Nearest just interval: Difference between revisions

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**Imported revision 146942725 - Original comment: garbage removed**
Wikispaces>xenwolf
**Imported revision 146943089 - 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:xenwolf|xenwolf]] and made on <tt>2010-06-04 04:50:47 UTC</tt>.<br>
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2010-06-04 04:55:23 UTC</tt>.<br>
: The original revision id was <tt>146942725</tt>.<br>
: The original revision id was <tt>146943089</tt>.<br>
: The revision comment was: <tt>garbage removed</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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The 600-cent interval (6 steps of [[12edo]], "Tritone") approximates following ratios:
The 600-cent interval (6 steps of [[12edo]], "Tritone") approximates following ratios:


|| **freq. ratio** || **log([[Tenney Height]])** || **size in cents** || **abs. "error"** ||
|| **freq. ratio** || **log([[Tenney Height]])** || **size in cents** || **"error"** (ct) ||
|| ... || ... || ... || ... ||
|| ... || ... || ... || ... ||
||= 3 / 2 ||= 2.585 ||= 701.96 ||= 101.96 ||
||= 3 / 2 ||= 2.585 ||= 701.96 ||= 101.96 ||
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         &lt;td&gt;&lt;strong&gt;size in cents&lt;/strong&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;size in cents&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;strong&gt;abs. &amp;quot;error&amp;quot;&lt;/strong&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;&amp;quot;error&amp;quot;&lt;/strong&gt; (ct)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;

Revision as of 04:55, 4 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 2010-06-04 04:55:23 UTC.
The original revision id was 146943089.
The revision comment was:

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"** (ct) ||
|| ... || ... || ... || ... ||
||= 3 / 2 ||= 2.585 ||= 701.96 ||= 101.96 ||
||= 4 / 3 ||= 3.585 ||= 498.04 ||= 101.96 ||
||= 7 / 5 ||= 5.129 ||= 582.51 ||= 17.49 ||
||= 10 / 7 ||= 6.129 ||= 617.49 ||= 17.49 ||
||= 17 / 12 ||= 7.672 ||= 603.00 ||= 3.000 ||
||= 24 / 17 ||= 8.672 ||= 597.00 ||= 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 in cents</strong><br />
</td>
        <td><strong>&quot;error&quot;</strong> (ct)<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;">4 / 3<br />
</td>
        <td style="text-align: center;">3.585<br />
</td>
        <td style="text-align: center;">498.04<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;">10 / 7<br />
</td>
        <td style="text-align: center;">6.129<br />
</td>
        <td style="text-align: center;">617.49<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 style="text-align: center;">24 / 17<br />
</td>
        <td style="text-align: center;">8.672<br />
</td>
        <td style="text-align: center;">597.00<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>