| |
| | 47.368
|-
| |
| | 4/100
| |
| | 48
|-
| |
| | 5/124
| |
| | 48.387
|-
| |
| | 6/148
| |
| | 48.649
|-
| |
| | 7/172
| |
| | 48.837
|-
| |
| | 8/196
| |
| | 48.98
|-
| |
| | 9/220
| |
| | 49.091
|-
| | 1/24
| |
| |
| | 50
|-
| |
| | 5/116
| |
| | 51.724
|-
| |
| | 4/92
| |
| | 52.174
|-
| |
| | 3/68
| |
| | 52.941
|-
| |
| | 2/44
| |
| | 54.5455
|-
| |
| |
| | 5/108
| | 55.556
|-
| |
| | 3/64
| |
| | 56.25
|-
| |
| | 4/84
| |
| | 57.143
|-
| |
| | 5/104
| |
| | 57.692
|-
| |
| | 6/124
| |
| | 58.0645
|-
| |
| | 7/144
| |
| | 58.333
|-
| |
| | 8/164
| |
| | 58.537
|-
| |
| | 9/184
| |
| | 58.696
|-
| |
| | 10/204
| |
| | 58.8235
|-
| |
| | 11/224
| |
| | 58.929
|-
| |
| | 12/244
| |
| | 59.016
|-
| |
| |
| |
| | 300/(2+pi)
|-
| | 1/20
| |
| |
| | 60
|-
| |
| |
| |
| | 300/(2+e)
|-
| |
| | 7/136
| |
| | 61.765
|-
| |
| | 6/116
| |
| | 62.069
|-
| |
| | 5/96
| |
| | 62.5
|-
| |
| | 4/76
| |
| | 63.158
|-
| |
| | 3/56
| |
| | 64.286
|-
| |
| |
| |
| | 300/(3+phi)
|-
| |
| |
| | 5/92
| | 65.217
|-
| |
| | 2/36
| |
| | 66.667
|-
| |
| |
| | 7/124
| | 67.742
|-
| |
| |
| | 5/88
| | 68.<span style="line-height: 1.5;">182</span>
|-
| |
| | 3/52
| |
| | 69.4615
|-
| |
| | 4/68
| |
| | 70.588
|-
| |
| | 5/84
| |
| | 71.429
|-
| |
| | 6/100
| |
| | 72
|-
| |
| | 7/116
| |
| | 72.414
|-
| |
| | 8/132
| |
| | 72.727
|-
| |
| | 9/148
| |
| | 72.973
|-
| |
| | 10/164
| |
| | 73.146
|-
| |
| | 11/180
| |
| | 73.333
|-
| |
| | 12/196
| |
| | 73.49
|-
| |
| | 13/212
| |
| | 73.585
|-
| |
| | 14/228
| |
| | 73.684
|-
| |
| | 15/244
| |
| | 73.7705
|-
| |
| | 16/260
| |
| | 73.864
|-
| |
| | 17/276
| |
| | 73.913
|-
| |
| | 18/292
| |
| | 73.973
|-
| |
| | 19/308
| |
| | 74.026
|-
| | 1/16
| |
| |
| | 75
|-
| |
| | 10/156
| |
| | 76.923
|-
| |
| | 9/140
| |
| | 77.143
|-
| |
| | 8/124
| |
| | 77.419
|-
| |
| | 7/108
| |
| | 77.778
|-
| |
| | 6/92
| |
| | 78.261
|-
| |
| | 5/76
| |
| | 78.947
|-
| |
| |
| | 9/136
| | 79.412
|-
| |
| | 4/60
| |
| | 80
|-
| |
| |
| |
| | 300/(2+sqrt(3))
|-
| |
| |
| | 7/104
| | 80.769
|-
| |
| | 3/44
| |
| | 81.818
|-
| |
| |
| | 8/116
| | 82.759
|-
| |
| |
| |
| | 300/(2+hpi)
|-
| |
| | 5/72
| |
| | 83.333
|-
| |
| |
| |
| | 300/(2+pi/2)
|-
| |
| |
| | 12/172
| | 83.721
|-
| |
| | 7/100
| |
| | 84
|-
| | 2/28
| |
| |
| | 85.714
|-
| |
| | 11/152
| |
| | 86.842
|-
| |
| | 9/124
| |
| | 87.097
|-
| |
| | 7/96
| |
| | 87.5
|-
| |
| | 5/68
| |
| | 88.235
|-
| |
| | 8/108
| |
| | 88.889
|-
| |
| | 11/148
| |
| | 89.096
|-
| | 3/40
| |
| |
| | 90
|-
| |
| | 7/92
| |
| | 91.304
|-
| | 4/52
| |
| |
| | 92.308
|-
| | 1/12
| |
| |
| | 100
|}
 
