Phoenix: Difference between revisions
Wikispaces>MasonGreen1 **Imported revision 567827413 - Original comment: ** |
Wikispaces>MasonGreen1 **Imported revision 567827445 - 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:MasonGreen1|MasonGreen1]] and made on <tt>2015-11-26 01: | : This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2015-11-26 01:57:24 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>567827445</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> | ||
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|| Minor thirty-fifth || 91 || || 5807.082 || 57:2 || | || Minor thirty-fifth || 91 || || 5807.082 || 57:2 || | ||
|| Neutral/major thirty-fifth || 92 || || 5870.896 || || | || Neutral/major thirty-fifth || 92 || || 5870.896 || || | ||
|| 31st harmonic | || 31st harmonic || 93 || || 5934.710 || 31:1 (wide-end only) || | ||
|| 32nd harmonic || 94 || || 5998.52 || 32:1 || | || 32nd harmonic || 94 || || 5998.52 || 32:1 || | ||
|| 33rd harmonic || 95 || || 6062.339 || 33:1 || | || 33rd harmonic || 95 || || 6062.339 || 33:1 || | ||
|| 34th harmonic || 96 || || 6126 || 34:1 | || 34th harmonic || 96 || || 6126.153 || 34:1 (narrow-end only) || | ||
Harmonics beyond the 34th are not matched well. | Harmonics beyond the 34th are not matched well. | ||
The wide end of the phoenix continuum matches 86 scale degrees to the 24th harmonic, whereas the narrow end matches 86 degrees to 47:2. The wide end of the continuum matches the 31st harmonic, the narrow end does not. On the other hand, the narrow end of the continuum matches the 34th harmonic, unlike the wide end.</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>Phoenix</title></head><body>The <strong>phoenix</strong> tuning continuum ranges consists of a range of equally-tempered scales ranging from 63.5998 cents (which divides the just 9:5 interval into 16 equal parts), to 63.8141 cents (which divides the perfect fifth into 11 equal parts, see <a class="wiki_link" href="/11edf">11edf</a>). All of these scales stretch the octave by around 8 to 12 cents. A distinctive feature of phoenix-tuned scales is that prime-numbered harmonics are, on average, approximated more reliably than composite ones. Concentrating the error around composites provides greater overall benefit to tempering.<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>Phoenix</title></head><body>The <strong>phoenix</strong> tuning continuum ranges consists of a range of equally-tempered scales ranging from 63.5998 cents (which divides the just 9:5 interval into 16 equal parts), to 63.8141 cents (which divides the perfect fifth into 11 equal parts, see <a class="wiki_link" href="/11edf">11edf</a>). All of these scales stretch the octave by around 8 to 12 cents. A distinctive feature of phoenix-tuned scales is that prime-numbered harmonics are, on average, approximated more reliably than composite ones. Concentrating the error around composites provides greater overall benefit to tempering.<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>31st harmonic | <td>31st harmonic<br /> | ||
</td> | </td> | ||
<td>93<br /> | <td>93<br /> | ||
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<td>5934.710<br /> | <td>5934.710<br /> | ||
</td> | </td> | ||
<td>31:1 | <td>31:1 (wide-end only)<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>6126<br /> | <td>6126.153<br /> | ||
</td> | </td> | ||
<td>34:1 | <td>34:1 (narrow-end only)<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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Harmonics beyond the 34th are not matched well.<br /> | Harmonics beyond the 34th are not matched well.<br /> | ||
<br /> | <br /> | ||
The wide end of the phoenix continuum matches 86 scale degrees to the 24th harmonic, whereas the narrow end matches 86 degrees to 47:2. The wide end of the continuum matches the 31st harmonic, the narrow end does not. On the other hand, the narrow end of the continuum matches the 34th harmonic, unlike the wide end.</body></html></pre></div> | |||