EDO
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=E.D.O.= EDO, used here, means //not// [[http://en.wikipedia.org/wiki/Edo_period|the period of Japanese history]] (and musical tradition), but [[Equal]] **D**ivisions of the [[Octave]]. =What are EDO scales like?= Very straightforward to work with, the step size being so even and all. Some find the monotony bland, others find it a safe stable footing for musicmaking. =How do I explore so many?= You will quickly find that the //factorization// of the total number of notes in each EDO has consequences for its structure and the way it relates to other EDOs. For example, 6 = 2 x 3, so 6-edo contains all of the intervals in both 2-edo and 3-edo. On the other hand, 7 is a prime number, so all of 7-edo intervals are un-redundant with smaller EDOs. The [[MOSScales|Moments of Symmetry]] paradigm is a fascinating way of thinking about building sub-scales of EDOs and relating them to non-EDO scales. When an edo divides the octave into fewer than 12 divisions (so that each step exceeds 100 cents), you might call it a [[macrotonal edos|macrotonal edo]]. Of these, 1, 2, 3, 4 and 6 divide 12 and so are already available to anyone wishing to explore them. The 5, 7 and 9 edos have arguably been used in various kinds of musical traditions in different parts of the world. On the other hand, if you use the edo to tune a scale or [[Regular temperaments|regular temperament]], the size of the edo does not matter so much, as you don't need to use all of it. Some of the edos which can be used to tune various temperaments are listed on the [[optimal patent val]] page. Tuning a scale in just intonation by one of these edos can be regarded as automatically tempering it to the corresponding regular temperament. All of these tools are also applicable to equal divisions of other ([[nonoctave]]) intervals as well. =Individual pages for EDOs= || [[1edo]] || [[2edo]] || [[3edo]] || [[4edo]] || [[5edo]] || [[6edo]] || [[7edo]] || [[8edo]] || [[9edo]] || [[10edo]] || [[11edo]] || [[12edo]] || || [[13edo]] || [[14edo]] || [[15edo]] || [[16edo]] || [[17edo]] || [[18edo]] || [[19edo]] || [[20edo]] || [[21edo]] || [[22edo]] || [[23edo]] || [[24edo]] || || [[25edo]] || [[26edo]] || [[27edo]] || [[28edo]] || [[29edo]] || [[30edo]] || [[31edo]] || [[32edo]] || [[33edo]] || [[34edo]] || [[35edo]] || [[36edo]] || || [[37edo]] || [[38edo]] || [[39edo]] || [[40edo]] || [[41edo]] || [[42edo]] || [[43edo]] || [[44edo]] || [[45edo]] || [[46edo]] || [[47edo]] || [[48edo]] || || [[49edo]] || [[50edo]] || [[51edo]] || [[52edo]] || [[53edo]] || [[54edo]] || [[55edo]] || [[56edo]] || [[57edo]] || [[58edo]] || [[59edo]] || [[60edo]] || || || || [[63edo]] || || [[65edo]] || || || [[68edo]] || || [[70edo]] || || [[72edo]] || || [[73edo]] || || [[75edo]] || || [[77edo]] || || || [[80edo]] || [[81edo]] || || || [[84edo]] || || [[85edo]] || || [[87edo]] || [[88edo]] || [[89edo]] || || [[91edo]] || || || [[94edo]] || || [[96edo]] || || || || [[99edo]] || || [[101edo]] || [[102edo]] || [[103edo]] || [[104edo]] || [[105edo]] || || || || || || || [[111edo]] || || [[113edo]] || || || || || [[118edo]] || || [[120edo]] || || [[121edo]] || || || || [[125edo]] || || [[127edo]] || [[128edo]] || || [[130edo]] || [[131edo]] || || || || || [[135edo]] || || [[137edo]] || || || [[140edo]] || || [[142edo]] || || || || || || [[147edo]] || || [[149edo]] || || || [[152edo]] || || [[154edo]] || || || and so on. Some larger systems include [[159edo]], [[166edo]], [[171edo]], [[177edo]], [[185edo]], [[190edo]], [[193edo]], [[197edo]] [[200edo]], [[202edo]], [[205edo]], [[224edo]], [[240edo]], [[253edo]], [[270edo]], [[284edo]], [[289edo]], [[311edo]], [[346edo]], [[347edo]], [[359edo]], [[383edo]], [[441edo]], [[494edo]], [[612edo]], [[665edo]], [[771edo]], [[940edo]], [[971edo]], [[2460edo]], [[2966edo]], [[6079edo]], [[15601edo]]
