9L 9s

From Xenharmonic Wiki
Jump to navigation Jump to search
↖ 8L 8s ↑ 9L 8s 10L 8s ↗
← 8L 9s 9L 9s 10L 9s →
↙ 8L 10s ↓ 9L 10s 10L 10s ↘ 
┌╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬┐
│║│║│║│║│║│║│║│║│║││
││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsLsLsLsLsLsLsLsLs
sLsLsLsLsLsLsLsLsL
Equave 2/1 (1200.0 ¢)
Period 1\9 (133.3 ¢)
Generator size
Bright 1\18 to 1\9 (66.7 ¢ to 133.3 ¢)
Dark 0\9 to 1\18 (0.0 ¢ to 66.7 ¢)
Related MOS scales
Parent none
Sister 9L 9s (self)
Daughters 18L 9s, 9L 18s
Neutralized 18edo
2-Flought 27L 9s, 9L 27s
Equal tunings
Equalized (L:s = 1:1) 1\18 (66.7 ¢)
Supersoft (L:s = 4:3) 4\63 (76.2 ¢)
Soft (L:s = 3:2) 3\45 (80.0 ¢)
Semisoft (L:s = 5:3) 5\72 (83.3 ¢)
Basic (L:s = 2:1) 2\27 (88.9 ¢)
Semihard (L:s = 5:2) 5\63 (95.2 ¢)
Hard (L:s = 3:1) 3\36 (100.0 ¢)
Superhard (L:s = 4:1) 4\45 (106.7 ¢)
Collapsed (L:s = 1:0) 1\9 (133.3 ¢)

9L 9s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 9 large steps and 9 small steps, with a period of 1 large step and 1 small step that repeats every 133.3 ¢, or 9 times every octave. Generators that produce this scale range from 66.7 ¢ to 133.3 ¢, or from 0 ¢ to 66.7 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.

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 9L 9s
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 133.3 ¢
2-mosstep Perfect 2-mosstep P2ms L + s 133.3 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 133.3 ¢ to 200.0 ¢
Major 3-mosstep M3ms 2L + s 200.0 ¢ to 266.7 ¢
4-mosstep Perfect 4-mosstep P4ms 2L + 2s 266.7 ¢
5-mosstep Minor 5-mosstep m5ms 2L + 3s 266.7 ¢ to 333.3 ¢
Major 5-mosstep M5ms 3L + 2s 333.3 ¢ to 400.0 ¢
6-mosstep Perfect 6-mosstep P6ms 3L + 3s 400.0 ¢
7-mosstep Minor 7-mosstep m7ms 3L + 4s 400.0 ¢ to 466.7 ¢
Major 7-mosstep M7ms 4L + 3s 466.7 ¢ to 533.3 ¢
8-mosstep Perfect 8-mosstep P8ms 4L + 4s 533.3 ¢
9-mosstep Minor 9-mosstep m9ms 4L + 5s 533.3 ¢ to 600.0 ¢
Major 9-mosstep M9ms 5L + 4s 600.0 ¢ to 666.7 ¢
10-mosstep Perfect 10-mosstep P10ms 5L + 5s 666.7 ¢
11-mosstep Minor 11-mosstep m11ms 5L + 6s 666.7 ¢ to 733.3 ¢
Major 11-mosstep M11ms 6L + 5s 733.3 ¢ to 800.0 ¢
12-mosstep Perfect 12-mosstep P12ms 6L + 6s 800.0 ¢
13-mosstep Minor 13-mosstep m13ms 6L + 7s 800.0 ¢ to 866.7 ¢
Major 13-mosstep M13ms 7L + 6s 866.7 ¢ to 933.3 ¢
14-mosstep Perfect 14-mosstep P14ms 7L + 7s 933.3 ¢
15-mosstep Minor 15-mosstep m15ms 7L + 8s 933.3 ¢ to 1000.0 ¢
Major 15-mosstep M15ms 8L + 7s 1000.0 ¢ to 1066.7 ¢
16-mosstep Perfect 16-mosstep P16ms 8L + 8s 1066.7 ¢
17-mosstep Minor 17-mosstep m17ms 8L + 9s 1066.7 ¢ to 1133.3 ¢
Major 17-mosstep M17ms 9L + 8s 1133.3 ¢ to 1200.0 ¢
18-mosstep Perfect 18-mosstep P18ms 9L + 9s 1200.0 ¢

