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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | The '''2460''' equal division divides the [[Octave|octave]] into 2460 equal parts of 0.4878 [[cent|cent]]s each. It has been used in [[Sagittal_notation|Sagittal notation]] to define the "olympian level" of JI notation, and has been proposed as the basis for a unit, the [[mina|mina]], which could be used in place of the [[cent|cent]]. It is uniquely [[consistent|consistent]] through to the [[27-limit|27-limit]], which is not very remarkable in itself ([[388edo|388edo]] is the first such system), but what is remarkable is the degree of accuracy to which it represents the 27-limit intervals. It is also a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta peak edo]] and has a lower 19-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]] than any edo until [[3395edo|3395]], and a lower 23-limit relative error than any until [[8269edo|8269]]. Also it has a lower 23-limit [[Tenney-Euclidean_metrics#Logflat TE badness| TE loglfat badness]] than any smaller edo and less than any until [[16808edo|16808]]. |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2015-08-20 13:51:53 UTC</tt>.<br>
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| : The original revision id was <tt>557051145</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| 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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| <h4>Original Wikitext content:</h4>
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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 [[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. It is also a [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta peak edo]] and has a lower 19-limit [[Tenney-Euclidean temperament measures#TE simple badness|relative error]] than any edo until [[3395edo|3395]], and a lower 23-limit relative error than any until [[8269edo|8269]]. Also it has a lower 23-limit [[Tenney-Euclidean metrics#Logflat TE badness| TE loglfat badness]] than any smaller edo and less than any until [[16808edo|16808]].
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| 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. | | 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. |
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| 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.</pre></div> | | 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|12edo]] is too well-known to need any introduction, [[41edo|41edo]] is an important system, and [[205edo|205edo]] has proponents such as [[Aaron_Andrew_Hunt|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|Mem]]). Aside from these, [[15edo|15edo]], [[20edo|20edo]], [[30edo|30edo]], [[60edo|60edo]], and [[164edo|164edo]] all have drawn some attention. Moreover a cent is exactly 2.05 [[mina|mina]]s, and a mem, 1\205 octaves, is exactly 12 minas. |
| <h4>Original HTML content:</h4>
| | [[Category:edo]] |
| <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 <strong>2460</strong> 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 &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 <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. It is also a <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists">zeta peak edo</a> and has a lower 19-limit <a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures#TE simple badness">relative error</a> than any edo until <a class="wiki_link" href="/3395edo">3395</a>, and a lower 23-limit relative error than any until <a class="wiki_link" href="/8269edo">8269</a>. Also it has a lower 23-limit <a class="wiki_link" href="/Tenney-Euclidean%20metrics#Logflat TE badness"> TE loglfat badness</a> than any smaller edo and less than any until <a class="wiki_link" href="/16808edo">16808</a>.<br />
| | [[Category:mina]] |
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| | [[Category:nano]] |
| 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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| 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></pre></div>
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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. It is also a zeta peak edo and has a lower 19-limit relative error than any edo until 3395, and a lower 23-limit relative error than any until 8269. Also it has a lower 23-limit TE loglfat badness than any smaller edo and less than any until 16808.
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 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 minas, and a mem, 1\205 octaves, is exactly 12 minas.