8L 4s

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↖7L 3s ↑8L 3s 9L 3s↗
←7L 4s8L 4s 9L 4s→
↙7L 5s ↓8L 5s 9L 5s↘
┌╥╥┬╥╥┬╥╥┬╥╥┬┐
│║║│║║│║║│║║││
││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLsLLsLLsLLs
sLLsLLsLLsLL
Equave 2/1 (1200.0¢)
Period 1\4 (300.0¢)
Generator size
Bright 1\12 to 1\8 (100.0¢ to 150.0¢)
Dark 1\8 to 2\12 (150.0¢ to 200.0¢)
TAMNAMS information
Descends from 4L 4s (tetrawood)
Required step ratio range 1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent 4L 4s
Sister 4L 8s
Daughters 12L 8s, 8L 12s
Neutralized 4L 8s
Equal tunings
Equalized (L:s = 1:1) 1\12 (100.0¢)
Supersoft (L:s = 4:3) 4\44 (109.1¢)
Soft (L:s = 3:2) 3\32 (112.5¢)
Semisoft (L:s = 5:3) 5\52 (115.4¢)
Basic (L:s = 2:1) 2\20 (120.0¢)
Semihard (L:s = 5:2) 5\48 (125.0¢)
Hard (L:s = 3:1) 3\28 (128.6¢)
Superhard (L:s = 4:1) 4\36 (133.3¢)
Collapsed (L:s = 1:0) 1\8 (150.0¢)

8L 4s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 8 large steps and 4 small steps, with a period of 2 large steps and 1 small step that repeats every 300.0¢, or 4 times every octave. 8L 4s is a child scale of 4L 4s, expanding it by 4 tones. Generators that produce this scale range from 100¢ to 150¢, or from 150¢ to 200¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.

This is the chromatic scale of Golden diminished temperament.

Modes

Modes of 8L 4s
UDP Rotational order Step pattern
8|0(4) 1 LLsLLsLLsLLs
4|4(4) 2 LsLLsLLsLLsL
0|8(4) 3 sLLsLLsLLsLL

Scale tree

Scale Tree and Tuning Spectrum of 8L 4s
Generator(edo) Cents Step Ratio Comments(always proper)
Bright Dark L:s Hardness
1\12 100.000 200.000 1:1 1.000 Equalized 8L 4s
6\68 105.882 194.118 6:5 1.200
5\56 107.143 192.857 5:4 1.250
9\100 108.000 192.000 9:7 1.286
4\44 109.091 190.909 4:3 1.333 Supersoft 8L 4s
11\120 110.000 190.000 11:8 1.375
7\76 110.526 189.474 7:5 1.400
10\108 111.111 188.889 10:7 1.429
3\32 112.500 187.500 3:2 1.500 Soft 8L 4s
11\116 113.793 186.207 11:7 1.571
8\84 114.286 185.714 8:5 1.600
13\136 114.706 185.294 13:8 1.625
5\52 115.385 184.615 5:3 1.667 Semisoft 8L 4s
12\124 116.129 183.871 12:7 1.714
7\72 116.667 183.333 7:4 1.750
9\92 117.391 182.609 9:5 1.800
2\20 120.000 180.000 2:1 2.000 Basic 8L 4s
9\88 122.727 177.273 9:4 2.250
7\68 123.529 176.471 7:3 2.333
12\116 124.138 175.862 12:5 2.400
5\48 125.000 175.000 5:2 2.500 Semihard 8L 4s
13\124 125.806 174.194 13:5 2.600
8\76 126.316 173.684 8:3 2.667
11\104 126.923 173.077 11:4 2.750
3\28 128.571 171.429 3:1 3.000 Hard 8L 4s
10\92 130.435 169.565 10:3 3.333
7\64 131.250 168.750 7:2 3.500
11\100 132.000 168.000 11:3 3.667
4\36 133.333 166.667 4:1 4.000 Superhard 8L 4s
9\80 135.000 165.000 9:2 4.500
5\44 136.364 163.636 5:1 5.000
6\52 138.462 161.538 6:1 6.000
1\8 150.000 150.000 1:0 → ∞ Collapsed 8L 4s