8L 10s

From Xenharmonic Wiki
Jump to navigation Jump to search
↖ 7L 9s ↑ 8L 9s 9L 9s ↗
← 7L 10s 8L 10s 9L 10s →
↙ 7L 11s ↓ 8L 11s 9L 11s ↘ 
┌╥┬╥┬╥┬╥┬┬╥┬╥┬╥┬╥┬┬┐
│║│║│║│║││║│║│║│║│││
││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsLsLsLssLsLsLsLss
ssLsLsLsLssLsLsLsL
Equave 2/1 (1200.0 ¢)
Period 1\2 (600.0 ¢)
Generator size
Bright 2\18 to 1\8 (133.3 ¢ to 150.0 ¢)
Dark 3\8 to 7\18 (450.0 ¢ to 466.7 ¢)
TAMNAMS information
Descends from 8L 2s (taric)
Ancestor's step ratio range 2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent 8L 2s
Sister 10L 8s
Daughters 18L 8s, 8L 18s
Neutralized 16L 2s
2-Flought 26L 10s, 8L 28s
Equal tunings
Equalized (L:s = 1:1) 2\18 (133.3 ¢)
Supersoft (L:s = 4:3) 7\62 (135.5 ¢)
Soft (L:s = 3:2) 5\44 (136.4 ¢)
Semisoft (L:s = 5:3) 8\70 (137.1 ¢)
Basic (L:s = 2:1) 3\26 (138.5 ¢)
Semihard (L:s = 5:2) 7\60 (140.0 ¢)
Hard (L:s = 3:1) 4\34 (141.2 ¢)
Superhard (L:s = 4:1) 5\42 (142.9 ¢)
Collapsed (L:s = 1:0) 1\8 (150.0 ¢)

8L 10s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 8 large steps and 10 small steps, with a period of 4 large steps and 5 small steps that repeats every 600.0 ¢, or twice every octave. 8L 10s is a child scale of 8L 2s, expanding it by 8 tones. Generators that produce this scale range from 133.3 ¢ to 150 ¢, or from 450 ¢ to 466.7 ¢.

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 10s
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 66.7 ¢
Major 1-mosstep M1ms L 66.7 ¢ to 150.0 ¢
2-mosstep Diminished 2-mosstep d2ms 2s 0.0 ¢ to 133.3 ¢
Perfect 2-mosstep P2ms L + s 133.3 ¢ to 150.0 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 150.0 ¢ to 200.0 ¢
Major 3-mosstep M3ms 2L + s 200.0 ¢ to 300.0 ¢
4-mosstep Minor 4-mosstep m4ms L + 3s 150.0 ¢ to 266.7 ¢
Major 4-mosstep M4ms 2L + 2s 266.7 ¢ to 300.0 ¢
5-mosstep Minor 5-mosstep m5ms 2L + 3s 300.0 ¢ to 333.3 ¢
Major 5-mosstep M5ms 3L + 2s 333.3 ¢ to 450.0 ¢
6-mosstep Minor 6-mosstep m6ms 2L + 4s 300.0 ¢ to 400.0 ¢
Major 6-mosstep M6ms 3L + 3s 400.0 ¢ to 450.0 ¢
7-mosstep Perfect 7-mosstep P7ms 3L + 4s 450.0 ¢ to 466.7 ¢
Augmented 7-mosstep A7ms 4L + 3s 466.7 ¢ to 600.0 ¢
8-mosstep Minor 8-mosstep m8ms 3L + 5s 450.0 ¢ to 533.3 ¢
Major 8-mosstep M8ms 4L + 4s 533.3 ¢ to 600.0 ¢
9-mosstep Perfect 9-mosstep P9ms 4L + 5s 600.0 ¢
10-mosstep Minor 10-mosstep m10ms 4L + 6s 600.0 ¢ to 666.7 ¢
Major 10-mosstep M10ms 5L + 5s 666.7 ¢ to 750.0 ¢
11-mosstep Diminished 11-mosstep d11ms 4L + 7s 600.0 ¢ to 733.3 ¢
Perfect 11-mosstep P11ms 5L + 6s 733.3 ¢ to 750.0 ¢
12-mosstep Minor 12-mosstep m12ms 5L + 7s 750.0 ¢ to 800.0 ¢
Major 12-mosstep M12ms 6L + 6s 800.0 ¢ to 900.0 ¢
13-mosstep Minor 13-mosstep m13ms 5L + 8s 750.0 ¢ to 866.7 ¢
Major 13-mosstep M13ms 6L + 7s 866.7 ¢ to 900.0 ¢
14-mosstep Minor 14-mosstep m14ms 6L + 8s 900.0 ¢ to 933.3 ¢
Major 14-mosstep M14ms 7L + 7s 933.3 ¢ to 1050.0 ¢
15-mosstep Minor 15-mosstep m15ms 6L + 9s 900.0 ¢ to 1000.0 ¢
Major 15-mosstep M15ms 7L + 8s 1000.0 ¢ to 1050.0 ¢
16-mosstep Perfect 16-mosstep P16ms 7L + 9s 1050.0 ¢ to 1066.7 ¢
Augmented 16-mosstep A16ms 8L + 8s 1066.7 ¢ to 1200.0 ¢
17-mosstep Minor 17-mosstep m17ms 7L + 10s 1050.0 ¢ to 1133.3 ¢
Major 17-mosstep M17ms 8L + 9s 1133.3 ¢ to 1200.0 ¢
18-mosstep Perfect 18-mosstep P18ms 8L + 10s 1200.0 ¢

