2460edo
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author xenwolf and made on 2011-06-30 09:01:10 UTC.
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Original Wikitext content:
The 2460 equal division divides the [[octave]] into 2460 equal parts of 0.4878 [[cent]]s 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. Since its prime factorization is 2^2*3*5*41, 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]] (and as a unit: [[Mem]]). Aside from these, [[15edo]], [[20edo]], [[30edo]], [[60edo]], and [[164edo]] all have drawn some attention. Moreover a cent is exactly 2.05 [[mina]]s, and a mem, 1/205 octaves, is exactly 12 minas.
Original HTML content:
<html><head><title>2460edo</title></head><body>The 2460 equal division divides the <a class="wiki_link" href="/octave">octave</a> into 2460 equal parts of 0.4878 <a class="wiki_link" href="/cent">cent</a>s each. It has been used in <a class="wiki_link" href="/Sagittal%20notation">Sagittal notation</a> to define the "olympian level" 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 <a class="wiki_link" href="/consistent">consistent</a> through to the <a class="wiki_link" href="/27-limit">27-limit</a>, which is not very remarkable in itself (<a class="wiki_link" href="/388edo">388edo</a> is the first such system), but what is remarkable is the degree of accuracy to which it represents the 27-limit intervals.<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.<br /> <br /> Since its prime factorization is 2^2*3*5*41, 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> (and as a unit: <a class="wiki_link" href="/Mem">Mem</a>). Aside from these, <a class="wiki_link" href="/15edo">15edo</a>, <a class="wiki_link" href="/20edo">20edo</a>, <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 <a class="wiki_link" href="/mina">mina</a>s, and a mem, 1/205 octaves, is exactly 12 minas.</body></html>