Original HTML content:
<html><head><title>EDO</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="E.D.O."></a><!-- ws:end:WikiTextHeadingRule:0 -->E.D.O.</h1>
<br />
EDO, used here, means <em>not</em> <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Edo_period" rel="nofollow">the period of Japanese history</a> (and musical tradition), but <a class="wiki_link" href="/Equal">Equal</a> <strong>D</strong>ivisions of the <a class="wiki_link" href="/Octave">Octave</a>.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="What are EDO scales like?"></a><!-- ws:end:WikiTextHeadingRule:2 -->What are EDO scales like?</h1>
<br />
Very straightforward to work with, the step size being so even and all. Some find the monotony bland, others find it a safe stable footing for musicmaking.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:<h1> --><h1 id="toc2"><a name="How do I explore so many?"></a><!-- ws:end:WikiTextHeadingRule:4 -->How do I explore so many?</h1>
<br />
You will quickly find that the <em>factorization</em> of the total number of notes in each EDO has consequences for its structure and the way it relates to other EDOs.<br />
<br />
For example, 6 = 2 x 3, so 6-edo contains all of the intervals in both 2-edo and 3-edo. On the other hand, 7 is a prime number, so all of 7-edo intervals are un-redundant with smaller EDOs.<br />
<br />
The <a class="wiki_link" href="/MOSScales">Moments of Symmetry</a> paradigm is a fascinating way of thinking about building sub-scales of EDOs and relating them to non-EDO scales.<br />
<br />
When an edo divides the octave into fewer than 12 divisions (so that each step exceeds 100 cents), you might call it a <a class="wiki_link" href="/macrotonal%20edos">macrotonal edo</a>. Of these, 1, 2, 3, 4 and 6 divide 12 and so are already available to anyone wishing to explore them. The 5, 7 and 9 edos have arguably been used in various kinds of musical traditions in different parts of the world. <br />
<br />
On the other hand, if you use the edo to tune a scale or <a class="wiki_link" href="/Regular%20temperaments">regular temperament</a>, the size of the edo does not matter so much, as you don't need to use all of it. Some of the edos which can be used to tune various temperaments are listed on the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> page. Tuning a scale in just intonation by one of these edos can be regarded as automatically tempering it to the corresponding regular temperament.<br />
<br />
All of these tools are also applicable to equal divisions of other (<a class="wiki_link" href="/nonoctave">nonoctave</a>) intervals as well.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="Individual pages for EDOs"></a><!-- ws:end:WikiTextHeadingRule:6 -->Individual pages for EDOs</h1>
<br />
<table class="wiki_table">
<tr>
<td><a class="wiki_link" href="/1edo">1edo</a><br />
</td>
<td><a class="wiki_link" href="/2edo">2edo</a><br />
</td>
<td><a class="wiki_link" href="/3edo">3edo</a><br />
</td>
<td><a class="wiki_link" href="/4edo">4edo</a><br />
</td>
<td><a class="wiki_link" href="/5edo">5edo</a><br />
</td>
<td><a class="wiki_link" href="/6edo">6edo</a><br />
</td>
<td><a class="wiki_link" href="/7edo">7edo</a><br />
</td>
<td><a class="wiki_link" href="/8edo">8edo</a><br />
</td>
<td><a class="wiki_link" href="/9edo">9edo</a><br />
</td>
<td><a class="wiki_link" href="/10edo">10edo</a><br />
</td>
<td><a class="wiki_link" href="/11edo">11edo</a><br />
</td>
<td><a class="wiki_link" href="/12edo">12edo</a><br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/13edo">13edo</a><br />
</td>
<td><a class="wiki_link" href="/14edo">14edo</a><br />
</td>
<td><a class="wiki_link" href="/15edo">15edo</a><br />
</td>
<td><a class="wiki_link" href="/16edo">16edo</a><br />
</td>
