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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: | : This revision was by author [[User:guest|guest]] and made on <tt>2012-02-10 09:55:27 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>300486972</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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One notable property of 53EDO is that it offers good approximations for both pure and pythagorean major thirds. | One notable property of 53EDO is that it offers good approximations for both pure and pythagorean major thirds. | ||
The perfect fifth is almost perfectly equal to the just interval 3/2, with only a 0.07 cent difference! 53EDO can be considered an extended Pythagorean tuning using the notes: 0, 4, 9, 13, 18, 22, 26/27, 31, 35, 40, 44, 49, 53. The thirds are close to just as well, and therefore 5-limit tuning can closely be approximated using the notes: 0, __5__, 9, __14__, __18__, 22, 26/27, 31, __36__, __39__, 44, __48__, 53. | |||
=Intervals= | =Intervals= | ||
| Line 164: | Line 166: | ||
<br /> | <br /> | ||
One notable property of 53EDO is that it offers good approximations for both pure and pythagorean major thirds.<br /> | One notable property of 53EDO is that it offers good approximations for both pure and pythagorean major thirds.<br /> | ||
<br /> | |||
The perfect fifth is almost perfectly equal to the just interval 3/2, with only a 0.07 cent difference! 53EDO can be considered an extended Pythagorean tuning using the notes: 0, 4, 9, 13, 18, 22, 26/27, 31, 35, 40, 44, 49, 53. The thirds are close to just as well, and therefore 5-limit tuning can closely be approximated using the notes: 0, <u>5</u>, 9, <u>14</u>, <u>18</u>, 22, 26/27, 31, <u>36</u>, <u>39</u>, 44, <u>48</u>, 53.<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:4 -->Intervals</h1> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:4 -->Intervals</h1> | ||
Revision as of 09:55, 10 February 2012
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author guest and made on 2012-02-10 09:55:27 UTC.
- The original revision id was 300486972.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
[[toc|flat]] =Theory= The famous //53 equal division// divides the octave into 53 equal comma-sized parts of 22.642 cents each. It is notable as a [[5-limit]] system, a fact apparently first noted by Isaac Newton, tempering out the schisma, 32805/32768, the kleisma, 15625/15552, the amity comma, 1600000/1594323 and the semicomma, 2109375/2097152. In the 7-limit it tempers out 225/224, 1728/1715 and 3125/3087, the marvel comma, the gariboh, and the orwell comma. In the 11-limit, it tempers out 99/98 and 121/120, and is the [[optimal patent val]] for [[Nuwell family|Big Brother]] temperament, which tempers out both, as well as 11-limit [[Semicomma family|orwell temperament]], which also tempers out the 11-limit comma 176/175. In the 13-limit, it tempers out 169/168 and 245/243, and gives the optimal patent val for [[Marvel family|athene temperament]]. It is the eighth [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta integral edo]] and the 16th [[prime numbers|prime]] edo, following [[47edo]] and coming before [[59edo]]. 53EDO has also found a certain dissemination as an EDO tuning for [[Arabic, Turkish, Persian|Arabic/Turkish/Persian music]] . [[http://en.wikipedia.org/wiki/53_equal_temperament|Wikipeda article about 53edo]] =Just Approximation= 53edo provides excellent approximations for the classic 5-limit [[just]] chords and scales, such as the Ptolemy-Zarlino "just major" scale. ||~ interval ||~ size ||~ diff || || perfect fifth ||= 31 || −0.07 cents || || major third ||= 17 || −1.40 cents || || minor third ||= 14 || +1.34 cents || || major tone ||= 9 || −0.14 cents || || major tone ||= 8 || −1.27 cents || || diat. semitone ||= 5 || +1.48 cents || One notable property of 53EDO is that it offers good approximations for both pure and pythagorean major thirds. The perfect fifth is almost perfectly equal to the just interval 3/2, with only a 0.07 cent difference! 