Glossary: Difference between revisions

; [[cent]] (¢) : A logarithmic [[Interval size measure|unit of measure of intervals]]. For a ratio R, 1200 · log₂(R).

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

; [[delta-rational]] (DR) : Of a chord, having at least two dyads which represent frequency differences which have a rational ratio. This property is thought to result in synchronized interference beating between the dyads.

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

; [[equave]] (interval of equivalence) : An interval considered to be equivalent to the unison, such as an [[octave]] (2/1 or 1200 cents).

; ''n''-form: An n-note [[constant structure]] scale.

; [[wikipedia: Frequency|Frequency]] : The number of oscillations per unit of time of a vibrating object.

; [[generator]]s : A set of intervals that generate a larger set through linear combination. e.g. the primes {2, 3} generate the Pythagorean scale.

; harmonic distance : A property of intervals other than size; a second type of distance, such that pitches separated by 'short' intervals are more likely to be confused (as by novice singers) than those separated by 'long' intervals. e.g. an octave is 'shorter' than a tritone. related to consonance. e.g. [[Benedetti_height|Tenney height]].

; [[wikipedia: Hertz|Hertz]] (Hz) : A unit of frequency defined as one oscillation per second.

; [[interval]] : The distance between two pitches, expressed as a ratio (of their associated frequencies in hertz) or as a logarithmic measure (e.g. cents).

; [[just intonation]] (JI) : The set of intervals expressible as rational numbers.

; [[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.

; [[mode]] : A particular rotation of a scale, e.g. Ionian, Dorian etc. for the diatonic scale.

; optimal tuning : A tuning of a temperament that optimizes some desired property (usually the accuracy of the temperament's approximations to just intonation). e.g. [[CTE tuning]].

; [[periodic scale]] : A scale that repeats at an interval of equivalence. Exactly what can be described by a [http://www.huygens-fokker.org/scala/scl_format.html Scala file].

; [[rank]] : The number of generators of a set of intervals, i.e. the set's dimensionality (not to be confused with the [[dimensionality]] of the temperament itself). 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}.

; [[scale]] : An ordered list of intervals.

; scale signature: An expression using the step sizes of a scale, where the coefficient in front of each step tells you how many of that step size the scale has. A [[mos]] scale has a scale signature of aL bs for step sizes L > s. Other scales may have more complex signatures such as 5L 2M 3s.

; [[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.

; [[tuning system|tuning]] of a temperament : A concrete realization of a(n abstract) 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.