User:Francium/8L 9s (3/1-equivalent)

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Revision as of 05:02, 15 May 2025 by Francium (talk | contribs) (Created page with "{{Infobox MOS|Tuning=8L 9s<3>}} {{MOS intro|Scale Signature=8L 9s<3>}} == Scale properties == {{TAMNAMS use|Scale Signature=8L 9s<3>}} === Intervals === {{MOS intervals|Scale Signature=8L 9s<3>}} === Generator chain === {{MOS genchain|Scale Signature=8L 9s<3>}} === Modes === {{MOS mode degrees|Scale Signature=8L 9s<3>}} == Scale tree == {{MOS tuning spectrum|Scale Signature=8L 9s<3>}}")
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↖ 7L 8s⟨3/1⟩ ↑ 8L 8s⟨3/1⟩ 9L 8s⟨3/1⟩ ↗
← 7L 9s⟨3/1⟩ 8L 9s (3/1-equivalent) 9L 9s⟨3/1⟩ →
↙ 7L 10s⟨3/1⟩ ↓ 8L 10s⟨3/1⟩ 9L 10s⟨3/1⟩ ↘
Scale structure
Step pattern LsLsLsLsLsLsLsLss
ssLsLsLsLsLsLsLsL
Equave 3/1 (1902.0 ¢)
Period 3/1 (1902.0 ¢)
Generator size(edt)
Bright 2\17 to 1\8 (223.8 ¢ to 237.7 ¢)
Dark 7\8 to 15\17 (1664.2 ¢ to 1678.2 ¢)
Related MOS scales
Parent 8L 1s⟨3/1⟩
Sister 9L 8s⟨3/1⟩
Daughters 17L 8s⟨3/1⟩, 8L 17s⟨3/1⟩
Neutralized 16L 1s⟨3/1⟩
2-Flought 25L 9s⟨3/1⟩, 8L 26s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1) 2\17 (223.8 ¢)
Supersoft (L:s = 4:3) 7\59 (225.7 ¢)
Soft (L:s = 3:2) 5\42 (226.4 ¢)
Semisoft (L:s = 5:3) 8\67 (227.1 ¢)
Basic (L:s = 2:1) 3\25 (228.2 ¢)
Semihard (L:s = 5:2) 7\58 (229.5 ¢)
Hard (L:s = 3:1) 4\33 (230.5 ¢)
Superhard (L:s = 4:1) 5\41 (231.9 ¢)
Collapsed (L:s = 1:0) 1\8 (237.7 ¢)
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8L 9s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 8 large steps and 9 small steps, repeating every interval of 3/1 (1902.0 ¢). Generators that produce this scale range from 223.8 ¢ to 237.7 ¢, or from 1664.2 ¢ to 1678.2 ¢.

