Nearest just interval: Difference between revisions
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Wikispaces>xenwolf **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: | : 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> | : The original revision id was <tt>146943089</tt>.<br> | ||
: The revision comment was: <tt> | : 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** || ** | || **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 || | ||
| Line 37: | Line 37: | ||
<td><strong>size in cents</strong><br /> | <td><strong>size in cents</strong><br /> | ||
</td> | </td> | ||
<td><strong> | <td><strong>&quot;error&quot;</strong> (ct)<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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:<h2> --><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>, "Tritone") 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>"error"</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>