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383edo: Difference between revisions

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**Imported revision 241202199 - Original comment: **
m Text replacement - "[[Helmholtz temperament|" to "[[Helmholtz (temperament)|"
 
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox ET}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
{{ED intro}}
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-07-13 14:27:36 UTC</tt>.<br>
 
: The original revision id was <tt>241202199</tt>.<br>
== Theory ==
: The revision comment was: <tt></tt><br>
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.
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
 
<h4>Original Wikitext content:</h4>
=== Prime harmonics ===
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The //383 equal division// divides the octave into 383 equal parts of 3.133 cents each. It is distinctly consistent through the 15-limit, and tempers out 32805/32768 in the 5-limit; 2401/2400 in the 7-limit; 6250/6237, 4000/3993 and 3025/3024 in the 11-limit; and 625/624, 1575/1573 and 2080/2079 in the 13-limit and it supports [[Schismatic family#Sesquiquartififths|sesquiquartififths]].</pre></div>
{{Harmonics in equal|383}}
<h4>Original HTML content:</h4>
 
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;383edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;383 equal division&lt;/em&gt; divides the octave into 383 equal parts of 3.133 cents each. It is distinctly consistent through the 15-limit, and tempers out 32805/32768 in the 5-limit; 2401/2400 in the 7-limit; 6250/6237, 4000/3993 and 3025/3024 in the 11-limit;  and 625/624, 1575/1573 and 2080/2079 in the 13-limit and it supports &lt;a class="wiki_link" href="/Schismatic%20family#Sesquiquartififths"&gt;sesquiquartififths&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
=== 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]]
Retrieved from "https://en.xen.wiki/w/383edo"