17edt: Difference between revisions

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Wikispaces>Kosmorsky
**Imported revision 268502024 - Original comment: well thats just not right**
Wikispaces>Kosmorsky
**Imported revision 280666756 - Original comment: **
Line 1: Line 1:
<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:Kosmorsky|Kosmorsky]] and made on <tt>2011-10-25 16:34:58 UTC</tt>.<br>
: This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2011-11-30 12:42:30 UTC</tt>.<br>
: The original revision id was <tt>268502024</tt>.<br>
: The original revision id was <tt>280666756</tt>.<br>
: The revision comment was: <tt>well thats just not right</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>
<h4>Original Wikitext content:</h4>
<h4>Original Wikitext content:</h4>
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=Intervals=  
=Intervals=  
|| degree of 17edt || cents value || cents value octave reduced ||
|| degree of 17edt ||  || cents value || cents value octave reduced ||
|| 0 || 0 ||  ||
|| 0 || C || 0 ||  ||
|| 1 || 111.9 ||  ||
|| 1 || Db = B# || 111.9 ||  ||
|| 2 || 223.8 ||  ||
|| 2 || Eb = C# || 223.8 ||  ||
|| 3 || 335.6 ||  ||
|| 3 || D || 335.6 ||  ||
|| 4 || 447.5 ||  ||
|| 4 || E || 447.5 ||  ||
|| 5 || 559.4 ||  ||
|| 5 || F = D# || 559.4 ||  ||
|| 6 || 671.3 ||  ||
|| 6 || Gb = E# || 671.3 ||  ||
|| 7 || 783.2 ||  ||
|| 7 || Hb = F# || 783.2 ||  ||
|| 8 || 895.1 ||  ||
|| 8 || G || 895.1 ||  ||
|| 9 || 1006.9 ||  ||
|| 9 || H || 1006.9 ||  ||
|| 10 || 1118.8 ||  ||
|| 10 || Jb = G# || 1118.8 ||  ||
|| 11 || 1230.7 || 30.7 ||
|| 11 || Ab = H# || 1230.7 || 30.7 ||
|| 12 || 1342.6 || 142.6 ||
|| 12 || J || 1342.6 || 142.6 ||
|| 13 || 1454.5 || 254.5 ||
|| 13 || A || 1454.5 || 254.5 ||
|| 14 || 1566.3 || 366.3 ||
|| 14 || Bb = J# || 1566.3 || 366.3 ||
|| 15 || 1678.2 || 478.2 ||
|| 15 || Cb = A# || 1678.2 || 478.2 ||
|| 16 || 1790.1 || 590.1 ||
|| 16 || B || 1790.1 || 590.1 ||
|| 17 || 1902.0 || 702.0 ||
|| 17 || C || 1902.0 || 702.0 ||
|| 18 || 2013.9 || 813.9 ||
|| 18 ||  || 2013.9 || 813.9 ||
|| 19 || 2125.8 || 925.8 ||
|| 19 ||  || 2125.8 || 925.8 ||
|| 20 || 2237.6 || 1037.6 ||
|| 20 ||  || 2237.6 || 1037.6 ||
|| 21 || 2349..5 || 1149.5 ||
|| 21 ||  || 2349..5 || 1149.5 ||
|| 22 || 2461.4 || 61.4 ||
|| 22 ||  || 2461.4 || 61.4 ||
|| 23 || 2573.2 || 173.2 ||
|| 23 ||  || 2573.2 || 173.2 ||
|| 24 || 2685.2 || 285.2 ||
|| 24 ||  || 2685.2 || 285.2 ||
|| 25 || 2797.1 || 397.1 ||
|| 25 ||  || 2797.1 || 397.1 ||
|| 26 || 2908.9 || 508.9 ||
|| 26 ||  || 2908.9 || 508.9 ||
|| 27 || 3020.8 || 620.8 ||
|| 27 ||  || 3020.8 || 620.8 ||
|| 28 || 3132.7 || 732.7 ||
|| 28 ||  || 3132.7 || 732.7 ||
|| 29 || 3244.6 || 844.6 ||
|| 29 ||  || 3244.6 || 844.6 ||
|| 30 || 3356.5 || 956.5 ||
|| 30 ||  || 3356.5 || 956.5 ||
|| 31 || 3468.3 || 1068.3 ||
|| 31 ||  || 3468.3 || 1068.3 ||
|| 32 || 3580.2 || 1180.2 ||
|| 32 ||  || 3580.2 || 1180.2 ||
|| 33 || 3692.1 || 92.1 ||
|| 33 ||  || 3692.1 || 92.1 ||
|| 34 || 3804.0 || 204.0 ||
|| 34 ||  || 3804.0 || 204.0 ||
 
