User:Francium/12L 7s (3/1-equivalent)

From Xenharmonic Wiki
Jump to navigation Jump to search
This user page is editable by any wiki editor.

As a general rule, most users expect their user space to be edited only by themselves, except for minor edits (e.g. maintenance), undoing obviously harmful edits such as vandalism or disruptive editing, and user talk pages.

However, by including this message box, the author of this user page has indicated that this page is open to contributions from other users (e.g. content-related edits).

↖ 11L 6s⟨3/1⟩ ↑ 12L 6s⟨3/1⟩ 13L 6s⟨3/1⟩ ↗
← 11L 7s⟨3/1⟩ 12L 7s (3/1-equivalent) 13L 7s⟨3/1⟩ →
↙ 11L 8s⟨3/1⟩ ↓ 12L 8s⟨3/1⟩ 13L 8s⟨3/1⟩ ↘ 
┌╥╥┬╥╥┬╥╥┬╥┬╥╥┬╥╥┬╥┬┐
│║║│║║│║║│║│║║│║║│║││
│││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLsLLsLLsLsLLsLLsLs
sLsLLsLLsLsLLsLLsLL
Equave 3/1 (1902.0 ¢)
Period 3/1 (1902.0 ¢)
Generator size(edt)
Bright 11\19 to 7\12 (1101.1 ¢ to 1109.5 ¢)
Dark 5\12 to 8\19 (792.5 ¢ to 800.8 ¢)
Related MOS scales
Parent 7L 5s⟨3/1⟩
Sister 7L 12s⟨3/1⟩
Daughters 19L 12s⟨3/1⟩, 12L 19s⟨3/1⟩
Neutralized 5L 14s⟨3/1⟩
2-Flought 31L 7s⟨3/1⟩, 12L 26s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1) 11\19 (1101.1 ¢)
Supersoft (L:s = 4:3) 40\69 (1102.6 ¢)
Soft (L:s = 3:2) 29\50 (1103.1 ¢)
Semisoft (L:s = 5:3) 47\81 (1103.6 ¢)
Basic (L:s = 2:1) 18\31 (1104.4 ¢)
Semihard (L:s = 5:2) 43\74 (1105.2 ¢)
Hard (L:s = 3:1) 25\43 (1105.8 ¢)
Superhard (L:s = 4:1) 32\55 (1106.6 ¢)
Collapsed (L:s = 1:0) 7\12 (1109.5 ¢)

12L 7s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 12 large steps and 7 small steps, repeating every interval of 3/1 (1902.0 ¢). Generators that produce this scale range from 1101.1 ¢ to 1109.5 ¢, or from 792.5 ¢ to 800.8 ¢.

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 interval regions.

Intervals

Intervals of 12L 7s⟨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 100.1 ¢
Major 1-mosstep M1ms L 100.1 ¢ to 158.5 ¢
2-mosstep Minor 2-mosstep m2ms L + s 158.5 ¢ to 200.2 ¢
Major 2-mosstep M2ms 2L 200.2 ¢ to 317.0 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 158.5 ¢ to 300.3 ¢
Major 3-mosstep M3ms 2L + s 300.3 ¢ to 317.0 ¢
4-mosstep Minor 4-mosstep m4ms 2L + 2s 317.0 ¢ to 400.4 ¢
Major 4-mosstep M4ms 3L + s 400.4 ¢ to 475.5 ¢
5-mosstep Minor 5-mosstep m5ms 3L + 2s 475.5 ¢ to 500.5 ¢
Major 5-mosstep M5ms 4L + s 500.5 ¢ to 634.0 ¢
6-mosstep Minor 6-mosstep m6ms 3L + 3s 475.5 ¢ to 600.6 ¢
Major 6-mosstep M6ms 4L + 2s 600.6 ¢ to 634.0 ¢
7-mosstep Minor 7-mosstep m7ms 4L + 3s 634.0 ¢ to 700.7 ¢
Major 7-mosstep M7ms 5L + 2s 700.7 ¢ to 792.5 ¢
8-mosstep Perfect 8-mosstep P8ms 5L + 3s 792.5 ¢ to 800.8 ¢
Augmented 8-mosstep A8ms 6L + 2s 800.8 ¢ to 951.0 ¢
9-mosstep Minor 9-mosstep m9ms 5L + 4s 792.5 ¢ to 900.9 ¢
Major 9-mosstep M9ms 6L + 3s 900.9 ¢ to 951.0 ¢
10-mosstep Minor 10-mosstep m10ms 6L + 4s 951.0 ¢ to 1001.0 ¢
Major 10-mosstep M10ms 7L + 3s 1001.0 ¢ to 1109.5 ¢
11-mosstep Diminished 11-mosstep d11ms 6L + 5s 951.0 ¢ to 1101.1 ¢
Perfect 11-mosstep P11ms 7L + 4s 1101.1 ¢ to 1109.5 ¢
12-mosstep Minor 12-mosstep m12ms 7L + 5s 1109.5 ¢ to 1201.2 ¢
Major 12-mosstep M12ms 8L + 4s 1201.2 ¢ to 1268.0 ¢
13-mosstep Minor 13-mosstep m13ms 8L + 5s 1268.0 ¢ to 1301.3 ¢
Major 13-mosstep M13ms 9L + 4s 1301.3 ¢ to 1426.5 ¢
14-mosstep Minor 14-mosstep m14ms 8L + 6s 1268.0 ¢ to 1401.4 ¢
Major 14-mosstep M14ms 9L + 5s 1401.4 ¢ to 1426.5 ¢
15-mosstep Minor 15-mosstep m15ms 9L + 6s 1426.5 ¢ to 1501.5 ¢
Major 15-mosstep M15ms 10L + 5s 1501.5 ¢ to 1585.0 ¢
16-mosstep Minor 16-mosstep m16ms 10L + 6s 1585.0 ¢ to 1601.6 ¢
Major 16-mosstep M16ms 11L + 5s 1601.6 ¢ to 1743.5 ¢
17-mosstep Minor 17-mosstep m17ms 10L + 7s 1585.0 ¢ to 1701.7 ¢
Major 17-mosstep M17ms 11L + 6s 1701.7 ¢ to 1743.5 ¢
18-mosstep Minor 18-mosstep m18ms 11L + 7s 1743.5 ¢ to 1801.9 ¢
Major 18-mosstep M18ms 12L + 6s 1801.9 ¢ to 1902.0 ¢
19-mosstep Perfect 19-mosstep P19ms 12L + 7s 1902.0 ¢

