Nearest just interval: Difference between revisions

Revision as of 04:50, 4 June 2010

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This revision was by author xenwolf and made on 2010-06-04 04:50:47 UTC.

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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** || **abs. "error"** ||
|| ... || ... || ... || ... ||
||= 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>abs. &quot;error&quot;</strong><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>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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 04:50:23 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2010-06-04 04:50:47 UTC</tt>.<br>
-: The original revision id was <tt>146942699</tt>.<br>
+: The original revision id was <tt>146942725</tt>.<br>
-: The revision comment was: <tt></tt><br>
+: The revision comment was: <tt>garbage removed</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>
@@ Line 20: / Line 20: @@
 ||= 24 / 17 ||= 8.672 ||= 597.00 ||= 3.000 ||
 || ... || ... || ... || ... ||
- approximates 7/5, 10/7, ...</pre></div>
+</pre></div>
 <h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Nearest just interval&lt;/title&gt;&lt;/head&gt;&lt;body&gt;An interval given by its logarhithmic size measure (like &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s or amount of edo-atoms) has an infinite list of &lt;em&gt;nearest just intervals&lt;/em&gt;&lt;br /&gt;
@@ Line 122: / Line 122: @@
 &lt;/table&gt;
- approximates 7/5, 10/7, ...&lt;/body&gt;&lt;/html&gt;</pre></div>
+&lt;/body&gt;&lt;/html&gt;</pre></div>

Nearest just interval: Difference between revisions

Revision as of 04:50, 4 June 2010

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