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Lucy tuning: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
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This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-06-19 06:44:12 UTC</tt>.<br>
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: The original revision id was <tt>237533881</tt>.<br>
 
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The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
\def\val#1{\left\langle\begin{matrix}#1\end{matrix}\right]}
<h4>Original Wikitext content:</h4>
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<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">[[http://www.lucytune.com|Link to Lucy Tuning website]]</pre></div>
'''Lucy tuning''' is the [[meantone]] tuning advocated by [[Charles Lucy]], with a fifth of precisely 600 + 300/π = 695.493 [[cent]]s. This is close to the [[88edo]] fifth of 695.455 [[cent]]s, and shares its general characteristics such as being a good tuning for [[Gamelismic clan#Mothra|mothra]] and [[Didymus rank three family#Euterpe|euterpe]] temperaments, providing a mothra generator, an approximate [[8/7]], of 200+100/π cents, which extends [[5-limit]] meantone Lucy tuning to a version with a mothra (1/3 meantone fifth) generator. As a tuning for 5-limit meantone, it has the softer quality characteristic of the flatter fifth meantones between [[50edo]] and [[19edo]]. It has a major third of 1200/π cents, or 1/π of an octave, 381.972 cents, 4.342 cents flat of [[5/4]], but 2.827 cents sharp of [[1/3-comma meantone]]'s major third.
<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;Lucy Tuning&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;a class="wiki_link_ext" href="http://www.lucytune.com" rel="nofollow"&gt;Link to Lucy Tuning website&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
A reasonable mapping for [[11-limit]] extended Lucy tuning would be
 
: <math>\val{1200 & 1800 + \frac{300}{π} & 2400 + \frac{1200}{π} & 3400 - \frac{100}{π} & 4400 - \frac{800}{π}}</math>
 
This tempers out the mothra [[comma]]s of 81/80, 1029/1024, 99/98 and 385/384. While Charles Lucy himself does not seem to consider the possibility of extending Lucy tuning, it should be noted that the mothra mapping above gives a 7/4 of 1000-100/π, a mere 0.659 cents flat of a [[7/4|just 7/4]]. Another way to extend Lucy tuning is meanpop:
 
: <math>\val{1200 & 1800 + \frac{300}{π} & 2400 + \frac{1200}{π} & 2400 + \frac{3000}{π} & 5400 - \frac{3900}{π}}</math>
 
Since this does not involve splitting the generator into thirds, it is closer to Lucy's 5-limit perspective.
 
== External links ==
* [http://www.lucytune.com Official website]
* [http://www.myspace.com/lucytuning Myspace profile]
* [http://tonalsoft.com/enc/l/lucy-tuning.aspx LucyTuning and 88-ed2 / 88-edo / 88-ET / 88-tone equal-temperament, and 3/10-comma meantone] on [[Tonalsoft Encyclopedia]]
 
[[Category:Lucy tuning| ]] <!-- main article -->
[[Category:Listen]]
[[Category:Meanpop]]
[[Category:Meantone]]
[[Category:Mothra]]
[[Category:Transcendental]]
[[Category:Historical]]
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