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

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'''4L 3s<3/1>''' (or '''electric''') refers to a [[tritave]]-repeating [[MOS]] scale with four large steps and three small steps. It is generated by any interval between 1\4edt and 2\7edt.  
'''4L 3s<3/1>''' (or '''electric''') refers to a [[tritave]]-repeating [[MOS]] scale with four large steps and three small steps. It is generated by any interval between 1\4edt and 2\7edt.  
== 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.
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 ==
{| class="wikitable"
{| class="wikitable"
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| 21\[[29edt]]
| 21\[[29edt]]
| 1377.2778
| 1377.2778
| 524.6772
| [[Tel:524.6772|524.6772]]
| 5
| 5
| 3
| 3
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| 17\[[23edt]]
| 17\[[23edt]]
| 1405.7928
| 1405.7928
| 496.1622
| [[Tel:496.1622|496.1622]]
| 5
| 5
| 1
| 1
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| 3\[[4edt]]
| 3\[[4edt]]
| 1426.4663
| 1426.4663
| 475.4888
| [[Tel:475.4888|475.4888]]
| 1
| 1
| 0
| 0

Revision as of 04:04, 5 March 2023

↖ 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 ¢)
ViewTalkEdit

4L 3s<3/1> (or electric) refers to a tritave-repeating MOS scale with four large steps and three small steps. It is generated by any interval between 1\4edt and 2\7edt.

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

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 [[1]] 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 [[2]] 5 1 5.0000
3\4edt 1426.4663 [[3]] 1 0 -> inf