Xenharmonic Wiki

299edo: Difference between revisions

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**Imported revision 240476789 - Original comment: **
 
m →Theory: adopt more specific link; misc. cleanup
 
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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>2011-07-08 02:09:16 UTC</tt>.<br>
 
: The original revision id was <tt>240476789</tt>.<br>
== Theory ==
: The revision comment was: <tt></tt><br>
299et [[tempering out|tempers out]] the kleisma, [[15625/15552]], in the [[5-limit]]; [[10976/10935]] in the [[7-limit]]; [[385/384]] in the [[11-limit]]; and [[325/324]], [[625/624]] and [[676/675]] in the [[13-limit]]. It provides the [[optimal patent val]] for the 13-limit rank-3 [[enlil]] temperament, and the rank-4 temperament tempering out 325/324 and 385/384.
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 //299 equal division// divides the octave into 299 parts of 4.013 cents each. In the 5-limit it tempers out the kleisma, 15625/15552, in the 7-limit 10976/10935, in the 11-limit 385/384; and in the 13-limit 325/324, 625/624 and 676/675.</pre></div>
{{Harmonics in equal|299}}
<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;299edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;299 equal division&lt;/em&gt; divides the octave into 299 parts of 4.013 cents each. In the 5-limit it tempers out the kleisma, 15625/15552, in the 7-limit 10976/10935, in the 11-limit 385/384; and in the 13-limit 325/324, 625/624 and 676/675.&lt;/body&gt;&lt;/html&gt;</pre></div>
=== Subsets and supersets ===
Since 299 factors into primes as {{nowrap| 13 × 23 }}, 299edo contains [[13edo]] and [[23edo]] as subset edos.
 
== 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| 474 -299 }}
| {{Mapping| 299 474 }}
| −0.1218
| 0.1218
| 3.04
|-
| 2.3.5
| 15625/15552, {{monzo| 80 -49 -1 }}
| {{Mapping| 299 474 694 }}
| +0.0665
| 0.2844
| 7.09
|-
| 2.3.5.7
| 10976/10935, 15625/15552, 823543/819200
| {{Mapping| 299 474 694 839 }}
| +0.1925
| 0.3291
| 8.20
|-
| 2.3.5.7.11
| 385/384, 6250/6237, 10976/10935, 12005/11979
| {{Mapping| 299 474 694 839 1034 }}
| +0.2399
| 0.3092
| 7.70
|-
| 2.3.5.7.11.13
| 325/324, 385/384, 625/624, 10648/10647, 10976/10935
| {{Mapping| 299 474 694 839 1034 1106 }}
| +0.2779
| 0.2948
| 7.34
|-
| 2.3.5.7.11.13.17
| 325/324, 385/384, 595/594, 625/624, 2058/2057, 8624/8619
| {{Mapping| 299 474 694 839 1034 1106 1222 }}
| +0.2595
| 0.2767
| 6.89
|-
| 2.3.5.7.11.13.17.19
| 325/324, 343/342, 385/384, 595/594, 625/624, 1216/1215, 1445/1444
| {{Mapping| 299 474 694 839 1034 1106 1222 1270 }}
| +0.2424
| 0.2627
| 6.54
|}
 
=== 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\299
| 100.33
| 1323/1250
| [[Heptacot]] (7-limit)
|-
| 1
| 79\299
| 317.06
| 6/5
| [[Hanson]]
|-
| 1
| 124\299
| 497.66
| 4/3
| [[Cotoneum]] (7-limit)
|-
| 1
| 124\299
| 505.69
| 75/56
| [[Marfifths]]
|}
<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
 
[[Category:Enlil]]
[[Category:Keenanismic]]
Retrieved from "https://en.xen.wiki/w/299edo"