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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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.

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 129: / Line 129: @@
 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.
+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 ==