7L 11s (3/1-equivalent)

From Xenharmonic Wiki
Jump to navigation Jump to search
Icon-Todo.png Todo: expand
This page is a WIP (work-in-progress).
↖ 6L 10s⟨3/1⟩ ↑ 7L 10s⟨3/1⟩ 8L 10s⟨3/1⟩ ↗
← 6L 11s⟨3/1⟩ 7L 11s (3/1-equivalent) 8L 11s⟨3/1⟩ →
↙ 6L 12s⟨3/1⟩ ↓ 7L 12s⟨3/1⟩ 8L 12s⟨3/1⟩ ↘ 
┌╥┬╥┬┬╥┬╥┬┬╥┬╥┬┬╥┬┬┐
│║│║││║│║││║│║││║│││
││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsLssLsLssLsLssLss
ssLssLsLssLsLssLsL
Equave 3/1 (1902.0¢)
Period 3/1 (1902.0¢)
Generator size(edt)
Bright 5\18 to 2\7 (528.3¢ to 543.4¢)
Dark 5\7 to 13\18 (1358.5¢ to 1373.6¢)
Related MOS scales
Parent 7L 4s⟨3/1⟩
Sister 11L 7s⟨3/1⟩
Daughters 18L 7s⟨3/1⟩, 7L 18s⟨3/1⟩
Neutralized 14L 4s⟨3/1⟩
2-Flought 25L 11s⟨3/1⟩, 7L 29s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1) 5\18 (528.3¢)
Supersoft (L:s = 4:3) 17\61 (530.1¢)
Soft (L:s = 3:2) 12\43 (530.8¢)
Semisoft (L:s = 5:3) 19\68 (531.4¢)
Basic (L:s = 2:1) 7\25 (532.5¢)
Semihard (L:s = 5:2) 16\57 (533.9¢)
Hard (L:s = 3:1) 9\32 (534.9¢)
Superhard (L:s = 4:1) 11\39 (536.4¢)
Collapsed (L:s = 1:0) 2\7 (543.4¢)

7L 11s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 7 large steps and 11 small steps, repeating every interval of 3/1 (1902.0¢). Generators that produce this scale range from 528.3¢ to 543.4¢, or from 1358.5¢ to 1373.6¢.

Temperaments

7L 11s⟨3/1⟩ MOS scales can be used for the Electra temperament, in which three generators down is approximately 13/11 and one generator up is approximately 15/11. If 11:13:15 is treated as the fundamental sonority of no-2's music, then Electra can be viewed as the analogue to meantone and 7L 11s⟨3/1⟩ can be viewed as the analogue to the diatonic scale. If twos are admitted, the hard end of the Electra heptatonic spectrum can be viewed as the subharmonic version of Pythagorean/Classical tuning.

Modes

Modes of 7L 11s⟨3/1⟩
UDP Cyclic
order		 Step
pattern
17|0 1 LsLssLsLssLsLssLss
16|1 6 LsLssLsLssLssLsLss
15|2 11 LsLssLssLsLssLsLss
14|3 16 LssLsLssLsLssLsLss
13|4 3 LssLsLssLsLssLssLs
12|5 8 LssLsLssLssLsLssLs
11|6 13 LssLssLsLssLsLssLs
10|7 18 sLsLssLsLssLsLssLs
9|8 5 sLsLssLsLssLssLsLs
8|9 10 sLsLssLssLsLssLsLs
7|10 15 sLssLsLssLsLssLsLs
6|11 2 sLssLsLssLsLssLssL
5|12 7 sLssLsLssLssLsLssL
4|13 12 sLssLssLsLssLsLssL
3|14 17 ssLsLssLsLssLsLssL
2|15 4 ssLsLssLsLssLssLsL
1|16 9 ssLsLssLssLsLssLsL
0|17 14 ssLssLsLssLsLssLsL

