Muddle
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A //Muddle// is a sort of second-order [[MOSScales|MOS Scale]] useful for generating usable subsets of larger MOS scales and for navigating [[Regular Temperaments]]. There are two necessary components: A **//parent MOS//** and an **//MOS shape//**. The parent MOS (or "parent scale") is any MOS scale large enough that taking subsets of it would be musically useful. The MOS shape is something like 12122, and it suggests a way of bunching intervals of the parent scale. If we apply the MOS shape to an equal-step scale, we arrive at a standard MOS. Eg. If our parent scale is [[8edo]] -- with steps 11111111 -- and our MOS shape is 12122, then the resulting MOS is (1)(11)(1)(11)(1)(11) = 12122 -- the same as our MOS shape. But if our parent scale is some other MOS, say 22222223 (a subset of [[17edo]]), applying the 12122 shape generates (2)(22)(2)(22)(23) = 24245. The latter scale, which we can call a //muddle//, has some melodic similarity to the MOS shape of 12122, but belongs to a different temperament family entirely. Choosing a different mode (rotation) of either the parent scale or the MOS shape may produce a different muddle. =Examples= ===1.=== To continue with our example of a parent scale of 22222223 and an MOS shape of 12122, here are all the muddles that can result from different rotations of the parent scale: * 22222223 parent with 12122 shape gives (2)(22)(2)(22)(23) = 24245 * 22222232 parent with 12122 shape gives (2)(22)(2)(22)(32) = 24245 * 22222322 parent with 12122 shape gives (2)(22)(2)(23)(22) = 24254 * 22223222 parent with 12122 shape gives (2)(22)(2)(32)(22) = 24254 * 22232222 parent with 12122 shape gives (2)(22)(3)(22)(22) = 24344 * 22322222 parent with 12122 shape gives (2)(23)(2)(22)(22) = 25244 * 23222222 parent with 12122 shape gives (2)(32)(2)(22)(22) = 25244 * 32222222 parent with 12122 shape gives (3)(22)(2)(22)(22) = 34244 Notice that not all of these rotations are different from each other. The unique muddles are 24245, 24254, 24344, 25244, and 34244. ===2.=== Here is a diagram showing the muddles available with 55755757 parent scale ([[Sensi]][8] of [[46edo]]) and 12122 MOS shape. Note that this combination produces MOS scales as well as muddles. [[image:sensi_pentatonics.png]] =Comments= Muddles always have more than two sizes of step -- either three or four sizes. Whereas MOS scales have two varieties of interval for each interval class (eg. a "large step" and a "small step"), muddles have potentially two varieties within each variety (eg. two sizes of "small step" and two sizes of "large step"). Parent MOS scales that are close to equal (eg. [[Maximal evenness|maximally even]] scales) will produce muddles that are closer in sound to the MOS shape. Larger parent scales contain more potential muddles than smaller ones, just as larger [[EDO]]s contain more potential MOS scales than smaller ones. =Variations= # One could muddle a muddle (a meta-muddle?). # One could muddle a [[MODMOS Scales|MODMOS scale]]. # One could muddle a non-MOS scale (muddle or non-muddle? ...still being decided...). ## <span class="commentBody"> For in</span><span class="text_exposed_show">stance, if you take overtones 16-32 as the parent scale, you can apply the 2322232 MOS shape and get 1/1, 9/8, 21/16, 23/16, 25/16, 27/16, 15/8, 2/1.</span>
Original HTML content:
<html><head><title>Muddle</title></head><body>A <em>Muddle</em> is a sort of second-order <a class="wiki_link" href="/MOSScales">MOS Scale</a> useful for generating usable subsets of larger MOS scales and for navigating <a class="wiki_link" href="/Regular%20Temperaments">Regular Temperaments</a>.