Xenharmonic Wiki

207edo: Difference between revisions

VisualWikitext
Wikispaces>genewardsmith
**Imported revision 541042640 - Original comment: **
 
m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"
 
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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>2015-02-15 18:40:45 UTC</tt>.<br>
 
: The original revision id was <tt>541042640</tt>.<br>
== Theory ==
: The revision comment was: <tt></tt><br>
207et [[tempering out|tempers out]] 32805/32768 ([[schisma]]) in the 5-limit, [[6144/6125]] and [[19683/19600]] in the 7-limit, [[441/440]] and 43923/43904 in the 11-limit, and [[351/350]], [[676/675]], [[729/728]], [[847/845]], [[1716/1715]] in the 13-limit. It serves as a tuning in the 11- and 13-limit for the [[swetneus]] temperament. It is significantly more accurate on the 2.3.7.11.13 [[subgroup]], a favorite of many people, and one which contains both 729/728 and [[10648/10647]], which it tempers out.
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 207 equal division of the octave, 207edo, divides the octave into 207 equal parts of size 5.797 cents each. It tempers out 32805/32768 in the 5-limit, 6144/6125 and 19683/19600 in the 7-limit, 441/440 and 43923/43904 in the 11-limit, and 351/350, 847/845, 676/675, 729/728, 1716/1715 in the 13-limit. It serves as the patent val in the 11- and 13-limits for [[Cataharry temperaments#Swetneus|swetneus temperament]]. It is significantly more accurate on the 2.3.7.11.13 subgroup, a favorite of many people, and one which contains both 729/728 and 10648/10647, which it tempers out.</pre></div>
{{Harmonics in equal|207}}
<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;207edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 207 equal division of the octave, 207edo, divides the octave into 207 equal parts of size 5.797 cents each. It tempers out 32805/32768 in the 5-limit, 6144/6125 and 19683/19600 in the 7-limit, 441/440 and 43923/43904 in the 11-limit, and 351/350, 847/845, 676/675, 729/728, 1716/1715 in the 13-limit. It serves as the patent val in the 11- and 13-limits for &lt;a class="wiki_link" href="/Cataharry%20temperaments#Swetneus"&gt;swetneus temperament&lt;/a&gt;. It is significantly more accurate on the 2.3.7.11.13 subgroup, a favorite of many people, and one which contains both 729/728 and 10648/10647, which it tempers out.&lt;/body&gt;&lt;/html&gt;</pre></div>
=== Subsets and supersets ===
Since 207 factors into {{factorisation|207}}, 207edo has subset edos {{EDOs| 3, 9, 23, and 69 }}.
 
== 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| -328 207 }}
| {{mapping| 207 328 }}
| +0.1595
| 0.1596
| 2.75
|-
| 2.3.5
| 32805/32768, {{monzo| 2 31 -22 }}
| {{mapping| 207 328 481 }}
| −0.1942
| 0.5166
| 8.91
|-
| 2.3.5.7
| 6144/6125, 19683/19600, 50421/50000
| {{mapping| 207 328 481 581 }}
| −0.0825
| 0.4874
| 8.41
|-
| 2.3.5.7.11
| 441/440, 3388/3375, 6144/6125, 19683/19600
| {{mapping| 207 328 481 581 716 }}
| −0.0317
| 0.4477
| 7.72
|-
| 2.3.5.7.11.13
| 351/350, 441/440, 676/675, 847/845, 3584/3575
| {{mapping| 207 328 481 581 716 766 }}
| −0.0287
| 0.4087
| 7.05
|-
| 2.3.5.7.11.13.17
| 351/350, 441/440, 561/560, 676/675, 847/845, 1089/1088
| {{mapping| 207 328 481 581 716 766 846 }}
| −0.0034
| 0.3834
| 6.61
|}
 
=== 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
| 25\207
| 144.93
| 49/45
| [[Swetneus]]
|-
| 1
| 43\207
| 249.28
| 15/13
| [[Hemischis]]
|-
| 1
| 86\207
| 498.55
| 4/3
| [[Helmholtz (temperament)|Helmholtz]]
|}
<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct
Retrieved from "https://en.xen.wiki/w/207edo"