8L 7s

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↙ 7L 8s ↓ 8L 8s 9L 8s ↘ 
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│║║│║│║│║│║│║│║││
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└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLsLsLsLsLsLsLs
sLsLsLsLsLsLsLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 13\15 to 7\8 (1040.0 ¢ to 1050.0 ¢)
Dark 1\8 to 2\15 (150.0 ¢ to 160.0 ¢)
TAMNAMS information
Related to 7L 1s (pine)
With tunings 1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent 7L 1s
Sister 7L 8s
Daughters 15L 8s, 8L 15s
Neutralized 1L 14s
2-Flought 23L 7s, 8L 22s
Equal tunings
Equalized (L:s = 1:1) 13\15 (1040.0 ¢)
Supersoft (L:s = 4:3) 46\53 (1041.5 ¢)
Soft (L:s = 3:2) 33\38 (1042.1 ¢)
Semisoft (L:s = 5:3) 53\61 (1042.6 ¢)
Basic (L:s = 2:1) 20\23 (1043.5 ¢)
Semihard (L:s = 5:2) 47\54 (1044.4 ¢)
Hard (L:s = 3:1) 27\31 (1045.2 ¢)
Superhard (L:s = 4:1) 34\39 (1046.2 ¢)
Collapsed (L:s = 1:0) 7\8 (1050.0 ¢)

8L 7s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 8 large steps and 7 small steps, repeating every octave. 8L 7s is a child scale of 7L 1s, expanding it by 7 tones. Generators that produce this scale range from 1040 ¢ to 1050 ¢, or from 150 ¢ to 160 ¢.

This scale is the chromatic scale of opossum temperament, where the tetrad 1/1-6/5-10/7-12/7 (0 ¢ – 316 ¢ – 617 ¢ – 933 ¢) can be formed by by stacking the dark generator 2, 4, and 6 times above the root. 8L 7s approximates this tetrad from 0 – 300 ¢ – 600 ¢ – 900 ¢ to 0 ¢ – 320 ¢ – 640 ¢ – 960 ¢.

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 diatonic interval categories.

Intervals

Intervals of 8L 7s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Minor 1-mosstep m1ms s 0.0 ¢ to 80.0 ¢
Major 1-mosstep M1ms L 80.0 ¢ to 150.0 ¢
2-mosstep Perfect 2-mosstep P2ms L + s 150.0 ¢ to 160.0 ¢
Augmented 2-mosstep A2ms 2L 160.0 ¢ to 300.0 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 150.0 ¢ to 240.0 ¢
Major 3-mosstep M3ms 2L + s 240.0 ¢ to 300.0 ¢
4-mosstep Minor 4-mosstep m4ms 2L + 2s 300.0 ¢ to 320.0 ¢
Major 4-mosstep M4ms 3L + s 320.0 ¢ to 450.0 ¢
5-mosstep Minor 5-mosstep m5ms 2L + 3s 300.0 ¢ to 400.0 ¢
Major 5-mosstep M5ms 3L + 2s 400.0 ¢ to 450.0 ¢
6-mosstep Minor 6-mosstep m6ms 3L + 3s 450.0 ¢ to 480.0 ¢
Major 6-mosstep M6ms 4L + 2s 480.0 ¢ to 600.0 ¢
7-mosstep Minor 7-mosstep m7ms 3L + 4s 450.0 ¢ to 560.0 ¢
Major 7-mosstep M7ms 4L + 3s 560.0 ¢ to 600.0 ¢
8-mosstep Minor 8-mosstep m8ms 4L + 4s 600.0 ¢ to 640.0 ¢
Major 8-mosstep M8ms 5L + 3s 640.0 ¢ to 750.0 ¢
9-mosstep Minor 9-mosstep m9ms 4L + 5s 600.0 ¢ to 720.0 ¢
Major 9-mosstep M9ms 5L + 4s 720.0 ¢ to 750.0 ¢
10-mosstep Minor 10-mosstep m10ms 5L + 5s 750.0 ¢ to 800.0 ¢
Major 10-mosstep M10ms 6L + 4s 800.0 ¢ to 900.0 ¢
11-mosstep Minor 11-mosstep m11ms 5L + 6s 750.0 ¢ to 880.0 ¢
Major 11-mosstep M11ms 6L + 5s 880.0 ¢ to 900.0 ¢
12-mosstep Minor 12-mosstep m12ms 6L + 6s 900.0 ¢ to 960.0 ¢
Major 12-mosstep M12ms 7L + 5s 960.0 ¢ to 1050.0 ¢
13-mosstep Diminished 13-mosstep d13ms 6L + 7s 900.0 ¢ to 1040.0 ¢
Perfect 13-mosstep P13ms 7L + 6s 1040.0 ¢ to 1050.0 ¢
14-mosstep Minor 14-mosstep m14ms 7L + 7s 1050.0 ¢ to 1120.0 ¢
Major 14-mosstep M14ms 8L + 6s 1120.0 ¢ to 1200.0 ¢
15-mosstep Perfect 15-mosstep P15ms 8L + 7s 1200.0 ¢