Intervals

Intervals of 7L 11s⟨3/1⟩
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 105.7¢
Major 1-mosstep M1ms L 105.7¢ to 271.7¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0¢ to 211.3¢
Major 2-mosstep M2ms L + s 211.3¢ to 271.7¢
3-mosstep Minor 3-mosstep m3ms L + 2s 271.7¢ to 317.0¢
Major 3-mosstep M3ms 2L + s 317.0¢ to 543.4¢
4-mosstep Minor 4-mosstep m4ms L + 3s 271.7¢ to 422.7¢
Major 4-mosstep M4ms 2L + 2s 422.7¢ to 543.4¢
5-mosstep Diminished 5-mosstep d5ms L + 4s 271.7¢ to 528.3¢
Perfect 5-mosstep P5ms 2L + 3s 528.3¢ to 543.4¢
6-mosstep Minor 6-mosstep m6ms 2L + 4s 543.4¢ to 634.0¢
Major 6-mosstep M6ms 3L + 3s 634.0¢ to 815.1¢
7-mosstep Minor 7-mosstep m7ms 2L + 5s 543.4¢ to 739.6¢
Major 7-mosstep M7ms 3L + 4s 739.6¢ to 815.1¢
8-mosstep Minor 8-mosstep m8ms 3L + 5s 815.1¢ to 845.3¢
Major 8-mosstep M8ms 4L + 4s 845.3¢ to 1086.8¢
9-mosstep Minor 9-mosstep m9ms 3L + 6s 815.1¢ to 951.0¢
Major 9-mosstep M9ms 4L + 5s 951.0¢ to 1086.8¢
10-mosstep Minor 10-mosstep m10ms 3L + 7s 815.1¢ to 1056.6¢
Major 10-mosstep M10ms 4L + 6s 1056.6¢ to 1086.8¢
11-mosstep Minor 11-mosstep m11ms 4L + 7s 1086.8¢ to 1162.3¢
Major 11-mosstep M11ms 5L + 6s 1162.3¢ to 1358.5¢
12-mosstep Minor 12-mosstep m12ms 4L + 8s 1086.8¢ to 1268.0¢
Major 12-mosstep M12ms 5L + 7s 1268.0¢ to 1358.5¢
13-mosstep Perfect 13-mosstep P13ms 5L + 8s 1358.5¢ to 1373.6¢
Augmented 13-mosstep A13ms 6L + 7s 1373.6¢ to 1630.2¢
14-mosstep Minor 14-mosstep m14ms 5L + 9s 1358.5¢ to 1479.3¢
Major 14-mosstep M14ms 6L + 8s 1479.3¢ to 1630.2¢
15-mosstep Minor 15-mosstep m15ms 5L + 10s 1358.5¢ to 1585.0¢
Major 15-mosstep M15ms 6L + 9s 1585.0¢ to 1630.2¢
16-mosstep Minor 16-mosstep m16ms 6L + 10s 1630.2¢ to 1690.6¢
Major 16-mosstep M16ms 7L + 9s 1690.6¢ to 1902.0¢
17-mosstep Minor 17-mosstep m17ms 6L + 11s 1630.2¢ to 1796.3¢
Major 17-mosstep M17ms 7L + 10s 1796.3¢ to 1902.0¢
18-mosstep Perfect 18-mosstep P18ms 7L + 11s 1902.0¢

Scale tree

Scale Tree and Tuning Spectrum of 7L 11s⟨3/1⟩
Generator(edt) Cents Step ratio Comments
Bright Dark L:s Hardness
5\18 528.321 1373.634 1:1 1.000 Equalized 7L 11s⟨3/1⟩
27\97 529.410 1372.545 6:5 1.200
22\79 529.658 1372.297 5:4 1.250
39\140 529.830 1372.125 9:7 1.286
17\61 530.053 1371.902 4:3 1.333 Supersoft 7L 11s⟨3/1⟩
46\165 530.242 1371.713 11:8 1.375
29\104 530.353 1371.602 7:5 1.400
41\147 530.477 1371.478 10:7 1.429
12\43 530.778 1371.177 3:2 1.500 Soft 7L 11s⟨3/1⟩
43\154 531.065 1370.890 11:7 1.571
31\111 531.177 1370.778 8:5 1.600
50\179 531.272 1370.683 13:8 1.625
19\68 531.429 1370.526 5:3 1.667 Semisoft 7L 11s⟨3/1⟩
45\161 531.602 1370.353 12:7 1.714
26\93 531.729 1370.226 7:4 1.750
33\118 531.903 1370.052 9:5 1.800
7\25 532.547 1369.408 2:1 2.000 Basic 7L 11s⟨3/1⟩
Scales with tunings softer than this are proper
30\107 533.258 1368.697 9:4 2.250
23\82 533.475 1368.480 7:3 2.333
39\139 533.642 1368.313 12:5 2.400
16\57 533.882 1368.073 5:2 2.500 Semihard 7L 11s⟨3/1⟩
41\146 534.111 1367.844 13:5 2.600
25\89 534.257 1367.698 8:3 2.667
34\121 534.434 1367.521 11:4 2.750
9\32 534.925 1367.030 3:1 3.000 Hard 7L 11s⟨3/1⟩
29\103 535.502 1366.453 10:3 3.333
20\71 535.762 1366.193 7:2 3.500
31\110 536.006 1365.950 11:3 3.667
11\39 536.449 1365.506 4:1 4.000 Superhard 7L 11s⟨3/1⟩
24\85 537.023 1364.932 9:2 4.500
13\46 537.509 1364.446 5:1 5.000
15\53 538.289 1363.666 6:1 6.000
2\7 543.416 1358.539 1:0 → ∞ Collapsed 7L 11s⟨3/1⟩
Retrieved from "https://en.xen.wiki/index.php?title=7L_11s_(3/1-equivalent)&oldid=176009"