[[Category:12-tone scales]]

Revision as of 23:39, 18 February 2024

↖ 3L 7s ↑ 4L 7s 5L 7s ↗
← 3L 8s 4L 8s 5L 8s →
↙ 3L 9s ↓ 4L 9s 5L 9s ↘
Scale structure
Step pattern LssLssLssLss
ssLssLssLssL
Equave 2/1 (1200.0 ¢)
Period 1\4 (300.0 ¢)
Generator size
Bright 2\12 to 1\4 (200.0 ¢ to 300.0 ¢)
Dark 0\4 to 1\12 (0.0 ¢ to 100.0 ¢)
TAMNAMS information
Related to 4L 4s (tetrawood)
With tunings 2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent 4L 4s
Sister 8L 4s
Daughters 12L 4s, 4L 12s
Neutralized 8L 4s
2-Flought 16L 8s, 4L 20s
Equal tunings
Equalized (L:s = 1:1) 2\12 (200.0 ¢)
Supersoft (L:s = 4:3) 7\40 (210.0 ¢)
Soft (L:s = 3:2) 5\28 (214.3 ¢)
Semisoft (L:s = 5:3) 8\44 (218.2 ¢)
Basic (L:s = 2:1) 3\16 (225.0 ¢)
Semihard (L:s = 5:2) 7\36 (233.3 ¢)
Hard (L:s = 3:1) 4\20 (240.0 ¢)
Superhard (L:s = 4:1) 5\24 (250.0 ¢)
Collapsed (L:s = 1:0) 1\4 (300.0 ¢)
View • Talk • Edit

4L 8s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 8 small steps, with a period of 1 large step and 2 small steps that repeats every 300.0 ¢, or 4 times every octave. 4L 8s is a child scale of 4L 4s, expanding it by 4 tones. Generators that produce this scale range from 200 ¢ to 300 ¢, or from 0 ¢ to 100 ¢. This is the minor chromatic scale of Diminished temperament. Its period of 300¢ (~6:5) is divided into L s s, making a universally proper scale, but the harmonic entropy minimum for it is not particularly low. The name for this MOS scale is p-chro tetrawood.

Modes

Modes of 4L 8s
UDP Cyclic
order		 Step
pattern
8|0(4) 1 LssLssLssLss
4|4(4) 3 sLssLssLssLs
0|8(4) 2 ssLssLssLssL

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 4L 8s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
2\12 200.000 100.000 1:1 1.000 Equalized 4L 8s
11\64 206.250 93.750 6:5 1.200
9\52 207.692 92.308 5:4 1.250
16\92 208.696 91.304 9:7 1.286
7\40 210.000 90.000 4:3 1.333 Supersoft 4L 8s
19\108 211.111 88.889 11:8 1.375
12\68 211.765 88.235 7:5 1.400
17\96 212.500 87.500 10:7 1.429
5\28 214.286 85.714 3:2 1.500 Soft 4L 8s
18\100 216.000 84.000 11:7 1.571
13\72 216.667 83.333 8:5 1.600
21\116 217.241 82.759 13:8 1.625
8\44 218.182 81.818 5:3 1.667 Semisoft 4L 8s
19\104 219.231 80.769 12:7 1.714
11\60 220.000 80.000 7:4 1.750
14\76 221.053 78.947 9:5 1.800
3\16 225.000 75.000 2:1 2.000 Basic 4L 8s
Scales with tunings softer than this are proper
13\68 229.412 70.588 9:4 2.250
10\52 230.769 69.231 7:3 2.333
17\88 231.818 68.182 12:5 2.400
7\36 233.333 66.667 5:2 2.500 Semihard 4L 8s
18\92 234.783 65.217 13:5 2.600
11\56 235.714 64.286 8:3 2.667
15\76 236.842 63.158 11:4 2.750
4\20 240.000 60.000 3:1 3.000 Hard 4L 8s
13\64 243.750 56.250 10:3 3.333
9\44 245.455 54.545 7:2 3.500
14\68 247.059 52.941 11:3 3.667
5\24 250.000 50.000 4:1 4.000 Superhard 4L 8s
11\52 253.846 46.154 9:2 4.500
6\28 257.143 42.857 5:1 5.000
7\32 262.500 37.500 6:1 6.000
1\4 300.000 0.000 1:0 → ∞ Collapsed 4L 8s
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