* Notes named so that C D E F G H J A B C = Lambda mode


=Z function=  
=Z function=  
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;degree of 17edt&lt;br /&gt;
         &lt;td&gt;degree of 17edt&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;cents value&lt;br /&gt;
         &lt;td&gt;cents value&lt;br /&gt;
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;0&lt;br /&gt;
         &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;C&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;0&lt;br /&gt;
         &lt;td&gt;0&lt;br /&gt;
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;1&lt;br /&gt;
         &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Db = B#&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;111.9&lt;br /&gt;
         &lt;td&gt;111.9&lt;br /&gt;
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;2&lt;br /&gt;
         &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Eb = C#&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;223.8&lt;br /&gt;
         &lt;td&gt;223.8&lt;br /&gt;
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;3&lt;br /&gt;
         &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;D&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;335.6&lt;br /&gt;
         &lt;td&gt;335.6&lt;br /&gt;
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;4&lt;br /&gt;
         &lt;td&gt;4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;E&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;447.5&lt;br /&gt;
         &lt;td&gt;447.5&lt;br /&gt;
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;5&lt;br /&gt;
         &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;F = D#&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;559.4&lt;br /&gt;
         &lt;td&gt;559.4&lt;br /&gt;
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;6&lt;br /&gt;
         &lt;td&gt;6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Gb = E#&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;671.3&lt;br /&gt;
         &lt;td&gt;671.3&lt;br /&gt;
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;7&lt;br /&gt;
         &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Hb = F#&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;783.2&lt;br /&gt;
         &lt;td&gt;783.2&lt;br /&gt;
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;8&lt;br /&gt;
         &lt;td&gt;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;895.1&lt;br /&gt;
         &lt;td&gt;895.1&lt;br /&gt;
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;9&lt;br /&gt;
         &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;H&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1006.9&lt;br /&gt;
         &lt;td&gt;1006.9&lt;br /&gt;
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;10&lt;br /&gt;
         &lt;td&gt;10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Jb = G#&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1118.8&lt;br /&gt;
         &lt;td&gt;1118.8&lt;br /&gt;
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;11&lt;br /&gt;
         &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Ab = H#&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1230.7&lt;br /&gt;
         &lt;td&gt;1230.7&lt;br /&gt;
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;12&lt;br /&gt;
         &lt;td&gt;12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;J&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1342.6&lt;br /&gt;
         &lt;td&gt;1342.6&lt;br /&gt;
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;13&lt;br /&gt;
         &lt;td&gt;13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1454.5&lt;br /&gt;
         &lt;td&gt;1454.5&lt;br /&gt;
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;14&lt;br /&gt;
         &lt;td&gt;14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Bb = J#&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1566.3&lt;br /&gt;
         &lt;td&gt;1566.3&lt;br /&gt;
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;15&lt;br /&gt;
         &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Cb = A#&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1678.2&lt;br /&gt;
         &lt;td&gt;1678.2&lt;br /&gt;
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;16&lt;br /&gt;
         &lt;td&gt;16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;B&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1790.1&lt;br /&gt;
         &lt;td&gt;1790.1&lt;br /&gt;
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;17&lt;br /&gt;
         &lt;td&gt;17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;C&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1902.0&lt;br /&gt;
