2L 10s

From Xenharmonic Wiki
Jump to navigation Jump to search
↖ 1L 9s ↑ 2L 9s 3L 9s ↗
← 1L 10s 2L 10s 3L 10s →
↙ 1L 11s ↓ 2L 11s 3L 11s ↘ 
┌╥┬┬┬┬┬╥┬┬┬┬┬┐
│║│││││║││││││
││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsssssLsssss
sssssLsssssL
Equave 2/1 (1200.0¢)
Period 1\2 (600.0¢)
Generator size
Bright 5\12 to 1\2 (500.0¢ to 600.0¢)
Dark 0\2 to 1\12 (0.0¢ to 100.0¢)
TAMNAMS information
Descends from 2L 8s (jaric)
Ancestor's step ratio range 2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent 2L 8s
Sister 10L 2s
Daughters 12L 2s, 2L 12s
Neutralized 4L 8s
2-Flought 14L 10s, 2L 22s
Equal tunings
Equalized (L:s = 1:1) 5\12 (500.0¢)
Supersoft (L:s = 4:3) 16\38 (505.3¢)
Soft (L:s = 3:2) 11\26 (507.7¢)
Semisoft (L:s = 5:3) 17\40 (510.0¢)
Basic (L:s = 2:1) 6\14 (514.3¢)
Semihard (L:s = 5:2) 13\30 (520.0¢)
Hard (L:s = 3:1) 7\16 (525.0¢)
Superhard (L:s = 4:1) 8\18 (533.3¢)
Collapsed (L:s = 1:0) 1\2 (600.0¢)

2L 10s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 10 small steps, with a period of 1 large step and 5 small steps that repeats every 600.0¢, or twice every octave. 2L 10s is a child scale of 2L 8s, expanding it by 2 tones. Generators that produce this scale range from 500¢ to 600¢, or from 0¢ to 100¢.

2L 10s appears as the chromatic scale of injera and shrutar temperaments, among others. Injera is the harmonic entropy minimum for this pattern, generating 5/4 by moving up four generators from the root. The name for this MOS scale is p-chro jaric.

Modes

Modes of 2L 10s
UDP Cyclic
order		 Step
pattern
10|0(2) 1 LsssssLsssss
8|2(2) 6 sLsssssLssss
6|4(2) 5 ssLsssssLsss
4|6(2) 4 sssLsssssLss
2|8(2) 3 ssssLsssssLs
0|10(2) 2 sssssLsssssL

Degrees

Scale degrees of the modes of 2L 10s 
UDP Cyclic
order		 Step
pattern		 Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12
10|0(2) 1 LsssssLsssss Perf. Aug. Maj. Maj. Maj. Perf. Perf. Aug. Maj. Maj. Maj. Perf. Perf.
8|2(2) 6 sLsssssLssss Perf. Perf. Maj. Maj. Maj. Perf. Perf. Perf. Maj. Maj. Maj. Perf. Perf.
6|4(2) 5 ssLsssssLsss Perf. Perf. Min. Maj. Maj. Perf. Perf. Perf. Min. Maj. Maj. Perf. Perf.
4|6(2) 4 sssLsssssLss Perf. Perf. Min. Min. Maj. Perf. Perf. Perf. Min. Min. Maj. Perf. Perf.
2|8(2) 3 ssssLsssssLs Perf. Perf. Min. Min. Min. Perf. Perf. Perf. Min. Min. Min. Perf. Perf.
0|10(2) 2 sssssLsssssL Perf. Perf. Min. Min. Min. Dim. Perf. Perf. Min. Min. Min. Dim. Perf.

Intervals

Intervals of 2L 10s
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 100.0¢
Augmented 1-mosstep A1ms L 100.0¢ to 600.0¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0¢ to 200.0¢
Major 2-mosstep M2ms L + s 200.0¢ to 600.0¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0¢ to 300.0¢
Major 3-mosstep M3ms L + 2s 300.0¢ to 600.0¢
4-mosstep Minor 4-mosstep m4ms 4s 0.0¢ to 400.0¢
Major 4-mosstep M4ms L + 3s 400.0¢ to 600.0¢
5-mosstep Diminished 5-mosstep d5ms 5s 0.0¢ to 500.0¢
Perfect 5-mosstep P5ms L + 4s 500.0¢ to 600.0¢
6-mosstep Perfect 6-mosstep P6ms L + 5s 600.0¢
7-mosstep Perfect 7-mosstep P7ms L + 6s 600.0¢ to 700.0¢
Augmented 7-mosstep A7ms 2L + 5s 700.0¢ to 1200.0¢
8-mosstep Minor 8-mosstep m8ms L + 7s 600.0¢ to 800.0¢
Major 8-mosstep M8ms 2L + 6s 800.0¢ to 1200.0¢
9-mosstep Minor 9-mosstep m9ms L + 8s 600.0¢ to 900.0¢
Major 9-mosstep M9ms 2L + 7s 900.0¢ to 1200.0¢
10-mosstep Minor 10-mosstep m10ms L + 9s 600.0¢ to 1000.0¢
Major 10-mosstep M10ms 2L + 8s 1000.0¢ to 1200.0¢
11-mosstep Diminished 11-mosstep d11ms L + 10s 600.0¢ to 1100.0¢
Perfect 11-mosstep P11ms 2L + 9s 1100.0¢ to 1200.0¢
12-mosstep Perfect 12-mosstep P12ms 2L + 10s 1200.0¢

Scale tree

Icon-Todo.png Todo: review
Review entries from past page revision and enter them into the scale tree.
Scale Tree and Tuning Spectrum of 2L 10s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
5\12 500.000 100.000 1:1 1.000 Equalized 2L 10s
26\62 503.226 96.774 6:5 1.200
21\50 504.000 96.000 5:4 1.250
37\88 504.545 95.455 9:7 1.286
16\38 505.263 94.737 4:3 1.333 Supersoft 2L 10s
43\102 505.882 94.118 11:8 1.375
27\64 506.250 93.750 7:5 1.400
38\90 506.667 93.333 10:7 1.429
11\26 507.692 92.308 3:2 1.500 Soft 2L 10s
39\92 508.696 91.304 11:7 1.571
28\66 509.091 90.909 8:5 1.600
45\106 509.434 90.566 13:8 1.625
17\40 510.000 90.000 5:3 1.667 Semisoft 2L 10s
40\94 510.638 89.362 12:7 1.714
23\54 511.111 88.889 7:4 1.750
29\68 511.765 88.235 9:5 1.800
6\14 514.286 85.714 2:1 2.000 Basic 2L 10s
Scales with tunings softer than this are proper
25\58 517.241 82.759 9:4 2.250
19\44 518.182 81.818 7:3 2.333
32\74 518.919 81.081 12:5 2.400
13\30 520.000 80.000 5:2 2.500 Semihard 2L 10s
33\76 521.053 78.947 13:5 2.600
20\46 521.739 78.261 8:3 2.667
27\62 522.581 77.419 11:4 2.750
7\16 525.000 75.000 3:1 3.000 Hard 2L 10s
22\50 528.000 72.000 10:3 3.333
15\34 529.412 70.588 7:2 3.500
23\52 530.769 69.231 11:3 3.667
8\18 533.333 66.667 4:1 4.000 Superhard 2L 10s
17\38 536.842 63.158 9:2 4.500
9\20 540.000 60.000 5:1 5.000
10\22 545.455 54.545 6:1 6.000
1\2 600.000 0.000 1:0 → ∞ Collapsed 2L 10s
Retrieved from "https://en.xen.wiki/index.php?title=2L_10s&oldid=170669"