Mapping: Difference between revisions
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Naively, one might think that a simple rounding function might be suitable for a mapping: let the "tempered version" of each JI pitch simply be the tempered pitch that is closest to it. However, this (usually) does not result in a regular temperament at all! The reason is that, although this mapping assigns a tempered pitch to each JI pitch, it does not do so in a ''consistent'' way – some instances of the same JI interval are represented by different tempered intervals if they occur in different places. A regular temperament mapping always represents each JI interval by the ''same'' tempered interval (even if that tempered interval is not the closest tempered interval to the JI interval). | Naively, one might think that a simple rounding function might be suitable for a mapping: let the "tempered version" of each JI pitch simply be the tempered pitch that is closest to it. However, this (usually) does not result in a regular temperament at all! The reason is that, although this mapping assigns a tempered pitch to each JI pitch, it does not do so in a ''consistent'' way – some instances of the same JI interval are represented by different tempered intervals if they occur in different places. A regular temperament mapping always represents each JI interval by the ''same'' tempered interval (even if that tempered interval is not the closest tempered interval to the JI interval). | ||
== A note on mathematical terminology == | |||
In mathematics generally, "mapping" is synonymous with "map" and "function". In RTT, "mapping" has the more specific meaning of a [[Wikipedia:Linear_map|''linear'' mapping]], which is a function that can be represented by a matrix. | |||
== Equal temperament mappings == | == Equal temperament mappings == | ||