88cET: 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:~~guest~~|~~guest~~]] and made on <tt>~~2008~~-12-20 18:42:54 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-07-03 20:34:02 UTC</tt>.<br>

: The original revision id was <tt>~~51651877~~</tt>.<br>

: The original revision id was <tt>151468937</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">=88cET ~~(equal division of the perfect fifth into 8 equal parts)~~=

<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">=88cET=

==Theory==

[[~~http:~~//~~www~~.~~tonalsoft~~.~~com~~/~~enc~~/~~number~~/88~~-cet~~.~~aspx|Article about 88cET in Joe Monzo's encyclopedia~~ of ~~microtonal music theory]]~~

88 cent equal temperament uses 88 cents, or 11/150 of an octave, to generate a nonoctave rank one scale. Since 88 cents is an excellent generator for [[Tetracot family|octacot temperament]], it can be viewed as the generator chain of octacot, stripped of octaves. However viewed, octacot and 88 cents equal temperament are very closely related.

Eight steps of 88 cents gives 704 cents, two cents sharp of 3/2, and eighteen gives 1584 cents, two cents flat of 5/2. Taken together this tells us that (5/2)^4/(3/2)^9 = 20000/19683, the minimal diesis or tetracot comma, must be being tempered out. Eleven steps of 88 cents gives 968 cents, less than a cent flat of 7/4, and this tells us that (7/4)^8/(3/2)^11 = 5764801/5668704 must be tempered out also. Taking this, multiplying it by the tetracot comma and taking the fourth root yields 245/243, which therefore must be tempered out also. The tetracot comma and 245/243 taken together define 7-limit octacot.

Continuing on, twenty steps of 88 cents gives 1760 cents, whioh we may compare to the 1751.3 cents of 11/4 and suggests 100/99 being tempered out, and four steps gives 352 cents, which may be compared to the 359.5 cents of 16/13, and suggestes 325/324 being tempered out. These would give an extended octacot, for which 88 cents would be an excellent generator tuning.

==Compositions==

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[[http://www.seraph.it/dep/int/88jinglebells.mp3|88 Jingle Bells]] by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/495ec175ce56cf38cb399d1cd24db164-17.html|blog entry]])</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>88cET</title></head><body><h1 id="toc0"><a name="x88cET ~~(equal division of the perfect fifth into 8 equal parts)~~"></a>88cET ~~(equal division of the perfect fifth into 8 equal parts)~~</h1>

<br />

<h2 id="toc1"><a name="x88cET-Theory"></a>Theory</h2>

<br />

<~~!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id~~="~~toc1~~"~~><a name~~="~~x88cET (equal division of the perfect fifth into 8 equal parts)-Theory~~"></a><~~!-- ws:end:WikiTextHeadingRule:2 --~~>~~Theory~~</h2>

88 cent equal temperament uses 88 cents, or 11/150 of an octave, to generate a nonoctave rank one scale. Since 88 cents is an excellent generator for <a class="wiki_link" href="/Tetracot%20family">octacot temperament</a>, it can be viewed as the generator chain of octacot, stripped of octaves. However viewed, octacot and 88 cents equal temperament are very closely related.<br />

~~<a class="wiki_link_ext" href="http:~~//~~www~~.~~tonalsoft~~.~~com~~/~~enc~~/~~number~~/88-~~cet~~.~~aspx" rel="nofollow"~~>~~Article about 88cET in Joe Monzo's encyclopedia of microtonal music theory~~</a><br />

<br />

Eight steps of 88 cents gives 704 cents, two cents sharp of 3/2, and eighteen gives 1584 cents, two cents flat of 5/2. Taken together this tells us that (5/2)^4/(3/2)^9 = 20000/19683, the minimal diesis or tetracot comma, must be being tempered out. Eleven steps of 88 cents gives 968 cents, less than a cent flat of 7/4, and this tells us that (7/4)^8/(3/2)^11 = 5764801/5668704 must be tempered out also. Taking this, multiplying it by the tetracot comma and taking the fourth root yields 245/243, which therefore must be tempered out also. The tetracot comma and 245/243 taken together define 7-limit octacot. <br />

<br />

Continuing on, twenty steps of 88 cents gives 1760 cents, whioh we may compare to the 1751.3 cents of 11/4 and suggests 100/99 being tempered out, and four steps gives 352 cents, which may be compared to the 359.5 cents of 16/13, and suggestes 325/324 being tempered out. These would give an extended octacot, for which 88 cents would be an excellent generator tuning.<br />

<br />

<h2 id="toc2"><a name="x88cET ~~(equal division of the perfect fifth into 8 equal parts)~~-Compositions"></a>Compositions</h2>

<h2 id="toc2"><a name="x88cET-Compositions"></a>Compositions</h2>

<a class="wiki_link_ext" href="http://www.seraph.it/dep/det/88east.mp3" rel="nofollow">88 East</a> by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a><br />

<a class="wiki_link_ext" href="http://www.seraph.it/dep/det/88vocoeast.mp3" rel="nofollow">88 VocoEast</a> by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a><br />

<a class="wiki_link_ext" href="http://www.seraph.it/dep/det/88Bulgarians.mp3" rel="nofollow">88 Bulgarians</a> by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a> (<a class="wiki_link_ext" href="http://www.seraph.it/blog_files/9660ca3450a996ea8b55713cbf36151f-15.html" rel="nofollow">blog entry</a>)<br />