Generator chain

Generator chain of 12L 7s⟨3/1⟩
Bright gens Scale degree Abbrev.
30 Augmented 7-mosdegree A7md
29 Augmented 15-mosdegree A15md
28 Augmented 4-mosdegree A4md
27 Augmented 12-mosdegree A12md
26 Augmented 1-mosdegree A1md
25 Augmented 9-mosdegree A9md
24 Augmented 17-mosdegree A17md
23 Augmented 6-mosdegree A6md
22 Augmented 14-mosdegree A14md
21 Augmented 3-mosdegree A3md
20 Augmented 11-mosdegree A11md
19 Augmented 0-mosdegree A0md
18 Augmented 8-mosdegree A8md
17 Major 16-mosdegree M16md
16 Major 5-mosdegree M5md
15 Major 13-mosdegree M13md
14 Major 2-mosdegree M2md
13 Major 10-mosdegree M10md
12 Major 18-mosdegree M18md
11 Major 7-mosdegree M7md
10 Major 15-mosdegree M15md
9 Major 4-mosdegree M4md
8 Major 12-mosdegree M12md
7 Major 1-mosdegree M1md
6 Major 9-mosdegree M9md
5 Major 17-mosdegree M17md
4 Major 6-mosdegree M6md
3 Major 14-mosdegree M14md
2 Major 3-mosdegree M3md
1 Perfect 11-mosdegree P11md
0 Perfect 0-mosdegree
Perfect 19-mosdegree		 P0md
P19md
−1 Perfect 8-mosdegree P8md
−2 Minor 16-mosdegree m16md
−3 Minor 5-mosdegree m5md
−4 Minor 13-mosdegree m13md
−5 Minor 2-mosdegree m2md
−6 Minor 10-mosdegree m10md
−7 Minor 18-mosdegree m18md
−8 Minor 7-mosdegree m7md
−9 Minor 15-mosdegree m15md
−10 Minor 4-mosdegree m4md
−11 Minor 12-mosdegree m12md
−12 Minor 1-mosdegree m1md
−13 Minor 9-mosdegree m9md
−14 Minor 17-mosdegree m17md
−15 Minor 6-mosdegree m6md
−16 Minor 14-mosdegree m14md
−17 Minor 3-mosdegree m3md
−18 Diminished 11-mosdegree d11md
−19 Diminished 19-mosdegree d19md
−20 Diminished 8-mosdegree d8md
−21 Diminished 16-mosdegree d16md
−22 Diminished 5-mosdegree d5md
−23 Diminished 13-mosdegree d13md
−24 Diminished 2-mosdegree d2md
−25 Diminished 10-mosdegree d10md
−26 Diminished 18-mosdegree d18md
−27 Diminished 7-mosdegree d7md
−28 Diminished 15-mosdegree d15md
−29 Diminished 4-mosdegree d4md
−30 Diminished 12-mosdegree d12md

