383edo: Difference between revisions
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{{Infobox ET}} | |||
{{ED intro}} | |||
== Theory == | |||
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 === | ||
[[Category: | {{Harmonics in equal|383}} | ||
=== Subsets and supersets === | |||
383edo is the 76th [[prime edo]]. | |||
== Regular temperament properties == | |||
{| class="wikitable center-4 center-5 center-6" | |||
|- | |||
! rowspan="2" | [[Subgroup]] | |||
! rowspan="2" | [[Comma list]] | |||
! rowspan="2" | [[Mapping]] | |||
! rowspan="2" | Optimal<br />8ve stretch (¢) | |||
! colspan="2" | Tuning error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |||
| 2.3 | |||
| {{monzo| -607 383 }} | |||
| {{mapping| 383 607 }} | |||
| +0.0402 | |||
| 0.0402 | |||
| 1.28 | |||
|- | |||
| 2.3.5 | |||
| 32805/32768, {{monzo| -8 -55 41}} | |||
| {{mapping| 383 607 889 }} | |||
| +0.1610 | |||
| 0.1741 | |||
| 5.55 | |||
|- | |||
| 2.3.5.7 | |||
| 2401/2400, 32805/32768, 68359375/68024448 | |||
| {{mapping| 383 607 889 1075 }} | |||
| +0.1813 | |||
| 0.1548 | |||
| 4.94 | |||
|- | |||
| 2.3.5.7.11 | |||
| 2401/2400, 3025/3024, 4000/3993, 32805/32768 | |||
| {{mapping| 383 607 889 1075 1325 }} | |||
| +0.1382 | |||
| 0.1631 | |||
| 5.20 | |||
|- | |||
| 2.3.5.7.11.13 | |||
| 625/624, 1575/1573, 2080/2079, 2401/2400, 10985/10976 | |||
| {{mapping| 383 607 889 1075 1325 1417 }} | |||
| +0.1531 | |||
| 0.1525 | |||
| 4.87 | |||
|} | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |||
|- | |||
! Periods<br />per 8ve | |||
! Generator* | |||
! Cents* | |||
! Associated<br />ratio* | |||
! Temperaments | |||
|- | |||
| 1 | |||
| 53\383 | |||
| 166.06 | |||
| 11/10 | |||
| [[Countertertiaschis]] | |||
|- | |||
| 1 | |||
| 56\383 | |||
| 175.46 | |||
| 448/405 | |||
| [[Sesquiquartififths]] | |||
|- | |||
| 1 | |||
| 133\383 | |||
| 416.71 | |||
| 14/11 | |||
| [[Unthirds]] | |||
|- | |||
| 1 | |||
| 159\383 | |||
| 498.17 | |||
| 4/3 | |||
| [[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:Countertertiaschis]] | |||