59edo: Difference between revisions

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:~~Andrew_Heathwaite~~|~~Andrew_Heathwaite~~]] and made on <tt>2012-05-~~21 02~~:08:28 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-06-01 03:40:06 UTC</tt>.<br>

: The original revision id was <tt>~~337752484~~</tt>.<br>

: The original revision id was <tt>341632678</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>

<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 //59 equal division// divides the octave into 59 equal steps of 20.339 cents each. Its best fifth is very (9.9 cents) sharp, and yet its [[major third]] is nearly pure. It is a good [[Porcupine family|porcupine]] tuning, giving in fact the [[optimal patent val]] for [[11-limit]] porcupine. This patent val tempers out 250/243 in the [[5-limit]], 64/63 and 16875/16807 in the [[7-limit]], and 55/54, 100/99 and 176/175 in the [[11-limit]]. 59edo is an ~~excelent~~ tuning for the 2.9.5.21.11 11-limit [[k*N subgroups|2*59 subgroup]], on which it takes the same tuning and tempers out the same commas as 118et. This can be extended to the 19-limit 2*59 subgroup 2.9.5.21.11.39.17.57, for which the 50&59 temperament with a subminor third generator provides an interesting 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 //59 equal division// divides the octave into 59 equal steps of 20.339 cents each. Its best fifth is very (9.9 cents) sharp, and yet its [[major third]] is nearly pure. It is a good [[Porcupine family|porcupine]] tuning, giving in fact the [[optimal patent val]] for [[11-limit]] porcupine. This patent val tempers out 250/243 in the [[5-limit]], 64/63 and 16875/16807 in the [[7-limit]], and 55/54, 100/99 and 176/175 in the [[11-limit]]. 59edo is an excellent tuning for the 2.9.5.21.11 11-limit [[k*N subgroups|2*59 subgroup]], on which it takes the same tuning and tempers out the same commas as 118et. This can be extended to the 19-limit 2*59 subgroup 2.9.5.21.11.39.17.57, for which the 50&59 temperament with a subminor third generator provides an interesting temperament.

Using the flat fifth instead of the sharp one allows for the 12&35 temperament, which is a kind of bizarre cousin to [[Schismatic family|garibaldi temperament]] with a generator of an approximate 15/14, tuned to the size of a whole tone, rather than a fifth.

Line 72:

|| 58 || 1179.661 ||</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>59edo</title></head><body>The <em>59 equal division</em> divides the octave into 59 equal steps of 20.339 cents each. Its best fifth is very (9.9 cents) sharp, and yet its <a class="wiki_link" href="/major%20third">major third</a> is nearly pure. It is a good <a class="wiki_link" href="/Porcupine%20family">porcupine</a> tuning, giving in fact the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for <a class="wiki_link" href="/11-limit">11-limit</a> porcupine. This patent val tempers out 250/243 in the <a class="wiki_link" href="/5-limit">5-limit</a>, 64/63 and 16875/16807 in the <a class="wiki_link" href="/7-limit">7-limit</a>, and 55/54, 100/99 and 176/175 in the <a class="wiki_link" href="/11-limit">11-limit</a>. 59edo is an ~~excelent~~ tuning for the 2.9.5.21.11 11-limit <a class="wiki_link" href="/k%2AN%20subgroups">2*59 subgroup</a>, on which it takes the same tuning and tempers out the same commas as 118et. This can be extended to the 19-limit 2*59 subgroup 2.9.5.21.11.39.17.57, for which the 50&amp;59 temperament with a subminor third generator provides an interesting temperament.<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>59edo</title></head><body>The <em>59 equal division</em> divides the octave into 59 equal steps of 20.339 cents each. Its best fifth is very (9.9 cents) sharp, and yet its <a class="wiki_link" href="/major%20third">major third</a> is nearly pure. It is a good <a class="wiki_link" href="/Porcupine%20family">porcupine</a> tuning, giving in fact the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for <a class="wiki_link" href="/11-limit">11-limit</a> porcupine. This patent val tempers out 250/243 in the <a class="wiki_link" href="/5-limit">5-limit</a>, 64/63 and 16875/16807 in the <a class="wiki_link" href="/7-limit">7-limit</a>, and 55/54, 100/99 and 176/175 in the <a class="wiki_link" href="/11-limit">11-limit</a>. 59edo is an excellent tuning for the 2.9.5.21.11 11-limit <a class="wiki_link" href="/k%2AN%20subgroups">2*59 subgroup</a>, on which it takes the same tuning and tempers out the same commas as 118et. This can be extended to the 19-limit 2*59 subgroup 2.9.5.21.11.39.17.57, for which the 50&amp;59 temperament with a subminor third generator provides an interesting temperament.<br />