<br /> <br /> There are two necessary components: A <strong><em>parent MOS</em></strong> and an <strong><em>MOS shape</em></strong>. The parent MOS (or "parent scale") is any MOS scale large enough that taking subsets of it would be musically useful. The MOS shape is something like 12122, and it suggests a way of bunching intervals of the parent scale. If we apply the MOS shape to an equal-step scale, we arrive at a standard MOS. Eg. If our parent scale is <a class="wiki_link" href="/8edo">8edo</a> -- with steps 11111111 -- and our MOS shape is 12122, then the resulting MOS is (1)(11)(1)(11)(1)(11) = 12122 -- the same as our MOS shape. But if our parent scale is some other MOS, say 22222223 (a subset of <a class="wiki_link" href="/17edo">17edo</a>), applying the 12122 shape generates (2)(22)(2)(22)(23) = 24245. The latter scale, which we can call a <em>muddle</em>, has some melodic similarity to the MOS shape of 12122, but belongs to a different temperament family entirely. Choosing a different mode (rotation) of either the parent scale or the MOS shape may produce a different muddle.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Examples"></a><!-- ws:end:WikiTextHeadingRule:0 -->Examples</h1> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h3> --><h3 id="toc1"><a name="Examples--1."></a><!-- ws:end:WikiTextHeadingRule:2 -->1.</h3> <br /> To continue with our example of a parent scale of 22222223 and an MOS shape of 12122, here are all the muddles that can result from different rotations of the parent scale:<br /> <ul><li>22222223 parent with 12122 shape gives (2)(22)(2)(22)(23) = 24245</li><li>22222232 parent with 12122 shape gives (2)(22)(2)(22)(32) = 24245</li><li>22222322 parent with 12122 shape gives (2)(22)(2)(23)(22) = 24254</li><li>22223222 parent with 12122 shape gives (2)(22)(2)(32)(22) = 24254</li><li>22232222 parent with 12122 shape gives (2)(22)(3)(22)(22) = 24344</li><li>22322222 parent with 12122 shape gives (2)(23)(2)(22)(22) = 25244</li><li>23222222 parent with 12122 shape gives (2)(32)(2)(22)(22) = 25244</li><li>32222222 parent with 12122 shape gives (3)(22)(2)(22)(22) = 34244</li></ul>Notice that not all of these rotations are different from each other. The unique muddles are 24245, 24254, 24344, 25244, and 34244.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h3> --><h3 id="toc2"><a name="Examples--2."></a><!-- ws:end:WikiTextHeadingRule:4 -->2.</h3> <br /> Here is a diagram showing the muddles available with 55755757 parent scale (<a class="wiki_link" href="/Sensi">Sensi</a>[8] of <a class="wiki_link" href="/46edo">46edo</a>) and 12122 MOS shape. Note that this combination produces MOS scales as well as muddles.<br /> <!-- ws:start:WikiTextLocalImageRule:40:<img src="/file/view/sensi_pentatonics.png/293730366/sensi_pentatonics.png" alt="" title="" /> --><img src="/file/view/sensi_pentatonics.png/293730366/sensi_pentatonics.png" alt="sensi_pentatonics.png" title="sensi_pentatonics.png" /><!-- ws:end:WikiTextLocalImageRule:40 --><br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="Comments"></a><!-- ws:end:WikiTextHeadingRule:6 -->Comments</h1> <br /> Muddles always have more than two sizes of step -- either three or four sizes. Whereas MOS scales have two varieties of interval for each interval class (eg. a "large step" and a "small step"), muddles have potentially two varieties within each variety (eg. two sizes of "small step" and two sizes of "large step"). Parent MOS scales that are close to equal (eg. <a class="wiki_link" href="/Maximal%20evenness">maximally even</a> scales) will produce muddles that are closer in sound to the MOS shape. Larger parent scales contain more potential muddles than smaller ones, just as larger <a class="wiki_link" href="/EDO">EDO</a>s contain more potential MOS scales than smaller ones.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h1> --><h1 id="toc4"><a name="Variations"></a><!-- ws:end:WikiTextHeadingRule:8 -->Variations</h1> <ol><li>One could muddle a muddle (a meta-muddle?).</li><li>One could muddle a <a class="wiki_link" href="/MODMOS%20Scales">MODMOS scale</a>.</li><li>One could muddle a non-MOS scale (muddle or non-muddle? ...still being decided...).<ol><li><span class="commentBody"> For in</span><span class="text_exposed_show">stance, if you take overtones 16-32 as the parent scale, you can apply the 2322232 MOS shape and get 1/1, 9/8, 21/16, 23/16, 25/16, 27/16, 15/8, 2/1.</span></li></ol></li></ol></body></html>