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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | The '''sqrtphi''' is a [[regular temperament|temperament]] for the 7-, 11-, 13-, 17-, and 19-limit. It is a member of [[kleismic family]], [[mirkwai clan]] and [[wizmic microtemperaments|wizmic temperaments]]. The name ''sqrtphi'' stands for square root of phi, which means the positive square root of the [[golden ratio]] <math>(\sqrt{\varphi} = \sqrt{\frac{1+\sqrt{5}}{2}})</math> as a frequency ratio. |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| |
| : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2012-12-12 17:10:04 UTC</tt>.<br>
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| : The original revision id was <tt>391766820</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>
| |
| <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">See [[Kleismic family#Sqrtphi]].
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| Gencom: [2 14/11; 325/324 364/363 375/374 400/399 442/441 595/594]
| | See [[Kleismic family #Sqrtphi]] for technical data. |
| Gencom map: [<1 12 11 16 17 28 27 -2|, <0 -30 -25 -38 -39 -70 -66 18|]
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| =Spectrum of Sqrtphi Tunings by Eigenmonzos= | | == Scales == |
| ||~ Eigenmonzo ||~ Undecimal Major Third ||
| | === Scala files === |
| || 26/21 || 415.12662 ||
| | * [[Sqrtphi17]] |
| || 17/13 || 416.10694 ||
| | * [[Sqrtphi23]] |
| || 18/13 || 416.33823 ||
| | * [[Sqrtphi49]] |
| || 15/11 || 416.44058 ||
| |
| || 13/11 || 416.47711 ||
| |
| || 18/17 || 416.49243 ||
| |
| || [[15_14|15/14]] || 416.50336 ||
| |
| || [[14_13|14/13]] || 416.50932 ||
| |
| || [[15_13|15/13]] || 416.51607 ||
| |
| || [[19_16|19/16]] || 416.52850 ||
| |
| || 22/17 || 416.53195 ||
| |
| || 13/12 || 416.53568 ||
| |
| || 20/19 || 416.53952 ||
| |
| || [[11_9|11/9]] || 416.54324 ||
| |
| || φ || 416.54515 ||
| |
| || [[5_4|5/4]] || 416.54745 ||
| |
| || 26/19 || 416.55665 ||
| |
| || 16/13 || 416.56389 ||
| |
| || 19/15 || 416.56499 ||
| |
| || 17/14 || 416.56680 ||
| |
| || 22/21 || 416.57024 ||
| |
| || 13/10 || 416.57302 (13, 15, 17, 19 and 21 limit minimax) ||
| |
| || 24/19 || 416.57413 ||
| |
| || 16/15 || 416.57693 ||
| |
| || 19/17 || 416.57807 ||
| |
| || 24/17 || 416.58332 ||
| |
| || 19/14 || 416.58370 ||
| |
| || 19/18 || 416.58465 ||
| |
| || [[9_7|9/7]] || 416.58709 ||
| |
| || 21/19 || 416.58991 ||
| |
| || 17/16 || 416.59158 ||
| |
| || 22/19 || 416.59991 ||
| |
| || [[4_3|4/3]] || 416.60150 (5 limit minimax) ||
| |
| || 21/16 || 416.60616 ||
| |
| || [[8_7|8/7]] || 416.60984 (7 and 9 limit minimax) ||
| |
| || 20/17 || 416.61850 ||
| |
| || [[11_8|11/8]] || 416.63287 (11 limit minimax) ||
| |
| || [[10_9|10/9]] || 416.64011 ||
| |
| || 21/20 || 416.64030 ||
| |
| || [[7_6|7/6]] || 416.64114 ||
| |
| || 17/15 || 416.66485 ||
| |
| || [[7_5|7/5]] || 416.72983 ||
| |
| || 12/11 || 416.73745 ||
| |
| || 11/10 || 416.78541 ||
| |
| || [[6_5|6/5]] || 416.87174 ||
| |
| || 21/17 || 417.08725 ||
| |
| || 14/11 || 417.50796 ||
| |
| </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>Sqrtphi</title></head><body>See <a class="wiki_link" href="/Kleismic%20family#Sqrtphi">Kleismic family</a>.<br />
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| <br />
| |
| Gencom: [2 14/11; 325/324 364/363 375/374 400/399 442/441 595/594]<br />
| |
| Gencom map: [&lt;1 12 11 16 17 28 27 -2|, &lt;0 -30 -25 -38 -39 -70 -66 18|]<br />
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| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Spectrum of Sqrtphi Tunings by Eigenmonzos"></a><!-- ws:end:WikiTextHeadingRule:0 -->Spectrum of Sqrtphi Tunings by Eigenmonzos</h1>
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|
| <table class="wiki_table">
| | == Tunings == |
