Regular temperament: Difference between revisions

Line 9:

A '''regular temperament''' ('''RT''') is an abstract [[tuning system]] that looks the same no matter which pitch you start from (or consider the [[tonic]]). In other words, unlimited free modulation is possible: any [[interval]] can be stacked as many times as you like. Regular temperaments generally have an infinite number of notes; and other than [[equal temperament]]s, every regular temperament actually has an infinite number of notes in between ''any two other notes''.

A regular temperament can usefully be thought of less as a ''tuning system'' and more as a set of rules for a tuning system to follow. For example, any regular tuning that follows the rule that ~3/2^4 = ~5/1 is a tuning of [[meantone]] temperament; if you change the rule to ~3/2^4 = ~36/7, then the same tuning can be treated as a tuning of [[archy]] temperament.

In addition to unlimited modulation, regular temperaments by definition are thought of as being approximations of some more complicated system of pure or target intervals, very often a [[just intonation]] (JI) [[subgroup]]. Each abstract interval is interpreted as a tempered, or detuned, version of the target interval (more accurately, a set of target intervals). A temperament only qualifies as a regular temperament if this interpretation works in a perfectly consistent way. For example, the sum of two tempered intervals must always be the tempered version of the sum of the JI intervals. Multiple pure intervals may be represented by the same tempered interval (so they are tempered together), but a single pure interval must never be represented by different tempered intervals; if so, the temperament is irregular.

@@ Line 9: / Line 9: @@
 A '''regular temperament''' ('''RT''') is an abstract [[tuning system]] that looks the same no matter which pitch you start from (or consider the [[tonic]]). In other words, unlimited free modulation is possible: any [[interval]] can be stacked as many times as you like. Regular temperaments generally have an infinite number of notes; and other than [[equal temperament]]s, every regular temperament actually has an infinite number of notes in between ''any two other notes''.
-A regular temperament can usefully be thought of less as a ''tuning system'' and more as a set of rules for a tuning system to follow. For example, any regular tuning that follows the rule that ~3/2^4 = ~5/1 is a tuning of [[meantone]] temperament; if you change the rule to ~3/2^4 = ~36/7, then the same tuning can be treated as a tuning of [[archy]] temperament.
 In addition to unlimited modulation, regular temperaments by definition are thought of as being approximations of some more complicated system of pure or target intervals, very often a [[just intonation]] (JI) [[subgroup]]. Each abstract interval is interpreted as a tempered, or detuned, version of the target interval (more accurately, a set of target intervals). A temperament only qualifies as a regular temperament if this interpretation works in a perfectly consistent way. For example, the sum of two tempered intervals must always be the tempered version of the sum of the JI intervals. Multiple pure intervals may be represented by the same tempered interval (so they are tempered together), but a single pure interval must never be represented by different tempered intervals; if so, the temperament is irregular.