<br />

Using the flat fifth instead of the sharp one allows for the 12&amp;35 temperament, which is a kind of bizarre cousin to <a class="wiki_link" href="/Schismatic%20family">garibaldi temperament</a> with a generator of an approximate 15/14, tuned to the size of a whole tone, rather than a fifth.<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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2012-05-21 02:08:28 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-06-01 03:40:06 UTC</tt>.<br>
-: The original revision id was <tt>337752484</tt>.<br>
+: The original revision id was <tt>341632678</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>
 <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 //59 equal division// divides the octave into 59 equal steps of 20.339 cents each. Its best fifth is very (9.9 cents) sharp, and yet its [[major third]] is nearly pure. It is a good [[Porcupine family|porcupine]] tuning, giving in fact the [[optimal patent val]] for [[11-limit]] porcupine. This patent val tempers out 250/243 in the [[5-limit]], 64/63 and 16875/16807 in the [[7-limit]], and 55/54, 100/99 and 176/175 in the [[11-limit]]. 59edo is an excelent tuning for the 2.9.5.21.11 11-limit [[k*N subgroups|2*59 subgroup]], on which it takes the same tuning and tempers out the same commas as 118et. This can be extended to the 19-limit 2*59 subgroup 2.9.5.21.11.39.17.57, for which the 50&amp;59 temperament with a subminor third generator provides an interesting 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 //59 equal division// divides the octave into 59 equal steps of 20.339 cents each. Its best fifth is very (9.9 cents) sharp, and yet its [[major third]] is nearly pure. It is a good [[Porcupine family|porcupine]] tuning, giving in fact the [[optimal patent val]] for [[11-limit]] porcupine. This patent val tempers out 250/243 in the [[5-limit]], 64/63 and 16875/16807 in the [[7-limit]], and 55/54, 100/99 and 176/175 in the [[11-limit]]. 59edo is an excellent tuning for the 2.9.5.21.11 11-limit [[k*N subgroups|2*59 subgroup]], on which it takes the same tuning and tempers out the same commas as 118et. This can be extended to the 19-limit 2*59 subgroup 2.9.5.21.11.39.17.57, for which the 50&amp;59 temperament with a subminor third generator provides an interesting temperament.
 Using the flat fifth instead of the sharp one allows for the 12&amp;35 temperament, which is a kind of bizarre cousin to [[Schismatic family|garibaldi temperament]] with a generator of an approximate 15/14, tuned to the size of a whole tone, rather than a fifth.
@@ Line 72: / Line 72: @@
 || 58 || 1179.661 ||</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;59edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;59 equal division&lt;/em&gt; divides the octave into 59 equal steps of 20.339 cents each. Its best fifth is very (9.9 cents) sharp, and yet its &lt;a class="wiki_link" href="/major%20third"&gt;major third&lt;/a&gt; is nearly pure. It is a good &lt;a class="wiki_link" href="/Porcupine%20family"&gt;porcupine&lt;/a&gt; tuning, giving in fact the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; porcupine. This patent val tempers out 250/243 in the &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt;, 64/63 and 16875/16807 in the &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt;, and 55/54, 100/99 and 176/175 in the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt;. 59edo is an excelent tuning for the 2.9.5.21.11 11-limit &lt;a class="wiki_link" href="/k%2AN%20subgroups"&gt;2*59 subgroup&lt;/a&gt;, on which it takes the same tuning and tempers out the same commas as 118et. This can be extended to the 19-limit 2*59 subgroup 2.9.5.21.11.39.17.57, for which the 50&amp;amp;59 temperament with a subminor third generator provides an interesting temperament.&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;59edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;59 equal division&lt;/em&gt; divides the octave into 59 equal steps of 20.339 cents each. Its best fifth is very (9.9 cents) sharp, and yet its &lt;a class="wiki_link" href="/major%20third"&gt;major third&lt;/a&gt; is nearly pure. It is a good &lt;a class="wiki_link" href="/Porcupine%20family"&gt;porcupine&lt;/a&gt; tuning, giving in fact the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; porcupine. This patent val tempers out 250/243 in the &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt;, 64/63 and 16875/16807 in the &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt;, and 55/54, 100/99 and 176/175 in the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt;. 59edo is an excellent tuning for the 2.9.5.21.11 11-limit &lt;a class="wiki_link" href="/k%2AN%20subgroups"&gt;2*59 subgroup&lt;/a&gt;, on which it takes the same tuning and tempers out the same commas as 118et. This can be extended to the 19-limit 2*59 subgroup 2.9.5.21.11.39.17.57, for which the 50&amp;amp;59 temperament with a subminor third generator provides an interesting temperament.&lt;br /&gt;
 &lt;br /&gt;
 Using the flat fifth instead of the sharp one allows for the 12&amp;amp;35 temperament, which is a kind of bizarre cousin to &lt;a class="wiki_link" href="/Schismatic%20family"&gt;garibaldi temperament&lt;/a&gt; with a generator of an approximate 15/14, tuned to the size of a whole tone, rather than a fifth.&lt;br /&gt;