Generator chain

Generator chain of 8L 10s
Bright gens Scale degree Abbrev. Scale degree Abbrev.
12 Augmented 6-mosdegree A6md Augmented 15-mosdegree A15md
11 Augmented 4-mosdegree A4md Augmented 13-mosdegree A13md
10 Augmented 2-mosdegree A2md Augmented 11-mosdegree A11md
9 Augmented 0-mosdegree A0md Augmented 9-mosdegree A9md
8 Augmented 7-mosdegree A7md Augmented 16-mosdegree A16md
7 Major 5-mosdegree M5md Major 14-mosdegree M14md
6 Major 3-mosdegree M3md Major 12-mosdegree M12md
5 Major 1-mosdegree M1md Major 10-mosdegree M10md
4 Major 8-mosdegree M8md Major 17-mosdegree M17md
3 Major 6-mosdegree M6md Major 15-mosdegree M15md
2 Major 4-mosdegree M4md Major 13-mosdegree M13md
1 Perfect 2-mosdegree P2md Perfect 11-mosdegree P11md
0 Perfect 0-mosdegree
Perfect 9-mosdegree		 P0md
P9md		 Perfect 9-mosdegree
Perfect 18-mosdegree		 P9md
P18md
−1 Perfect 7-mosdegree P7md Perfect 16-mosdegree P16md
−2 Minor 5-mosdegree m5md Minor 14-mosdegree m14md
−3 Minor 3-mosdegree m3md Minor 12-mosdegree m12md
−4 Minor 1-mosdegree m1md Minor 10-mosdegree m10md
−5 Minor 8-mosdegree m8md Minor 17-mosdegree m17md
−6 Minor 6-mosdegree m6md Minor 15-mosdegree m15md
−7 Minor 4-mosdegree m4md Minor 13-mosdegree m13md
−8 Diminished 2-mosdegree d2md Diminished 11-mosdegree d11md
−9 Diminished 9-mosdegree d9md Diminished 18-mosdegree d18md
−10 Diminished 7-mosdegree d7md Diminished 16-mosdegree d16md
−11 Diminished 5-mosdegree d5md Diminished 14-mosdegree d14md
−12 Diminished 3-mosdegree d3md Diminished 12-mosdegree d12md

