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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
The '''sqrtphi''' is a temperament for the 7, 11, 13, 17, and 19 prime limits. 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:genewardsmith|genewardsmith]] and made on <tt>2012-11-04 17:14:27 UTC</tt>.<br>
: The original revision id was <tt>379113424</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">See [[Kleismic family#Sqrtphi]].


=Spectrum of Sqrtphi Tunings by Eigenmonzos=
See [[Kleismic family #Sqrtphi|Kleismic family]] for more technical data.
||~ Eigenmonzo ||~ Undecimal Major Third ||
|| 26/21 || 415.12662 ||
|| 17/13 || 416.10694 ||
|| 18/13 || 416.33823 ||
|| 15/11 || 416.44058 ||
|| 13/11 || 416.47711 ||
|| 18/17 || 416.49243 ||
|| 15/14 || 416.50336 ||
|| 14/13 || 416.50932 ||
|| 15/13 || 416.51607 ||
|| 19/16 || 416.52850 ||
|| 22/17 || 416.53195 ||
|| 13/12 || 416.53568 ||
|| 20/19 || 416.53952 ||
|| 11/9 || 416.54324 ||
|| φ || 416.54515 ||
|| 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 || 416.58709 ||
|| 21/19 || 416.58991 ||
|| 17/16 || 416.59158 ||
|| 22/19 || 416.59991 ||
|| 4/3 || 416.60150 (5 limit minimax) ||
|| 21/16 || 416.60616 ||
|| 8/7 || 416.60984 (7 and 9 limit minimax) ||
|| 20/17 || 416.61850 ||
|| 11/8 || 416.63287 (11 limit minimax) ||
|| 10/9 || 416.64011 ||
|| 21/20 || 416.64030 ||
|| 7/6 || 416.64114 ||
|| 17/15 || 416.66485 ||
|| 7/5 || 416.72983 ||
|| 12/11 || 416.73745 ||
|| 11/10 || 416.78541 ||
|| 6/5 || 416.87174 ||
|| 21/17 || 417.08725 ||
|| 14/11 || 417.50796 ||


</pre></div>
== Tuning spectrum ==
<h4>Original HTML content:</h4>
Gencom: [2 14/11; 325/324 364/363 375/374 400/399 442/441 595/594]
<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;Sqrtphi&lt;/title&gt;&lt;/head&gt;&lt;body&gt;See &lt;a class="wiki_link" href="/Kleismic%20family#Sqrtphi"&gt;Kleismic family&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Spectrum of Sqrtphi Tunings by Eigenmonzos"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Spectrum of Sqrtphi Tunings by Eigenmonzos&lt;/h1&gt;


&lt;table class="wiki_table"&gt;
Gencom mapping: [{{val|1 12 11 16 17 28 27 -2}}, {{val|0 -30 -25 -38 -39 -70 -66 18}}]
    &lt;tr&gt;
        &lt;th&gt;Eigenmonzo&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Undecimal Major Third&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;26/21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;415.12662&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;17/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.10694&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;18/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.33823&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.44058&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.47711&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;18/17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.49243&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.50336&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.50932&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.51607&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;19/16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.52850&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;22/17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.53195&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13/12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.53568&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;20/19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.53952&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.54324&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;φ&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.54515&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.54745&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;26/19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.55665&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.56389&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;19/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.56499&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;17/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.56680&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;22/21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.57024&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.57302 (13, 15, 17, 19 and 21 limit minimax)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;24/19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.57413&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.57693&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;19/17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.57807&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;24/17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.58332&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;19/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.58370&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;19/18&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.58465&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.58709&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;21/19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.58991&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;17/16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.59158&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;22/19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.59991&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.60150 (5 limit minimax)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;21/16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.60616&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.60984 (7 and 9 limit minimax)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;20/17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.61850&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.63287 (11 limit minimax)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.64011&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;21/20&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.64030&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7/6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.64114&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;17/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.66485&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.72983&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;12/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.73745&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.78541&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;416.87174&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;21/17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;417.08725&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;417.50796&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
{| class="wikitable center-all"
|-
! | [[eigenmonzo|eigenmonzo<br>(unchanged-interval]])
! | undecimal<br>major third (¢)
! | comments
|-
| | 26/21
| | 415.12662
| |
|-
| | 17/13
| | 416.10694
| |
|-
| | 18/13
| | 416.33823
| |
|-
| | 15/11
| | 416.44058
| |
|-
| | 13/11
| | 416.47711
| |
|-
| | 18/17
| | 416.49243
| |
|-
| | 15/14
| | 416.50336
| |
|-
| | 14/13
| | 416.50932
| |
|-
| | 15/13
| | 416.51607
| |
|-
| | 19/16
| | 416.52850
| |
|-
| | 22/17
| | 416.53195
| |
|-
| | 13/12
| | 416.53568
| |
|-
| | 20/19
| | 416.53952
| |
|-
| | 11/9
| | 416.54324
| |
|-
| | (φ)
| | 416.54515
| | square root of phi
|-
| | 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-odd-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
| | 416.58709
| |
|-
| | 21/19
| | 416.58991
| |
|-
| | 17/16
| | 416.59158
| |
|-
| | 22/19
| | 416.59991
| |
|-
| | 4/3
| | 416.60150
| | 5-odd-limit minimax
|-
| | 21/16
| | 416.60616
| |
|-
| | 8/7
| | 416.60984
| | 7 and 9-odd-limit minimax
|-
| | 20/17
| | 416.61850
| |
|-
| | 11/8
| | 416.63287
| | 11-odd-limit minimax
|-
| | 10/9
| | 416.64011
| |
|-
| | 21/20
| | 416.64030
| |
|-
| | 7/6
| | 416.64114
| |
|-
| | 17/15
| | 416.66485
| |
|-
| | 7/5
| | 416.72983
| |
|-
| | 12/11
| | 416.73745
| |
|-
| | 11/10
| | 416.78541
| |
|-
| | 6/5
| | 416.87174
| |
|-
| | 21/17
| | 417.08725
| |
|-
| | 14/11
| | 417.50796
| |
|}
 
== Scales ==
* [[Sqrtphi17]]
* [[Sqrtphi23]]
* [[Sqrtphi49]]
 
== Music ==
'''[[Vito Sicurella]]'''
* [http://micro.soonlabel.com/gene_ward_smith/Others/Sicurella/A%20Fight%20For%20Phi.mp3 A Fight for Phi]
'''[[Chris Vaisvil]]'''
* [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:Golden ratio]]
Retrieved from "https://en.xen.wiki/w/Sqrtphi"