Muddle: Difference between revisions

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''~~Muddling~~'' ~~refers to~~ a ~~process of~~ mapping one [[periodic scale]] onto another one~~; the scale thus produced is~~ a ''~~'muddle'~~''~~. By periodic scale is meant a scale that repeats "at the something" (octave, tritave, something else)~~. There are two necessary components: a ''parent scale'' and a ''target shape'', or simply "parent" and "target". The parent scale can be any periodic scale at all; the target ~~scale~~ is not exactly a scale – it is the outline or ''shape'' of a scale – and it must be defined in terms of units or degrees which comprise the steps. If the period is an octave, this means the target scale will be a subset of an [[edo]].

A '''muddle''' is a scale that results from mapping one [[periodic scale]] onto another one by a process called ''muddling''. There are two necessary components: a ''parent scale'' and a ''target shape'', or simply "parent" and "target". The parent scale can be any periodic scale at all; the target is not exactly a scale – it is the outline or ''shape'' of a scale – and it must be defined in terms of units or degrees which comprise the steps. If the period is an octave, this means the target scale will be a subset of an [[edo]].

The simplest sort of muddle is a mos muddle, which is a sort of second-order [[mos scale]] and is useful for generating usable subsets of larger mos scales and for navigating [[regular temperament]]s. This article will mostly deal with mos muddles, but ~~it should be remembered that~~ this process can be generalized to arbitrary sequences of steps.

The simplest sort of muddle is a mos muddle, which is a sort of second-order [[mos scale]] and is useful for generating usable subsets of larger mos scales and for navigating [[regular temperament]]s. This article will mostly deal with mos muddles, but this process can be generalized to arbitrary sequences of steps.

== Construction ==

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== Comments ==

With the exception of trivial muddles, 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~~.

With the exception of trivial muddles, 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 "L" and a small step "s"), a secondary scale can have two varieties for each size step of the target scale (eg. the targets "s" and "L" steps become "s", "S", "l" and "L"). It is very common for a large small step (S) to be smaller than a small large step (l) but this isn't necessarily the case if the parent scale is less even than the target scale, if the parent MOS scale is generated from an equal temperament it is even possible for S and l to be the same size.

Parent scales that are close to equal (eg. [[Maximal_evenness|maximally even]] scales) will produce muddles that are melodically closer 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 one.

As every note in the muddle is also in the parent scale it will have share any temperament properties and therefore the harmonic relationships of the parent scale, however depending on the choice of the target, specific low generator intervals can be absent from the scale.

== History ==

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-''Muddling'' refers to a process of mapping one [[periodic scale]] onto another one; the scale thus produced is a '''muddle'''. By periodic scale is meant a scale that repeats "at the something" (octave, tritave, something else). There are two necessary components: a ''parent scale'' and a ''target shape'', or simply "parent" and "target". The parent scale can be any periodic scale at all; the target scale is not exactly a scale – it is the outline or ''shape'' of a scale – and it must be defined in terms of units or degrees which comprise the steps. If the period is an octave, this means the target scale will be a subset of an [[edo]].
+A '''muddle''' is a scale that results from mapping one [[periodic scale]] onto another one by a process called ''muddling''. There are two necessary components: a ''parent scale'' and a ''target shape'', or simply "parent" and "target". The parent scale can be any periodic scale at all; the target is not exactly a scale – it is the outline or ''shape'' of a scale – and it must be defined in terms of units or degrees which comprise the steps. If the period is an octave, this means the target scale will be a subset of an [[edo]].
-The simplest sort of muddle is a mos muddle, which is a sort of second-order [[mos scale]] and is useful for generating usable subsets of larger mos scales and for navigating [[regular temperament]]s. This article will mostly deal with mos muddles, but it should be remembered that this process can be generalized to arbitrary sequences of steps.
+The simplest sort of muddle is a mos muddle, which is a sort of second-order [[mos scale]] and is useful for generating usable subsets of larger mos scales and for navigating [[regular temperament]]s. This article will mostly deal with mos muddles, but this process can be generalized to arbitrary sequences of steps.
 == Construction ==
@@ Line 125: / Line 125: @@
 == Comments ==
-With the exception of trivial muddles, 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.
+With the exception of trivial muddles, 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 "L" and a small step "s"), a secondary scale can have two varieties for each size step of the target scale  (eg. the targets "s" and "L" steps become "s", "S", "l" and "L"). It is very common for a large small step (S) to be smaller than a small large step (l) but this isn't necessarily the case if the parent scale is less even than the target scale, if the parent MOS scale is generated from an equal temperament it is even possible for  S and l to be the same size.
+Parent scales that are close to equal (eg. [[Maximal_evenness|maximally even]] scales) will produce muddles that are melodically closer 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 one.
+As every note in the muddle is also in the parent scale it will have share any temperament properties and therefore the harmonic relationships of the parent scale, however depending on the choice of the target, specific low generator intervals can be absent from the scale.
 == History ==