Muddle: Difference between revisions

Let the target scale T be a sequence of steps [ t1, t2, t3, ... , tm ], the parent scale P be a sequence of steps [ p1, p2, p3, ... , pn ], and the resulting muddle scale S be a sequence of steps [ s1, s2, s3, ... , sm ]. Note that the number of steps in P must be equal to the sum of all ti from T. Also note that both ti and pi are both numeric values, as with si.

In the case of a MOS muddle, the parent scale is any MOS scale large enough that taking subsets of it would be musically useful. The target scale is something like 12122. This could be the form of an actual scale (an MOS subset of [[8edo|8edo]], in this example), but as a target scale, we are interested in its general ''shape'', which suggests a way of bunching intervals of the parent scale. If we apply the target to an equal-step scale, we arrive at a standard MOS. Eg. If our parent scale is [[8edo|8edo]] -- with steps 11111111 -- and our target scale is 12122, then the resulting scale is (1)(11)(1)(11)(11) = 12122 -- the same as our target scale. But if our parent scale is some other MOS scale, say 22222223 (a subset of [[17edo|17edo]]), applying the 12122 target scale generates (2)(22)(2)(22)(23) = 24245 -- not an MOS scale. The latter scale, which we can call a ''muddle'', has some melodic similarity to the target scale of 12122, but belongs to a different temperament family entirely. Choosing a different mode (rotation) of either the parent scale or the target scale may produce a different muddle.

===1.===

[[File:sensi_pentatonics.png|alt=sensi_pentatonics.png|sensi_pentatonics.png]]

MOS 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 scales that are close to equal (eg. [[Maximal_evenness|maximally even]] scales) will produce muddles that are closer in sound to the target scale. Larger parent scales contain more potential muddles than smaller ones, just as larger [[EDO]]s contain more potential MOS scales than smaller ones.

MOS muddles seem to be as old as MOS, although the name "muddle" is new. Page six of [[Erv_Wilson|Erv Wilson]]'s [http://www.anaphoria.com/mos.PDF seminal article on MOS scales] shows a 17-tone MOS subset of [[41edo|41edo]] as "parent scale" and a 7-tone MOS pattern as "target scale shape". They are also present in the work of [[Kraig_Grady|Kraig Grady]], who prefers the term "bi-level" (see [https://anaphoriasouth.blogspot.com/2011/05/pentatonic-family-pt-1.html this blog entry] and [https://anaphoriasouth.blogspot.com/2012/01/pentatonic-family-pt2.html this one]). The word "muddle" comes from [[Gene_Ward_Smith|Gene Ward Smith]].

As mentioned at the beginning, in a muddle, the parent scale can be any kind of periodic scale at all, including but not limited to [[MODMOS_Scales|MODMOS scales]], [[MOS_Cradle|MOS Cradle scales]], other muddles, scales of [[Regular_Temperaments|temperaments]] with rank higher than 2, [[Just_intonation|Just Intonation]] scales, etc. The target scale is a little less flexible, but it could be at least a MODMOS scale, a MOS Cradle scale or any other MOS subset or subset of a periodic equal-step scale. It's just important that the total number of "units" in the target scale (eg. the MOS Cradle 23132 has 2+3+1+3+2=11 units) be the same as the number of tones in the parent scale (thus the 23132 target scale must be applied to a scale of 11 tones).

<span style="">As one example of a muddle with a non-MOS parent</span><span style="">, if you take overtones 16-32 as the parent scale, you can apply a 2322232 target scale and get 1/1, 9/8, 21/16, 23/16, 25/16, 27/16, 15/8, 2/1.</span>