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EDO: Difference between revisions

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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:genewardsmith|genewardsmith]] and made on <tt>2014-05-30 12:37:29 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-05-30 12:38:20 UTC</tt>.<br>
: The original revision id was <tt>512141408</tt>.<br>
: The original revision id was <tt>512141702</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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If you are interested in exploring the unique merits and challenges of each EDO, irrespective of any desire to approximate Just intonation (or any other a priori musical goal), starting at the bottom and working your way up can be a most illuminating exercise.
If you are interested in exploring the unique merits and challenges of each EDO, irrespective of any desire to approximate Just intonation (or any other a priori musical goal), starting at the bottom and working your way up can be a most illuminating exercise.


If you're a classically-trained musician and you'd like to start with some EDOs that have some relationship to common-practice tonal music, starting with reasonably-low EDOs that give a good approximation to [[3_2|3/2]] (the perfect 5th) can be rewarding. These include [[12edo]], [[17edo|17]], [[19edo|19]], [[22edo|22]], [[29edo|29]], [[31edo|31]], [[39edo|39]], [[41edo|41]], [[43edo|43]], [[45edo|45]], [[46edo|46]], [[49edo|49]], [[50edo|50]] and [[53edo|53]]. All of these can be notated with some variant on the [[Nominal-Accidental Chains#A-G%20circle-of-fifths%20notation|A-G "circle of fifths" notation]], while other EDOs, including [[24edo|24]], [[34edo|34]], [[36edo|36]], [[38edo|38]], [[44edo|44]], [[48edo|48]], or [[51edo|51]] involve more than one such circle.
If you're a classically-trained musician and you'd like to start with some EDOs that have some relationship to common-practice tonal music, starting with reasonably-low EDOs that give a good approximation to [[3_2|3/2]] (the perfect 5th) can be rewarding. These include [[12edo|12]], [[17edo|17]], [[19edo|19]], [[22edo|22]], [[29edo|29]], [[31edo|31]], [[39edo|39]], [[41edo|41]], [[43edo|43]], [[45edo|45]], [[46edo|46]], [[49edo|49]], [[50edo|50]] and [[53edo|53]]. All of these can be notated with some variant on the [[Nominal-Accidental Chains#A-G%20circle-of-fifths%20notation|A-G "circle of fifths" notation]], while other EDOs, including [[24edo|24]], [[34edo|34]], [[36edo|36]], [[38edo|38]], [[44edo|44]], [[48edo|48]], or [[51edo|51]] involve more than one such circle.