<td><a class="wiki_link" href="/17edo">17edo</a><br />
</td>
<td><a class="wiki_link" href="/18edo">18edo</a><br />
</td>
<td><a class="wiki_link" href="/19edo">19edo</a><br />
</td>
<td><a class="wiki_link" href="/20edo">20edo</a><br />
</td>
<td><a class="wiki_link" href="/21edo">21edo</a><br />
</td>
<td><a class="wiki_link" href="/22edo">22edo</a><br />
</td>
<td><a class="wiki_link" href="/23edo">23edo</a><br />
</td>
<td><a class="wiki_link" href="/24edo">24edo</a><br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/25edo">25edo</a><br />
</td>
<td><a class="wiki_link" href="/26edo">26edo</a><br />
</td>
<td><a class="wiki_link" href="/27edo">27edo</a><br />
</td>
<td><a class="wiki_link" href="/28edo">28edo</a><br />
</td>
<td><a class="wiki_link" href="/29edo">29edo</a><br />
</td>
<td><a class="wiki_link" href="/30edo">30edo</a><br />
</td>
<td><a class="wiki_link" href="/31edo">31edo</a><br />
</td>
<td><a class="wiki_link" href="/32edo">32edo</a><br />
</td>
<td><a class="wiki_link" href="/33edo">33edo</a><br />
</td>
<td><a class="wiki_link" href="/34edo">34edo</a><br />
</td>
<td><a class="wiki_link" href="/35edo">35edo</a><br />
</td>
<td><a class="wiki_link" href="/36edo">36edo</a><br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/37edo">37edo</a><br />
</td>
<td><a class="wiki_link" href="/38edo">38edo</a><br />
</td>
<td><a class="wiki_link" href="/39edo">39edo</a><br />
</td>
<td><a class="wiki_link" href="/40edo">40edo</a><br />
</td>
<td><a class="wiki_link" href="/41edo">41edo</a><br />
</td>
<td><a class="wiki_link" href="/42edo">42edo</a><br />
</td>
<td><a class="wiki_link" href="/43edo">43edo</a><br />
</td>
<td><a class="wiki_link" href="/44edo">44edo</a><br />
</td>
<td><a class="wiki_link" href="/45edo">45edo</a><br />
</td>
<td><a class="wiki_link" href="/46edo">46edo</a><br />
</td>
<td><a class="wiki_link" href="/47edo">47edo</a><br />
</td>
<td><a class="wiki_link" href="/48edo">48edo</a><br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/49edo">49edo</a><br />
</td>
<td><a class="wiki_link" href="/50edo">50edo</a><br />
</td>
<td><a class="wiki_link" href="/51edo">51edo</a><br />
</td>
<td><a class="wiki_link" href="/52edo">52edo</a><br />
</td>
<td><a class="wiki_link" href="/53edo">53edo</a><br />
</td>
<td><a class="wiki_link" href="/54edo">54edo</a><br />
</td>
<td><a class="wiki_link" href="/55edo">55edo</a><br />
</td>
<td><a class="wiki_link" href="/56edo">56edo</a><br />
</td>
<td><a class="wiki_link" href="/57edo">57edo</a><br />
</td>
<td><a class="wiki_link" href="/58edo">58edo</a><br />
</td>
<td><a class="wiki_link" href="/59edo">59edo</a><br />
</td>
<td><a class="wiki_link" href="/60edo">60edo</a><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><a class="wiki_link" href="/63edo">63edo</a><br />
</td>
<td><br />
</td>
<td><a class="wiki_link" href="/65edo">65edo</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><a class="wiki_link" href="/68edo">68edo</a><br />
</td>
<td><br />
</td>
<td><a class="wiki_link" href="/70edo">70edo</a><br />
</td>
<td><br />
</td>
<td><a class="wiki_link" href="/72edo">72edo</a><br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/73edo">73edo</a><br />
</td>
<td><br />
</td>
<td><a class="wiki_link" href="/75edo">75edo</a><br />
</td>
<td><br />
</td>
<td><a class="wiki_link" href="/77edo">77edo</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><a class="wiki_link" href="/80edo">80edo</a><br />
</td>
<td><a class="wiki_link" href="/81edo">81edo</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><a class="wiki_link" href="/84edo">84edo</a><br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/85edo">85edo</a><br />
</td>
<td><br />
</td>
<td><a class="wiki_link" href="/87edo">87edo</a><br />
</td>
<td><a class="wiki_link" href="/88edo">88edo</a><br />
</td>
