2L 20s

From Xenharmonic Wiki
Jump to navigation Jump to search
↖ 1L 19s ↑ 2L 19s 3L 19s ↗
← 1L 20s 2L 20s 3L 20s →
↙ 1L 21s ↓ 2L 21s 3L 21s ↘ 
┌╥┬┬┬┬┬┬┬┬┬┬╥┬┬┬┬┬┬┬┬┬┬┐
│║││││││││││║│││││││││││
││││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LssssssssssLssssssssss
ssssssssssLssssssssssL
Equave 2/1 (1200.0 ¢)
Period 1\2 (600.0 ¢)
Generator size
Bright 10\22 to 1\2 (545.5 ¢ to 600.0 ¢)
Dark 0\2 to 1\22 (0.0 ¢ to 54.5 ¢)
TAMNAMS information
Descends from 2L 8s
Ancestor's step ratio range 7:1 to 1:0
Related MOS scales
Parent 2L 18s
Sister 20L 2s
Daughters 22L 2s, 2L 22s
Neutralized 4L 18s
2-Flought 24L 20s, 2L 42s
Equal tunings
Equalized (L:s = 1:1) 10\22 (545.5 ¢)
Supersoft (L:s = 4:3) 31\68 (547.1 ¢)
Soft (L:s = 3:2) 21\46 (547.8 ¢)
Semisoft (L:s = 5:3) 32\70 (548.6 ¢)
Basic (L:s = 2:1) 11\24 (550.0 ¢)
Semihard (L:s = 5:2) 23\50 (552.0 ¢)
Hard (L:s = 3:1) 12\26 (553.8 ¢)
Superhard (L:s = 4:1) 13\28 (557.1 ¢)
Collapsed (L:s = 1:0) 1\2 (600.0 ¢)

2L 20s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 20 small steps, with a period of 1 large step and 10 small steps that repeats every 600.0 ¢, or twice every octave. 2L 20s is related to 2L 8s, expanding it by 12 tones. Generators that produce this scale range from 545.5 ¢ to 600 ¢, or from 0 ¢ to 54.5 ¢.

This scale is the quarter tone scale of Shrutar.

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

The intervals of 2L 20s are named after the number of mossteps (L and s) they subtend. Each interval, apart from the period intervals (perfect 0-mosstep, perfect 11-mosstep, and perfect 22-mosstep), has two varieties, or sizes, each. Interval varieties are named major and minor for the large and small sizes, respectively, and augmented, perfect, and diminished for the scale's generators.

