Harmony of 23edo: Difference between revisions
Wikispaces>guest **Imported revision 138905941 - Original comment: ** |
Wikispaces>guest **Imported revision 138907681 - 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:guest|guest]] and made on <tt>2010-05-03 00: | : This revision was by author [[User:guest|guest]] and made on <tt>2010-05-03 00:39:53 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>138907681</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">If you take a look at the intervals of [[23edo]], you'll find that this system does not contain good representations of harmonics 3, 5, 7, 11, or 13, which appear as central in most just intonation systems. Rather than trivialize 23edo by calling it "atonal" or "nonharmonic," I'd like to consider higher-limit harmonies that could serve as useful sonorities, perhaps even "consonances," in the context of careful composition. [[23edo]] contains intervals which approach harmonics 9, 17, 21, 23, 33, | <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">If you take a look at the intervals of [[23edo]], you'll find that this system does not contain good representations of harmonics 3, 5, 7, 11, or 13, which appear as central in most just intonation systems. Rather than trivialize 23edo by calling it "atonal" or "nonharmonic," I'd like to consider higher-limit harmonies that could serve as useful sonorities, perhaps even "consonances," in the context of careful composition. [[23edo]] contains intervals which approach harmonics 9, 17, 21, 23, 33, 43, 63 & 117. Let's compare the cents values to see how close 23edo intervals come to these harmonics. | ||
|| degrees of 23edo || cents || nearest harmonic || cents || "error" || | || degrees of 23edo || cents || nearest harmonic || cents || "error" || | ||
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|| 3 || 156.522 || 23/21 || 157.493 || -0.971 || | || 3 || 156.522 || 23/21 || 157.493 || -0.971 || | ||
|| **4** || **208.696** || **9/8** || **203.910** || **+4.786** || | || **4** || **208.696** || **9/8** || **203.910** || **+4.786** || | ||
|| 7 || 365.217 || | || 7 || 365.217 || 63/51 || 365.825 || -.608 || | ||
|| **9** || **469.565** || **21/16** || **470.781** || **-1.216** || | || **9** || **469.565** || **21/16** || **470.781** || **-1.216** || | ||
|| **12** || **626.087** || **23/16** || **628.274** || **-2.187** || | || **12** || **626.087** || **23/16** || **628.274** || **-2.187** || | ||
| Line 136: | Line 136: | ||
23/21 (157.493, error: -.971)</pre></div> | 23/21 (157.493, error: -.971)</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>Harmony of 23edo</title></head><body>If you take a look at the intervals of <a class="wiki_link" href="/23edo">23edo</a>, you'll find that this system does not contain good representations of harmonics 3, 5, 7, 11, or 13, which appear as central in most just intonation systems. Rather than trivialize 23edo by calling it &quot;atonal&quot; or &quot;nonharmonic,&quot; I'd like to consider higher-limit harmonies that could serve as useful sonorities, perhaps even &quot;consonances,&quot; in the context of careful composition. <a class="wiki_link" href="/23edo">23edo</a> contains intervals which approach harmonics 9, 17, 21, 23, 33, | <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>Harmony of 23edo</title></head><body>If you take a look at the intervals of <a class="wiki_link" href="/23edo">23edo</a>, you'll find that this system does not contain good representations of harmonics 3, 5, 7, 11, or 13, which appear as central in most just intonation systems. Rather than trivialize 23edo by calling it &quot;atonal&quot; or &quot;nonharmonic,&quot; I'd like to consider higher-limit harmonies that could serve as useful sonorities, perhaps even &quot;consonances,&quot; in the context of careful composition. <a class="wiki_link" href="/23edo">23edo</a> contains intervals which approach harmonics 9, 17, 21, 23, 33, 43, 63 &amp; 117. Let's compare the cents values to see how close 23edo intervals come to these harmonics.<br /> | ||
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<td>365.217<br /> | <td>365.217<br /> | ||
</td> | </td> | ||
<td> | <td>63/51<br /> | ||
</td> | </td> | ||
<td> | <td>365.825<br /> | ||
</td> | </td> | ||
<td> | <td>-.608<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||