Xenharmonic Wiki

List of superparticular intervals: Difference between revisions

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Wikispaces>guest
**Imported revision 309253554 - Original comment: **
Wikispaces>JosephRuhf
**Imported revision 350990950 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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>2012-03-08 19:47:40 UTC</tt>.<br>
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2012-07-06 21:48:59 UTC</tt>.<br>
: The original revision id was <tt>309253554</tt>.<br>
: The original revision id was <tt>350990950</tt>.<br>
: The revision comment was: <tt></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>
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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|| 154/153 || 11.278 || (2*7*11)/(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17) ||  ||
|| 154/153 || 11.278 || (2*7*11)/(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17) ||  ||
|| 170/169 || 10.214 || (2*5*17)/13&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt; ||  ||
|| 170/169 || 10.214 || (2*5*17)/13&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt; ||  ||
|| 221/220 || 7.8514 || (13*17)/(2^2*5*11) ||  ||
|| 221/220 || 7.8514 || (13*17)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5*11) ||  ||
|| 256/255 || 6.7759 || (2^8)/(3*5*17) || 255th subharmonic ||
|| 256/255 || 6.7759 || (2^8)/(3*5*17) || 255th subharmonic ||
|| 273/272 || 6.3532 || (3*7*13)/(2^4*17) ||  ||
|| 273/272 || 6.3532 || (3*7*13)/(2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*17) ||  ||
|| 289/288 || 6.0008 || 17&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;/(2^5*3^2) ||  ||
|| 289/288 || 6.0008 || 17&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;/(2&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;) ||  ||
|| 375/374 || 4.6228 || (3*5&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;)/(2*11*17) ||  ||
|| 375/374 || 4.6228 || (3*5&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;)/(2*11*17) ||  ||
|| 442/441 || 3.9213 || (2*13*17)/(3*7)&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt; ||  ||
|| 442/441 || 3.9213 || (2*13*17)/(3*7)&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt; ||  ||
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|| [[77_76|77/76]] || 22.631 || (7*11)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*19) ||  ||
|| [[77_76|77/76]] || 22.631 || (7*11)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*19) ||  ||
|| [[96_95|96/95]] || 18.128 || (2&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;*3)/(5*19) ||  ||
|| [[96_95|96/95]] || 18.128 || (2&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;*3)/(5*19) ||  ||
|| 133/132 || 13.066 || (19*7)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3*11) ||  ||
|| 153/152 || 11.352 || (3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17)/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*19) ||  ||
|| 171/170 || 10.154 || (3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*19)/(2*5*17) ||  ||
|| 190/189 || 9.1358 || (2*5*19)/(3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*7) ||  ||
|| 209/208 || 8.3033 || (11*19)/(2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*13) ||  ||
|| 210/209 || 8.2637 || (2*3*5*7)/(11*19) ||  ||
|| 286/285 || 6.0639 || (2*11*13)/(3*5*19) ||  ||
|| 400/399 || 4.3335 || (2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/(3*7*19) ||  ||
|| 456/455 || 3.8007 || (2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3*19)/(5*7*13) ||  ||
|| 476/475 || 3.6409 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*7*17)/(5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*19) ||  ||
|| 495/494 || 3.501 || (3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5*11)/(2*13*19) ||  ||
|| 513/512 || 3.378 || &lt;span style="vertical-align: super;"&gt;(3^3*19)/2&lt;/span&gt;&lt;span style="vertical-align: super;"&gt;^9&lt;/span&gt; || 513th harmonic ||
||||||||~ 23-limit (incomplete) ||
||||||||~ 23-limit (incomplete) ||
|| [[23_22|23/22]] || 76.956 || 23/(2*11) ||  ||
|| [[23_22|23/22]] || 76.956 || 23/(2*11) ||  ||
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         &lt;td&gt;7.8514&lt;br /&gt;
         &lt;td&gt;7.8514&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(13*17)/(2^2*5*11)&lt;br /&gt;
         &lt;td&gt;(13*17)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5*11)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
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         &lt;td&gt;6.3532&lt;br /&gt;
         &lt;td&gt;6.3532&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3*7*13)/(2^4*17)&lt;br /&gt;
         &lt;td&gt;(3*7*13)/(2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*17)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
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         &lt;td&gt;6.0008&lt;br /&gt;
         &lt;td&gt;6.0008&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;17&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;/(2^5*3^2)&lt;br /&gt;
         &lt;td&gt;17&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;/(2&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;133/132&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13.066&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;(19*7)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3*11)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;153/152&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11.352&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17)/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*19)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;171/170&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10.154&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*19)/(2*5*17)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;190/189&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9.1358&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;(2*5*19)/(3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*7)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;209/208&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8.3033&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;(11*19)/(2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*13)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;210/209&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8.2637&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;(2*3*5*7)/(11*19)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;286/285&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6.0639&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;(2*11*13)/(3*5*19)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;400/399&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4.3335&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/(3*7*19)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;456/455&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3.8007&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3*19)/(5*7*13)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;476/475&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3.6409&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*7*17)/(5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*19)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;495/494&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3.501&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5*11)/(2*13*19)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;513/512&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3.378&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;span style="vertical-align: super;"&gt;(3^3*19)/2&lt;/span&gt;&lt;span style="vertical-align: super;"&gt;^9&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;513th harmonic&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Retrieved from "https://en.xen.wiki/w/List_of_superparticular_intervals"