Xenharmonic Wiki

225edo: Difference between revisions

VisualWikitext
Wikispaces>hstraub
**Imported revision 238144507 - Original comment: **
 
Eliora (talk | contribs)
autopatrolled, emailconfirmed
3,582 edits
 
(13 intermediate revisions by 11 users not shown)
Line 1: Line 1:
<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:hstraub|hstraub]] and made on <tt>2011-06-22 07:23:30 UTC</tt>.<br>
 
: The original revision id was <tt>238144507</tt>.<br>
== Theory ==
: The revision comment was: <tt></tt><br>
225edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with rather large errors in [[harmonic]]s [[3/1|3]], [[5/1|5]], [[7/1|7]], [[11/1|11]], and [[13/1|13]].  
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>
In fact, 225edo sets the sequential record for being worst for integer harmonics as a whole, when evaluated using how close are its harmonic errors to <math>1 - \phi</math> = 38.1966%, the golden ratio, the number most difficult to approximate with rationals. While other edos with poor approximation usually end up approximating the square of that harmonic well, 225edo performs worst due to it setting a record of how close its harmonic errors are to 38.1966%.
<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">=Scales=
 
[[bossier8]]
It has three mappings usable for the 7-limit:  
[[bossier11]]
* {{val| 225 357 522 632 }} ([[patent val]]),
[[bossier14]]</pre></div>
* {{val| 225 '''356''' 522 '''631''' }} (225bd),
<h4>Original HTML content:</h4>
* {{val| 225 357 '''523''' 632 }} (225c).
<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;225edo&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="Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Scales&lt;/h1&gt;
 
&lt;a class="wiki_link" href="/bossier8"&gt;bossier8&lt;/a&gt;&lt;br /&gt;
Using the patent val, it tempers out 20000/19683 and 2109375/2097152 in the 5-limit; 3125/3087, 10976/10935, and 589824/588245 in the 7-limit.
&lt;a class="wiki_link" href="/bossier11"&gt;bossier11&lt;/a&gt;&lt;br /&gt;
 
&lt;a class="wiki_link" href="/bossier14"&gt;bossier14&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
Using the 225bd val, it tempers out 78732/78125 (sensipent comma) and {{monzo| -52 27 4 }} in the 5-limit; 225/224, 177147/175000, and 40353607/40000000 in the 7-limit.
 
Using the 225c val, it tempers out 131072000/129140163 (rodan comma) and 30958682112/30517578125 (trisedodge comma) in the 5-limit; 2401/2400, 4375/4374, and 2097152/2066715 in the 7-limit.
 
=== Odd harmonics ===
{{Harmonics in equal|225}}
 
== Scales ==
* [[Bossier scales]]
 
[[Category:Bossier]]
Retrieved from "https://en.xen.wiki/w/225edo"