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 8L 9s⟨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 111.9 ¢
Major 1-mosstep M1ms L 111.9 ¢ to 237.7 ¢
2-mosstep Diminished 2-mosstep d2ms 2s 0.0 ¢ to 223.8 ¢
Perfect 2-mosstep P2ms L + s 223.8 ¢ to 237.7 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 237.7 ¢ to 335.6 ¢
Major 3-mosstep M3ms 2L + s 335.6 ¢ to 475.5 ¢
4-mosstep Minor 4-mosstep m4ms L + 3s 237.7 ¢ to 447.5 ¢
Major 4-mosstep M4ms 2L + 2s 447.5 ¢ to 475.5 ¢
5-mosstep Minor 5-mosstep m5ms 2L + 3s 475.5 ¢ to 559.4 ¢
Major 5-mosstep M5ms 3L + 2s 559.4 ¢ to 713.2 ¢
6-mosstep Minor 6-mosstep m6ms 2L + 4s 475.5 ¢ to 671.3 ¢
Major 6-mosstep M6ms 3L + 3s 671.3 ¢ to 713.2 ¢
7-mosstep Minor 7-mosstep m7ms 3L + 4s 713.2 ¢ to 783.2 ¢
Major 7-mosstep M7ms 4L + 3s 783.2 ¢ to 951.0 ¢
8-mosstep Minor 8-mosstep m8ms 3L + 5s 713.2 ¢ to 895.0 ¢
Major 8-mosstep M8ms 4L + 4s 895.0 ¢ to 951.0 ¢
9-mosstep Minor 9-mosstep m9ms 4L + 5s 951.0 ¢ to 1006.9 ¢
Major 9-mosstep M9ms 5L + 4s 1006.9 ¢ to 1188.7 ¢
10-mosstep Minor 10-mosstep m10ms 4L + 6s 951.0 ¢ to 1118.8 ¢
Major 10-mosstep M10ms 5L + 5s 1118.8 ¢ to 1188.7 ¢
11-mosstep Minor 11-mosstep m11ms 5L + 6s 1188.7 ¢ to 1230.7 ¢
Major 11-mosstep M11ms 6L + 5s 1230.7 ¢ to 1426.5 ¢
12-mosstep Minor 12-mosstep m12ms 5L + 7s 1188.7 ¢ to 1342.6 ¢
Major 12-mosstep M12ms 6L + 6s 1342.6 ¢ to 1426.5 ¢
13-mosstep Minor 13-mosstep m13ms 6L + 7s 1426.5 ¢ to 1454.4 ¢
Major 13-mosstep M13ms 7L + 6s 1454.4 ¢ to 1664.2 ¢
14-mosstep Minor 14-mosstep m14ms 6L + 8s 1426.5 ¢ to 1566.3 ¢
Major 14-mosstep M14ms 7L + 7s 1566.3 ¢ to 1664.2 ¢
15-mosstep Perfect 15-mosstep P15ms 7L + 8s 1664.2 ¢ to 1678.2 ¢
Augmented 15-mosstep A15ms 8L + 7s 1678.2 ¢ to 1902.0 ¢
16-mosstep Minor 16-mosstep m16ms 7L + 9s 1664.2 ¢ to 1790.1 ¢
Major 16-mosstep M16ms 8L + 8s 1790.1 ¢ to 1902.0 ¢
17-mosstep Perfect 17-mosstep P17ms 8L + 9s 1902.0 ¢

Generator chain

Generator chain of 8L 9s⟨3/1⟩
Bright gens Scale degree Abbrev.
24 Augmented 14-mosdegree A14md
23 Augmented 12-mosdegree A12md
22 Augmented 10-mosdegree A10md
21 Augmented 8-mosdegree A8md
20 Augmented 6-mosdegree A6md
19 Augmented 4-mosdegree A4md
18 Augmented 2-mosdegree A2md
17 Augmented 0-mosdegree A0md
16 Augmented 15-mosdegree A15md
15 Major 13-mosdegree M13md
14 Major 11-mosdegree M11md
13 Major 9-mosdegree M9md
12 Major 7-mosdegree M7md
11 Major 5-mosdegree M5md
10 Major 3-mosdegree M3md
9 Major 1-mosdegree M1md
8 Major 16-mosdegree M16md
7 Major 14-mosdegree M14md
6 Major 12-mosdegree M12md
5 Major 10-mosdegree M10md
4 Major 8-mosdegree M8md
3 Major 6-mosdegree M6md
2 Major 4-mosdegree M4md
1 Perfect 2-mosdegree P2md
0 Perfect 0-mosdegree
Perfect 17-mosdegree		 P0md
P17md
−1 Perfect 15-mosdegree P15md
−2 Minor 13-mosdegree m13md
−3 Minor 11-mosdegree m11md
−4 Minor 9-mosdegree m9md
−5 Minor 7-mosdegree m7md
−6 Minor 5-mosdegree m5md
−7 Minor 3-mosdegree m3md
−8 Minor 1-mosdegree m1md
−9 Minor 16-mosdegree m16md
−10 Minor 14-mosdegree m14md
−11 Minor 12-mosdegree m12md
−12 Minor 10-mosdegree m10md
−13 Minor 8-mosdegree m8md
−14 Minor 6-mosdegree m6md
−15 Minor 4-mosdegree m4md
−16 Diminished 2-mosdegree d2md
−17 Diminished 17-mosdegree d17md
−18 Diminished 15-mosdegree d15md
−19 Diminished 13-mosdegree d13md
−20 Diminished 11-mosdegree d11md
−21 Diminished 9-mosdegree d9md
−22 Diminished 7-mosdegree d7md
−23 Diminished 5-mosdegree d5md
−24 Diminished 3-mosdegree d3md

