Nearest just interval: Difference between revisions

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Wikispaces>xenwolf
**Imported revision 146943113 - Original comment: **
Wikispaces>xenwolf
**Imported revision 147266335 - Original comment: the inverse isn't so interesting...**
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:xenwolf|xenwolf]] and made on <tt>2010-06-04 04:55:48 UTC</tt>.<br>
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2010-06-06 17:12:15 UTC</tt>.<br>
: The original revision id was <tt>146943113</tt>.<br>
: The original revision id was <tt>147266335</tt>.<br>
: The revision comment was: <tt></tt><br>
: The revision comment was: <tt>the inverse isn't so interesting...</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>
Line 14: Line 14:
|| ... || ... || ... || ... ||
|| ... || ... || ... || ... ||
||= 3 / 2 ||= 2.585 ||= 701.96 ||= 101.96 ||
||= 3 / 2 ||= 2.585 ||= 701.96 ||= 101.96 ||
||= 4 / 3 ||= 3.585 ||= 498.04 ||= 101.96 ||
||= 7 / 5 ||= 5.129 ||= 582.51 ||= 17.49 ||
||= 7 / 5 ||= 5.129 ||= 582.51 ||= 17.49 ||
||= 10 / 7 ||= 6.129 ||= 617.49 ||= 17.49 ||
||= 17 / 12 ||= 7.672 ||= 603.00 ||= 3.000 ||
||= 17 / 12 ||= 7.672 ||= 603.00 ||= 3.000 ||
||= 24 / 17 ||= 8.672 ||= 597.00 ||= 3.000 ||
|| ... || ... || ... || ... ||
|| ... || ... || ... || ... ||
</pre></div>
</pre></div>
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;701.96&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;701.96&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;101.96&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;4 / 3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3.585&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;498.04&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;101.96&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;101.96&lt;br /&gt;
Line 76: Line 63:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;582.51&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;582.51&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;17.49&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;10 / 7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6.129&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;617.49&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;17.49&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;17.49&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;603.00&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;603.00&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3.000&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;24 / 17&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;8.672&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;597.00&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;3.000&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;3.000&lt;br /&gt;

Revision as of 17:12, 6 June 2010

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author xenwolf and made on 2010-06-06 17:12:15 UTC.
The original revision id was 147266335.
The revision comment was: the inverse isn't so interesting...

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

An interval given by its logarhithmic size measure (like [[cent]]s or amount of edo-atoms) has an infinite list of //nearest just intervals//

==Example==
The 600-cent interval (6 steps of [[12edo]], "Tritone") approximates following ratios:

|| **freq. ratio** || **log([[Tenney Height]])** || **size** in cents || **"error"** in cents ||
|| ... || ... || ... || ... ||
||= 3 / 2 ||= 2.585 ||= 701.96 ||= 101.96 ||
||= 7 / 5 ||= 5.129 ||= 582.51 ||= 17.49 ||
||= 17 / 12 ||= 7.672 ||= 603.00 ||= 3.000 ||
|| ... || ... || ... || ... ||

Original HTML content:

<html><head><title>Nearest just interval</title></head><body>An interval given by its logarhithmic size measure (like <a class="wiki_link" href="/cent">cent</a>s or amount of edo-atoms) has an infinite list of <em>nearest just intervals</em><br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Example"></a><!-- ws:end:WikiTextHeadingRule:0 -->Example</h2>
The 600-cent interval (6 steps of <a class="wiki_link" href="/12edo">12edo</a>, &quot;Tritone&quot;) approximates following ratios:<br />
<br />


<table class="wiki_table">
    <tr>
        <td><strong>freq. ratio</strong><br />
</td>
        <td><strong>log(<a class="wiki_link" href="/Tenney%20Height">Tenney Height</a>)</strong><br />
</td>
        <td><strong>size</strong> in cents<br />
</td>
        <td><strong>&quot;error&quot;</strong> in cents<br />
</td>
    </tr>
    <tr>
        <td>...<br />
</td>
        <td>...<br />
</td>
        <td>...<br />
</td>
        <td>...<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">3 / 2<br />
</td>
        <td style="text-align: center;">2.585<br />
</td>
        <td style="text-align: center;">701.96<br />
</td>
        <td style="text-align: center;">101.96<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">7 / 5<br />
</td>
        <td style="text-align: center;">5.129<br />
</td>
        <td style="text-align: center;">582.51<br />
</td>
        <td style="text-align: center;">17.49<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">17 / 12<br />
</td>
        <td style="text-align: center;">7.672<br />
</td>
        <td style="text-align: center;">603.00<br />
</td>
        <td style="text-align: center;">3.000<br />
</td>
    </tr>
    <tr>
        <td>...<br />
</td>
        <td>...<br />
</td>
        <td>...<br />
</td>
        <td>...<br />
</td>
    </tr>
</table>

</body></html>