3L 7s (3/1-equivalent)

From Xenharmonic Wiki
Jump to navigation Jump to search
↖ 2L 6s⟨3/1⟩ ↑ 3L 6s⟨3/1⟩ 4L 6s⟨3/1⟩ ↗
← 2L 7s⟨3/1⟩ 3L 7s (3/1-equivalent) 4L 7s⟨3/1⟩ →
↙ 2L 8s⟨3/1⟩ ↓ 3L 8s⟨3/1⟩ 4L 8s⟨3/1⟩ ↘ 
┌╥┬┬╥┬┬╥┬┬┬┐
│║││║││║││││
││││││││││││
└┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LssLssLsss
sssLssLssL
Equave 3/1 (1902.0 ¢)
Period 3/1 (1902.0 ¢)
Generator size(edt)
Bright 3\10 to 1\3 (570.6 ¢ to 634.0 ¢)
Dark 2\3 to 7\10 (1268.0 ¢ to 1331.4 ¢)
Related MOS scales
Parent 3L 4s⟨3/1⟩
Sister 7L 3s⟨3/1⟩
Daughters 10L 3s⟨3/1⟩, 3L 10s⟨3/1⟩
Neutralized 6L 4s⟨3/1⟩
2-Flought 13L 7s⟨3/1⟩, 3L 17s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1) 3\10 (570.6 ¢)
Supersoft (L:s = 4:3) 10\33 (576.4 ¢)
Soft (L:s = 3:2) 7\23 (578.9 ¢)
Semisoft (L:s = 5:3) 11\36 (581.2 ¢)
Basic (L:s = 2:1) 4\13 (585.2 ¢)
Semihard (L:s = 5:2) 9\29 (590.3 ¢)
Hard (L:s = 3:1) 5\16 (594.4 ¢)
Superhard (L:s = 4:1) 6\19 (600.6 ¢)
Collapsed (L:s = 1:0) 1\3 (634.0 ¢)

3L 7s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 3 large steps and 7 small steps, repeating every interval of 3/1 (1902.0 ¢). Generators that produce this scale range from 570.6 ¢ to 634 ¢, or from 1268 ¢ to 1331.4 ¢.

It is the decatonic scale of the 7/5-generated Canopus temperament, one of the most notable no-twos temperaments after Bohlen-Pierce-Stearns. Basic 3L 7s〈3/1〉 is in 13edt (Bohlen-Pierce).

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.

{{subst:MOS data temporary}}

Scale tree

Scale tree and tuning spectrum of 3L 7s⟨3/1⟩
Generator(edt) Cents Step ratio Comments
Bright Dark L:s Hardness
3\10 570.587 1331.369 1:1 1.000 Equalized 3L 7s⟨3/1⟩
16\53 574.175 1327.780 6:5 1.200
13\43 575.010 1326.945 5:4 1.250
23\76 575.592 1326.363 9:7 1.286
10\33 576.350 1325.605 4:3 1.333 Supersoft 3L 7s⟨3/1⟩
27\89 576.998 1324.957 11:8 1.375
17\56 577.379 1324.576 7:5 1.400
24\79 577.809 1324.146 10:7 1.429
7\23 578.856 1323.099 3:2 1.500 Soft 3L 7s⟨3/1⟩
25\82 579.864 1322.091 11:7 1.571
18\59 580.257 1321.698 8:5 1.600
29\95 580.597 1321.358 13:8 1.625
11\36 581.153 1320.802 5:3 1.667 Semisoft 3L 7s⟨3/1⟩
26\85 581.774 1320.181 12:7 1.714
15\49 582.231 1319.724 7:4 1.750
19\62 582.857 1319.098 9:5 1.800
4\13 585.217 1316.738 2:1 2.000 Basic 3L 7s⟨3/1⟩
Scales with tunings softer than this are proper
Canopus is around here
17\55 587.877 1314.078 9:4 2.250
13\42 588.700 1313.255 7:3 2.333
22\71 589.338 1312.617 12:5 2.400
9\29 590.262 1311.693 5:2 2.500 Semihard 3L 7s⟨3/1⟩
23\74 591.148 1310.807 13:5 2.600
14\45 591.719 1310.236 8:3 2.667
19\61 592.412 1309.543 11:4 2.750
5\16 594.361 1307.594 3:1 3.000 Hard 3L 7s⟨3/1⟩
16\51 596.692 1305.263 10:3 3.333
11\35 597.757 1304.198 7:2 3.500
17\54 598.764 1303.191 11:3 3.667
6\19 600.617 1301.338 4:1 4.000 Superhard 3L 7s⟨3/1⟩
13\41 603.059 1298.896 9:2 4.500
7\22 605.168 1296.788 5:1 5.000
8\25 608.626 1293.329 6:1 6.000
1\3 633.985 1267.970 1:0 → ∞ Collapsed 3L 7s⟨3/1⟩
Retrieved from "https://en.xen.wiki/index.php?title=3L_7s_(3/1-equivalent)&oldid=184234"