78edo: Difference between revisions

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Wikispaces>xenwolf
**Imported revision 214058754 - Original comment: **
Wikispaces>MasonGreen1
**Imported revision 585778963 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-03-25 15:08:17 UTC</tt>.<br>
: This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2016-06-18 10:43:29 UTC</tt>.<br>
: The original revision id was <tt>214058754</tt>.<br>
: The original revision id was <tt>585778963</tt>.<br>
: The revision comment was: <tt></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>
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>
<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">The 78 equal division divides the octave into 78 equal parts of size 15.385 [[cent]]s each. It tempers out 2048/2025 in the [[5-limit]]; 875/864 and 2401/2400 in the [[7-limit]]; and 100/99, 385/384 and 1375/1372 in the [[11-limit]]. It provides the [[optimal patent val]] for 11-limit [[Diaschismic family|keen temperament]].</pre></div>
<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 78 equal division divides the octave into 78 equal parts of size 15.385 [[cent]]s each. It tempers out 2048/2025 in the [[5-limit]]; 875/864 and 2401/2400 in the [[7-limit]]; and 100/99, 385/384 and 1375/1372 in the [[11-limit]]. It provides the [[optimal patent val]] for 11-limit [[Diaschismic family|keen temperament]].
 
Much like [[100edo|100bddd]], the 78ddd val can be used to construct an alternative to 22edo for pajara. The large and small step sizes in this case have ratio 4:3. The width of the tempered perfect fifth is 707.7 cents. The major third is 384.6 cents; less than two cents flat of just. The harmonic seventh is 984.6 cents, or about 15.8 cents sharp; hence this tuning prioritizes the 3- and 5-limits over the 7-limit, while still ensuring that no basic 7-limit intervals other than the tritones are more than 16 cents off. The 22-note 2MOS generated in this way could be used to build straight-fretted guitars that would be [[https://en.wikipedia.org/wiki/Augmented-fourths_tuning|tuned in tritones]]. The appeal of this scale is that it is less xenharmonic than [[22edo]] is, for listeners accustomed to 12edo. In particular, the 163.6¢ "flat minor whole tone" of 22edo is now 169.2¢, making it more clearly a //whole// tone (albeit noticeably flat), rather than a neutral second.</pre></div>
<h4>Original HTML content:</h4>
<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;78edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 78 equal division divides the octave into 78 equal parts of size 15.385 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s each. It tempers out 2048/2025 in the &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt;; 875/864 and 2401/2400 in the &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt;; and 100/99, 385/384 and 1375/1372 in the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt;. It provides the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for 11-limit &lt;a class="wiki_link" href="/Diaschismic%20family"&gt;keen temperament&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
<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;78edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 78 equal division divides the octave into 78 equal parts of size 15.385 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s each. It tempers out 2048/2025 in the &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt;; 875/864 and 2401/2400 in the &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt;; and 100/99, 385/384 and 1375/1372 in the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt;. It provides the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for 11-limit &lt;a class="wiki_link" href="/Diaschismic%20family"&gt;keen temperament&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
Much like &lt;a class="wiki_link" href="/100edo"&gt;100bddd&lt;/a&gt;, the 78ddd val can be used to construct an alternative to 22edo for pajara. The large and small step sizes in this case have ratio 4:3. The width of the tempered perfect fifth is 707.7 cents. The major third is 384.6 cents; less than two cents flat of just. The harmonic seventh is 984.6 cents, or about 15.8 cents sharp; hence this tuning prioritizes the 3- and 5-limits over the 7-limit, while still ensuring that no basic 7-limit intervals other than the tritones are more than 16 cents off. The 22-note 2MOS generated in this way could be used to build straight-fretted guitars that would be &lt;a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Augmented-fourths_tuning" rel="nofollow"&gt;tuned in tritones&lt;/a&gt;. The appeal of this scale is that it is less xenharmonic than &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt; is, for listeners accustomed to 12edo. In particular, the 163.6¢ &amp;quot;flat minor whole tone&amp;quot; of 22edo is now 169.2¢, making it more clearly a &lt;em&gt;whole&lt;/em&gt; tone (albeit noticeably flat), rather than a neutral second.&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 10:43, 18 June 2016

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author MasonGreen1 and made on 2016-06-18 10:43:29 UTC.
The original revision id was 585778963.
The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

The 78 equal division divides the octave into 78 equal parts of size 15.385 [[cent]]s each. It tempers out 2048/2025 in the [[5-limit]]; 875/864 and 2401/2400 in the [[7-limit]]; and 100/99, 385/384 and 1375/1372 in the [[11-limit]]. It provides the [[optimal patent val]] for 11-limit [[Diaschismic family|keen temperament]].

Much like [[100edo|100bddd]], the 78ddd val can be used to construct an alternative to 22edo for pajara. The large and small step sizes in this case have ratio 4:3. The width of the tempered perfect fifth is 707.7 cents. The major third is 384.6 cents; less than two cents flat of just. The harmonic seventh is 984.6 cents, or about 15.8 cents sharp; hence this tuning prioritizes the 3- and 5-limits over the 7-limit, while still ensuring that no basic 7-limit intervals other than the tritones are more than 16 cents off. The 22-note 2MOS generated in this way could be used to build straight-fretted guitars that would be [[https://en.wikipedia.org/wiki/Augmented-fourths_tuning|tuned in tritones]]. The appeal of this scale is that it is less xenharmonic than [[22edo]] is, for listeners accustomed to 12edo. In particular, the 163.6¢ "flat minor whole tone" of 22edo is now 169.2¢, making it more clearly a //whole// tone (albeit noticeably flat), rather than a neutral second.

Original HTML content:

<html><head><title>78edo</title></head><body>The 78 equal division divides the octave into 78 equal parts of size 15.385 <a class="wiki_link" href="/cent">cent</a>s each. It tempers out 2048/2025 in the <a class="wiki_link" href="/5-limit">5-limit</a>; 875/864 and 2401/2400 in the <a class="wiki_link" href="/7-limit">7-limit</a>; and 100/99, 385/384 and 1375/1372 in the <a class="wiki_link" href="/11-limit">11-limit</a>. It provides the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for 11-limit <a class="wiki_link" href="/Diaschismic%20family">keen temperament</a>.<br />
<br />
Much like <a class="wiki_link" href="/100edo">100bddd</a>, the 78ddd val can be used to construct an alternative to 22edo for pajara. The large and small step sizes in this case have ratio 4:3. The width of the tempered perfect fifth is 707.7 cents. The major third is 384.6 cents; less than two cents flat of just. The harmonic seventh is 984.6 cents, or about 15.8 cents sharp; hence this tuning prioritizes the 3- and 5-limits over the 7-limit, while still ensuring that no basic 7-limit intervals other than the tritones are more than 16 cents off. The 22-note 2MOS generated in this way could be used to build straight-fretted guitars that would be <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Augmented-fourths_tuning" rel="nofollow">tuned in tritones</a>. The appeal of this scale is that it is less xenharmonic than <a class="wiki_link" href="/22edo">22edo</a> is, for listeners accustomed to 12edo. In particular, the 163.6¢ &quot;flat minor whole tone&quot; of 22edo is now 169.2¢, making it more clearly a <em>whole</em> tone (albeit noticeably flat), rather than a neutral second.</body></html>