Lucy tuning: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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

: This revision was by author [[User:~~genewardsmith~~|~~genewardsmith~~]] and made on <tt>2011-06-~~19 16~~:46:14 UTC</tt>.<br>

: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-22 15:44:51 UTC</tt>.<br>

: The original revision id was <tt>~~237586837~~</tt>.<br>

: The original revision id was <tt>238240749</tt>.<br>

: The revision comment was: <tt></tt><br>

: The revision comment was: <tt>some links added</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">LucyTuning is the meantone tuning advocated by [[Charles Lucy]], with a fifth of precisely 600 + 300/pi = 695.493 ~~cents~~. This is close to the [[88edo]] fifth of 695.455 cents, and shares its general characteristics such as being a good tuning for [[Meantone family|mothra]] and [[Didymus rank three family|eupterpe]] temperaments, providing a mothra generator, an approximate 8/7, of 200+100/pi cents, which extends [[5-limit]] meantone LucyTuning 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/pi cents, or 1/pi of an octave, 381.972 cents, 4.342 cents flat of 5/4.

<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">LucyTuning is the meantone tuning advocated by [[Charles Lucy]], with a fifth of precisely 600 + 300/pi = 695.493 [[cent]]s. This is close to the [[88edo]] fifth of 695.455 cents, and shares its general characteristics such as being a good tuning for [[Meantone family|mothra]] and [[Didymus rank three family|eupterpe]] temperaments, providing a mothra generator, an approximate [[8_7|8/7]], of 200+100/pi cents, which extends [[5-limit]] meantone LucyTuning 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/pi cents, or 1/pi of an octave, 381.972 cents, 4.342 cents flat of [[5_4|5/4]].

A reasonable mapping for [[11-limit]] extended LucyTuning would be

<1200 1800+300/pi 2400+1200/pi 3400-100/pi 4400-800/pi|

This tempers out the mothra ~~commas~~ of 81/80, 1029/1024, 99/98 and 385/384. While Charles Lucy himself does not seem to consider the possibility of extending LucyTuning, it should be noted that the mothra mapping above gives a 7/4 of 1000-100/pi, a mere 0.659 cents flat of a just 7/4. Another way to extend LucyTuning is meanpop:

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 LucyTuning, it should be noted that the mothra mapping above gives a 7/4 of 1000-100/pi, a mere 0.659 cents flat of a [[7_4|just 7/4]]. Another way to extend LucyTuning is meanpop:

<1200 1800+300/pi 2400+1200/pi 2400+3000/pi 5400-3900/pi|

Since this does not involve splitting the generator into thirds it is closer to Lucy's 5-limit perspective.

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[[http://www.myspace.com/lucytuning]]</pre></div>

<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"><html><head><title>Lucy Tuning</title></head><body>LucyTuning is the meantone tuning advocated by <a class="wiki_link" href="/Charles%20Lucy">Charles Lucy</a>, with a fifth of precisely 600 + 300/pi = 695.493 ~~cents~~. This is close to the <a class="wiki_link" href="/88edo">88edo</a> fifth of 695.455 cents, and shares its general characteristics such as being a good tuning for <a class="wiki_link" href="/Meantone%20family">mothra</a> and <a class="wiki_link" href="/Didymus%20rank%20three%20family">eupterpe</a> temperaments, providing a mothra generator, an approximate 8/7, of 200+100/pi cents, which extends <a class="wiki_link" href="/5-limit">5-limit</a> meantone LucyTuning 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 <a class="wiki_link" href="/50edo">50edo</a> and <a class="wiki_link" href="/19edo">19edo</a>. It has a major third of 1200/pi cents, or 1/pi of an octave, 381.972 cents, 4.342 cents flat of 5/4.<br />

