User:Francium/6L 13s (3/1-equivalent)

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Revision as of 15:09, 13 May 2025 by Francium (talk | contribs) (Created page with "{{Infobox MOS|Tuning=6L 13s<3>}} {{MOS intro|Scale Signature=6L 13s<3>}} == Scale properties == {{TAMNAMS use|Scale Signature=6L 13s<3>}} === Intervals === {{MOS intervals|Scale Signature=6L 13s<3>}} === Generator chain === {{MOS genchain|Scale Signature=6L 13s<3>}} === Modes === {{MOS mode degrees|Scale Signature=6L 13s<3>}} == Scale tree == {{MOS tuning spectrum|Scale Signature=6L 13s<3>}}")
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↖ 5L 12s⟨3/1⟩ ↑ 6L 12s⟨3/1⟩ 7L 12s⟨3/1⟩ ↗
← 5L 13s⟨3/1⟩ 6L 13s (3/1-equivalent) 7L 13s⟨3/1⟩ →
↙ 5L 14s⟨3/1⟩ ↓ 6L 14s⟨3/1⟩ 7L 14s⟨3/1⟩ ↘
Scale structure
Step pattern LssLssLssLssLssLsss
sssLssLssLssLssLssL
Equave 3/1 (1902.0 ¢)
Period 3/1 (1902.0 ¢)
Generator size(edt)
Bright 3\19 to 1\6 (300.3 ¢ to 317.0 ¢)
Dark 5\6 to 16\19 (1585.0 ¢ to 1601.6 ¢)
Related MOS scales
Parent 6L 7s⟨3/1⟩
Sister 13L 6s⟨3/1⟩
Daughters 19L 6s⟨3/1⟩, 6L 19s⟨3/1⟩
Neutralized 12L 7s⟨3/1⟩
2-Flought 25L 13s⟨3/1⟩, 6L 32s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1) 3\19 (300.3 ¢)
Supersoft (L:s = 4:3) 10\63 (301.9 ¢)
Soft (L:s = 3:2) 7\44 (302.6 ¢)
Semisoft (L:s = 5:3) 11\69 (303.2 ¢)
Basic (L:s = 2:1) 4\25 (304.3 ¢)
Semihard (L:s = 5:2) 9\56 (305.7 ¢)
Hard (L:s = 3:1) 5\31 (306.8 ¢)
Superhard (L:s = 4:1) 6\37 (308.4 ¢)
Collapsed (L:s = 1:0) 1\6 (317.0 ¢)
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6L 13s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 6 large steps and 13 small steps, repeating every interval of 3/1 (1902.0 ¢). Generators that produce this scale range from 300.3 ¢ to 317 ¢, or from 1585 ¢ to 1601.6 ¢.

