29edo: Difference between revisions

Revision as of 19:58, 17 November 2010

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Original Wikitext content:

29edo divides the 2:1 octave into 29 equal steps of approximately 41.37931 cents.

29 is the lowest edo which approximates the 3:2 just fifth more accurately than 12edo: 3/2 = 701.955... cents; 17 degrees of 29edo = 703.448... cents. Since the fifth is slightly sharp, 29edo is a [[positive temperament]] -- a Superpythagorean instead of a Meantone system. 

The third (and of course second) is the only harmonic, of the intelligibly low ones anyway, that 29-edo approximates, and it does so stunningly well. Accordingly it's best use is as an equally tempered pythagorean scale, which despite yall's focus on insane xenharmonic stuff is still a good thing to have around. It does give some good approximations of other just ratios, but without the harmonics themselves, making them into actual chords in sensible progressions is impossible.

==Intervals of 29edo== 
|| degrees of 29edo || cents value ||
|| 0 || 0 ||
|| 1 || 41.379 ||
|| 2 || 82.759 ||
|| 3 || 124.138 ||
|| 4 || 165.517 ||
|| 5 || 206.897 ||
|| 6 || 248.276 ||
|| 7 || 289.655 ||
|| 8 || 331.034 ||
|| 9 || 372.414 ||
|| 10 || 413.793 ||
|| 11 || 455.172 ||
|| 12 || 496.552 ||
|| 13 || 537.931 ||
|| 14 || 579.310 ||
|| 15 || 620.690 ||
|| 16 || 662.069 ||
|| 17 || 703.448 ||
|| 18 || 744.828 ||
|| 19 || 786.207 ||
|| 20 || 827.586 ||
|| 21 || 868.966 ||
|| 22 || 910.345 ||
|| 23 || 951.724 ||
|| 24 || 993.103 ||
|| 25 || 1034.483 ||
|| 26 || 1075.862 ||
|| 27 || 1117.241 ||
|| 28 || 1158.621 ||

Original HTML content:

<html><head><title>29edo</title></head><body>29edo divides the 2:1 octave into 29 equal steps of approximately 41.37931 cents.<br />
<br />
29 is the lowest edo which approximates the 3:2 just fifth more accurately than 12edo: 3/2 = 701.955... cents; 17 degrees of 29edo = 703.448... cents. Since the fifth is slightly sharp, 29edo is a <a class="wiki_link" href="/positive%20temperament">positive temperament</a> -- a Superpythagorean instead of a Meantone system. <br />
<br />
The third (and of course second) is the only harmonic, of the intelligibly low ones anyway, that 29-edo approximates, and it does so stunningly well. Accordingly it's best use is as an equally tempered pythagorean scale, which despite yall's focus on insane xenharmonic stuff is still a good thing to have around. It does give some good approximations of other just ratios, but without the harmonics themselves, making them into actual chords in sensible progressions is impossible.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Intervals of 29edo"></a><!-- ws:end:WikiTextHeadingRule:0 -->Intervals of 29edo</h2>
 

<table class="wiki_table">
    <tr>
        <td>degrees of 29edo<br />
</td>
        <td>cents value<br />
</td>
    </tr>
    <tr>
        <td>0<br />
</td>
        <td>0<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>41.379<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>82.759<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>124.138<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>165.517<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>206.897<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>248.276<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>289.655<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>331.034<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>372.414<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>413.793<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>455.172<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>496.552<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>537.931<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>579.310<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>620.690<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>662.069<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>703.448<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>744.828<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>786.207<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>827.586<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>868.966<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>910.345<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>951.724<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>993.103<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>1034.483<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>1075.862<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>1117.241<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>1158.621<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:guest|guest]] and made on <tt>2010-11-17 19:58:16 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2010-11-17 19:58:34 UTC</tt>.<br>
-: The original revision id was <tt>180616779</tt>.<br>
+: The original revision id was <tt>180616867</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>
@@ Line 10: / Line 10: @@
 is the lowest edo which approximates the 3:2 just fifth more accurately than 12edo: 3/2 = 701.955... cents; 17 degrees of 29edo = 703.448... cents. Since the fifth is slightly sharp, 29edo is a [[positive temperament]] -- a Superpythagorean instead of a Meantone system.
-The third (and of course second) is the only harmonic, of the intelligibly low ones anyway, that 29-edo approximates, and it does so stunningly well. Accordingly it's best use is as an equally tempered pythagorean scale, which despite yall's focus on insane microtonal stuff is still a good thing to have around. It does give some good approximations of other just ratios, but without the harmonics themselves, making them into actual chords in sensible progressions is impossible.
+The third (and of course second) is the only harmonic, of the intelligibly low ones anyway, that 29-edo approximates, and it does so stunningly well. Accordingly it's best use is as an equally tempered pythagorean scale, which despite yall's focus on insane xenharmonic stuff is still a good thing to have around. It does give some good approximations of other just ratios, but without the harmonics themselves, making them into actual chords in sensible progressions is impossible.
 ==Intervals of 29edo==
@@ Line 48: / Line 48: @@
 is the lowest edo which approximates the 3:2 just fifth more accurately than 12edo: 3/2 = 701.955... cents; 17 degrees of 29edo = 703.448... cents. Since the fifth is slightly sharp, 29edo is a &lt;a class="wiki_link" href="/positive%20temperament"&gt;positive temperament&lt;/a&gt; -- a Superpythagorean instead of a Meantone system. &lt;br /&gt;
 &lt;br /&gt;
-The third (and of course second) is the only harmonic, of the intelligibly low ones anyway, that 29-edo approximates, and it does so stunningly well. Accordingly it's best use is as an equally tempered pythagorean scale, which despite yall's focus on insane microtonal stuff is still a good thing to have around. It does give some good approximations of other just ratios, but without the harmonics themselves, making them into actual chords in sensible progressions is impossible.&lt;br /&gt;
+The third (and of course second) is the only harmonic, of the intelligibly low ones anyway, that 29-edo approximates, and it does so stunningly well. Accordingly it's best use is as an equally tempered pythagorean scale, which despite yall's focus on insane xenharmonic stuff is still a good thing to have around. It does give some good approximations of other just ratios, but without the harmonics themselves, making them into actual chords in sensible progressions is impossible.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Intervals of 29edo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Intervals of 29edo&lt;/h2&gt;

29edo: Difference between revisions

Revision as of 19:58, 17 November 2010

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