Modes

Scale degrees of the modes of 12L 7s⟨3/1⟩
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
18|0 1 LLsLLsLLsLsLLsLLsLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
17|1 12 LLsLLsLsLLsLLsLLsLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
16|2 4 LLsLLsLsLLsLLsLsLLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Maj. Perf.
15|3 15 LLsLsLLsLLsLLsLsLLs Perf. Maj. Maj. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Maj. Perf.
14|4 7 LLsLsLLsLLsLsLLsLLs Perf. Maj. Maj. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf.
13|5 18 LsLLsLLsLLsLsLLsLLs Perf. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf.
12|6 10 LsLLsLLsLsLLsLLsLLs Perf. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Maj. Min. Perf. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf.
11|7 2 LsLLsLLsLsLLsLLsLsL Perf. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Maj. Min. Perf. Maj. Min. Maj. Maj. Min. Maj. Min. Perf.
10|8 13 LsLLsLsLLsLLsLLsLsL Perf. Maj. Min. Maj. Maj. Min. Maj. Min. Perf. Maj. Min. Perf. Maj. Min. Maj. Maj. Min. Maj. Min. Perf.
9|9 5 LsLLsLsLLsLLsLsLLsL Perf. Maj. Min. Maj. Maj. Min. Maj. Min. Perf. Maj. Min. Perf. Maj. Min. Maj. Min. Min. Maj. Min. Perf.
8|10 16 LsLsLLsLLsLLsLsLLsL Perf. Maj. Min. Maj. Min. Min. Maj. Min. Perf. Maj. Min. Perf. Maj. Min. Maj. Min. Min. Maj. Min. Perf.
7|11 8 LsLsLLsLLsLsLLsLLsL Perf. Maj. Min. Maj. Min. Min. Maj. Min. Perf. Maj. Min. Perf. Min. Min. Maj. Min. Min. Maj. Min. Perf.
6|12 19 sLLsLLsLLsLsLLsLLsL Perf. Min. Min. Maj. Min. Min. Maj. Min. Perf. Maj. Min. Perf. Min. Min. Maj. Min. Min. Maj. Min. Perf.
5|13 11 sLLsLLsLsLLsLLsLLsL Perf. Min. Min. Maj. Min. Min. Maj. Min. Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Maj. Min. Perf.
4|14 3 sLLsLLsLsLLsLLsLsLL Perf. Min. Min. Maj. Min. Min. Maj. Min. Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Min. Min. Perf.
3|15 14 sLLsLsLLsLLsLLsLsLL Perf. Min. Min. Maj. Min. Min. Min. Min. Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Min. Min. Perf.
2|16 6 sLLsLsLLsLLsLsLLsLL Perf. Min. Min. Maj. Min. Min. Min. Min. Perf. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Perf.
1|17 17 sLsLLsLLsLLsLsLLsLL Perf. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Perf.
0|18 9 sLsLLsLLsLsLLsLLsLL Perf. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Dim. Min. Min. Min. Min. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 12L 7s⟨3/1⟩
Generator(edt) Cents Step ratio Comments
Bright Dark L:s Hardness
11\19 1101.132 800.823 1:1 1.000 Equalized 12L 7s⟨3/1⟩
62\107 1102.067 799.888 6:5 1.200
51\88 1102.269 799.686 5:4 1.250
91\157 1102.407 799.548 9:7 1.286
40\69 1102.583 799.372 4:3 1.333 Supersoft 12L 7s⟨3/1⟩
109\188 1102.729 799.226 11:8 1.375
69\119 1102.814 799.141 7:5 1.400
98\169 1102.909 799.046 10:7 1.429
29\50 1103.134 798.821 3:2 1.500 Soft 12L 7s⟨3/1⟩
105\181 1103.344 798.611 11:7 1.571
76\131 1103.424 798.531 8:5 1.600
123\212 1103.493 798.462 13:8 1.625
47\81 1103.604 798.351 5:3 1.667 Semisoft 12L 7s⟨3/1⟩
112\193 1103.725 798.230 12:7 1.714
65\112 1103.813 798.142 7:4 1.750
83\143 1103.932 798.023 9:5 1.800
18\31 1104.361 797.594 2:1 2.000 Basic 12L 7s⟨3/1⟩
Scales with tunings softer than this are proper
79\136 1104.812 797.143 9:4 2.250
61\105 1104.945 797.010 7:3 2.333
104\179 1105.046 796.909 12:5 2.400
43\74 1105.190 796.765 5:2 2.500 Semihard 12L 7s⟨3/1⟩
111\191 1105.325 796.630 13:5 2.600
68\117 1105.410 796.545 8:3 2.667
93\160 1105.511 796.444 11:4 2.750
25\43 1105.788 796.167 3:1 3.000 Hard 12L 7s⟨3/1⟩
82\141 1106.101 795.854 10:3 3.333
57\98 1106.239 795.716 7:2 3.500
89\153 1106.366 795.589 11:3 3.667
32\55 1106.592 795.363 4:1 4.000 Superhard 12L 7s⟨3/1⟩
71\122 1106.875 795.080 9:2 4.500
39\67 1107.108 794.847 5:1 5.000
46\79 1107.467 794.488 6:1 6.000
7\12 1109.474 792.481 1:0 → ∞ Collapsed 12L 7s⟨3/1⟩
Retrieved from "https://en.xen.wiki/index.php?title=User:Francium/12L_7s_(3/1-equivalent)&oldid=197657"