Regular temperament: Difference between revisions
Cmloegcmluin (talk | contribs) extract mathematical theory from main regular temperament page; combine introductory material from original page with introductory material that used to live on the Tour of Regular Temperaments page |
remove unnecessary newline |
||
| Line 5: | Line 5: | ||
| ja = レギュラーテンペラメント | | ja = レギュラーテンペラメント | ||
}} | }} | ||
A '''regular temperament''' is a mathematical object that maps an infinite set of intervals in to a smaller, though still infinite, set of [[tempering out|tempered]] intervals. Typically, the source set is assumed to be some [[Harmonic Limit|''p''-limit]] [[just intonation]] — or any [[Just intonation subgroups|subgroup]] thereof — AKA rational numbers, and tempering is done by deliberately mistuning some of the ratios such that a [[comma]] or set of commas vanishes by becoming a unison (it is "tempered out" in the temperament). The utility of regular temperament is partly to produce scales that are simpler and have more consonances than strict JI, while maintaining a high level of concordance (or similarity to JI), and partly to introduce useful "puns" as commas are tempered out. Temperaments effectively reduce the "dimensionality" of JI, thereby simplifying the pitch relationships. | A '''regular temperament''' is a mathematical object that maps an infinite set of intervals in to a smaller, though still infinite, set of [[tempering out|tempered]] intervals. Typically, the source set is assumed to be some [[Harmonic Limit|''p''-limit]] [[just intonation]] — or any [[Just intonation subgroups|subgroup]] thereof — AKA rational numbers, and tempering is done by deliberately mistuning some of the ratios such that a [[comma]] or set of commas vanishes by becoming a unison (it is "tempered out" in the temperament). The utility of regular temperament is partly to produce scales that are simpler and have more consonances than strict JI, while maintaining a high level of concordance (or similarity to JI), and partly to introduce useful "puns" as commas are tempered out. Temperaments effectively reduce the "dimensionality" of JI, thereby simplifying the pitch relationships. | ||