Generator chain

Generator chain of 8L 7s
Bright gens Scale degree Abbrev.
22 Augmented 1-mosdegree A1md
21 Augmented 3-mosdegree A3md
20 Augmented 5-mosdegree A5md
19 Augmented 7-mosdegree A7md
18 Augmented 9-mosdegree A9md
17 Augmented 11-mosdegree A11md
16 Augmented 13-mosdegree A13md
15 Augmented 0-mosdegree A0md
14 Augmented 2-mosdegree A2md
13 Major 4-mosdegree M4md
12 Major 6-mosdegree M6md
11 Major 8-mosdegree M8md
10 Major 10-mosdegree M10md
9 Major 12-mosdegree M12md
8 Major 14-mosdegree M14md
7 Major 1-mosdegree M1md
6 Major 3-mosdegree M3md
5 Major 5-mosdegree M5md
4 Major 7-mosdegree M7md
3 Major 9-mosdegree M9md
2 Major 11-mosdegree M11md
1 Perfect 13-mosdegree P13md
0 Perfect 0-mosdegree
Perfect 15-mosdegree		 P0md
P15md
−1 Perfect 2-mosdegree P2md
−2 Minor 4-mosdegree m4md
−3 Minor 6-mosdegree m6md
−4 Minor 8-mosdegree m8md
−5 Minor 10-mosdegree m10md
−6 Minor 12-mosdegree m12md
−7 Minor 14-mosdegree m14md
−8 Minor 1-mosdegree m1md
−9 Minor 3-mosdegree m3md
−10 Minor 5-mosdegree m5md
−11 Minor 7-mosdegree m7md
−12 Minor 9-mosdegree m9md
−13 Minor 11-mosdegree m11md
−14 Diminished 13-mosdegree d13md
−15 Diminished 15-mosdegree d15md
−16 Diminished 2-mosdegree d2md
−17 Diminished 4-mosdegree d4md
−18 Diminished 6-mosdegree d6md
−19 Diminished 8-mosdegree d8md
−20 Diminished 10-mosdegree d10md
−21 Diminished 12-mosdegree d12md
−22 Diminished 14-mosdegree d14md

Modes

Scale degrees of the modes of 8L 7s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
14|0 1 LLsLsLsLsLsLsLs Perf. Maj. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
13|1 14 LsLLsLsLsLsLsLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
12|2 12 LsLsLLsLsLsLsLs Perf. Maj. Perf. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
11|3 10 LsLsLsLLsLsLsLs Perf. Maj. Perf. Maj. Min. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
10|4 8 LsLsLsLsLLsLsLs Perf. Maj. Perf. Maj. Min. Maj. Min. Maj. Min. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
9|5 6 LsLsLsLsLsLLsLs Perf. Maj. Perf. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Maj. Perf. Maj. Perf.
8|6 4 LsLsLsLsLsLsLLs Perf. Maj. Perf. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Perf. Maj. Perf.
7|7 2 LsLsLsLsLsLsLsL Perf. Maj. Perf. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Perf. Min. Perf.
6|8 15 sLLsLsLsLsLsLsL Perf. Min. Perf. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Perf. Min. Perf.
5|9 13 sLsLLsLsLsLsLsL Perf. Min. Perf. Min. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Perf. Min. Perf.
4|10 11 sLsLsLLsLsLsLsL Perf. Min. Perf. Min. Min. Min. Min. Maj. Min. Maj. Min. Maj. Min. Perf. Min. Perf.
3|11 9 sLsLsLsLLsLsLsL Perf. Min. Perf. Min. Min. Min. Min. Min. Min. Maj. Min. Maj. Min. Perf. Min. Perf.
2|12 7 sLsLsLsLsLLsLsL Perf. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Maj. Min. Perf. Min. Perf.
1|13 5 sLsLsLsLsLsLLsL Perf. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Perf.
0|14 3 sLsLsLsLsLsLsLL Perf. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Dim. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 8L 7s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
13\15 1040.000 160.000 1:1 1.000 Equalized 8L 7s
72\83 1040.964 159.036 6:5 1.200
59\68 1041.176 158.824 5:4 1.250
105\121 1041.322 158.678 9:7 1.286
46\53 1041.509 158.491 4:3 1.333 Supersoft 8L 7s
125\144 1041.667 158.333 11:8 1.375
79\91 1041.758 158.242 7:5 1.400
112\129 1041.860 158.140 10:7 1.429
33\38 1042.105 157.895 3:2 1.500 Soft 8L 7s
119\137 1042.336 157.664 11:7 1.571
86\99 1042.424 157.576 8:5 1.600
139\160 1042.500 157.500 13:8 1.625
53\61 1042.623 157.377 5:3 1.667 Semisoft 8L 7s
126\145 1042.759 157.241 12:7 1.714
73\84 1042.857 157.143 7:4 1.750
93\107 1042.991 157.009 9:5 1.800
20\23 1043.478 156.522 2:1 2.000 Basic 8L 7s
Scales with tunings softer than this are proper
87\100 1044.000 156.000 9:4 2.250
67\77 1044.156 155.844 7:3 2.333
114\131 1044.275 155.725 12:5 2.400
47\54 1044.444 155.556 5:2 2.500 Semihard 8L 7s
121\139 1044.604 155.396 13:5 2.600
74\85 1044.706 155.294 8:3 2.667
101\116 1044.828 155.172 11:4 2.750
27\31 1045.161 154.839 3:1 3.000 Hard 8L 7s
Nusecond is around here
88\101 1045.545 154.455 10:3 3.333
61\70 1045.714 154.286 7:2 3.500
95\109 1045.872 154.128 11:3 3.667
34\39 1046.154 153.846 4:1 4.000 Superhard 8L 7s
75\86 1046.512 153.488 9:2 4.500
41\47 1046.809 153.191 5:1 5.000
48\55 1047.273 152.727 6:1 6.000
7\8 1050.000 150.000 1:0 → ∞ Collapsed 8L 7s
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