Modes

Scale degrees of the modes of 8L 9s⟨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
16|0 1 LsLsLsLsLsLsLsLss Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Perf.
15|1 3 LsLsLsLsLsLsLssLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
14|2 5 LsLsLsLsLsLssLsLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Perf. Maj. Perf.
13|3 7 LsLsLsLsLssLsLsLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf.
12|4 9 LsLsLsLssLsLsLsLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf.
11|5 11 LsLsLssLsLsLsLsLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf.
10|6 13 LsLssLsLsLsLsLsLs Perf. Maj. Perf. Maj. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf.
9|7 15 LssLsLsLsLsLsLsLs Perf. Maj. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf.
8|8 17 sLsLsLsLsLsLsLsLs Perf. Min. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf.
7|9 2 sLsLsLsLsLsLsLssL Perf. Min. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Min. Perf.
6|10 4 sLsLsLsLsLsLssLsL Perf. Min. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Min. Perf. Min. Perf.
5|11 6 sLsLsLsLsLssLsLsL Perf. Min. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Min. Min. Min. Perf. Min. Perf.
4|12 8 sLsLsLsLssLsLsLsL Perf. Min. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Min. Min. Min. Min. Min. Perf. Min. Perf.
3|13 10 sLsLsLssLsLsLsLsL Perf. Min. Perf. Min. Maj. Min. Maj. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Perf.
2|14 12 sLsLssLsLsLsLsLsL Perf. Min. Perf. Min. Maj. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Perf.
1|15 14 sLssLsLsLsLsLsLsL Perf. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Perf.
0|16 16 ssLsLsLsLsLsLsLsL Perf. Min. Dim. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 8L 9s⟨3/1⟩
Generator(edt) Cents Step ratio Comments
Bright Dark L:s Hardness
2\17 223.759 1678.196 1:1 1.000 Equalized 8L 9s⟨3/1⟩
11\93 224.962 1676.993 6:5 1.200
9\76 225.232 1676.723 5:4 1.250
16\135 225.417 1676.538 9:7 1.286
7\59 225.656 1676.299 4:3 1.333 Supersoft 8L 9s⟨3/1⟩
19\160 225.857 1676.098 11:8 1.375
12\101 225.975 1675.980 7:5 1.400
17\143 226.107 1675.848 10:7 1.429
5\42 226.423 1675.532 3:2 1.500 Soft 8L 9s⟨3/1⟩
18\151 226.723 1675.232 11:7 1.571
13\109 226.839 1675.116 8:5 1.600
21\176 226.938 1675.017 13:8 1.625
8\67 227.099 1674.856 5:3 1.667 Semisoft 8L 9s⟨3/1⟩
19\159 227.278 1674.677 12:7 1.714
11\92 227.408 1674.547 7:4 1.750
14\117 227.584 1674.371 9:5 1.800
3\25 228.235 1673.720 2:1 2.000 Basic 8L 9s⟨3/1⟩
Scales with tunings softer than this are proper
13\108 228.939 1673.016 9:4 2.250
10\83 229.151 1672.804 7:3 2.333
17\141 229.314 1672.641 12:5 2.400
7\58 229.546 1672.409 5:2 2.500 Semihard 8L 9s⟨3/1⟩
18\149 229.766 1672.189 13:5 2.600
11\91 229.907 1672.048 8:3 2.667
15\124 230.075 1671.880 11:4 2.750
4\33 230.540 1671.415 3:1 3.000 Hard 8L 9s⟨3/1⟩
13\107 231.079 1670.876 10:3 3.333
9\74 231.319 1670.636 7:2 3.500
14\115 231.542 1670.413 11:3 3.667
5\41 231.946 1670.009 4:1 4.000 Superhard 8L 9s⟨3/1⟩
11\90 232.461 1669.494 9:2 4.500
6\49 232.892 1669.063 5:1 5.000
7\57 233.573 1668.382 6:1 6.000
1\8 237.744 1664.211 1:0 → ∞ Collapsed 8L 9s⟨3/1⟩
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