4L 15s

From Xenharmonic Wiki
Jump to navigation Jump to search
↖ 3L 14s ↑ 4L 14s 5L 14s ↗
← 3L 15s 4L 15s 5L 15s →
↙ 3L 16s ↓ 4L 16s 5L 16s ↘ 
┌╥┬┬┬╥┬┬┬┬╥┬┬┬┬╥┬┬┬┬┐
│║│││║││││║││││║│││││
│││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsssLssssLssssLssss
ssssLssssLssssLsssL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 14\19 to 3\4 (884.2¢ to 900.0¢)
Dark 1\4 to 5\19 (300.0¢ to 315.8¢)
TAMNAMS information
Descends from 4L 3s (smitonic)
Ancestor's step ratio range 4:1 to 1:0 (ultrahard)
Related MOS scales
Parent 4L 11s
Sister 15L 4s
Daughters 19L 4s, 4L 19s
Neutralized 8L 11s
2-Flought 23L 15s, 4L 34s
Equal tunings
Equalized (L:s = 1:1) 14\19 (884.2¢)
Supersoft (L:s = 4:3) 45\61 (885.2¢)
Soft (L:s = 3:2) 31\42 (885.7¢)
Semisoft (L:s = 5:3) 48\65 (886.2¢)
Basic (L:s = 2:1) 17\23 (887.0¢)
Semihard (L:s = 5:2) 37\50 (888.0¢)
Hard (L:s = 3:1) 20\27 (888.9¢)
Superhard (L:s = 4:1) 23\31 (890.3¢)
Collapsed (L:s = 1:0) 3\4 (900.0¢)

4L 15s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 15 small steps, repeating every octave. 4L 15s is a great-grandchild scale of 4L 3s, expanding it by 12 tones. Generators that produce this scale range from 884.2¢ to 900¢, or from 300¢ to 315.8¢.

This scale is associated with myna temperament (pronounced /'maɪnə/), where stacking two bright generators and octave-reducing produces 7/5 (~582¢).

Modes

Modes of 4L 15s
UDP Cyclic
order		 Step
pattern
18|0 1 LsssLssssLssssLssss
17|1 15 LssssLsssLssssLssss
16|2 10 LssssLssssLsssLssss
15|3 5 LssssLssssLssssLsss
14|4 19 sLsssLssssLssssLsss
13|5 14 sLssssLsssLssssLsss
12|6 9 sLssssLssssLsssLsss
11|7 4 sLssssLssssLssssLss
10|8 18 ssLsssLssssLssssLss
9|9 13 ssLssssLsssLssssLss
8|10 8 ssLssssLssssLsssLss
7|11 3 ssLssssLssssLssssLs
6|12 17 sssLsssLssssLssssLs
5|13 12 sssLssssLsssLssssLs
4|14 7 sssLssssLssssLsssLs
3|15 2 sssLssssLssssLssssL
2|16 16 ssssLsssLssssLssssL
1|17 11 ssssLssssLsssLssssL
0|18 6 ssssLssssLssssLsssL

