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131edo: Difference between revisions

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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:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2010-09-19 00:56:39 UTC</tt>.<br>
: The original revision id was <tt>163684829</tt>.<br>
: The revision comment was: <tt></tt><br>
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>
<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">=&lt;span style="display: block; line-height: 0px; overflow: hidden;"&gt;&lt;/span&gt;131 tone equal temperament &lt;span style="display: block; line-height: 0px; overflow: hidden;"&gt;&lt;/span&gt;=


23 23 8 23 23 23 8 : Pytagorean tuning (comparable with 17edo)
== Theory ==
21 21 13 21 21 21 13 : Meantone tuning (comparable with 50edo)
131edo is in[[consistent]] to the [[5-odd-limit]] and the error of [[harmonic]] [[3/1|3]] is quite large. However, it is the next [[edo]] after [[81edo]] on the [[Golden meantone|Golden Tone System]] (''[[Das Goldene Tonsystem]]'') of Thorvald Kornerup, using the 131b [[val]]. The [[patent val]] has a fifth sharp by 3.389 cents rather than flat like the meantone fifth; rather than tempering out [[81/80]] it tempers out the [[immunity comma]], 1638400/1594323. In the 7-limit it tempers out [[3125/3087]] and [[245/243]], so that it [[support]]s [[bohpier]].
17 17 17 6 17 17 17 17 6 : Armodue tuning (comparable with 23edo)</pre></div>
 
<h4>Original HTML content:</h4>
131edo is also notable for having a good approximation to [[natave|acoustic ''e'']], at 189\131, which is a [[semiconvergent]]. This number of steps, 189, is particularly well-factorizable, and logarithmic divisors of acoustic ''e'' form a sequence of rapidly converging approximations to small rationals. Among these are [[4/3]] (2\7[[EDN|edn]] = 54\131), [[5/4]] (2\9edn = 42\131), [[15/13]] (1\7edn = 27\131), [[19/17]] (1\9edn = 21\131), [[11/10]] (2\21edn = 18\131), [[14/13]] (2\27edn = 14\131), and [[32/31]] (2\63edn = 6\131), with accuracy increasing the smaller the fraction.
<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;131edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x131 tone equal temperament "&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;span style="display: block; line-height: 0px; overflow: hidden;"&gt;&lt;/span&gt;131 tone equal temperament &lt;span style="display: block; line-height: 0px; overflow: hidden;"&gt;&lt;/span&gt;&lt;/h1&gt;
 
&lt;br /&gt;
=== Odd harmonics ===
23 23 8 23 23 23 8 : Pytagorean tuning (comparable with 17edo)&lt;br /&gt;
{{Harmonics in equal|131|columns=15}}
21 21 13 21 21 21 13 : Meantone tuning (comparable with 50edo)&lt;br /&gt;
 
17 17 17 6 17 17 17 17 6 : Armodue tuning (comparable with 23edo)&lt;/body&gt;&lt;/html&gt;</pre></div>
=== Subsets and supersets ===
131edo is the 32nd [[prime]] edo, following [[127edo]] and before [[137edo]].
 
== Scales ==
=== Mos scales ===
{| class="wikitable"
|-
| 33 16 33 33 16
| [[3L_2s|Pentatonic]] (comparable with [[8edo]] and [[99edo]])
|-
| 23 23 8 23 23 23 8
| [[5L_2s|Pythagorean tuning]] (comparable with [[17edo]])
|-
| 21 21 13 21 21 21 13
| [[5L_2s|Meantone tuning]] (comparable with [[50edo]])
|-
| 19 12 19 19 12 19 19 12
| [[5L_3s|Oneirotonic tuning]] (comparable with [[55edo]])
|-
| 18 18 18 18 18 18 18 5
| [[7L_1s|Porcupine tuning]] (comparable with [[29edo]] and [[80edo]])
|-
| 17 17 17 6 17 17 17 17 6
| [[7L_2s|Superdiatonic tuning]] (comparable with [[23edo]])
|-
| 16 16 16 16 16 16 16 16 3
| [[8L 1s|Bohpier tuning]] (comparable with [[41edo]])
|-
| 13 13 9 13 13 13 9 13 13 13 9
| [[8L 3s|Sensi-11 Tuning]]
|-
| 11 11 11 11 11 5 11 11 11 11 11 11 5
| De Vries 13-tone Tuning
|-
| 10 10 10 7 10 10 10 10 7 10 10 10 10 7
| [[11L_3s|Ketradektriatoh Tuning]]
|-
| 21 17 21 17 17 21 17
| [[mohaha7]]
|-
| 4 17 17 17 4 17 17 4 17 17
| [[mohaha10]]
|}
 
[[Category:Bohpier]]
[[Category:Immunity]]
[[Category:Meantone]]
[[Category:Golden meantone]]
Retrieved from "https://en.xen.wiki/w/131edo"