Intervals of 2L 20s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Perfect 1-mosstep P1ms s 0.0 ¢ to 54.5 ¢
Augmented 1-mosstep A1ms L 54.5 ¢ to 600.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 109.1 ¢
Major 2-mosstep M2ms L + s 109.1 ¢ to 600.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 163.6 ¢
Major 3-mosstep M3ms L + 2s 163.6 ¢ to 600.0 ¢
4-mosstep Minor 4-mosstep m4ms 4s 0.0 ¢ to 218.2 ¢
Major 4-mosstep M4ms L + 3s 218.2 ¢ to 600.0 ¢
5-mosstep Minor 5-mosstep m5ms 5s 0.0 ¢ to 272.7 ¢
Major 5-mosstep M5ms L + 4s 272.7 ¢ to 600.0 ¢
6-mosstep Minor 6-mosstep m6ms 6s 0.0 ¢ to 327.3 ¢
Major 6-mosstep M6ms L + 5s 327.3 ¢ to 600.0 ¢
7-mosstep Minor 7-mosstep m7ms 7s 0.0 ¢ to 381.8 ¢
Major 7-mosstep M7ms L + 6s 381.8 ¢ to 600.0 ¢
8-mosstep Minor 8-mosstep m8ms 8s 0.0 ¢ to 436.4 ¢
Major 8-mosstep M8ms L + 7s 436.4 ¢ to 600.0 ¢
9-mosstep Minor 9-mosstep m9ms 9s 0.0 ¢ to 490.9 ¢
Major 9-mosstep M9ms L + 8s 490.9 ¢ to 600.0 ¢
10-mosstep Diminished 10-mosstep d10ms 10s 0.0 ¢ to 545.5 ¢
Perfect 10-mosstep P10ms L + 9s 545.5 ¢ to 600.0 ¢
11-mosstep Perfect 11-mosstep P11ms L + 10s 600.0 ¢
12-mosstep Perfect 12-mosstep P12ms L + 11s 600.0 ¢ to 654.5 ¢
Augmented 12-mosstep A12ms 2L + 10s 654.5 ¢ to 1200.0 ¢
13-mosstep Minor 13-mosstep m13ms L + 12s 600.0 ¢ to 709.1 ¢
Major 13-mosstep M13ms 2L + 11s 709.1 ¢ to 1200.0 ¢
14-mosstep Minor 14-mosstep m14ms L + 13s 600.0 ¢ to 763.6 ¢
Major 14-mosstep M14ms 2L + 12s 763.6 ¢ to 1200.0 ¢
15-mosstep Minor 15-mosstep m15ms L + 14s 600.0 ¢ to 818.2 ¢
Major 15-mosstep M15ms 2L + 13s 818.2 ¢ to 1200.0 ¢
16-mosstep Minor 16-mosstep m16ms L + 15s 600.0 ¢ to 872.7 ¢
Major 16-mosstep M16ms 2L + 14s 872.7 ¢ to 1200.0 ¢
17-mosstep Minor 17-mosstep m17ms L + 16s 600.0 ¢ to 927.3 ¢
Major 17-mosstep M17ms 2L + 15s 927.3 ¢ to 1200.0 ¢
18-mosstep Minor 18-mosstep m18ms L + 17s 600.0 ¢ to 981.8 ¢
Major 18-mosstep M18ms 2L + 16s 981.8 ¢ to 1200.0 ¢
19-mosstep Minor 19-mosstep m19ms L + 18s 600.0 ¢ to 1036.4 ¢
Major 19-mosstep M19ms 2L + 17s 1036.4 ¢ to 1200.0 ¢
20-mosstep Minor 20-mosstep m20ms L + 19s 600.0 ¢ to 1090.9 ¢
Major 20-mosstep M20ms 2L + 18s 1090.9 ¢ to 1200.0 ¢
21-mosstep Diminished 21-mosstep d21ms L + 20s 600.0 ¢ to 1145.5 ¢
Perfect 21-mosstep P21ms 2L + 19s 1145.5 ¢ to 1200.0 ¢
22-mosstep Perfect 22-mosstep P22ms 2L + 20s 1200.0 ¢

Generator chain

A chain of bright generators, each a perfect 10-mosstep, produces the following scale degrees. A chain of 11 bright generators from each period contains the scale degrees of one of the modes of 2L 20s. Expanding each chain to 12 scale degrees produces the modes of either 22L 2s (for soft-of-basic tunings) or 2L 22s (for hard-of-basic tunings).

Generator chain of 2L 20s
Bright gens Scale degree Abbrev. Scale degree Abbrev.
11 Augmented 0-mosdegree A0md Augmented 11-mosdegree A11md
10 Augmented 1-mosdegree A1md Augmented 12-mosdegree A12md
9 Major 2-mosdegree M2md Major 13-mosdegree M13md
8 Major 3-mosdegree M3md Major 14-mosdegree M14md
7 Major 4-mosdegree M4md Major 15-mosdegree M15md
6 Major 5-mosdegree M5md Major 16-mosdegree M16md
5 Major 6-mosdegree M6md Major 17-mosdegree M17md
4 Major 7-mosdegree M7md Major 18-mosdegree M18md
3 Major 8-mosdegree M8md Major 19-mosdegree M19md
2 Major 9-mosdegree M9md Major 20-mosdegree M20md
1 Perfect 10-mosdegree P10md Perfect 21-mosdegree P21md
0 Perfect 0-mosdegree
Perfect 11-mosdegree		 P0md
P11md		 Perfect 11-mosdegree
Perfect 22-mosdegree		 P11md
P22md
−1 Perfect 1-mosdegree P1md Perfect 12-mosdegree P12md
−2 Minor 2-mosdegree m2md Minor 13-mosdegree m13md
−3 Minor 3-mosdegree m3md Minor 14-mosdegree m14md
−4 Minor 4-mosdegree m4md Minor 15-mosdegree m15md
−5 Minor 5-mosdegree m5md Minor 16-mosdegree m16md
−6 Minor 6-mosdegree m6md Minor 17-mosdegree m17md
−7 Minor 7-mosdegree m7md Minor 18-mosdegree m18md
−8 Minor 8-mosdegree m8md Minor 19-mosdegree m19md
−9 Minor 9-mosdegree m9md Minor 20-mosdegree m20md
−10 Diminished 10-mosdegree d10md Diminished 21-mosdegree d21md
−11 Diminished 11-mosdegree d11md Diminished 22-mosdegree d22md