Intervals

Intervals of 4L 15s
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 63.2¢
Major 1-mosstep M1ms L 63.2¢ to 300.0¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0¢ to 126.3¢
Major 2-mosstep M2ms L + s 126.3¢ to 300.0¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0¢ to 189.5¢
Major 3-mosstep M3ms L + 2s 189.5¢ to 300.0¢
4-mosstep Minor 4-mosstep m4ms 4s 0.0¢ to 252.6¢
Major 4-mosstep M4ms L + 3s 252.6¢ to 300.0¢
5-mosstep Perfect 5-mosstep P5ms L + 4s 300.0¢ to 315.8¢
Augmented 5-mosstep A5ms 2L + 3s 315.8¢ to 600.0¢
6-mosstep Minor 6-mosstep m6ms L + 5s 300.0¢ to 378.9¢
Major 6-mosstep M6ms 2L + 4s 378.9¢ to 600.0¢
7-mosstep Minor 7-mosstep m7ms L + 6s 300.0¢ to 442.1¢
Major 7-mosstep M7ms 2L + 5s 442.1¢ to 600.0¢
8-mosstep Minor 8-mosstep m8ms L + 7s 300.0¢ to 505.3¢
Major 8-mosstep M8ms 2L + 6s 505.3¢ to 600.0¢
9-mosstep Minor 9-mosstep m9ms L + 8s 300.0¢ to 568.4¢
Major 9-mosstep M9ms 2L + 7s 568.4¢ to 600.0¢
10-mosstep Minor 10-mosstep m10ms 2L + 8s 600.0¢ to 631.6¢
Major 10-mosstep M10ms 3L + 7s 631.6¢ to 900.0¢
11-mosstep Minor 11-mosstep m11ms 2L + 9s 600.0¢ to 694.7¢
Major 11-mosstep M11ms 3L + 8s 694.7¢ to 900.0¢
12-mosstep Minor 12-mosstep m12ms 2L + 10s 600.0¢ to 757.9¢
Major 12-mosstep M12ms 3L + 9s 757.9¢ to 900.0¢
13-mosstep Minor 13-mosstep m13ms 2L + 11s 600.0¢ to 821.1¢
Major 13-mosstep M13ms 3L + 10s 821.1¢ to 900.0¢
14-mosstep Diminished 14-mosstep d14ms 2L + 12s 600.0¢ to 884.2¢
Perfect 14-mosstep P14ms 3L + 11s 884.2¢ to 900.0¢
15-mosstep Minor 15-mosstep m15ms 3L + 12s 900.0¢ to 947.4¢
Major 15-mosstep M15ms 4L + 11s 947.4¢ to 1200.0¢
16-mosstep Minor 16-mosstep m16ms 3L + 13s 900.0¢ to 1010.5¢
Major 16-mosstep M16ms 4L + 12s 1010.5¢ to 1200.0¢
17-mosstep Minor 17-mosstep m17ms 3L + 14s 900.0¢ to 1073.7¢
Major 17-mosstep M17ms 4L + 13s 1073.7¢ to 1200.0¢
18-mosstep Minor 18-mosstep m18ms 3L + 15s 900.0¢ to 1136.8¢
Major 18-mosstep M18ms 4L + 14s 1136.8¢ to 1200.0¢
19-mosstep Perfect 19-mosstep P19ms 4L + 15s 1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 4L 15s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
14\19 884.211 315.789 1:1 1.000 Equalized 4L 15s
73\99 884.848 315.152 6:5 1.200
59\80 885.000 315.000 5:4 1.250
104\141 885.106 314.894 9:7 1.286
45\61 885.246 314.754 4:3 1.333 Supersoft 4L 15s
121\164 885.366 314.634 11:8 1.375
76\103 885.437 314.563 7:5 1.400
107\145 885.517 314.483 10:7 1.429
31\42 885.714 314.286 3:2 1.500 Soft 4L 15s
110\149 885.906 314.094 11:7 1.571
79\107 885.981 314.019 8:5 1.600
127\172 886.047 313.953 13:8 1.625
48\65 886.154 313.846 5:3 1.667 Semisoft 4L 15s
113\153 886.275 313.725 12:7 1.714
65\88 886.364 313.636 7:4 1.750
82\111 886.486 313.514 9:5 1.800
17\23 886.957 313.043 2:1 2.000 Basic 4L 15s
Scales with tunings softer than this are proper
71\96 887.500 312.500 9:4 2.250
54\73 887.671 312.329 7:3 2.333
91\123 887.805 312.195 12:5 2.400
37\50 888.000 312.000 5:2 2.500 Semihard 4L 15s
94\127 888.189 311.811 13:5 2.600
57\77 888.312 311.688 8:3 2.667
77\104 888.462 311.538 11:4 2.750
20\27 888.889 311.111 3:1 3.000 Hard 4L 15s
63\85 889.412 310.588 10:3 3.333
43\58 889.655 310.345 7:2 3.500
66\89 889.888 310.112 11:3 3.667
23\31 890.323 309.677 4:1 4.000 Superhard 4L 15s
49\66 890.909 309.091 9:2 4.500
26\35 891.429 308.571 5:1 5.000
29\39 892.308 307.692 6:1 6.000
3\4 900.000 300.000 1:0 → ∞ Collapsed 4L 15s
Retrieved from "https://en.xen.wiki/index.php?title=4L_15s&oldid=170785"