<a class="wiki_link_ext" href="http://www.seraph.it/dep/int/88jinglebells.mp3" rel="nofollow">88 Jingle Bells</a> by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a> (<a class="wiki_link_ext" href="http://www.seraph.it/blog_files/495ec175ce56cf38cb399d1cd24db164-17.html" rel="nofollow">blog entry</a>)</body></html></pre></div>

@@ 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:guest|guest]] and made on <tt>2008-12-20 18:42:54 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-07-03 20:34:02 UTC</tt>.<br>
-: The original revision id was <tt>51651877</tt>.<br>
+: The original revision id was <tt>151468937</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">=88cET (equal division of the perfect fifth into 8 equal parts)=
+<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">=88cET=
 ==Theory==
-[[http://www.tonalsoft.com/enc/number/88-cet.aspx|Article about 88cET in Joe Monzo's encyclopedia of microtonal music theory]]
+cent equal temperament uses 88 cents, or 11/150 of an octave, to generate a nonoctave rank one scale. Since 88 cents is an excellent generator for [[Tetracot family|octacot temperament]], it can be viewed as the generator chain of octacot, stripped of octaves. However viewed, octacot and 88 cents equal temperament are very closely related.
+Eight steps of 88 cents gives 704 cents, two cents sharp of 3/2, and eighteen gives 1584 cents, two cents flat of 5/2. Taken together this tells us that (5/2)^4/(3/2)^9 = 20000/19683, the minimal diesis or tetracot comma, must be being tempered out. Eleven steps of 88 cents gives 968 cents, less than a cent flat of 7/4, and this tells us that (7/4)^8/(3/2)^11 = 5764801/5668704 must be tempered out also. Taking this, multiplying it by the tetracot comma and taking the fourth root yields 245/243, which therefore must be tempered out also. The tetracot comma and 245/243 taken together define 7-limit octacot.
+Continuing on, twenty steps of 88 cents gives 1760 cents, whioh we may compare to the 1751.3 cents of 11/4 and suggests 100/99 being tempered out, and four steps gives 352 cents, which may be compared to the 359.5 cents of 16/13, and suggestes 325/324 being tempered out. These would give an extended octacot, for which 88 cents would be an excellent generator tuning.
 ==Compositions==
@@ Line 17: / Line 22: @@
 [[http://www.seraph.it/dep/int/88jinglebells.mp3|88 Jingle Bells]] by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/495ec175ce56cf38cb399d1cd24db164-17.html|blog entry]])</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;88cET&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x88cET (equal division of the perfect fifth into 8 equal parts)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;88cET (equal division of the perfect fifth into 8 equal parts)&lt;/h1&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;88cET&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x88cET"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;88cET&lt;/h1&gt;
+ &lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x88cET-Theory"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Theory&lt;/h2&gt;
   &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x88cET (equal division of the perfect fifth into 8 equal parts)-Theory"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Theory&lt;/h2&gt;
+cent equal temperament uses 88 cents, or 11/150 of an octave, to generate a nonoctave rank one scale. Since 88 cents is an excellent generator for &lt;a class="wiki_link" href="/Tetracot%20family"&gt;octacot temperament&lt;/a&gt;, it can be viewed as the generator chain of octacot, stripped of octaves. However viewed, octacot and 88 cents equal temperament are very closely related.&lt;br /&gt;
- &lt;a class="wiki_link_ext" href="http://www.tonalsoft.com/enc/number/88-cet.aspx" rel="nofollow"&gt;Article about 88cET in Joe Monzo's encyclopedia of microtonal music theory&lt;/a&gt;&lt;br /&gt;
+&lt;br /&gt;
+Eight steps of 88 cents gives 704 cents, two cents sharp of 3/2, and eighteen gives 1584 cents, two cents flat of 5/2. Taken together this tells us that (5/2)^4/(3/2)^9 = 20000/19683, the minimal diesis or tetracot comma, must be being tempered out. Eleven steps of 88 cents gives 968 cents, less than a cent flat of 7/4, and this tells us that (7/4)^8/(3/2)^11 = 5764801/5668704 must be tempered out also. Taking this, multiplying it by the tetracot comma and taking the fourth root yields 245/243, which therefore must be tempered out also. The tetracot comma and 245/243 taken together define 7-limit octacot. &lt;br /&gt;
+&lt;br /&gt;
+Continuing on, twenty steps of 88 cents gives 1760 cents, whioh we may compare to the 1751.3 cents of 11/4 and suggests 100/99 being tempered out, and four steps gives 352 cents, which may be compared to the 359.5 cents of 16/13, and suggestes 325/324 being tempered out. These would give an extended octacot, for which 88 cents would be an excellent generator tuning.&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x88cET (equal division of the perfect fifth into 8 equal parts)-Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Compositions&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x88cET-Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Compositions&lt;/h2&gt;
   &lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/det/88east.mp3" rel="nofollow"&gt;88 East&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt;&lt;br /&gt;
 &lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/det/88vocoeast.mp3" rel="nofollow"&gt;88 VocoEast&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt;&lt;br /&gt;
 &lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/det/88Bulgarians.mp3" rel="nofollow"&gt;88 Bulgarians&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/9660ca3450a996ea8b55713cbf36151f-15.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
 &lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/int/88jinglebells.mp3" rel="nofollow"&gt;88 Jingle Bells&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/495ec175ce56cf38cb399d1cd24db164-17.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;/body&gt;&lt;/html&gt;</pre></div>