53EDO can be considered an extended Pythagorean tuning using the notes: 0, 4, 9, 13, 18, 22, 26/27, 31, 35, 40, 44, 49, 53. The thirds are close to just as well, and therefore 5-limit tuning can closely be approximated using the notes: 0, __5__, 9, __14__, __18__, 22, 26/27, 31, __36__, __39__, 44, __48__, 53. =Intervals= || degrees of 53edo || cents value || generator for || || 0 || 0.00 || || || 1 || 22.64 || || || 2 || 45.28 || [[Quartonic]] || || 3 || 67.92 || || || 4 || 90.57 || || || 5 || 113.21 || || || 6 || 135.85 || || || 7 || 158.49 || [[Hemikleismic]] || || 8 || 181.13 || || || 9 || 203.77 || || || 10 || 226.42 || || || 11 || 249.06 || [[Hemischis]] || || 12 || 271.70 || [[Orwell]] || || 13 || 294.34 || || || 14 || 316.98 || [[Hanson]]/[[Catakleismic]] || || 15 || 339.62 || [[Amity]]/[[Hitchcock]] || || 16 || 362.26 || || || 17 || 384.91 || || || 18 || 407.55 || || || 19 || 430.19 || || || 20 || 452.83 || || || 21 || 475.47 || [[Vulture]]/[[Buzzard]] || || 22 || 498.11 || || || 23 || 520.75 || || || 24 || 543.40 || || || 25 || 566.04 || [[Tricot]] || || 26 || 588.68 || || || 27 || 611.32 || || || 28 || 633.96 || || || 29 || 656.60 || || || 30 || 679.25 || || || 31 || 701.89 || [[Helmholtz]]/[[Garibaldi]] || || 32 || 724.53 || || || 33 || 747.17 || || || 34 || 769.81 || || || 35 || 792.45 || || || 36 || 815.09 || || || 37 || 837.74 || || || 38 || 860.38 || || || 39 || 883.02 || || || 40 || 905.66 || || || 41 || 928.30 || || || 42 || 950.94 || || || 43 || 973.58 || || || 44 || 996.23 || || || 45 || 1018.87 || || || 46 || 1041.51 || || || 47 || 1064.15 || || || 48 || 1086.79 || || || 49 || 1109.43 || || || 50 || 1132.08 || || || 51 || 1154.72 || || || 52 || 1177.36 || || =Compositions= [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Khramov/prelude1-53.mp3|Bach WTC1 Prelude 1 in 53]] by Bach and [[Mykhaylo Khramov]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Khramov/fugue1-53.mp3|Bach WTC1 Fugue 1 in 53]] by Bach and Mykhaylo Khramov [[http://www.geocities.com/Bernalorg/Excerpts/n53.wav|53edo guitar study]] by Novaro <-- broken link? [[http://bumpermusic.blogspot.com/2007/05/whisper-song-in-53-edo-now-526-slower.html|Whisper Song in 53EDO]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Prent/sing53-c5-slow.mp3|play]] by [[Prent Rodgers]] [[http://www.archive.org/details/TrioInOrwell|Trio in Orwell]] [[http://www.archive.org/download/TrioInOrwell/TrioInOrwell.mp3|play]] by [[Gene Ward Smith]] [[http://www.akjmusic.com/audio/desert_prayer.mp3|Desert Prayer]] by [[http://www.akjmusic.com|Aaron Krister Johnson]]
Original HTML content:
<html><head><title>53edo</title></head><body><!-- ws:start:WikiTextTocRule:8:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:8 --><!-- ws:start:WikiTextTocRule:9: --><a href="#Theory">Theory</a><!-- ws:end:WikiTextTocRule:9 --><!-- ws:start:WikiTextTocRule:10: --> | <a href="#Just Approximation">Just Approximation</a><!-- ws:end:WikiTextTocRule:10 --><!-- ws:start:WikiTextTocRule:11: --> | <a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:11 --><!-- ws:start:WikiTextTocRule:12: --> | <a href="#Compositions">Compositions</a><!-- ws:end:WikiTextTocRule:12 --><!-- ws:start:WikiTextTocRule:13: -->
<!-- ws:end:WikiTextTocRule:13 --><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Theory"></a><!-- ws:end:WikiTextHeadingRule:0 -->Theory</h1>
The famous <em>53 equal division</em> divides the octave into 53 equal comma-sized parts of 22.642 cents each. It is notable as a <a class="wiki_link" href="/5-limit">5-limit</a> system, a fact apparently first noted by Isaac Newton, tempering out the schisma, 32805/32768, the kleisma, 15625/15552, the amity comma, 1600000/1594323 and the semicomma, 2109375/2097152. In the 7-limit it tempers out 225/224, 1728/1715 and 3125/3087, the marvel comma, the gariboh, and the orwell comma. In the 11-limit, it tempers out 99/98 and 121/120, and is the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for <a class="wiki_link" href="/Nuwell%20family">Big Brother</a> temperament, which tempers out both, as well as 11-limit <a class="wiki_link" href="/Semicomma%20family">orwell temperament</a>, which also tempers out the 11-limit comma 176/175. In the 13-limit, it tempers out 169/168 and 245/243, and gives the optimal patent val for <a class="wiki_link" href="/Marvel%20family">athene temperament</a>. It is the eighth <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta integral edo</a> and the 16th <a class="wiki_link" href="/prime%20numbers">prime</a> edo, following <a class="wiki_link" href="/47edo">47edo</a> and coming before <a class="wiki_link" href="/59edo">59edo</a>.<br />
