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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>2011-08-31 12:27:15 UTC</tt>.<br>
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| : The original revision id was <tt>249724240</tt>.<br>
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| : The revision comment was: <tt></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>
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| <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">The //175 equal division// divides the octave into 175 equal parts of 6.857 cents each. It tempers out 1029/1024 and 225/224, so that it supports 7-limit [[Gamelsimic clan#Miracle|miracle temperament]], and in fact provides an excellent alternative to [[72edo]] for 7-limit miracle. In the 11-limit, it tempers out 243/242, 385/384, 441/440 and 540/439, and supports 11-limit miracle. In the 13-limit, 175f tempers out 351/350 just as 72 does.
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| =Music= | | == Theory == |
| http://www.archive.org/details/RachmaninoffPlaysBlackjack
| | 175et [[tempering out|tempers out]] [[225/224]] and [[1029/1024]], so that it [[support]]s 7-limit [[miracle]], and in fact provides an excellent alternative to [[72edo]] for 7-limit miracle with improved [[5/1|5]] and [[7/1|7]] at the cost of a slightly flatter [[3/1|3]]. In the 11-limit, it tempers out [[243/242]], [[385/384]], [[441/440]] and [[540/539]], and supports 11-limit miracle. In the 13-limit, the 175f val, {{val| 175 277 406 491 605 '''647''' }} tempers out [[351/350]] just as 72 does, and provides a tuning for [[benediction]] temperament very close to the POTE tuning. |
| [[http://www.archive.org/download/RachmaninoffPlaysBlackjack/rachman.mp3|play]]</pre></div> | | |
| <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>175edo</title></head><body>The <em>175 equal division</em> divides the octave into 175 equal parts of 6.857 cents each. It tempers out 1029/1024 and 225/224, so that it supports 7-limit <a class="wiki_link" href="/Gamelsimic%20clan#Miracle">miracle temperament</a>, and in fact provides an excellent alternative to <a class="wiki_link" href="/72edo">72edo</a> for 7-limit miracle. In the 11-limit, it tempers out 243/242, 385/384, 441/440 and 540/439, and supports 11-limit miracle. In the 13-limit, 175f tempers out 351/350 just as 72 does.<br />
| | {{Harmonics in equal|175}} |
| <br />
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| <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:0 -->Music</h1>
| | === Subsets and supersets === |
| <!-- ws:start:WikiTextUrlRule:8:http://www.archive.org/details/RachmaninoffPlaysBlackjack --><a class="wiki_link_ext" href="http://www.archive.org/details/RachmaninoffPlaysBlackjack" rel="nofollow">http://www.archive.org/details/RachmaninoffPlaysBlackjack</a><!-- ws:end:WikiTextUrlRule:8 --><br />
| | Since 175 factors into {{factorization|175}}, 175edo has subset edos {{EDOs| 5, 7, 25, and 35 }}. |
| <a class="wiki_link_ext" href="http://www.archive.org/download/RachmaninoffPlaysBlackjack/rachman.mp3" rel="nofollow">play</a></body></html></pre></div>
| | |
| | == Music == |
| | ; [[Gene Ward Smith]] |
| | * ''Rachmaninoff Plays Blackjack'' (archived 2010) – [http://www.archive.org/details/RachmaninoffPlaysBlackjack detail] | [http://www.archive.org/download/RachmaninoffPlaysBlackjack/rachman.mp3 play] – [[Blackjack]] in 175edo tuning |
| Prime factorization
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52 × 7
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| Step size
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6.85714 ¢
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| Fifth
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102\175 (699.429 ¢)
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| Semitones (A1:m2)
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14:15 (96 ¢ : 102.9 ¢)
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| Dual sharp fifth
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103\175 (706.286 ¢)
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| Dual flat fifth
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102\175 (699.429 ¢)
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| Dual major 2nd
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30\175 (205.714 ¢) (→ 6\35)
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| Consistency limit
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7
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| Distinct consistency limit
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7
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175 equal divisions of the octave (abbreviated 175edo or 175ed2), also called 175-tone equal temperament (175tet) or 175 equal temperament (175et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 175 equal parts of about 6.86 ¢ each. Each step represents a frequency ratio of 21/175, or the 175th root of 2.
Theory
175et tempers out 225/224 and 1029/1024, so that it supports 7-limit miracle, and in fact provides an excellent alternative to 72edo for 7-limit miracle with improved 5 and 7 at the cost of a slightly flatter 3. In the 11-limit, it tempers out 243/242, 385/384, 441/440 and 540/539, and supports 11-limit miracle. In the 13-limit, the 175f val, ⟨175 277 406 491 605 647] tempers out 351/350 just as 72 does, and provides a tuning for benediction temperament very close to the POTE tuning.
Odd harmonics
Approximation of odd harmonics in 175edo
| Harmonic
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3
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5
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7
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9
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11
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13
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15
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17
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19
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21
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23
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| Error
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Absolute (¢)
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-2.53
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-2.31
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-1.97
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+1.80
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-2.75
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+2.90
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+2.02
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-2.10
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-2.66
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+2.36
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+2.58
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| Relative (%)
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-36.8
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-33.7
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-28.7
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+26.3
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-40.1
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+42.3
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+29.4
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-30.6
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-38.7
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+34.4
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+37.7
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Steps
(reduced)
|
277
(102)
|
406
(56)
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491
(141)
|
555
(30)
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605
(80)
|
648
(123)
|
684
(159)
|
715
(15)
|
743
(43)
|
769
(69)
|
792
(92)
|
Subsets and supersets
Since 175 factors into 52 × 7, 175edo has subset edos 5, 7, 25, and 35.
Music
- Gene Ward Smith