Glossary: Difference between revisions

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; [[just intonation subgroup]] : The set of JI ratios obtainable by stacking (finitely many) copies of a finite set of JI generators up or down. For example, 7/6 and 49/32 are both in the 2.3.7 subgroup, the set of JI ratios obtained by stacking copies of 2/1, 3/1 and 7/1 up and down.

; [[temperament]] : A mapping from a [[domain]] (such as a [[prime limit]] or [[just intonation subgroup]]) to a set of intervals with fewer generators. ~~expressible~~ as a [[mapping|mapping matrix]] whose columns are generators of the just intonation and whose rows are generators of the temperament. In particular, the row vectors are called [[val]]s or [[map]]s.

; [[temperament]] : A mapping from a [[domain]] (such as a [[prime limit]] or [[just intonation subgroup]]) to a set of intervals with fewer generators. Expressible as a [[mapping|mapping matrix]] whose columns are generators of the just intonation and whose rows are generators of the temperament. In particular, the row vectors are called [[val]]s or [[map]]s.

; [[comma]] : A rational number that maps to 1/1 in a given temperament.

; [[rank]] : The number of generators of a set of intervals, i.e. the set's ~~cardinality~~. For example, 12edo 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, i.e. the set's dimensionality. For example, 12edo 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]].

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 ; [[just intonation subgroup]] : The set of JI ratios obtainable by stacking (finitely many) copies of a finite set of JI generators up or down. For example, 7/6 and 49/32 are both in the 2.3.7 subgroup, the set of JI ratios obtained by stacking copies of 2/1, 3/1 and 7/1 up and down.
-; [[temperament]] : A mapping from a [[domain]] (such as a [[prime limit]] or [[just intonation subgroup]]) to a set of intervals with fewer generators. expressible as a [[mapping|mapping matrix]] whose columns are generators of the just intonation and whose rows are generators of the temperament. In particular, the row vectors are called [[val]]s or [[map]]s.
+; [[temperament]] : A mapping from a [[domain]] (such as a [[prime limit]] or [[just intonation subgroup]]) to a set of intervals with fewer generators. Expressible as a [[mapping|mapping matrix]] whose columns are generators of the just intonation and whose rows are generators of the temperament. In particular, the row vectors are called [[val]]s or [[map]]s.
 ; [[comma]] : A rational number that maps to 1/1 in a given temperament.
-; [[rank]] : The number of generators of a set of intervals, i.e. the set's cardinality. For example, 12edo 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, i.e. the set's dimensionality. For example, 12edo 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]].