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| <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:genewardsmith|genewardsmith]] and made on <tt>2011-08-24 21:01:09 UTC</tt>.<br>
| | |
| : The original revision id was <tt>248303395</tt>.<br>
| | == Theory == |
| : The revision comment was: <tt></tt><br>
| | 150edo is [[contorted]] in the 5-limit, [[tempering out]] the same commas as [[75edo]], including [[20000/19683]] and [[2109375/2097152]]. However, every 11th step of 150edo is equal to the [[88cET]] nonoctave tuning, which is also represented as [[octacot]] through a regular temperament theory perspective. It provides a good tuning for octacot, for which 88{{c}} provides a generator. |
| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
| | The equal temperament tempers out [[245/243]], [[2401/2400]], and [[4000/3969]] in the 7-limit, [[385/384]], [[896/891]], and [[1375/1372]] in the 11-limit, and [[352/351]], [[364/363]], [[676/675]] and [[1575/1573]] in the 13-limit. |
| <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 //150 equal division// divides the octave into 150 equal steps exactly 8 cents each. This means eleven such steps are 88 cents, relating 150edo to the [[88cET]] nonoctave tuning. It tempers out 245/243, 4000/3969 and 2401/2400 in the 7-limit, 896/891, 385/384 and 1375/1372 in the 11-limit, and 352/351, 364/363, 676/675 and 1575/1573 in the 134-limit. It is contorted in the 5-limit, tempering out the same commas as [[75edo]], including 20000/19683 and 2109375/2097152. It provides a good tuning for [[Tetracot family#Octacot]], for which 88 cents provides a generator.</pre></div>
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| <h4>Original HTML content:</h4>
| | === Odd harmonics === |
| <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>150edo</title></head><body>The <em>150 equal division</em> divides the octave into 150 equal steps exactly 8 cents each. This means eleven such steps are 88 cents, relating 150edo to the <a class="wiki_link" href="/88cET">88cET</a> nonoctave tuning. It tempers out 245/243, 4000/3969 and 2401/2400 in the 7-limit, 896/891, 385/384 and 1375/1372 in the 11-limit, and 352/351, 364/363, 676/675 and 1575/1573 in the 134-limit. It is contorted in the 5-limit, tempering out the same commas as <a class="wiki_link" href="/75edo">75edo</a>, including 20000/19683 and 2109375/2097152. It provides a good tuning for <a class="wiki_link" href="/Tetracot%20family#Octacot">Tetracot family</a>, for which 88 cents provides a generator.</body></html></pre></div>
| | {{Harmonics in equal|150|columns=10}} |
| | |
| | === Subsets and supersets === |
| | Since 150 factors into 2 × 3 × 5<sup>2</sup>, 150edo has subset edos {{EDOs| 2, 3, 5, 6, 10, 15, 25, 30, 50, and 75 }}. |
| | |
| | == Regular temperament properties == |
| | === Rank-2 temperaments === |
| | {| class="wikitable center-all left-5" |
| | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator |
| | |- |
| | ! Periods<br />per 8ve |
| | ! Generator* |
| | ! Cents* |
| | ! Associated<br />ratio* |
| | ! Temperaments |
| | |- |
| | | 1 |
| | | 11\150 |
| | | 88.00 |
| | | 21/20 |
| | | [[Octacot]] (150e) / [[october]] (150) |
| | |- |
| | | 1 |
| | | 29\150 |
| | | 232.00 |
| | | 8/7 |
| | | [[Quadrawell]] |
| | |- |
| | | 10 |
| | | 31\150<br />(1\150) |
| | | 248.00<br />(8.00) |
| | | 15/13<br />(176/175) |
| | | [[Decoid]] (150e) |
| | |} |
| | <nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct |