4L 3s (3/1-equivalent): Difference between revisions

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{{MOS intro|Other Names=electric}}
{{MOS intro|Other Names=electric}}
{{todo|improve synopsis}}
== Temperaments ==
== Temperaments ==
4L 3s<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 4L 3s<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.
4L 3s<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 4L 3s<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 ==
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{{todo|inline=1|complete table}}
== Intervals ==
{{MOS intervals}}
== Scales ==
== Scales ==
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[[Category:7-tone scales]]
[[Category:7-tone scales]]
[[Category:Tritave]]
[[Category:Tritave]]

Revision as of 00:17, 16 December 2024

↖ 3L 2s⟨3/1⟩ ↑ 4L 2s⟨3/1⟩ 5L 2s⟨3/1⟩ ↗
← 3L 3s⟨3/1⟩ 4L 3s (3/1-equivalent) 5L 3s⟨3/1⟩ →
↙ 3L 4s⟨3/1⟩ ↓ 4L 4s⟨3/1⟩ 5L 4s⟨3/1⟩ ↘
Scale structure
Step pattern LLsLsLs
sLsLsLL
Equave 3/1 (1902.0 ¢)
Period 3/1 (1902.0 ¢)
Generator size(edt)
Bright 5\7 to 3\4 (1358.5 ¢ to 1426.5 ¢)
Dark 1\4 to 2\7 (475.5 ¢ to 543.4 ¢)
Related MOS scales
Parent 3L 1s⟨3/1⟩
Sister 3L 4s⟨3/1⟩
Daughters 7L 4s⟨3/1⟩, 4L 7s⟨3/1⟩
Neutralized 1L 6s⟨3/1⟩
2-Flought 11L 3s⟨3/1⟩, 4L 10s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1) 5\7 (1358.5 ¢)
Supersoft (L:s = 4:3) 18\25 (1369.4 ¢)
Soft (L:s = 3:2) 13\18 (1373.6 ¢)
Semisoft (L:s = 5:3) 21\29 (1377.3 ¢)
Basic (L:s = 2:1) 8\11 (1383.2 ¢)
Semihard (L:s = 5:2) 19\26 (1389.9 ¢)
Hard (L:s = 3:1) 11\15 (1394.8 ¢)
Superhard (L:s = 4:1) 14\19 (1401.4 ¢)
Collapsed (L:s = 1:0) 3\4 (1426.5 ¢)
View • Talk • Edit

4L 3s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 4 large steps and 3 small steps, repeating every interval of 3/1 (1902.0 ¢). Generators that produce this scale range from 1358.5 ¢ to 1426.5 ¢, or from 475.5 ¢ to 543.4 ¢.

Temperaments

4L 3s<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 4L 3s<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

Mode UDP Name
LLsLsLs 6|0
LsLLsLs 5|1
LsLsLLs 4|2
LsLsLsL 3|3
sLLsLsL 2|4
sLsLLsL 1|5
sLsLsLL 0|6
Todo: complete table

Intervals

Intervals of 4L 3s⟨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 271.7 ¢
Major 1-mosstep M1ms L 271.7 ¢ to 475.5 ¢
2-mosstep Perfect 2-mosstep P2ms L + s 475.5 ¢ to 543.4 ¢
Augmented 2-mosstep A2ms 2L 543.4 ¢ to 951.0 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 475.5 ¢ to 815.1 ¢
Major 3-mosstep M3ms 2L + s 815.1 ¢ to 951.0 ¢
4-mosstep Minor 4-mosstep m4ms 2L + 2s 951.0 ¢ to 1086.8 ¢
Major 4-mosstep M4ms 3L + s 1086.8 ¢ to 1426.5 ¢
5-mosstep Diminished 5-mosstep d5ms 2L + 3s 951.0 ¢ to 1358.5 ¢
Perfect 5-mosstep P5ms 3L + 2s 1358.5 ¢ to 1426.5 ¢
6-mosstep Minor 6-mosstep m6ms 3L + 3s 1426.5 ¢ to 1630.2 ¢
Major 6-mosstep M6ms 4L + 2s 1630.2 ¢ to 1902.0 ¢
7-mosstep Perfect 7-mosstep P7ms 4L + 3s 1902.0 ¢

Scales

Generator (chroma-positive) Cents (chroma-positive) Cents (chroma-negative) L s L/s Comments
5\7edt 1358.539 543.416 1 1 1.0000
23\32edt 1367.03 534.925 5 4 1.2500
18\25edt 1369.41 532.55 4 3 1.3333 Electra is in this region
13\18edt 1373.634 528.321 3 2 1.5000
21\29edt 1377.2778 524.6772 5 3 1.6667
8\11edt 1383.2 518.7 2 1 2.0000 Basic electric (generators smaller than this are proper)
19\26edt 1389.9 512.1 5 2 2.5000
11\15edt 1394.767 507.188 3 1 3.0000
14\19edt 1401.441 500.514 4 1 4.0000
17\23edt 1405.7928 496.1622 5 1 5.0000
3\4edt 1426.4663 475.4888 1 0 -> inf
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