Modes

Scale degrees of the modes of 2L 20s 
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 19 20 21 22
20|0(2) 1 LssssssssssLssssssssss Perf. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
18|2(2) 11 sLssssssssssLsssssssss Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
16|4(2) 10 ssLssssssssssLssssssss Perf. Perf. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Perf. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
14|6(2) 9 sssLssssssssssLsssssss Perf. Perf. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Perf. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
12|8(2) 8 ssssLssssssssssLssssss Perf. Perf. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Perf. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
10|10(2) 7 sssssLssssssssssLsssss Perf. Perf. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Perf. Perf. Perf. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Perf. Perf.
8|12(2) 6 ssssssLssssssssssLssss Perf. Perf. Min. Min. Min. Min. Min. Maj. Maj. Maj. Perf. Perf. Perf. Min. Min. Min. Min. Min. Maj. Maj. Maj. Perf. Perf.
6|14(2) 5 sssssssLssssssssssLsss Perf. Perf. Min. Min. Min. Min. Min. Min. Maj. Maj. Perf. Perf. Perf. Min. Min. Min. Min. Min. Min. Maj. Maj. Perf. Perf.
4|16(2) 4 ssssssssLssssssssssLss Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Maj. Perf. Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Maj. Perf. Perf.
2|18(2) 3 sssssssssLssssssssssLs Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Perf.
0|20(2) 2 ssssssssssLssssssssssL Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Dim. Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Dim. Perf.

Scale tree

Scale tree and tuning spectrum of 2L 20s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
10\22 545.455 54.545 1:1 1.000 Equalized 2L 20s
51\112 546.429 53.571 6:5 1.200
41\90 546.667 53.333 5:4 1.250
72\158 546.835 53.165 9:7 1.286
31\68 547.059 52.941 4:3 1.333 Supersoft 2L 20s
83\182 547.253 52.747 11:8 1.375
52\114 547.368 52.632 7:5 1.400
73\160 547.500 52.500 10:7 1.429
21\46 547.826 52.174 3:2 1.500 Soft 2L 20s
74\162 548.148 51.852 11:7 1.571
53\116 548.276 51.724 8:5 1.600
85\186 548.387 51.613 13:8 1.625
32\70 548.571 51.429 5:3 1.667 Semisoft 2L 20s
75\164 548.780 51.220 12:7 1.714
43\94 548.936 51.064 7:4 1.750
54\118 549.153 50.847 9:5 1.800
11\24 550.000 50.000 2:1 2.000 Basic 2L 20s
Scales with tunings softer than this are proper
45\98 551.020 48.980 9:4 2.250
34\74 551.351 48.649 7:3 2.333
57\124 551.613 48.387 12:5 2.400
23\50 552.000 48.000 5:2 2.500 Semihard 2L 20s
58\126 552.381 47.619 13:5 2.600
35\76 552.632 47.368 8:3 2.667
47\102 552.941 47.059 11:4 2.750
12\26 553.846 46.154 3:1 3.000 Hard 2L 20s
37\80 555.000 45.000 10:3 3.333
25\54 555.556 44.444 7:2 3.500
38\82 556.098 43.902 11:3 3.667
13\28 557.143 42.857 4:1 4.000 Superhard 2L 20s
27\58 558.621 41.379 9:2 4.500
14\30 560.000 40.000 5:1 5.000
15\32 562.500 37.500 6:1 6.000
1\2 600.000 0.000 1:0 → ∞ Collapsed 2L 20s
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=2L_20s&oldid=183776"