29edo: Difference between revisions
Wikispaces>guest **Imported revision 180616867 - Original comment: ** |
Wikispaces>Osmiorisbendi **Imported revision 210044612 - 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: | : This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2011-03-13 16:11:40 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>210044612</tt>.<br> | ||
: The revision comment was: <tt></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> | ||
<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;white-space: pre-wrap ! important" class="old-revision-html">29edo divides the 2:1 octave into 29 equal steps of approximately 41.37931 cents. | <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;white-space: pre-wrap ! important" class="old-revision-html">=<span style="color: #ff4700; font-size: 103%;">29 tone equal temperament</span>= | ||
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. | 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. | ||
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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. | 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 | ==Intervals== | ||
|| | || Degrees of 29-EDO || Cents value || | ||
|| 0 || 0 || | || 0 || 0 || | ||
|| 1 || 41.379 || | || 1 || 41.379 || | ||
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|| 28 || 1158.621 ||</pre></div> | || 28 || 1158.621 ||</pre></div> | ||
<h4>Original HTML content:</h4> | <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"><html><head><title>29edo</title></head><body>29edo divides the 2:1 octave into 29 equal steps of approximately 41.37931 cents.<br /> | <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"><html><head><title>29edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x29 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #ff4700; font-size: 103%;">29 tone equal temperament</span></h1> | ||
<br /> | |||
29edo divides the 2:1 octave into 29 equal steps of approximately 41.37931 cents.<br /> | |||
<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 /> | 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 /> | ||
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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 /> | 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 /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x29 tone equal temperament-Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals</h2> | ||
<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<td> | <td>Degrees of 29-EDO<br /> | ||
</td> | </td> | ||
<td> | <td>Cents value<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||