<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"><html><head><title>Lucy Tuning</title></head><body>LucyTuning is the meantone tuning advocated by <a class="wiki_link" href="/Charles%20Lucy">Charles Lucy</a>, with a fifth of precisely 600 + 300/pi = 695.493 <a class="wiki_link" href="/cent">cent</a>s. This is close to the <a class="wiki_link" href="/88edo">88edo</a> fifth of 695.455 cents, and shares its general characteristics such as being a good tuning for <a class="wiki_link" href="/Meantone%20family">mothra</a> and <a class="wiki_link" href="/Didymus%20rank%20three%20family">eupterpe</a> temperaments, providing a mothra generator, an approximate <a class="wiki_link" href="/8_7">8/7</a>, of 200+100/pi cents, which extends <a class="wiki_link" href="/5-limit">5-limit</a> meantone LucyTuning 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 <a class="wiki_link" href="/50edo">50edo</a> and <a class="wiki_link" href="/19edo">19edo</a>. It has a major third of 1200/pi cents, or 1/pi of an octave, 381.972 cents, 4.342 cents flat of <a class="wiki_link" href="/5_4">5/4</a>.<br />

<br />

A reasonable mapping for <a class="wiki_link" href="/11-limit">11-limit</a> extended LucyTuning would be<br />

&lt;1200 1800+300/pi 2400+1200/pi 3400-100/pi 4400-800/pi|<br />

This tempers out the mothra ~~commas~~ of 81/80, 1029/1024, 99/98 and 385/384. While Charles Lucy himself does not seem to consider the possibility of extending LucyTuning, it should be noted that the mothra mapping above gives a 7/4 of 1000-100/pi, a mere 0.659 cents flat of a just 7/4. Another way to extend LucyTuning is meanpop:<br />

This tempers out the mothra <a class="wiki_link" href="/comma">comma</a>s of 81/80, 1029/1024, 99/98 and 385/384. While Charles Lucy himself does not seem to consider the possibility of extending LucyTuning, it should be noted that the mothra mapping above gives a 7/4 of 1000-100/pi, a mere 0.659 cents flat of a <a class="wiki_link" href="/7_4">just 7/4</a>. Another way to extend LucyTuning is meanpop:<br />

&lt;1200 1800+300/pi 2400+1200/pi 2400+3000/pi 5400-3900/pi|<br />

Since this does not involve splitting the generator into thirds it is closer to Lucy's 5-limit perspective.<br />