         &lt;td&gt;1902.0&lt;br /&gt;
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;18&lt;br /&gt;
         &lt;td&gt;18&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;2013.9&lt;br /&gt;
         &lt;td&gt;2013.9&lt;br /&gt;
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;19&lt;br /&gt;
         &lt;td&gt;19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;2125.8&lt;br /&gt;
         &lt;td&gt;2125.8&lt;br /&gt;
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;20&lt;br /&gt;
         &lt;td&gt;20&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;2237.6&lt;br /&gt;
         &lt;td&gt;2237.6&lt;br /&gt;
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;21&lt;br /&gt;
         &lt;td&gt;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;2349..5&lt;br /&gt;
         &lt;td&gt;2349..5&lt;br /&gt;
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;22&lt;br /&gt;
         &lt;td&gt;22&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;2461.4&lt;br /&gt;
         &lt;td&gt;2461.4&lt;br /&gt;
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;23&lt;br /&gt;
         &lt;td&gt;23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;2573.2&lt;br /&gt;
         &lt;td&gt;2573.2&lt;br /&gt;
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;24&lt;br /&gt;
         &lt;td&gt;24&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;2685.2&lt;br /&gt;
         &lt;td&gt;2685.2&lt;br /&gt;
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;25&lt;br /&gt;
         &lt;td&gt;25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;2797.1&lt;br /&gt;
         &lt;td&gt;2797.1&lt;br /&gt;
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;26&lt;br /&gt;
         &lt;td&gt;26&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;2908.9&lt;br /&gt;
         &lt;td&gt;2908.9&lt;br /&gt;
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;27&lt;br /&gt;
         &lt;td&gt;27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3020.8&lt;br /&gt;
         &lt;td&gt;3020.8&lt;br /&gt;
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;28&lt;br /&gt;
         &lt;td&gt;28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3132.7&lt;br /&gt;
         &lt;td&gt;3132.7&lt;br /&gt;
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;29&lt;br /&gt;
         &lt;td&gt;29&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3244.6&lt;br /&gt;
         &lt;td&gt;3244.6&lt;br /&gt;
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;30&lt;br /&gt;
         &lt;td&gt;30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3356.5&lt;br /&gt;
         &lt;td&gt;3356.5&lt;br /&gt;
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;31&lt;br /&gt;
         &lt;td&gt;31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3468.3&lt;br /&gt;
         &lt;td&gt;3468.3&lt;br /&gt;
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;32&lt;br /&gt;
         &lt;td&gt;32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3580.2&lt;br /&gt;
         &lt;td&gt;3580.2&lt;br /&gt;
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;33&lt;br /&gt;
         &lt;td&gt;33&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3692.1&lt;br /&gt;
         &lt;td&gt;3692.1&lt;br /&gt;
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     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;34&lt;br /&gt;
         &lt;td&gt;34&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3804.0&lt;br /&gt;
         &lt;td&gt;3804.0&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;Notes named so that C D E F G H J A B C = Lambda mode&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Z function"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Z function&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Z function"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Z function&lt;/h1&gt;
  Below is a plot of the &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Removing%20primes"&gt;no-twos Z function&lt;/a&gt; in the vicinity of 17edt.&lt;br /&gt;
  Below is a plot of the &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Removing%20primes"&gt;no-twos Z function&lt;/a&gt; in the vicinity of 17edt.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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&lt;!-- ws:start:WikiTextLocalImageRule:380:&amp;lt;img src=&amp;quot;/file/view/17edt.png/250611032/17edt.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/17edt.png/250611032/17edt.png" alt="17edt.png" title="17edt.png" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:380 --&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 12:42, 30 November 2011