<br />
53EDO has also found a certain dissemination as an EDO tuning for <a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian">Arabic/Turkish/Persian music</a> .<br />
<br />
<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/53_equal_temperament" rel="nofollow">Wikipeda article about 53edo</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Just Approximation"></a><!-- ws:end:WikiTextHeadingRule:2 -->Just Approximation</h1>
53edo provides excellent approximations for the classic 5-limit <a class="wiki_link" href="/just">just</a> chords and scales, such as the Ptolemy-Zarlino "just major" scale.<br />
<table class="wiki_table">
<tr>
<th>interval<br />
</th>
<th>size<br />
</th>
<th>diff<br />
</th>
</tr>
<tr>
<td>perfect fifth<br />
</td>
<td style="text-align: center;">31<br />
</td>
<td>−0.07 cents<br />
</td>
</tr>
<tr>
<td>major third<br />
</td>
<td style="text-align: center;">17<br />
</td>
<td>−1.40 cents<br />
</td>
</tr>
<tr>
<td>minor third<br />
</td>
<td style="text-align: center;">14<br />
</td>
<td>+1.34 cents<br />
</td>
</tr>
<tr>
<td>major tone<br />
</td>
<td style="text-align: center;">9<br />
</td>
<td>−0.14 cents<br />
</td>
</tr>
<tr>
<td>major tone<br />
</td>
<td style="text-align: center;">8<br />
</td>
<td>−1.27 cents<br />
</td>
</tr>
<tr>
<td>diat. semitone<br />
</td>
<td style="text-align: center;">5<br />
</td>
<td>+1.48 cents<br />
</td>
</tr>
</table>
<br />
One notable property of 53EDO is that it offers good approximations for both pure and pythagorean major thirds.<br />
<br />
The perfect fifth is almost perfectly equal to the just interval 3/2, with only a 0.07 cent difference! 53EDO can be considered an extended Pythagorean tuning using the notes: 0, 4, 9, 13, 18, 22, 26/27, 31, 35, 40, 44, 49, 53. The thirds are close to just as well, and therefore 5-limit tuning can closely be approximated using the notes: 0, <u>5</u>, 9, <u>14</u>, <u>18</u>, 22, 26/27, 31, <u>36</u>, <u>39</u>, 44, <u>48</u>, 53.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:<h1> --><h1 id="toc2"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:4 -->Intervals</h1>
<table class="wiki_table">
<tr>
<td>degrees of 53edo<br />
</td>
<td>cents value<br />
</td>
<td>generator for<br />
</td>
</tr>
<tr>
<td>0<br />
</td>
<td>0.00<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>22.64<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>45.28<br />
</td>
<td><a class="wiki_link" href="/Quartonic">Quartonic</a><br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>67.92<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>90.57<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>113.21<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>135.85<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>158.49<br />
</td>
<td><a class="wiki_link" href="/Hemikleismic">Hemikleismic</a><br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>181.13<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>203.77<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>226.42<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>249.06<br />
</td>
<td><a class="wiki_link" href="/Hemischis">Hemischis</a><br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>271.70<br />
</td>
<td><a class="wiki_link" href="/Orwell">Orwell</a><br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>294.34<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>316.98<br />
</td>
<td><a class="wiki_link" href="/Hanson">Hanson</a>/<a class="wiki_link" href="/Catakleismic">Catakleismic</a><br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>339.62<br />
</td>