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-19 16:46:14 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-22 15:44:51 UTC</tt>.<br>
-: The original revision id was <tt>237586837</tt>.<br>
+: The original revision id was <tt>238240749</tt>.<br>
-: The revision comment was: <tt></tt><br>
+: The revision comment was: <tt>some links added</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">LucyTuning is the meantone tuning advocated by [[Charles Lucy]], with a fifth of precisely 600 + 300/pi = 695.493 cents. This is close to the [[88edo]] fifth of 695.455 cents, and shares its general characteristics such as being a good tuning for [[Meantone family|mothra]] and [[Didymus rank three family|eupterpe]] temperaments, providing a mothra generator, an approximate 8/7, of 200+100/pi cents, which extends [[5-limit]] meantone LucyTuning 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/pi cents, or 1/pi of an octave, 381.972 cents, 4.342 cents flat of 5/4.
+<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">LucyTuning is the meantone tuning advocated by [[Charles Lucy]], with a fifth of precisely 600 + 300/pi = 695.493 [[cent]]s. This is close to the [[88edo]] fifth of 695.455 cents, and shares its general characteristics such as being a good tuning for [[Meantone family|mothra]] and [[Didymus rank three family|eupterpe]] temperaments, providing a mothra generator, an approximate [[8_7|8/7]], of 200+100/pi cents, which extends [[5-limit]] meantone LucyTuning 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/pi cents, or 1/pi of an octave, 381.972 cents, 4.342 cents flat of [[5_4|5/4]].
 A reasonable mapping for [[11-limit]] extended LucyTuning would be
 &lt;1200 1800+300/pi 2400+1200/pi 3400-100/pi 4400-800/pi|
-This tempers out the mothra commas of 81/80, 1029/1024, 99/98 and 385/384. While Charles Lucy himself does not seem to consider the possibility of extending LucyTuning, it should be noted that the mothra mapping above gives a 7/4 of 1000-100/pi, a mere 0.659 cents flat of a just 7/4. Another way to extend LucyTuning is meanpop:
+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 LucyTuning, it should be noted that the mothra mapping above gives a 7/4 of 1000-100/pi, a mere 0.659 cents flat of a [[7_4|just 7/4]]. Another way to extend LucyTuning is meanpop:
 &lt;1200 1800+300/pi 2400+1200/pi 2400+3000/pi 5400-3900/pi|
 Since this does not involve splitting the generator into thirds it is closer to Lucy's 5-limit perspective.
@@ Line 19: / Line 19: @@
 [[http://www.myspace.com/lucytuning]]</pre></div>
 <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;LucyTuning is the meantone tuning advocated by &lt;a class="wiki_link" href="/Charles%20Lucy"&gt;Charles Lucy&lt;/a&gt;, with a fifth of precisely 600 + 300/pi = 695.493 cents. This is close to the &lt;a class="wiki_link" href="/88edo"&gt;88edo&lt;/a&gt; fifth of 695.455 cents, and shares its general characteristics such as being a good tuning for &lt;a class="wiki_link" href="/Meantone%20family"&gt;mothra&lt;/a&gt; and &lt;a class="wiki_link" href="/Didymus%20rank%20three%20family"&gt;eupterpe&lt;/a&gt; temperaments, providing a mothra generator, an approximate 8/7, of 200+100/pi cents, which extends &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; meantone LucyTuning 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 &lt;a class="wiki_link" href="/50edo"&gt;50edo&lt;/a&gt; and &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;. It has a major third of 1200/pi cents, or 1/pi of an octave, 381.972 cents, 4.342 cents flat of 5/4.&lt;br /&gt;
+<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;LucyTuning is the meantone tuning advocated by &lt;a class="wiki_link" href="/Charles%20Lucy"&gt;Charles Lucy&lt;/a&gt;, with a fifth of precisely 600 + 300/pi = 695.493 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s. This is close to the &lt;a class="wiki_link" href="/88edo"&gt;88edo&lt;/a&gt; fifth of 695.455 cents, and shares its general characteristics such as being a good tuning for &lt;a class="wiki_link" href="/Meantone%20family"&gt;mothra&lt;/a&gt; and &lt;a class="wiki_link" href="/Didymus%20rank%20three%20family"&gt;eupterpe&lt;/a&gt; temperaments, providing a mothra generator, an approximate &lt;a class="wiki_link" href="/8_7"&gt;8/7&lt;/a&gt;, of 200+100/pi cents, which extends &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; meantone LucyTuning 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 &lt;a class="wiki_link" href="/50edo"&gt;50edo&lt;/a&gt; and &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;. It has a major third of 1200/pi cents, or 1/pi of an octave, 381.972 cents, 4.342 cents flat of &lt;a class="wiki_link" href="/5_4"&gt;5/4&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
 A reasonable mapping for &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; extended LucyTuning would be&lt;br /&gt;
 &amp;lt;1200 1800+300/pi 2400+1200/pi 3400-100/pi 4400-800/pi|&lt;br /&gt;
-This tempers out the mothra commas of 81/80, 1029/1024, 99/98 and 385/384. While Charles Lucy himself does not seem to consider the possibility of extending LucyTuning, it should be noted that the mothra mapping above gives a 7/4 of 1000-100/pi, a mere 0.659 cents flat of a just 7/4. Another way to extend LucyTuning is meanpop:&lt;br /&gt;
+This tempers out the mothra &lt;a class="wiki_link" href="/comma"&gt;comma&lt;/a&gt;s of 81/80, 1029/1024, 99/98 and 385/384. While Charles Lucy himself does not seem to consider the possibility of extending LucyTuning, it should be noted that the mothra mapping above gives a 7/4 of 1000-100/pi, a mere 0.659 cents flat of a &lt;a class="wiki_link" href="/7_4"&gt;just 7/4&lt;/a&gt;. Another way to extend LucyTuning is meanpop:&lt;br /&gt;
 &amp;lt;1200 1800+300/pi 2400+1200/pi 2400+3000/pi 5400-3900/pi|&lt;br /&gt;
 Since this does not involve splitting the generator into thirds it is closer to Lucy's 5-limit perspective.&lt;br /&gt;