<td><a class="wiki_link" href="/89edo">89edo</a><br />
</td>
<td><br />
</td>
<td><a class="wiki_link" href="/91edo">91edo</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><a class="wiki_link" href="/94edo">94edo</a><br />
</td>
<td><br />
</td>
<td><a class="wiki_link" href="/96edo">96edo</a><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><a class="wiki_link" href="/99edo">99edo</a><br />
</td>
<td><br />
</td>
<td><a class="wiki_link" href="/101edo">101edo</a><br />
</td>
<td><a class="wiki_link" href="/102edo">102edo</a><br />
</td>
<td><a class="wiki_link" href="/103edo">103edo</a><br />
</td>
<td><a class="wiki_link" href="/104edo">104edo</a><br />
</td>
<td><a class="wiki_link" href="/105edo">105edo</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><a class="wiki_link" href="/111edo">111edo</a><br />
</td>
<td><br />
</td>
<td><a class="wiki_link" href="/113edo">113edo</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><a class="wiki_link" href="/118edo">118edo</a><br />
</td>
<td><br />
</td>
<td><a class="wiki_link" href="/120edo">120edo</a><br />
</td>
</tr>
<tr>
<td><a class="wiki_link" href="/121edo">121edo</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><a class="wiki_link" href="/125edo">125edo</a><br />
</td>
<td><br />
</td>
<td><a class="wiki_link" href="/127edo">127edo</a><br />
</td>
<td><a class="wiki_link" href="/128edo">128edo</a><br />
</td>
<td><br />
</td>
<td><a class="wiki_link" href="/130edo">130edo</a><br />
</td>
<td><a class="wiki_link" href="/131edo">131edo</a><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><a class="wiki_link" href="/135edo">135edo</a><br />
</td>
<td><br />
</td>
<td><a class="wiki_link" href="/137edo">137edo</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><a class="wiki_link" href="/140edo">140edo</a><br />
</td>
<td><br />
</td>
<td><a class="wiki_link" href="/142edo">142edo</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
</table>
|| || || <a class="wiki_link" href="/147edo">147edo</a> || || <a class="wiki_link" href="/149edo">149edo</a> || || || <a class="wiki_link" href="/152edo">152edo</a> || || <a class="wiki_link" href="/154edo">154edo</a> || || || <br />
and so on. Some larger systems include <a class="wiki_link" href="/159edo">159edo</a>, <a class="wiki_link" href="/166edo">166edo</a>, <a class="wiki_link" href="/171edo">171edo</a>, <a class="wiki_link" href="/177edo">177edo</a>, <a class="wiki_link" href="/185edo">185edo</a>, <a class="wiki_link" href="/190edo">190edo</a>, <a class="wiki_link" href="/193edo">193edo</a>, <a class="wiki_link" href="/197edo">197edo</a> <a class="wiki_link" href="/200edo">200edo</a>, <a class="wiki_link" href="/202edo">202edo</a>, <a class="wiki_link" href="/205edo">205edo</a>, <a class="wiki_link" href="/224edo">224edo</a>, <a class="wiki_link" href="/240edo">240edo</a>, <a class="wiki_link" href="/253edo">253edo</a>, <a class="wiki_link" href="/270edo">270edo</a>, <a class="wiki_link" href="/284edo">284edo</a>, <a class="wiki_link" href="/289edo">289edo</a>, <a class="wiki_link" href="/311edo">311edo</a>, <a class="wiki_link" href="/346edo">346edo</a>, <a class="wiki_link" href="/347edo">347edo</a>, <a class="wiki_link" href="/359edo">359edo</a>, <a class="wiki_link" href="/383edo">383edo</a>, <a class="wiki_link" href="/441edo">441edo</a>, <a class="wiki_link" href="/494edo">494edo</a>, <a class="wiki_link" href="/612edo">612edo</a>, <a class="wiki_link" href="/665edo">665edo</a>, <a class="wiki_link" href="/771edo">771edo</a>, <a class="wiki_link" href="/940edo">940edo</a>, <a class="wiki_link" href="/971edo">971edo</a>, <a class="wiki_link" href="/2460edo">2460edo</a>, <a class="wiki_link" href="/2966edo">2966edo</a>, <a class="wiki_link" href="/6079edo">6079edo</a>, <a class="wiki_link" href="/15601edo">15601edo</a></body></html>