Modes

Scale degrees of the modes of 8L 10s
UDP Cyclic
order		 Step
pattern		 Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
16|0(2) 1 LsLsLsLssLsLsLsLss Perf. Maj. Perf. Maj. Maj. Maj. Maj. Aug. Maj. Perf. Maj. Perf. Maj. Maj. Maj. Maj. Aug. Maj. Perf.
14|2(2) 3 LsLsLssLsLsLsLssLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Perf. Maj. Perf. Maj. Perf. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
12|4(2) 5 LsLssLsLsLsLssLsLs Perf. Maj. Perf. Maj. Maj. Min. Maj. Perf. Maj. Perf. Maj. Perf. Maj. Maj. Min. Maj. Perf. Maj. Perf.
10|6(2) 7 LssLsLsLsLssLsLsLs Perf. Maj. Perf. Min. Maj. Min. Maj. Perf. Maj. Perf. Maj. Perf. Min. Maj. Min. Maj. Perf. Maj. Perf.
8|8(2) 9 sLsLsLsLssLsLsLsLs Perf. Min. Perf. Min. Maj. Min. Maj. Perf. Maj. Perf. Min. Perf. Min. Maj. Min. Maj. Perf. Maj. Perf.
6|10(2) 2 sLsLsLssLsLsLsLssL Perf. Min. Perf. Min. Maj. Min. Maj. Perf. Min. Perf. Min. Perf. Min. Maj. Min. Maj. Perf. Min. Perf.
4|12(2) 4 sLsLssLsLsLsLssLsL Perf. Min. Perf. Min. Maj. Min. Min. Perf. Min. Perf. Min. Perf. Min. Maj. Min. Min. Perf. Min. Perf.
2|14(2) 6 sLssLsLsLsLssLsLsL Perf. Min. Perf. Min. Min. Min. Min. Perf. Min. Perf. Min. Perf. Min. Min. Min. Min. Perf. Min. Perf.
0|16(2) 8 ssLsLsLsLssLsLsLsL Perf. Min. Dim. Min. Min. Min. Min. Perf. Min. Perf. Min. Dim. Min. Min. Min. Min. Perf. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 8L 10s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
2\18 133.333 466.667 1:1 1.000 Equalized 8L 10s
11\98 134.694 465.306 6:5 1.200
9\80 135.000 465.000 5:4 1.250
16\142 135.211 464.789 9:7 1.286
7\62 135.484 464.516 4:3 1.333 Supersoft 8L 10s
19\168 135.714 464.286 11:8 1.375
12\106 135.849 464.151 7:5 1.400
17\150 136.000 464.000 10:7 1.429
5\44 136.364 463.636 3:2 1.500 Soft 8L 10s
18\158 136.709 463.291 11:7 1.571
13\114 136.842 463.158 8:5 1.600
21\184 136.957 463.043 13:8 1.625
8\70 137.143 462.857 5:3 1.667 Semisoft 8L 10s
19\166 137.349 462.651 12:7 1.714
11\96 137.500 462.500 7:4 1.750
14\122 137.705 462.295 9:5 1.800
3\26 138.462 461.538 2:1 2.000 Basic 8L 10s
Scales with tunings softer than this are proper
13\112 139.286 460.714 9:4 2.250
10\86 139.535 460.465 7:3 2.333
17\146 139.726 460.274 12:5 2.400
7\60 140.000 460.000 5:2 2.500 Semihard 8L 10s
18\154 140.260 459.740 13:5 2.600
11\94 140.426 459.574 8:3 2.667
15\128 140.625 459.375 11:4 2.750
4\34 141.176 458.824 3:1 3.000 Hard 8L 10s
13\110 141.818 458.182 10:3 3.333
9\76 142.105 457.895 7:2 3.500
14\118 142.373 457.627 11:3 3.667
5\42 142.857 457.143 4:1 4.000 Superhard 8L 10s
11\92 143.478 456.522 9:2 4.500
6\50 144.000 456.000 5:1 5.000
7\58 144.828 455.172 6:1 6.000
1\8 150.000 450.000 1:0 → ∞ Collapsed 8L 10s
Icon-Stub.png This page is a stub. You can help the Xenharmonic Wiki by expanding it.
Retrieved from "https://en.xen.wiki/index.php?title=8L_10s&oldid=184293"