383edo: Difference between revisions
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{{Infobox ET}} | |||
{{ED intro}} | |||
== Theory == | == Theory == | ||
383edo is | 383edo is [[consistency|distinctly consistent]] through the [[15-odd-limit]] with a flat tendency. As an equal temperament, it [[tempering out|tempers out]] 32805/32768 ([[schisma]]) in the [[5-limit]]; [[2401/2400]] in the [[7-limit]]; [[3025/3024]], [[4000/3993]] and [[6250/6237]] in the [[11-limit]]; and [[625/624]], [[1575/1573]] and [[2080/2079]] in the [[13-limit]]. It provides the [[optimal patent val]] for the [[countertertiaschis]] temperament, and a good tuning for [[sesquiquartififths]] in the higher limits. | ||
=== Prime harmonics === | |||
{{Harmonics in equal|383}} | |||
=== Subsets and supersets === | |||
383edo is the 76th [[prime edo]]. | 383edo is the 76th [[prime edo]]. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
! rowspan="2" | Subgroup | |- | ||
! rowspan="2" | [[Subgroup]] | |||
! rowspan="2" | [[Comma list]] | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br>8ve stretch (¢) | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
! colspan="2" | Tuning error | ! colspan="2" | Tuning error | ||
|- | |- | ||
| Line 22: | Line 25: | ||
| 2.3 | | 2.3 | ||
| {{monzo| -607 383 }} | | {{monzo| -607 383 }} | ||
| | | {{mapping| 383 607 }} | ||
| +0.0402 | | +0.0402 | ||
| 0.0402 | | 0.0402 | ||
| Line 29: | Line 32: | ||
| 2.3.5 | | 2.3.5 | ||
| 32805/32768, {{monzo| -8 -55 41}} | | 32805/32768, {{monzo| -8 -55 41}} | ||
| | | {{mapping| 383 607 889 }} | ||
| +0.1610 | | +0.1610 | ||
| 0.1741 | | 0.1741 | ||
| Line 36: | Line 39: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 2401/2400, 32805/32768, 68359375/68024448 | | 2401/2400, 32805/32768, 68359375/68024448 | ||
| | | {{mapping| 383 607 889 1075 }} | ||
| +0.1813 | | +0.1813 | ||
| 0.1548 | | 0.1548 | ||
| Line 43: | Line 46: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 2401/2400, 3025/3024, 4000/3993, 32805/32768 | | 2401/2400, 3025/3024, 4000/3993, 32805/32768 | ||
| | | {{mapping| 383 607 889 1075 1325 }} | ||
| +0.1382 | | +0.1382 | ||
| 0.1631 | | 0.1631 | ||
| Line 50: | Line 53: | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 625/624, 1575/1573, 2080/2079, 2401/2400, 10985/10976 | | 625/624, 1575/1573, 2080/2079, 2401/2400, 10985/10976 | ||
| | | {{mapping| 383 607 889 1075 1325 1417 }} | ||
| +0.1531 | | +0.1531 | ||
| 0.1525 | | 0.1525 | ||
| Line 58: | Line 61: | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
|+Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
! Periods<br>per | |- | ||
! Generator | ! Periods<br />per 8ve | ||
! Cents | ! Generator* | ||
! Associated<br>ratio | ! Cents* | ||
! Associated<br />ratio* | |||
! Temperaments | ! Temperaments | ||
|- | |||
| 1 | |||
| 53\383 | |||
| 166.06 | |||
| 11/10 | |||
| [[Countertertiaschis]] | |||
|- | |- | ||
| 1 | | 1 | ||
| Line 72: | Line 82: | ||
|- | |- | ||
| 1 | | 1 | ||
| 133\ | | 133\383 | ||
| 416.71 | | 416.71 | ||
| 14/11 | | 14/11 | ||
| Line 81: | Line 91: | ||
| 498.17 | | 498.17 | ||
| 4/3 | | 4/3 | ||
| [[Helmholtz]] | | [[Helmholtz (temperament)|Helmholtz]] | ||
|} | |} | ||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | |||
== Music == | |||
; [[Francium]] | |||
* "Mark A Player" from ''I Want To'' (2025) – [https://open.spotify.com/track/1M3LmqPfXRjpxuuTRgEufN Spotify] | [https://francium223.bandcamp.com/track/mark-a-player Bandcamp] | [https://www.youtube.com/watch?v=ePR_S5cNZvI YouTube] – in Marconic, 383edo tuning | |||
[[Category: | [[Category:Countertertiaschis]] | ||