Xenharmonic Wiki

78edo: Difference between revisions

← Older edit
VisualWikitext
Wikispaces>xenwolf
**Imported revision 214058754 - Original comment: **
Overthink (talk | contribs)
autopatrolled
2,764 edits
mNo edit summary
 
(20 intermediate revisions by 13 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:xenwolf|xenwolf]] and made on <tt>2011-03-25 15:08:17 UTC</tt>.<br>
 
: The original revision id was <tt>214058754</tt>.<br>
== Theory ==
: The revision comment was: <tt></tt><br>
78edo is [[consistent]] to the [[7-odd-limit]], but the error of [[harmonic]] [[3/1|3]], inherited from [[39edo]], is quite large for the size of the system.  
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>
This tuning [[tempering out|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 [[keen]] temperament.
<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>
 
<h4>Original HTML content:</h4>
Much like [[100edo|100bddd]], the 78dd 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 [[cent]]s. 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 {{w|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 cents "flat minor whole tone" of 22edo is now 169.2 cents, making it more clearly a ''whole'' tone (albeit noticeably flat), rather than a neutral second.
<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>
 
=== Odd harmonics ===
{{Harmonics in equal|78}}
 
=== Subsets and supersets ===
Since 78 factors into {{factorization|78}}, 78edo has subset edos {{EDOs| 2, 3, 6, 13, 26, and 39 }}. [[156edo]], which doubles it, is a notable tuning.
 
== Intervals ==
{{Interval table}}
 
== Scales ==
* [[Maeve Gutierrez|Gutierrez Moonglade scale]]
 
== Instruments ==
 
[[Lumatone mapping for 78edo|Lumatone mappings for 78edo]] are available.
[[Category:Keen]]
 
== Music ==
; [[Bryan Deister]]
* [https://www.youtube.com/shorts/jxYRAo6jHaE ''microtonal improvisation in 78edo''] (2025)
Retrieved from "https://en.xen.wiki/w/78edo"