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Original Wikitext content:

[[toc|flat]]
=Properties= 
17edt divides 3, the tritave, into 17 equal parts of 111.880 cents each, corresponding to 10.726 edo. It tempers out 245/243 and 16807/15625 in the 7-limit, 77/75 and 1331/1323 in the 11-limit, and 175/169 and 121/117 in the 13-limit. It supports the no-twos temperament tempering out 245/243 and 77/75, which in terms of tritave patent vals could be written 17&21.

17edt is the sixth [[The Riemann Zeta Function and Tuning#Removing%20primes|zeta peak tritave division]].

=Discussion= 
17edt is closely related [[13edt]], the Bohlen-Pierce division, because they share the feature of tempering out 245/243. Both 13edt and 17edt have 4L+5s nonatonic modes, but whereas the ratio of large to small steps in 13edt is a calm 2:1, in 17edt it is a hard 3:1. Thus, the approximation of 5/3 and 7/3 suffers slightly, in return for a very good approximation of 11/9, which is in fact the size of the large step.

=Intervals= 
|| degree of 17edt ||   || cents value || cents value octave reduced ||
|| 0 || C || 0 ||   ||
|| 1 || Db = B# || 111.9 ||   ||
|| 2 || Eb = C# || 223.8 ||   ||
|| 3 || D || 335.6 ||   ||
|| 4 || E || 447.5 ||   ||
|| 5 || F = D# || 559.4 ||   ||
|| 6 || Gb = E# || 671.3 ||   ||
|| 7 || Hb = F# || 783.2 ||   ||
|| 8 || G || 895.1 ||   ||
|| 9 || H || 1006.9 ||   ||
|| 10 || Jb = G# || 1118.8 ||   ||
|| 11 || Ab = H# || 1230.7 || 30.7 ||
|| 12 || J || 1342.6 || 142.6 ||
|| 13 || A || 1454.5 || 254.5 ||
|| 14 || Bb = J# || 1566.3 || 366.3 ||
|| 15 || Cb = A# || 1678.2 || 478.2 ||
|| 16 || B || 1790.1 || 590.1 ||
|| 17 || C || 1902.0 || 702.0 ||
|| 18 ||   || 2013.9 || 813.9 ||
|| 19 ||   || 2125.8 || 925.8 ||
|| 20 ||   || 2237.6 || 1037.6 ||
|| 21 ||   || 2349..5 || 1149.5 ||
|| 22 ||   || 2461.4 || 61.4 ||
|| 23 ||   || 2573.2 || 173.2 ||
|| 24 ||   || 2685.2 || 285.2 ||
|| 25 ||   || 2797.1 || 397.1 ||
|| 26 ||   || 2908.9 || 508.9 ||
|| 27 ||   || 3020.8 || 620.8 ||
|| 28 ||   || 3132.7 || 732.7 ||
|| 29 ||   || 3244.6 || 844.6 ||
|| 30 ||   || 3356.5 || 956.5 ||
|| 31 ||   || 3468.3 || 1068.3 ||
|| 32 ||   || 3580.2 || 1180.2 ||
|| 33 ||   || 3692.1 || 92.1 ||
|| 34 ||   || 3804.0 || 204.0 ||

* Notes named so that C D E F G H J A B C = Lambda mode

=Z function= 
Below is a plot of the [[The Riemann Zeta Function and Tuning#Removing%20primes|no-twos Z function]] in the vicinity of 17edt.

[[image:17edt.png]]

Original HTML content:

<html><head><title>17edt</title></head><body><!-- ws:start:WikiTextTocRule:8:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:8 --><!-- ws:start:WikiTextTocRule:9: --><a href="#Properties">Properties</a><!-- ws:end:WikiTextTocRule:9 --><!-- ws:start:WikiTextTocRule:10: --> | <a href="#Discussion">Discussion</a><!-- ws:end:WikiTextTocRule:10 --><!-- ws:start:WikiTextTocRule:11: --> | <a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:11 --><!-- ws:start:WikiTextTocRule:12: --> | <a href="#Z function">Z function</a><!-- ws:end:WikiTextTocRule:12 --><!-- ws:start:WikiTextTocRule:13: -->
<!-- ws:end:WikiTextTocRule:13 --><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Properties"></a><!-- ws:end:WikiTextHeadingRule:0 -->Properties</h1>
 17edt divides 3, the tritave, into 17 equal parts of 111.880 cents each, corresponding to 10.726 edo. It tempers out 245/243 and 16807/15625 in the 7-limit, 77/75 and 1331/1323 in the 11-limit, and 175/169 and 121/117 in the 13-limit. It supports the no-twos temperament tempering out 245/243 and 77/75, which in terms of tritave patent vals could be written 17&amp;21.<br />
<br />
17edt is the sixth <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Removing%20primes">zeta peak tritave division</a>.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Discussion"></a><!-- ws:end:WikiTextHeadingRule:2 -->Discussion</h1>
 17edt is closely related <a class="wiki_link" href="/13edt">13edt</a>, the Bohlen-Pierce division, because they share the feature of tempering out 245/243. Both 13edt and 17edt have 4L+5s nonatonic modes, but whereas the ratio of large to small steps in 13edt is a calm 2:1, in 17edt it is a hard 3:1. Thus, the approximation of 5/3 and 7/3 suffers slightly, in return for a very good approximation of 11/9, which is in fact the size of the large step.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:4 -->Intervals</h1>
 

