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]].

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]] ||
||   ||   ||   ||   || [[65edo]] ||   ||   || [[68edo]] ||   || [[70edo]] ||   || [[72edo]] ||
||   ||   ||   || [[76edo]] || [[77edo]] ||   || [[79edo]] || [[80edo]] ||   ||   ||   ||   ||
||   ||   || [[87edo]] || [[88edo]] || [[89edo]] ||   ||   ||   ||   || [[94edo]] ||   || [[96edo]] ||
||   ||   || [[99edo]] ||   || [[101edo]] ||   ||   || [[104edo]] ||   ||   ||   ||   ||
||   ||   || [[111edo]] ||   || [[113edo]] ||   ||   ||   ||   || [[118edo]] ||   || [[120edo]] ||
||   ||   ||   ||   || [[125edo]] ||   || [[127edo]] ||   ||   || [[130edo]] ||   ||   ||
||   ||   || [[135edo]] ||   || [[137edo]] ||   ||   || [[140edo]] ||   || [[142edo]] ||   ||   ||
||   ||   || [[147edo]] ||   || [[149edo]] ||   ||   || [[152edo]] ||   ||   ||   ||   ||
and so on. Some larger systems include [[159edo]], [[166edo]], [[171edo]], [[185edo]], [[190edo]], [[197edo]], [[200edo]], [[202edo]], [[205edo]], [[224edo]], [[240edo]], [[253edo]], [[270edo]], [[284edo]], [[289edo]], [[311edo]], [[346edo]], [[441edo]], [[494edo]], [[612edo]], [[665edo]]

Original HTML content:

<html><head><title>EDO</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><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:&lt;h1&gt; --><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:&lt;h1&gt; --><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>.<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:&lt;h1&gt; --><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><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><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><a class="wiki_link" href="/76edo">76edo</a><br />
</td>
        <td><a class="wiki_link" href="/77edo">77edo</a><br />
</td>
        <td><br />
</td>
        <td><a class="wiki_link" href="/79edo">79edo</a><br />
</td>
        <td><a class="wiki_link" href="/80edo">80edo</a><br />
</td>
        <td><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="/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><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><br />
</td>
        <td><br />
</td>
        <td><a class="wiki_link" href="/104edo">104edo</a><br />
</td>
        <td><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><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><br />
</td>
        <td><br />
</td>
        <td><a class="wiki_link" href="/130edo">130edo</a><br />
</td>
        <td><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>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><a class="wiki_link" href="/147edo">147edo</a><br />
</td>
        <td><br />
</td>
        <td><a class="wiki_link" href="/149edo">149edo</a><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><a class="wiki_link" href="/152edo">152edo</a><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
</table>

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="/185edo">185edo</a>, <a class="wiki_link" href="/190edo">190edo</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="/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></body></html>
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