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" | ||
| Line 89: | Line 89: | ||
| 21\[[29edt]] | | 21\[[29edt]] | ||
| 1377.2778 | | 1377.2778 | ||
| 524.6772 | | [[Tel:524.6772|524.6772]] | ||
| 5 | | 5 | ||
| 3 | | 3 | ||
| Line 129: | Line 129: | ||
| 17\[[23edt]] | | 17\[[23edt]] | ||
| 1405.7928 | | 1405.7928 | ||
| 496.1622 | | [[Tel:496.1622|496.1622]] | ||
| 5 | | 5 | ||
| 1 | | 1 | ||
| Line 137: | Line 137: | ||
| 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
sLsLsLL
Generator size(edt)
Related MOS scales
Equal tunings(edt)
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 |