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 6L 13s⟨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 317.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 200.2 ¢
Major 2-mosstep M2ms L + s 200.2 ¢ to 317.0 ¢
3-mosstep Diminished 3-mosstep d3ms 3s 0.0 ¢ to 300.3 ¢
Perfect 3-mosstep P3ms L + 2s 300.3 ¢ to 317.0 ¢
4-mosstep Minor 4-mosstep m4ms L + 3s 317.0 ¢ to 400.4 ¢
Major 4-mosstep M4ms 2L + 2s 400.4 ¢ to 634.0 ¢
5-mosstep Minor 5-mosstep m5ms L + 4s 317.0 ¢ to 500.5 ¢
Major 5-mosstep M5ms 2L + 3s 500.5 ¢ to 634.0 ¢
6-mosstep Minor 6-mosstep m6ms L + 5s 317.0 ¢ to 600.6 ¢
Major 6-mosstep M6ms 2L + 4s 600.6 ¢ to 634.0 ¢
7-mosstep Minor 7-mosstep m7ms 2L + 5s 634.0 ¢ to 700.7 ¢
Major 7-mosstep M7ms 3L + 4s 700.7 ¢ to 951.0 ¢
8-mosstep Minor 8-mosstep m8ms 2L + 6s 634.0 ¢ to 800.8 ¢
Major 8-mosstep M8ms 3L + 5s 800.8 ¢ to 951.0 ¢
9-mosstep Minor 9-mosstep m9ms 2L + 7s 634.0 ¢ to 900.9 ¢
Major 9-mosstep M9ms 3L + 6s 900.9 ¢ to 951.0 ¢
10-mosstep Minor 10-mosstep m10ms 3L + 7s 951.0 ¢ to 1001.0 ¢
Major 10-mosstep M10ms 4L + 6s 1001.0 ¢ to 1268.0 ¢
11-mosstep Minor 11-mosstep m11ms 3L + 8s 951.0 ¢ to 1101.1 ¢
Major 11-mosstep M11ms 4L + 7s 1101.1 ¢ to 1268.0 ¢
12-mosstep Minor 12-mosstep m12ms 3L + 9s 951.0 ¢ to 1201.2 ¢
Major 12-mosstep M12ms 4L + 8s 1201.2 ¢ to 1268.0 ¢
13-mosstep Minor 13-mosstep m13ms 4L + 9s 1268.0 ¢ to 1301.3 ¢
Major 13-mosstep M13ms 5L + 8s 1301.3 ¢ to 1585.0 ¢
14-mosstep Minor 14-mosstep m14ms 4L + 10s 1268.0 ¢ to 1401.4 ¢
Major 14-mosstep M14ms 5L + 9s 1401.4 ¢ to 1585.0 ¢
15-mosstep Minor 15-mosstep m15ms 4L + 11s 1268.0 ¢ to 1501.5 ¢
Major 15-mosstep M15ms 5L + 10s 1501.5 ¢ to 1585.0 ¢
16-mosstep Perfect 16-mosstep P16ms 5L + 11s 1585.0 ¢ to 1601.6 ¢
Augmented 16-mosstep A16ms 6L + 10s 1601.6 ¢ to 1902.0 ¢
17-mosstep Minor 17-mosstep m17ms 5L + 12s 1585.0 ¢ to 1701.7 ¢
Major 17-mosstep M17ms 6L + 11s 1701.7 ¢ to 1902.0 ¢
18-mosstep Minor 18-mosstep m18ms 5L + 13s 1585.0 ¢ to 1801.9 ¢
Major 18-mosstep M18ms 6L + 12s 1801.9 ¢ to 1902.0 ¢
19-mosstep Perfect 19-mosstep P19ms 6L + 13s 1902.0 ¢

Generator chain

Generator chain of 6L 13s⟨3/1⟩
Bright gens Scale degree Abbrev.
24 Augmented 15-mosdegree A15md
23 Augmented 12-mosdegree A12md
22 Augmented 9-mosdegree A9md
21 Augmented 6-mosdegree A6md
20 Augmented 3-mosdegree A3md
19 Augmented 0-mosdegree A0md
18 Augmented 16-mosdegree A16md
17 Major 13-mosdegree M13md
16 Major 10-mosdegree M10md
15 Major 7-mosdegree M7md
14 Major 4-mosdegree M4md
13 Major 1-mosdegree M1md
12 Major 17-mosdegree M17md
11 Major 14-mosdegree M14md
10 Major 11-mosdegree M11md
9 Major 8-mosdegree M8md
8 Major 5-mosdegree M5md
7 Major 2-mosdegree M2md
6 Major 18-mosdegree M18md
5 Major 15-mosdegree M15md
4 Major 12-mosdegree M12md
3 Major 9-mosdegree M9md
2 Major 6-mosdegree M6md
1 Perfect 3-mosdegree P3md
0 Perfect 0-mosdegree
Perfect 19-mosdegree		 P0md
P19md
−1 Perfect 16-mosdegree P16md
−2 Minor 13-mosdegree m13md
−3 Minor 10-mosdegree m10md
−4 Minor 7-mosdegree m7md
−5 Minor 4-mosdegree m4md
−6 Minor 1-mosdegree m1md
−7 Minor 17-mosdegree m17md
−8 Minor 14-mosdegree m14md
−9 Minor 11-mosdegree m11md
−10 Minor 8-mosdegree m8md
−11 Minor 5-mosdegree m5md
−12 Minor 2-mosdegree m2md
−13 Minor 18-mosdegree m18md
−14 Minor 15-mosdegree m15md
−15 Minor 12-mosdegree m12md
−16 Minor 9-mosdegree m9md
−17 Minor 6-mosdegree m6md
−18 Diminished 3-mosdegree d3md
−19 Diminished 19-mosdegree d19md
−20 Diminished 16-mosdegree d16md
−21 Diminished 13-mosdegree d13md
−22 Diminished 10-mosdegree d10md
−23 Diminished 7-mosdegree d7md
−24 Diminished 4-mosdegree d4md

