23edf

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Revision as of 05:23, 13 June 2015 by Wikispaces>toddiharrop (**Imported revision 553808036 - Original comment: **)
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This revision was by author toddiharrop and made on 2015-06-13 05:23:10 UTC.
The original revision id was 553808036.
The revision comment was:

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Original Wikitext content:

Twenty-three equal divisions of the perfect fifth (23ed3/2)

Rank 1 scale with step size of 30.52 cents.
Close to 39ed2 and/or 62ed3, however, the respective
octave and twelfth would need to be nearly 10 cents flat.
A proponent of this scale is Petr Pařízek.

Some intervals in table below, selected on the basis of
single-use of primes (for most cases):
||= **Step** ||= **Size** 
**(cents)** ||= **Approx.** 
**(JI) ratio** ||= **Error from** 
**ratio (cents)** ||
||= 19 ||= 579.9 ||= 7/5 ||= –2.6¢ ||
||= 23 ||= 702 ||= 3/2 ||=   ||
||= 24 ||= 732.5 ||= 29/19 ||= +0.4¢ ||
||= 29 ||= 885.1 ||= 5/3 ||= +0.7¢ ||
||= 31 ||= 946.1 ||= 19/11 ||= –0.1¢ ||
||= 35 ||= 1068 ||= 13/7 ||= –3.5¢ ||
||= 46 ||= 1404 ||= 9/4 ||=   ||
||= 48 ||= 1465 ||= 7/3 ||= –1.9¢ ||
||= 52 ||= 1587 ||= 5/2 ||= +0.7¢ ||
||= 55 ||= 1679 ||= 29/11 ||= +0.3¢ ||
||= 58 ||= 1770 ||= 25/9 ||= +1.4¢ ||
||= 71 ||= 2167 ||= 7/2 ||= –1.9¢ ||
||=   ||=   ||=   ||=   ||
–Todd Harrop (June 2015)

Original HTML content:

<html><head><title>23edf</title></head><body>Twenty-three equal divisions of the perfect fifth (23ed3/2)<br />
<br />
Rank 1 scale with step size of 30.52 cents.<br />
Close to 39ed2 and/or 62ed3, however, the respective<br />
octave and twelfth would need to be nearly 10 cents flat.<br />
A proponent of this scale is Petr Pařízek.<br />
<br />
Some intervals in table below, selected on the basis of<br />
single-use of primes (for most cases):<br />


<table class="wiki_table">
    <tr>
        <td style="text-align: center;"><strong>Step</strong><br />
</td>
        <td style="text-align: center;"><strong>Size</strong> <br />
<strong>(cents)</strong><br />
</td>
        <td style="text-align: center;"><strong>Approx.</strong> <br />
<strong>(JI) ratio</strong><br />
</td>
        <td style="text-align: center;"><strong>Error from</strong> <br />
<strong>ratio (cents)</strong><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">19<br />
</td>
        <td style="text-align: center;">579.9<br />
</td>
        <td style="text-align: center;">7/5<br />
</td>
        <td style="text-align: center;">–2.6¢<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">23<br />
</td>
        <td style="text-align: center;">702<br />
</td>
        <td style="text-align: center;">3/2<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">24<br />
</td>
        <td style="text-align: center;">732.5<br />
</td>
        <td style="text-align: center;">29/19<br />
</td>
        <td style="text-align: center;">+0.4¢<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">29<br />
</td>
        <td style="text-align: center;">885.1<br />
</td>
        <td style="text-align: center;">5/3<br />
</td>
        <td style="text-align: center;">+0.7¢<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">31<br />
</td>
        <td style="text-align: center;">946.1<br />
</td>
        <td style="text-align: center;">19/11<br />
</td>
        <td style="text-align: center;">–0.1¢<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">35<br />
</td>
        <td style="text-align: center;">1068<br />
</td>
        <td style="text-align: center;">13/7<br />
</td>
        <td style="text-align: center;">–3.5¢<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">46<br />
</td>
        <td style="text-align: center;">1404<br />
</td>
        <td style="text-align: center;">9/4<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">48<br />
</td>
        <td style="text-align: center;">1465<br />
</td>
        <td style="text-align: center;">7/3<br />
</td>
        <td style="text-align: center;">–1.9¢<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">52<br />
</td>
        <td style="text-align: center;">1587<br />
</td>
        <td style="text-align: center;">5/2<br />
</td>
        <td style="text-align: center;">+0.7¢<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">55<br />
</td>
        <td style="text-align: center;">1679<br />
</td>
        <td style="text-align: center;">29/11<br />
</td>
        <td style="text-align: center;">+0.3¢<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">58<br />
</td>
        <td style="text-align: center;">1770<br />
</td>
        <td style="text-align: center;">25/9<br />
</td>
        <td style="text-align: center;">+1.4¢<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">71<br />
</td>
        <td style="text-align: center;">2167<br />
</td>
        <td style="text-align: center;">7/2<br />
</td>
        <td style="text-align: center;">–1.9¢<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
</table>

–Todd Harrop (June 2015)</body></html>
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