2460edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 236640090 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 236681132 - 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:genewardsmith|genewardsmith]] and made on <tt>2011-06-14 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-14 18:09:22 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>236681132</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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<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">The 2460 equal division divides the octave into 2460 equal parts of 0.4878 cents each. It has been used in [[Sagittal notation]] to define the "olympian level" of JI notation, and has been proposed as the basis for a unit, the [[mina]], which could be used in place of the [[cent]]. It is uniquely consistent through to the 27-limit, which is not very remarkable in itself (388edo is the first such system), but what is remarkable is the degree of accuracy to which it represents the 27-limit intervals. | <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">The 2460 equal division divides the octave into 2460 equal parts of 0.4878 cents each. It has been used in [[Sagittal notation]] to define the "olympian level" of JI notation, and has been proposed as the basis for a unit, the [[mina]], which could be used in place of the [[cent]]. It is uniquely consistent through to the 27-limit, which is not very remarkable in itself (388edo is the first such system), but what is remarkable is the degree of accuracy to which it represents the 27-limit intervals. | ||
As a micro (or nano) temperament, it is a landscape system in the 7-limit, tempering out 250047/250000, and in the 11-limit it tempers out 9801/9800. Beyond that, 10648/10647 in the 13-limit, 12376/12375 in the 17-limit, 5929/5928 and 6860/6859 in the 19-limit and 8281/8280 in the 23-limit.</pre></div> | As a micro (or nano) temperament, it is a landscape system in the 7-limit, tempering out 250047/250000, and in the 11-limit it tempers out 9801/9800. Beyond that, 10648/10647 in the 13-limit, 12376/12375 in the 17-limit, 5929/5928 and 6860/6859 in the 19-limit and 8281/8280 in the 23-limit. | ||
2460 is divisible by 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 41, 60, 82, 123, 164, 205, 246, 410, 492, 615, 820, and 1230. Of these, [[12edo]] is too well-known to need any introduction, [[41edo]] is an important system, and [[205edo]] has proponents such as [[Aaron Andrew Hunt]], who uses it as the default tuning for [[http://www.h-pi.com/theory/measurement3.html|Hi-pi Instruments]]. Aside from these, [[15edo]], [20edo]], [[30edo]], [[60edo]], and [[164edo]] all have drawn some attention. Moreover a cent is exactly 2.05 minas, and a mem, 1/205 octaves, is exactly 12 minas. | |||
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<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>2460edo</title></head><body>The 2460 equal division divides the octave into 2460 equal parts of 0.4878 cents each. It has been used in <a class="wiki_link" href="/Sagittal%20notation">Sagittal notation</a> to define the &quot;olympian level&quot; of JI notation, and has been proposed as the basis for a unit, the <a class="wiki_link" href="/mina">mina</a>, which could be used in place of the <a class="wiki_link" href="/cent">cent</a>. It is uniquely consistent through to the 27-limit, which is not very remarkable in itself (388edo is the first such system), but what is remarkable is the degree of accuracy to which it represents the 27-limit intervals.<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>2460edo</title></head><body>The 2460 equal division divides the octave into 2460 equal parts of 0.4878 cents each. It has been used in <a class="wiki_link" href="/Sagittal%20notation">Sagittal notation</a> to define the &quot;olympian level&quot; of JI notation, and has been proposed as the basis for a unit, the <a class="wiki_link" href="/mina">mina</a>, which could be used in place of the <a class="wiki_link" href="/cent">cent</a>. It is uniquely consistent through to the 27-limit, which is not very remarkable in itself (388edo is the first such system), but what is remarkable is the degree of accuracy to which it represents the 27-limit intervals.<br /> | ||
<br /> | <br /> | ||
As a micro (or nano) temperament, it is a landscape system in the 7-limit, tempering out 250047/250000, and in the 11-limit it tempers out 9801/9800. Beyond that, 10648/10647 in the 13-limit, 12376/12375 in the 17-limit, 5929/5928 and 6860/6859 in the 19-limit and 8281/8280 in the 23-limit.</body></html></pre></div> | As a micro (or nano) temperament, it is a landscape system in the 7-limit, tempering out 250047/250000, and in the 11-limit it tempers out 9801/9800. Beyond that, 10648/10647 in the 13-limit, 12376/12375 in the 17-limit, 5929/5928 and 6860/6859 in the 19-limit and 8281/8280 in the 23-limit.<br /> | ||
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2460 is divisible by 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 41, 60, 82, 123, 164, 205, 246, 410, 492, 615, 820, and 1230. Of these, <a class="wiki_link" href="/12edo">12edo</a> is too well-known to need any introduction, <a class="wiki_link" href="/41edo">41edo</a> is an important system, and <a class="wiki_link" href="/205edo">205edo</a> has proponents such as <a class="wiki_link" href="/Aaron%20Andrew%20Hunt">Aaron Andrew Hunt</a>, who uses it as the default tuning for <a class="wiki_link_ext" href="http://www.h-pi.com/theory/measurement3.html" rel="nofollow">Hi-pi Instruments</a>. Aside from these, <a class="wiki_link" href="/15edo">15edo</a>, [20edo]], <a class="wiki_link" href="/30edo">30edo</a>, <a class="wiki_link" href="/60edo">60edo</a>, and <a class="wiki_link" href="/164edo">164edo</a> all have drawn some attention. Moreover a cent is exactly 2.05 minas, and a mem, 1/205 octaves, is exactly 12 minas.</body></html></pre></div> | |||