| <tr>
| | === Tuning spectrum === |
| <th>Eigenmonzo<br />
| | {| class="wikitable center-all left-3" |
| </th>
| | |- |
| <th>Undecimal Major Third<br />
| | ! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval]]) |
| </th>
| | ! Generator (¢) |
| </tr>
| | ! Comments |
| <tr>
| | |- |
| <td>26/21<br />
| | | 26/21 |
| </td>
| | | 415.12662 |
| <td>415.12662<br />
| | | |
| </td>
| | |- |
| </tr>
| | | 17/13 |
| <tr>
| | | 416.10694 |
| <td>17/13<br />
| | | |
| </td>
| | |- |
| <td>416.10694<br />
| | | 18/13 |
| </td>
| | | 416.33823 |
| </tr>
| | | |
| <tr>
| | |- |
| <td>18/13<br />
| | | 15/11 |
| </td>
| | | 416.44058 |
| <td>416.33823<br />
| | | |
| </td>
| | |- |
| </tr>
| | | 13/11 |
| <tr>
| | | 416.47711 |
| <td>15/11<br />
| | | |
| </td>
| | |- |
| <td>416.44058<br />
| | | 18/17 |
| </td>
| | | 416.49243 |
| </tr>
| | | |
| <tr>
| | |- |
| <td>13/11<br />
| | | 15/14 |
| </td>
| | | 416.50336 |
| <td>416.47711<br />
| | | |
| </td>
| | |- |
| </tr>
| | | 14/13 |
| <tr>
| | | 416.50932 |
| <td>18/17<br />
| | | |
| </td>
| | |- |
| <td>416.49243<br />
| | | 15/13 |
| </td>
| | | 416.51607 |
| </tr>
| | | |
| <tr>
| | |- |
| <td><a class="wiki_link" href="/15_14">15/14</a><br />
| | | 19/16 |
| </td>
| | | 416.52850 |
| <td>416.50336<br />
| | | |
| </td>
| | |- |
| </tr>
| | | 22/17 |
| <tr>
| | | 416.53195 |
| <td><a class="wiki_link" href="/14_13">14/13</a><br />
| | | |
| </td>
| | |- |
| <td>416.50932<br />
| | | 13/12 |
| </td>
| | | 416.53568 |
| </tr>
| | | |
| <tr>
| | |- |
| <td><a class="wiki_link" href="/15_13">15/13</a><br />
| | | 20/19 |
| </td>
| | | 416.53952 |
| <td>416.51607<br />
| | | |
| </td>
| | |- |
| </tr>
| | | 11/9 |
| <tr>
| | | 416.54324 |
| <td><a class="wiki_link" href="/19_16">19/16</a><br />
| | | |
| </td>
| | |- |
| <td>416.52850<br />
| | | (φ) |
| </td>
| | | 416.54515 |
| </tr>
| | | square root of phi |
| <tr>
| | |- |
| <td>22/17<br />
| | | 5/4 |
| </td>
| | | 416.54745 |
| <td>416.53195<br />
| | | |
| </td>
| | |- |
| </tr>
| | | 26/19 |
| <tr>
| | | 416.55665 |
| <td>13/12<br />
| | | |
| </td>
| | |- |
| <td>416.53568<br />
| | | 16/13 |
| </td>
| | | 416.56389 |
| </tr>
| | | |
| <tr>
| | |- |
| <td>20/19<br />
| | | 19/15 |
| </td>
| | | 416.56499 |
| <td>416.53952<br />
| | | |
| </td>
| | |- |
| </tr>
| | | 17/14 |
| <tr>
| | | 416.56680 |
| <td><a class="wiki_link" href="/11_9">11/9</a><br />
| | | |
| </td>
| | |- |
| <td>416.54324<br />
| | | 22/21 |
| </td>
| | | 416.57024 |
| </tr>
| | | |
| <tr>
| | |- |
| <td>φ<br />
| | | 13/10 |
| </td>
| | | 416.57302 |
| <td>416.54515<br />
| | | 13, 15, 17, 19 and 21-odd-limit minimax |
| </td>
| | |- |
| </tr>
| | | 24/19 |
| <tr>
| | | 416.57413 |
| <td><a class="wiki_link" href="/5_4">5/4</a><br />
| | | |
| </td>
| | |- |
| <td>416.54745<br />
| | | 16/15 |
| </td>
| | | 416.57693 |
| </tr>
| | | |
| <tr>
| | |- |
| <td>26/19<br />
| | | 19/17 |
| </td>
| | | 416.57807 |
| <td>416.55665<br />
| | | |
| </td>
| | |- |
| </tr>
| | | 24/17 |
| <tr>
| | | 416.58332 |
| <td>16/13<br />
| | | |
| </td>
| | |- |
| <td>416.56389<br />
| | | 19/14 |
| </td>
| | | 416.58370 |
| </tr>
| | | |
| <tr>
| | |- |
| <td>19/15<br />
| | | 19/18 |
| </td>
| | | 416.58465 |
| <td>416.56499<br />
| | | |
| </td>
| | |- |
| </tr>
| | | 9/7 |
| <tr>
| | | 416.58709 |
| <td>17/14<br />
| | | |
| </td>
| | |- |
| <td>416.56680<br />
| | | 21/19 |
| </td>
| | | 416.58991 |
| </tr>
| | | |
| <tr>
| | |- |
| <td>22/21<br />
| | | 17/16 |
| </td>
| | | 416.59158 |
| <td>416.57024<br />
| | | |
| </td>
| | |- |
| </tr>
| | | 22/19 |
| <tr>
| | | 416.59991 |
| <td>13/10<br />
| | | |
| </td>
| | |- |
| <td>416.57302 (13, 15, 17, 19 and 21 limit minimax)<br />
| | | 4/3 |
| </td>
| | | 416.60150 |
| </tr>
| | | 5-odd-limit minimax |
| <tr>