<td><a class="wiki_link" href="/Amity">Amity</a>/<a class="wiki_link" href="/Hitchcock">Hitchcock</a><br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>362.26<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>384.91<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>407.55<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>430.19<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>452.83<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>475.47<br />
</td>
<td><a class="wiki_link" href="/Vulture">Vulture</a>/<a class="wiki_link" href="/Buzzard">Buzzard</a><br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>498.11<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>520.75<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>543.40<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>566.04<br />
</td>
<td><a class="wiki_link" href="/Tricot">Tricot</a><br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>588.68<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>611.32<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>633.96<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>656.60<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>679.25<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>701.89<br />
</td>
<td><a class="wiki_link" href="/Helmholtz">Helmholtz</a>/<a class="wiki_link" href="/Garibaldi">Garibaldi</a><br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>724.53<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>747.17<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>769.81<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>792.45<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>815.09<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>837.74<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>860.38<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td>883.02<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td>905.66<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>41<br />
</td>
<td>928.30<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>42<br />
</td>
<td>950.94<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>43<br />
</td>
<td>973.58<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>44<br />
</td>
<td>996.23<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>45<br />
</td>
<td>1018.87<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>46<br />
</td>
<td>1041.51<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>47<br />
</td>
<td>1064.15<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>48<br />
</td>
<td>1086.79<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>49<br />
</td>
<td>1109.43<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>50<br />
</td>
<td>1132.08<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>51<br />
</td>
<td>1154.72<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>52<br />
</td>
<td>1177.36<br />
</td>
<td><br />
</td>
</tr>
</table>
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:6 -->Compositions</h1>
<a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Khramov/prelude1-53.mp3" rel="nofollow">Bach WTC1 Prelude 1 in 53</a> by Bach and <a class="wiki_link" href="/Mykhaylo%20Khramov">Mykhaylo Khramov</a><br />
<a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Khramov/fugue1-53.mp3" rel="nofollow">Bach WTC1 Fugue 1 in 53</a> by Bach and Mykhaylo Khramov<br />
<a class="wiki_link_ext" href="http://www.geocities.com/Bernalorg/Excerpts/n53.wav" rel="nofollow">53edo guitar study</a> by Novaro <-- broken link?<br />
<a class="wiki_link_ext" href="http://bumpermusic.blogspot.com/2007/05/whisper-song-in-53-edo-now-526-slower.html" rel="nofollow">Whisper Song in 53EDO</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Prent/sing53-c5-slow.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="/Prent%20Rodgers">Prent Rodgers</a><br />
<a class="wiki_link_ext" href="http://www.archive.org/details/TrioInOrwell" rel="nofollow">Trio in Orwell</a> <a class="wiki_link_ext" href="http://www.archive.org/download/TrioInOrwell/TrioInOrwell.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="/Gene%20Ward%20Smith">Gene Ward Smith</a><br />
<a class="wiki_link_ext" href="http://www.akjmusic.com/audio/desert_prayer.mp3" rel="nofollow">Desert Prayer</a> by <a class="wiki_link_ext" href="http://www.akjmusic.com" rel="nofollow">Aaron Krister Johnson</a></body></html>