Generator chain

Generator chain of 9L 9s
Bright gens Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev.
2 Augmented 0-mosdegree A0md Augmented 2-mosdegree A2md Augmented 4-mosdegree A4md Augmented 6-mosdegree A6md Augmented 8-mosdegree A8md Augmented 10-mosdegree A10md Augmented 12-mosdegree A12md Augmented 14-mosdegree A14md Augmented 16-mosdegree A16md
1 Major 1-mosdegree M1md Major 3-mosdegree M3md Major 5-mosdegree M5md Major 7-mosdegree M7md Major 9-mosdegree M9md Major 11-mosdegree M11md Major 13-mosdegree M13md Major 15-mosdegree M15md Major 17-mosdegree M17md
0 Perfect 0-mosdegree
Perfect 2-mosdegree		 P0md
P2md		 Perfect 2-mosdegree
Perfect 4-mosdegree		 P2md
P4md		 Perfect 4-mosdegree
Perfect 6-mosdegree		 P4md
P6md		 Perfect 6-mosdegree
Perfect 8-mosdegree		 P6md
P8md		 Perfect 8-mosdegree
Perfect 10-mosdegree		 P8md
P10md		 Perfect 10-mosdegree
Perfect 12-mosdegree		 P10md
P12md		 Perfect 12-mosdegree
Perfect 14-mosdegree		 P12md
P14md		 Perfect 14-mosdegree
Perfect 16-mosdegree		 P14md
P16md		 Perfect 16-mosdegree
Perfect 18-mosdegree		 P16md
P18md
−1 Minor 1-mosdegree m1md Minor 3-mosdegree m3md Minor 5-mosdegree m5md Minor 7-mosdegree m7md Minor 9-mosdegree m9md Minor 11-mosdegree m11md Minor 13-mosdegree m13md Minor 15-mosdegree m15md Minor 17-mosdegree m17md
−2 Diminished 2-mosdegree d2md Diminished 4-mosdegree d4md Diminished 6-mosdegree d6md Diminished 8-mosdegree d8md Diminished 10-mosdegree d10md Diminished 12-mosdegree d12md Diminished 14-mosdegree d14md Diminished 16-mosdegree d16md Diminished 18-mosdegree d18md

Modes

Scale degrees of the modes of 9L 9s
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
9|0(9) 1 LsLsLsLsLsLsLsLsLs Perf. Maj. Perf. Maj. Perf. Maj. Perf. Maj. Perf. Maj. Perf. Maj. Perf. Maj. Perf. Maj. Perf. Maj. Perf.
0|9(9) 2 sLsLsLsLsLsLsLsLsL Perf. Min. Perf. Min. Perf. Min. Perf. Min. Perf. Min. Perf. Min. Perf. Min. Perf. Min. Perf. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 9L 9s
Generator(edo) Cents Step ratio Comments(always proper)
Bright Dark L:s Hardness
1\18 66.667 66.667 1:1 1.000 Equalized 9L 9s
6\99 72.727 60.606 6:5 1.200
5\81 74.074 59.259 5:4 1.250
9\144 75.000 58.333 9:7 1.286
4\63 76.190 57.143 4:3 1.333 Supersoft 9L 9s
11\171 77.193 56.140 11:8 1.375
7\108 77.778 55.556 7:5 1.400
10\153 78.431 54.902 10:7 1.429
3\45 80.000 53.333 3:2 1.500 Soft 9L 9s
11\162 81.481 51.852 11:7 1.571
8\117 82.051 51.282 8:5 1.600
13\189 82.540 50.794 13:8 1.625
5\72 83.333 50.000 5:3 1.667 Semisoft 9L 9s
12\171 84.211 49.123 12:7 1.714
7\99 84.848 48.485 7:4 1.750
9\126 85.714 47.619 9:5 1.800
2\27 88.889 44.444 2:1 2.000 Basic 9L 9s
9\117 92.308 41.026 9:4 2.250
7\90 93.333 40.000 7:3 2.333
12\153 94.118 39.216 12:5 2.400
5\63 95.238 38.095 5:2 2.500 Semihard 9L 9s
13\162 96.296 37.037 13:5 2.600
8\99 96.970 36.364 8:3 2.667
11\135 97.778 35.556 11:4 2.750
3\36 100.000 33.333 3:1 3.000 Hard 9L 9s
10\117 102.564 30.769 10:3 3.333
7\81 103.704 29.630 7:2 3.500
11\126 104.762 28.571 11:3 3.667
4\45 106.667 26.667 4:1 4.000 Superhard 9L 9s
9\99 109.091 24.242 9:2 4.500
5\54 111.111 22.222 5:1 5.000
6\63 114.286 19.048 6:1 6.000
1\9 133.333 0.000 1:0 → ∞ Collapsed 9L 9s
This page is a stub. You can help the Xenharmonic Wiki by expanding it.
Retrieved from "https://en.xen.wiki/index.php?title=9L_9s&oldid=195422"