User:VectorGraphics/Periodicity: Difference between revisions

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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}.

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''', which tells you which pairs of accidentals you'll need to notate music in that scale. So, for example, our 12-well temperament has the chroma basis {81/80, 128/125}.

A lot of other JI scales (and scales in general, using a tempered lattice) can be constructed as periodicity blocks. For example, the just zarlino scale can be constructed with the chroma basis {81/80, 25/24}. Porcupine temperament equates these two chromas by tempering out the porcupine comma, so the zarlino periodicity block can be placed into a lattice representing porcupine temperament to obtain the porcupine zarlino scale (a MODMOS of porcupine's "Onyx" MOS itself).

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 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}.
+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''', which tells you which pairs of accidentals you'll need to notate music in that scale. So, for example, our 12-well temperament has the chroma basis {81/80, 128/125}.
 A lot of other JI scales (and scales in general, using a tempered lattice) can be constructed as periodicity blocks. For example, the just zarlino scale can be constructed with the chroma basis {81/80, 25/24}. Porcupine temperament equates these two chromas by tempering out the porcupine comma, so the zarlino periodicity block can be placed into a lattice representing porcupine temperament to obtain the porcupine zarlino scale (a MODMOS of porcupine's "Onyx" MOS itself).