| | |- |
| <td>24/19<br />
| | | 21/16 |
| </td>
| | | 416.60616 |
| <td>416.57413<br />
| | | |
| </td>
| | |- |
| </tr>
| | | 8/7 |
| <tr>
| | | 416.60984 |
| <td>16/15<br />
| | | 7 and 9-odd-limit minimax |
| </td>
| | |- |
| <td>416.57693<br />
| | | 20/17 |
| </td>
| | | 416.61850 |
| </tr>
| | | |
| <tr>
| | |- |
| <td>19/17<br />
| | | 11/8 |
| </td>
| | | 416.63287 |
| <td>416.57807<br />
| | | 11-odd-limit minimax |
| </td>
| | |- |
| </tr>
| | | 10/9 |
| <tr>
| | | 416.64011 |
| <td>24/17<br />
| | | |
| </td>
| | |- |
| <td>416.58332<br />
| | | 21/20 |
| </td>
| | | 416.64030 |
| </tr>
| | | |
| <tr>
| | |- |
| <td>19/14<br />
| | | 7/6 |
| </td>
| | | 416.64114 |
| <td>416.58370<br />
| | | |
| </td>
| | |- |
| </tr>
| | | 17/15 |
| <tr>
| | | 416.66485 |
| <td>19/18<br />
| | | |
| </td>
| | |- |
| <td>416.58465<br />
| | | 7/5 |
| </td>
| | | 416.72983 |
| </tr>
| | | |
| <tr>
| | |- |
| <td><a class="wiki_link" href="/9_7">9/7</a><br />
| | | 12/11 |
| </td>
| | | 416.73745 |
| <td>416.58709<br />
| | | |
| </td>
| | |- |
| </tr>
| | | 11/10 |
| <tr>
| | | 416.78541 |
| <td>21/19<br />
| | | |
| </td>
| | |- |
| <td>416.58991<br />
| | | 6/5 |
| </td>
| | | 416.87174 |
| </tr>
| | | |
| <tr>
| | |- |
| <td>17/16<br />
| | | 21/17 |
| </td>
| | | 417.08725 |
| <td>416.59158<br />
| | | |
| </td>
| | |- |
| </tr>
| | | 14/11 |
| <tr>
| | | 417.50796 |
| <td>22/19<br />
| | | |
| </td>
| | |} |
| <td>416.59991<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/4_3">4/3</a><br />
| |
| </td>
| |
| <td>416.60150 (5 limit minimax)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>21/16<br />
| |
| </td>
| |
| <td>416.60616<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/8_7">8/7</a><br />
| |
| </td>
| |
| <td>416.60984 (7 and 9 limit minimax)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>20/17<br />
| |
| </td>
| |
| <td>416.61850<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/11_8">11/8</a><br />
| |
| </td>
| |
| <td>416.63287 (11 limit minimax)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/10_9">10/9</a><br />
| |
| </td>
| |
| <td>416.64011<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>21/20<br />
| |
| </td>
| |
| <td>416.64030<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/7_6">7/6</a><br />
| |
| </td>
| |
| <td>416.64114<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
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| <td>17/15<br />
| |
| </td>
| |
| <td>416.66485<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/7_5">7/5</a><br />
| |
| </td>
| |
| <td>416.72983<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12/11<br />
| |
| </td>
| |
| <td>416.73745<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11/10<br />
| |
| </td>
| |
| <td>416.78541<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/6_5">6/5</a><br />
| |
| </td>
| |
| <td>416.87174<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>21/17<br />
| |
| </td>
| |
| <td>417.08725<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14/11<br />
| |
| </td>
| |
| <td>417.50796<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| </body></html></pre></div>
| | == Music == |
| | ; [[Vito Sicurella]] |
| | * [https://web.archive.org/web/20201127014110/http://micro.soonlabel.com/gene_ward_smith/Others/Sicurella/A%20Fight%20For%20Phi.mp3 ''A Fight for Phi''] |
| | |
| | ; [[Chris Vaisvil]] |
| | * [https://web.archive.org/web/20201127012408/http://micro.soonlabel.com/sqrt_phi/daily20111123a-sqrt-phi-17.mp3 ''Prelude for Piano in Square root of Phi Tuning''] |
| | |
| | [[Category:Sqrtphi| ]] <!-- main article --> |
| | [[Category:Rank-2 temperaments]] |
| | [[Category:Kleismic family]] |
| | [[Category:Canopic clan]] |
| | [[Category:Wizmic microtemperaments]] |
| | [[Category:Golden ratio]] |