4L 8s

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↖3L 7s ↑4L 7s 5L 7s↗
←3L 8s4L 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
Descends from 4L 4s (tetrawood)
Required step ratio range 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
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¢)

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 Rotational order Step pattern
8|0(4) 1 LssLssLssLss
4|4(4) 3 sLssLssLssLs
0|8(4) 2 ssLssLssLssL

Scale tree

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