8L 4s

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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
Related to 4L 4s (tetrawood)
With tunings 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
2-Flought 20L 4s, 8L 16s
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.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

Intervals

Intervals of 8L 4s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Diminished 1-mosstep d1ms s 0.0 ¢ to 100.0 ¢
Perfect 1-mosstep P1ms L 100.0 ¢ to 150.0 ¢
2-mosstep Perfect 2-mosstep P2ms L + s 150.0 ¢ to 200.0 ¢
Augmented 2-mosstep A2ms 2L 200.0 ¢ to 300.0 ¢
3-mosstep Perfect 3-mosstep P3ms 2L + s 300.0 ¢
4-mosstep Diminished 4-mosstep d4ms 2L + 2s 300.0 ¢ to 400.0 ¢
Perfect 4-mosstep P4ms 3L + s 400.0 ¢ to 450.0 ¢
5-mosstep Perfect 5-mosstep P5ms 3L + 2s 450.0 ¢ to 500.0 ¢
Augmented 5-mosstep A5ms 4L + s 500.0 ¢ to 600.0 ¢
6-mosstep Perfect 6-mosstep P6ms 4L + 2s 600.0 ¢
7-mosstep Diminished 7-mosstep d7ms 4L + 3s 600.0 ¢ to 700.0 ¢
Perfect 7-mosstep P7ms 5L + 2s 700.0 ¢ to 750.0 ¢
8-mosstep Perfect 8-mosstep P8ms 5L + 3s 750.0 ¢ to 800.0 ¢
Augmented 8-mosstep A8ms 6L + 2s 800.0 ¢ to 900.0 ¢
9-mosstep Perfect 9-mosstep P9ms 6L + 3s 900.0 ¢
10-mosstep Diminished 10-mosstep d10ms 6L + 4s 900.0 ¢ to 1000.0 ¢
Perfect 10-mosstep P10ms 7L + 3s 1000.0 ¢ to 1050.0 ¢
11-mosstep Perfect 11-mosstep P11ms 7L + 4s 1050.0 ¢ to 1100.0 ¢
Augmented 11-mosstep A11ms 8L + 3s 1100.0 ¢ to 1200.0 ¢
12-mosstep Perfect 12-mosstep P12ms 8L + 4s 1200.0 ¢

Generator chain

Generator chain of 8L 4s
Bright gens Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev.
4 Augmented 1-mosdegree A1md Augmented 4-mosdegree A4md Augmented 7-mosdegree A7md Augmented 10-mosdegree A10md
3 Augmented 0-mosdegree A0md Augmented 3-mosdegree A3md Augmented 6-mosdegree A6md Augmented 9-mosdegree A9md
2 Augmented 2-mosdegree A2md Augmented 5-mosdegree A5md Augmented 8-mosdegree A8md Augmented 11-mosdegree A11md
1 Perfect 1-mosdegree P1md Perfect 4-mosdegree P4md Perfect 7-mosdegree P7md Perfect 10-mosdegree P10md
0 Perfect 0-mosdegree
Perfect 3-mosdegree		 P0md
P3md		 Perfect 3-mosdegree
Perfect 6-mosdegree		 P3md
P6md		 Perfect 6-mosdegree
Perfect 9-mosdegree		 P6md
P9md		 Perfect 9-mosdegree
Perfect 12-mosdegree		 P9md
P12md
−1 Perfect 2-mosdegree P2md Perfect 5-mosdegree P5md Perfect 8-mosdegree P8md Perfect 11-mosdegree P11md
−2 Diminished 1-mosdegree d1md Diminished 4-mosdegree d4md Diminished 7-mosdegree d7md Diminished 10-mosdegree d10md
−3 Diminished 3-mosdegree d3md Diminished 6-mosdegree d6md Diminished 9-mosdegree d9md Diminished 12-mosdegree d12md
−4 Diminished 2-mosdegree d2md Diminished 5-mosdegree d5md Diminished 8-mosdegree d8md Diminished 11-mosdegree d11md

Modes

Scale degrees of the modes of 8L 4s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12
8|0(4) 1 LLsLLsLLsLLs Perf. Perf. Aug. Perf. Perf. Aug. Perf. Perf. Aug. Perf. Perf. Aug. Perf.
4|4(4) 2 LsLLsLLsLLsL Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf.
0|8(4) 3 sLLsLLsLLsLL Perf. Dim. Perf. Perf. Dim. Perf. Perf. Dim. Perf. Perf. Dim. Perf. Perf.

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
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