User:VectorGraphics/Periodicity: Difference between revisions

Line 24:

== From temperaments to scales ==

[[File:12 well 5limit.png|left|thumb|337x337px|A well temperament of 12-edo defined from a Fokker periodicity block, in ratios and in cents. (Both possible mappings of 600c have been provided.)]]

Such a block can then be placed back into a less restrictive temperament or into just intonation, to define a scale, sort of like a MOS scale but generalized to a higher dimension. For example, one might describe a 12-tone well temperament in 5-limit just intonation by placing a periodicity block representing 12edo into a JI lattice, and seeing what intervals lie within it.

Such a block can then be placed back into a less restrictive temperament or into just intonation, to define a scale, sort of like a MOS scale but generalized to a higher dimension. For example, one might describe a 12-tone well temperament in 5-limit just intonation by placing a periodicity block representing 12edo into a JI lattice, and seeing what intervals lie within it. This can be treated as a scale on its own (a just chromatic scale), outside of the context of being a 12edo detemper.

In the context of constructing a scale (as opposed to defining a temperament), the intervals chosen at which to repeat the table are called '''chromas''' instead of commas, and they define a '''chroma basis'''. So, for example, our 12-well temperament has the chroma basis {81/80, 128/125}.

@@ Line 24: / Line 24: @@
 == From temperaments to scales ==
 [[File:12 well 5limit.png|left|thumb|337x337px|A well temperament of 12-edo defined from a Fokker periodicity block, in ratios and in cents. (Both possible mappings of 600c have been provided.)]]
-Such a block can then be placed back into a less restrictive temperament or into just intonation, to define a scale, sort of like a MOS scale but generalized to a higher dimension. For example, one might describe a 12-tone well temperament in 5-limit just intonation by placing a periodicity block representing 12edo into a JI lattice, and seeing what intervals lie within it.
+Such a block can then be placed back into a less restrictive temperament or into just intonation, to define a scale, sort of like a MOS scale but generalized to a higher dimension. For example, one might describe a 12-tone well temperament in 5-limit just intonation by placing a periodicity block representing 12edo into a JI lattice, and seeing what intervals lie within it. This can be treated as a scale on its own (a just chromatic scale), outside of the context of being a 12edo detemper.
 In the context of constructing a scale (as opposed to defining a temperament), the intervals chosen at which to repeat the table are called '''chromas''' instead of commas, and they define a '''chroma basis'''. So, for example, our 12-well temperament has the chroma basis {81/80, 128/125}.