<table class="wiki_table">
    <tr>
        <td>degree of 17edt<br />
</td>
        <td><br />
</td>
        <td>cents value<br />
</td>
        <td>cents value octave reduced<br />
</td>
    </tr>
    <tr>
        <td>0<br />
</td>
        <td>C<br />
</td>
        <td>0<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>Db = B#<br />
</td>
        <td>111.9<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>Eb = C#<br />
</td>
        <td>223.8<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>D<br />
</td>
        <td>335.6<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>E<br />
</td>
        <td>447.5<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>F = D#<br />
</td>
        <td>559.4<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>Gb = E#<br />
</td>
        <td>671.3<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>Hb = F#<br />
</td>
        <td>783.2<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>G<br />
</td>
        <td>895.1<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>H<br />
</td>
        <td>1006.9<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>Jb = G#<br />
</td>
        <td>1118.8<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>Ab = H#<br />
</td>
        <td>1230.7<br />
</td>
        <td>30.7<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>J<br />
</td>
        <td>1342.6<br />
</td>
        <td>142.6<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>A<br />
</td>
        <td>1454.5<br />
</td>
        <td>254.5<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>Bb = J#<br />
</td>
        <td>1566.3<br />
</td>
        <td>366.3<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>Cb = A#<br />
</td>
        <td>1678.2<br />
</td>
        <td>478.2<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>B<br />
</td>
        <td>1790.1<br />
</td>
        <td>590.1<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>C<br />
</td>
        <td>1902.0<br />
</td>
        <td>702.0<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td><br />
</td>
        <td>2013.9<br />
</td>
        <td>813.9<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td><br />
</td>
        <td>2125.8<br />
</td>
        <td>925.8<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td><br />
</td>
        <td>2237.6<br />
</td>
        <td>1037.6<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td><br />
</td>
        <td>2349..5<br />
</td>
        <td>1149.5<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td><br />
</td>
        <td>2461.4<br />
</td>
        <td>61.4<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td><br />
</td>
        <td>2573.2<br />
</td>
        <td>173.2<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td><br />
</td>
        <td>2685.2<br />
</td>
        <td>285.2<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td><br />
</td>
        <td>2797.1<br />
</td>
        <td>397.1<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td><br />
</td>
        <td>2908.9<br />
</td>
        <td>508.9<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td><br />
</td>
        <td>3020.8<br />
</td>
        <td>620.8<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td><br />
</td>
        <td>3132.7<br />
</td>
        <td>732.7<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td><br />
</td>
        <td>3244.6<br />
</td>
        <td>844.6<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td><br />
</td>
        <td>3356.5<br />
</td>
        <td>956.5<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td><br />
</td>
        <td>3468.3<br />
</td>
        <td>1068.3<br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td><br />
</td>
        <td>3580.2<br />
</td>
        <td>1180.2<br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td><br />
</td>
        <td>3692.1<br />
</td>
        <td>92.1<br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td><br />
</td>
        <td>3804.0<br />
</td>
        <td>204.0<br />
</td>
    </tr>
</table>

<br />
<ul><li>Notes named so that C D E F G H J A B C = Lambda mode</li></ul><br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Z function"></a><!-- ws:end:WikiTextHeadingRule:6 -->Z function</h1>
 Below is a plot of the <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Removing%20primes">no-twos Z function</a> in the vicinity of 17edt.<br />
<br />
<!-- ws:start:WikiTextLocalImageRule:380:&lt;img src=&quot;/file/view/17edt.png/250611032/17edt.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/17edt.png/250611032/17edt.png" alt="17edt.png" title="17edt.png" /><!-- ws:end:WikiTextLocalImageRule:380 --></body></html>