Val: Difference between revisions
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Vals are important because they provide a way to mathematically formalize how, specifically, the intervals in a random chain of generators are viewed as the tempered versions of more fundamental just intonation intervals. They can also be viewed as a way to map JI "onto" the chain, imbuing it with a harmonic context. Vals will enable you to figure out what commas your temperament eliminates, what [[comma pump]]s are available in the temperament, what the most consonant chords in the temperament are, how to optimize the octave stretch of the temperament to minimize tuning error, what EDOs support your temperament, and other operations as of yet undiscovered. | Vals are important because they provide a way to mathematically formalize how, specifically, the intervals in a random chain of generators are viewed as the tempered versions of more fundamental just intonation intervals. They can also be viewed as a way to map JI "onto" the chain, imbuing it with a harmonic context. Vals will enable you to figure out what commas your temperament eliminates, what [[comma pump]]s are available in the temperament, what the most consonant chords in the temperament are, how to optimize the octave stretch of the temperament to minimize tuning error, what EDOs support your temperament, and other operations as of yet undiscovered. | ||
For a more mathematically intensive introduction to vals, see [[ | For a more mathematically intensive introduction to vals, see [[vals and tuning space]]. For the characterization of higher rank temperaments, see [[mapping]]. | ||
== Example EDO == | == Example EDO == | ||
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== See also == | == See also == | ||
* [[Mapping]] | * [[Mapping]] | ||
* [[Vals and | * [[Vals and tuning space]] | ||
* [[Monzos and | * [[Monzos and interval space]] | ||
* [[Patent val]] | * [[Patent val]] | ||