Glossary: Difference between revisions

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'''comma''' - A rational number that maps to 1/1 in a given temperament.

'''rank''' - The number of generators of a set of intervals. e.g. 12-tone equal temperament is rank-1 because it can be generated by the semitone; the Pythagorean scale is rank-2 because it can be generated by the primes {2, 3}

'''rank''' - The number of generators of a set of intervals. e.g. 12-tone equal temperament is rank-1 because it can be generated by the semitone; the Pythagorean scale is rank-2 because it can be generated by the primes {2, 3}.

'''equal temperament''' - A rank-1 temperament. The temperament-agnostic term is [[equal-step tuning]].

'''tuning of a temperament''' - ~~The~~ concrete realization of a temperament, with concrete cent values (for each basis element of the temperament). A temperament's character does not depend on the exact choice of tuning, e.g. a semitone of 100.1 cents produces a scale similar to that produced by a semitone of 100.0 cents.

'''tuning of a temperament''' - A concrete realization of a temperament, with concrete cent values (for each basis element of the temperament). A temperament's character does not depend on the exact choice of tuning, e.g. a semitone of 100.1 cents produces a scale similar to that produced by a semitone of 100.0 cents.

'''optimal tuning''' - A tuning that optimizes some desired property (usually the accuracy of the temperament's approximations to just intonation). e.g. [[POTE_tuning|POTE tuning]].

@@ Line 29: / Line 29: @@
 '''comma''' - A rational number that maps to 1/1 in a given temperament.
-'''rank''' - The number of generators of a set of intervals. e.g. 12-tone equal temperament is rank-1 because it can be generated by the semitone; the Pythagorean scale is rank-2 because it can be generated by the primes {2, 3}
+'''rank''' - The number of generators of a set of intervals. e.g. 12-tone equal temperament is rank-1 because it can be generated by the semitone; the Pythagorean scale is rank-2 because it can be generated by the primes {2, 3}.
 '''equal temperament''' - A rank-1 temperament. The temperament-agnostic term is [[equal-step tuning]].
-'''tuning of a temperament''' - The concrete realization of a temperament, with concrete cent values (for each basis element of the temperament). A temperament's character does not depend on the exact choice of tuning, e.g. a semitone of 100.1 cents produces a scale similar to that produced by a semitone of 100.0 cents.
+'''tuning of a temperament''' - A concrete realization of a temperament, with concrete cent values (for each basis element of the temperament). A temperament's character does not depend on the exact choice of tuning, e.g. a semitone of 100.1 cents produces a scale similar to that produced by a semitone of 100.0 cents.
 '''optimal tuning''' - A tuning that optimizes some desired property (usually the accuracy of the temperament's approximations to just intonation). e.g. [[POTE_tuning|POTE tuning]].