Modes

Scale degrees of the modes of 6L 13s⟨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 LssLssLssLssLssLsss Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Maj. Perf.
17|1 4 LssLssLssLssLsssLss Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf.
16|2 7 LssLssLssLsssLssLss Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf.
15|3 10 LssLssLsssLssLssLss Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf.
14|4 13 LssLsssLssLssLssLss Perf. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf.
13|5 16 LsssLssLssLssLssLss Perf. Maj. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf.
12|6 19 sLssLssLssLssLssLss Perf. Min. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf.
11|7 3 sLssLssLssLssLsssLs Perf. Min. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Min. Maj. Perf.
10|8 6 sLssLssLssLsssLssLs Perf. Min. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Min. Maj. Perf. Min. Maj. Perf.
9|9 9 sLssLssLsssLssLssLs Perf. Min. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Min. Min. Maj. Min. Min. Maj. Perf. Min. Maj. Perf.
8|10 12 sLssLsssLssLssLssLs Perf. Min. Maj. Perf. Min. Maj. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Perf. Min. Maj. Perf.
7|11 15 sLsssLssLssLssLssLs Perf. Min. Maj. Perf. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Perf. Min. Maj. Perf.
6|12 18 ssLssLssLssLssLssLs Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Perf. Min. Maj. Perf.
5|13 2 ssLssLssLssLssLsssL Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Perf. Min. Min. Perf.
4|14 5 ssLssLssLssLsssLssL Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Perf.
3|15 8 ssLssLssLsssLssLssL Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Maj. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf.
2|16 11 ssLssLsssLssLssLssL Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf.
1|17 14 ssLsssLssLssLssLssL Perf. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf.
0|18 17 sssLssLssLssLssLssL Perf. Min. Min. Dim. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 6L 13s⟨3/1⟩
Generator(edt) Cents Step ratio Comments
Bright Dark L:s Hardness
3\19 300.309 1601.646 1:1 1.000 Equalized 6L 13s⟨3/1⟩
16\101 301.300 1600.655 6:5 1.200
13\82 301.529 1600.426 5:4 1.250
23\145 301.689 1600.266 9:7 1.286
10\63 301.898 1600.057 4:3 1.333 Supersoft 6L 13s⟨3/1⟩
27\170 302.075 1599.880 11:8 1.375
17\107 302.180 1599.775 7:5 1.400
24\151 302.297 1599.658 10:7 1.429
7\44 302.584 1599.371 3:2 1.500 Soft 6L 13s⟨3/1⟩
25\157 302.859 1599.096 11:7 1.571
18\113 302.966 1598.989 8:5 1.600
29\182 303.059 1598.896 13:8 1.625
11\69 303.210 1598.745 5:3 1.667 Semisoft 6L 13s⟨3/1⟩
26\163 303.379 1598.576 12:7 1.714
15\94 303.503 1598.452 7:4 1.750
19\119 303.673 1598.282 9:5 1.800
4\25 304.313 1597.642 2:1 2.000 Basic 6L 13s⟨3/1⟩
Scales with tunings softer than this are proper
17\106 305.031 1596.924 9:4 2.250
13\81 305.252 1596.703 7:3 2.333
22\137 305.423 1596.532 12:5 2.400
9\56 305.671 1596.284 5:2 2.500 Semihard 6L 13s⟨3/1⟩
23\143 305.909 1596.046 13:5 2.600
14\87 306.062 1595.893 8:3 2.667
19\118 306.247 1595.708 11:4 2.750
5\31 306.767 1595.188 3:1 3.000 Hard 6L 13s⟨3/1⟩
16\99 307.387 1594.568 10:3 3.333
11\68 307.669 1594.286 7:2 3.500
17\105 307.936 1594.019 11:3 3.667
6\37 308.425 1593.530 4:1 4.000 Superhard 6L 13s⟨3/1⟩
13\80 309.068 1592.887 9:2 4.500
7\43 309.621 1592.334 5:1 5.000
8\49 310.523 1591.432 6:1 6.000
1\6 316.993 1584.963 1:0 → ∞ Collapsed 6L 13s⟨3/1⟩
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