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381edo: Difference between revisions

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**Imported revision 246765587 - Original comment: **
m Text replacement - "Octave-reduced form, reduced to the first half-octave" to "Octave-reduced form, reduced to the first half-octave"
 
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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>2011-08-18 14:41:37 UTC</tt>.<br>
 
: The original revision id was <tt>246765587</tt>.<br>
== Theory ==
: The revision comment was: <tt></tt><br>
381edo is [[consistent]] to the [[13-odd-limit]] and almost the [[15-odd-limit]]; the only inconsistently mapped intervals in the 15-odd-limit are [[15/11]] and its [[octave complement]]. It has a sharp tendency, with odd [[harmonic]]s 3 through 15 all tuned sharp except for 11, which is very slightly flat.
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>
As an equal temperament, it [[tempering out|tempers out]] the [[vulture comma]], {{monzo| 24 -21 4 }}, in the 5-limit and 6144/6125 ([[porwell comma]]) and 250047/250000 ([[landscape comma]]) in the 7-limit. It provides the [[optimal patent val]] for the porwell planar temperament tempering out 6144/6125, and [[nessafof]], the {{nowrap| 99 & 282 }} temperament tempering out it and the landscape comma 250047/250000.
<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 //381 equal division// divides the octave into 381 equal parts of 3.150 cents each. It tempers out the vulture comma, |24 -21 4&gt;, in the 5-limit and 6144/6125 and 250047/250000 in the 7-limit. It provides the [[optimal patent val]] for the porwell planar temperament tempering out 6144/6125, and [[Porwell temperaments#Nessafof|nessafof]], the 15&amp;69 tempering out it and the landscape comma 250047/250000.</pre></div>
 
<h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;381edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;381 equal division&lt;/em&gt; divides the octave into 381 equal parts of 3.150 cents each. It tempers out the vulture comma, |24 -21 4&amp;gt;, in the 5-limit and 6144/6125 and 250047/250000 in the 7-limit. It provides the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for the porwell planar temperament tempering out 6144/6125, and &lt;a class="wiki_link" href="/Porwell%20temperaments#Nessafof"&gt;nessafof&lt;/a&gt;, the 15&amp;amp;69 tempering out it and the landscape comma 250047/250000.&lt;/body&gt;&lt;/html&gt;</pre></div>
{{Harmonics in equal|381|intervals=prime}}
 
=== Subsets and supersets ===
Since 381 factors into primes as {{nowrap| 3 × 127 }}, 381edo contains [[3edo]] and [[127edo]] as subsets.
 
== 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| 604 -381 }}
| {{Mapping| 381 604 }}
| −0.1285
| 0.1284
| 4.08
|-
| 2.3.5
| {{Monzo| 24 -21 4 }}, {{monzo| 25 15 -21 }}
| {{Mapping| 381 604 885 }}
| −0.2418
| 0.1915
| 6.08
|-
| 2.3.5.7
| 6144/6125, 250047/250000, 43046721/43025920
| {{Mapping| 381 604 885 1070 }}
| −0.2929
| 0.1880
| 5.97
|-
| 2.3.5.7.11
| 3025/3024, 6144/6125, 19712/19683, 160083/160000
| {{Mapping| 381 604 885 1070 1318 }}
| −0.2264
| 0.2144
| 6.81
|-
| 2.3.5.7.11.13
| 676/675, 1001/1000, 3025/3024, 6144/6125, 10985/10976
| {{Mapping| 381 604 885 1070 1318 1410 }}
| −0.2075
| 0.2002
| 6.36
|}
 
=== 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
| 151\381
| 475.59
| 320/243
| [[Vulture]] (5-limit)
|-
| 3
| 24\381
| 475.59<br>(75.59)
| 320/243<br>(117/112)
| [[Terture]]
|-
| 3
| 50\381
| 157.48
| 35/32
| [[Nessafof]]
|}
<nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[Normal forms|minimal form]] in parentheses if distinct
 
[[Category:Porwell]]
[[Category:Nessafof]]
Retrieved from "https://en.xen.wiki/w/381edo"