Some EDOs, such as [[26edo|26]], [[27edo|27]], [[32edo|32]], [[33edo|33]], or [[37edo|37]] have fifths which are reasonably good but quite audibly not just. Other EDOs, such as [[11edo|11]], [[13edo|13]], [[14edo|14]], [[15edo|15]], [[16edo|16]], [[18edo|18]], [[20edo|20]], [[21edo|21]], [[23edo|23]] or [[25edo|25]], are of interest to the avid seeker of totally unusual sounds that have next-to-no connection with the common practice.
Some EDOs, such as [[26edo|26]], [[27edo|27]], [[32edo|32]], [[33edo|33]], or [[37edo|37]] have fifths which are reasonably good but quite audibly not just. Other EDOs, such as [[11edo|11]], [[13edo|13]], [[14edo|14]], [[15edo|15]], [[16edo|16]], [[18edo|18]], [[20edo|20]], [[21edo|21]], [[23edo|23]] or [[25edo|25]], are of interest to the avid seeker of totally unusual sounds that have next-to-no connection with the common practice.
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If you are interested in exploring the unique merits and challenges of each EDO, irrespective of any desire to approximate Just intonation (or any other a priori musical goal), starting at the bottom and working your way up can be a most illuminating exercise.&lt;br /&gt;
If you are interested in exploring the unique merits and challenges of each EDO, irrespective of any desire to approximate Just intonation (or any other a priori musical goal), starting at the bottom and working your way up can be a most illuminating exercise.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
If you're a classically-trained musician and you'd like to start with some EDOs that have some relationship to common-practice tonal music, starting with reasonably-low EDOs that give a good approximation to &lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt; (the perfect 5th) can be rewarding. These include &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;, &lt;a class="wiki_link" href="/17edo"&gt;17&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22&lt;/a&gt;, &lt;a class="wiki_link" href="/29edo"&gt;29&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/39edo"&gt;39&lt;/a&gt;, &lt;a class="wiki_link" href="/41edo"&gt;41&lt;/a&gt;, &lt;a class="wiki_link" href="/43edo"&gt;43&lt;/a&gt;, &lt;a class="wiki_link" href="/45edo"&gt;45&lt;/a&gt;, &lt;a class="wiki_link" href="/46edo"&gt;46&lt;/a&gt;, &lt;a class="wiki_link" href="/49edo"&gt;49&lt;/a&gt;, &lt;a class="wiki_link" href="/50edo"&gt;50&lt;/a&gt; and &lt;a class="wiki_link" href="/53edo"&gt;53&lt;/a&gt;. All of these can be notated with some variant on the &lt;a class="wiki_link" href="/Nominal-Accidental%20Chains#A-G%20circle-of-fifths%20notation"&gt;A-G &amp;quot;circle of fifths&amp;quot; notation&lt;/a&gt;, while other EDOs, including &lt;a class="wiki_link" href="/24edo"&gt;24&lt;/a&gt;, &lt;a class="wiki_link" href="/34edo"&gt;34&lt;/a&gt;, &lt;a class="wiki_link" href="/36edo"&gt;36&lt;/a&gt;, &lt;a class="wiki_link" href="/38edo"&gt;38&lt;/a&gt;, &lt;a class="wiki_link" href="/44edo"&gt;44&lt;/a&gt;, &lt;a class="wiki_link" href="/48edo"&gt;48&lt;/a&gt;, or &lt;a class="wiki_link" href="/51edo"&gt;51&lt;/a&gt; involve more than one such circle.&lt;br /&gt;
If you're a classically-trained musician and you'd like to start with some EDOs that have some relationship to common-practice tonal music, starting with reasonably-low EDOs that give a good approximation to &lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt; (the perfect 5th) can be rewarding. These include &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/17edo"&gt;17&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22&lt;/a&gt;, &lt;a class="wiki_link" href="/29edo"&gt;29&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/39edo"&gt;39&lt;/a&gt;, &lt;a class="wiki_link" href="/41edo"&gt;41&lt;/a&gt;, &lt;a class="wiki_link" href="/43edo"&gt;43&lt;/a&gt;, &lt;a class="wiki_link" href="/45edo"&gt;45&lt;/a&gt;, &lt;a class="wiki_link" href="/46edo"&gt;46&lt;/a&gt;, &lt;a class="wiki_link" href="/49edo"&gt;49&lt;/a&gt;, &lt;a class="wiki_link" href="/50edo"&gt;50&lt;/a&gt; and &lt;a class="wiki_link" href="/53edo"&gt;53&lt;/a&gt;. All of these can be notated with some variant on the &lt;a class="wiki_link" href="/Nominal-Accidental%20Chains#A-G%20circle-of-fifths%20notation"&gt;A-G &amp;quot;circle of fifths&amp;quot; notation&lt;/a&gt;, while other EDOs, including &lt;a class="wiki_link" href="/24edo"&gt;24&lt;/a&gt;, &lt;a class="wiki_link" href="/34edo"&gt;34&lt;/a&gt;, &lt;a class="wiki_link" href="/36edo"&gt;36&lt;/a&gt;, &lt;a class="wiki_link" href="/38edo"&gt;38&lt;/a&gt;, &lt;a class="wiki_link" href="/44edo"&gt;44&lt;/a&gt;, &lt;a class="wiki_link" href="/48edo"&gt;48&lt;/a&gt;, or &lt;a class="wiki_link" href="/51edo"&gt;51&lt;/a&gt; involve more than one such circle.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Some EDOs, such as &lt;a class="wiki_link" href="/26edo"&gt;26&lt;/a&gt;, &lt;a class="wiki_link" href="/27edo"&gt;27&lt;/a&gt;, &lt;a class="wiki_link" href="/32edo"&gt;32&lt;/a&gt;, &lt;a class="wiki_link" href="/33edo"&gt;33&lt;/a&gt;, or &lt;a class="wiki_link" href="/37edo"&gt;37&lt;/a&gt; have fifths which are reasonably good but quite audibly not just. Other EDOs, such as &lt;a class="wiki_link" href="/11edo"&gt;11&lt;/a&gt;, &lt;a class="wiki_link" href="/13edo"&gt;13&lt;/a&gt;, &lt;a class="wiki_link" href="/14edo"&gt;14&lt;/a&gt;, &lt;a class="wiki_link" href="/15edo"&gt;15&lt;/a&gt;, &lt;a class="wiki_link" href="/16edo"&gt;16&lt;/a&gt;, &lt;a class="wiki_link" href="/18edo"&gt;18&lt;/a&gt;, &lt;a class="wiki_link" href="/20edo"&gt;20&lt;/a&gt;, &lt;a class="wiki_link" href="/21edo"&gt;21&lt;/a&gt;, &lt;a class="wiki_link" href="/23edo"&gt;23&lt;/a&gt; or &lt;a class="wiki_link" href="/25edo"&gt;25&lt;/a&gt;, are of interest to the avid seeker of totally unusual sounds that have next-to-no connection with the common practice.&lt;br /&gt;
Some EDOs, such as &lt;a class="wiki_link" href="/26edo"&gt;26&lt;/a&gt;, &lt;a class="wiki_link" href="/27edo"&gt;27&lt;/a&gt;, &lt;a class="wiki_link" href="/32edo"&gt;32&lt;/a&gt;, &lt;a class="wiki_link" href="/33edo"&gt;33&lt;/a&gt;, or &lt;a class="wiki_link" href="/37edo"&gt;37&lt;/a&gt; have fifths which are reasonably good but quite audibly not just. Other EDOs, such as &lt;a class="wiki_link" href="/11edo"&gt;11&lt;/a&gt;, &lt;a class="wiki_link" href="/13edo"&gt;13&lt;/a&gt;, &lt;a class="wiki_link" href="/14edo"&gt;14&lt;/a&gt;, &lt;a class="wiki_link" href="/15edo"&gt;15&lt;/a&gt;, &lt;a class="wiki_link" href="/16edo"&gt;16&lt;/a&gt;, &lt;a class="wiki_link" href="/18edo"&gt;18&lt;/a&gt;, &lt;a class="wiki_link" href="/20edo"&gt;20&lt;/a&gt;, &lt;a class="wiki_link" href="/21edo"&gt;21&lt;/a&gt;, &lt;a class="wiki_link" href="/23edo"&gt;23&lt;/a&gt; or &lt;a class="wiki_link" href="/25edo"&gt;25&lt;/a&gt;, are of interest to the avid seeker of totally unusual sounds that have next-to-no connection with the common practice.&lt;br /&gt;
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