Glossary: Difference between revisions

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A concise list of essential terms in xenharmonic music theory

~~'''hertz''' -~~ A unit ~~for~~ frequency~~; counts~~ per second.

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

~~'''~~pitch~~''' -~~ The property of some sounds that allows them to be ordered on a one-dimensional 'pitch axis'. Often measured by the frequency (in hertz) of a sine wave having the same pitch.

; [[wikipedia:Pitch (music)|pitch]] : The property of some sounds that allows them to be ordered on a one-dimensional 'pitch axis'. Often measured by the frequency (in hertz) of a sine wave having the same pitch.

~~'''~~cents~~''' -~~ A logarithmic unit of measure. For a ratio R, 1200 * log2(R).

; [[cents]] (¢) : A logarithmic [[Interval size measure|unit of measure of intervals]]. For a ratio R, 1200 · log<sub>2</sub>(R).

~~'''~~interval~~''' -~~ The distance between two pitches, expressed as a ratio (of their associated frequencies in hertz) or in cents.

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

~~'''~~scale~~''' -~~ An ordered list of intervals.

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

~~'''~~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]].

; 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]].

~~'''~~equave~~''' or '''~~interval of equivalence~~''' -~~ An interval considered to be equivalent to the unison, such as an octave (~~pitch ratio~~ 2/1 or 1200 cents).

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

~~'''~~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].

; [[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].

~~'''~~mode~~''' -~~ A particular rotation of a scale, e.g. ~~ionian~~, ~~dorian~~ etc. for the diatonic scale.

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

~~'''~~just intonation~~''' -~~ The set of intervals expressible as rational numbers.

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

~~'''generators''' -~~ A set of intervals that generate a larger set through linear combination. e.g. the primes {2, 3} generate the Pythogorean scale.

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

~~'''~~just intonation subgroup~~''' -~~ The set of JI ratios obtainable by stacking (finitely many) copies of a finite set of 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.

; [[just intonation subgroup]] : The set of JI ratios obtainable by stacking (finitely many) copies of a finite set of 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 [[just intonation subgroup]] to a set of intervals with fewer generators. expressible as a [[Intro_to_Mappings|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 [[Vals_and_Tuning_Space|vals]].

; [[temperament]] : A mapping from a [[just intonation subgroup]] to a set of intervals with fewer generators. expressible as a [[Intro_to_Mappings|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 [[Vals_and_Tuning_Space|vals]].

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

; [[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 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}.

; [[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]].

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

~~'''~~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.

; [[tuning system|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]].

; 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]].

~~'''~~subtend~~''' -~~ Of an interval size, to occur as a certain number of steps in a given scale.

; subtend : Of an interval size, to occur as a certain number of steps in a given scale.

:''In the diatonic scale, the perfect fifth always subtends 4 steps.''

: ''In the diatonic scale, the perfect fifth always subtends 4 steps.''

[[Category:terminology]]

[[Category:Terms]]

@@ Line 1: / Line 1: @@
 A concise list of essential terms in xenharmonic music theory
-'''hertz''' - A unit for frequency; counts per second.
+; [[wikipedia:Hertz|Hertz]] (Hz) : A unit of frequency defined as one cycle per second.
-'''pitch''' - The property of some sounds that allows them to be ordered on a one-dimensional 'pitch axis'. Often measured by the frequency (in hertz) of a sine wave having the same pitch.
+; [[wikipedia:Pitch (music)|pitch]] : The property of some sounds that allows them to be ordered on a one-dimensional 'pitch axis'. Often measured by the frequency (in hertz) of a sine wave having the same pitch.
-'''cents''' - A logarithmic unit of measure. For a ratio R, 1200 * log2(R).
+; [[cents]] (¢) : A logarithmic [[Interval size measure|unit of measure of intervals]]. For a ratio R, 1200 · log<sub>2</sub>(R).
-'''interval''' - The distance between two pitches, expressed as a ratio (of their associated frequencies in hertz) or in cents.
+; [[interval]] : The distance between two pitches, expressed as a ratio (of their associated frequencies in hertz) or as a logarithmic measure (e.g. cents).
-'''scale''' - An ordered list of intervals.
+; [[scale]] : An ordered list of intervals.
-'''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]].
+; 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]].
-'''equave''' or '''interval of equivalence''' - An interval considered to be equivalent to the unison, such as an octave (pitch ratio 2/1 or 1200 cents).
+; [[equave]] (interval of equivalence) : An interval considered to be equivalent to the unison, such as an [[octave]] (2/1 or 1200 cents).
-'''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].
+; [[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].
-'''mode''' - A particular rotation of a scale, e.g. ionian, dorian etc. for the diatonic scale.
+; [[mode]] : A particular rotation of a scale, e.g. Ionian, Dorian etc. for the diatonic scale.
-'''just intonation''' - The set of intervals expressible as rational numbers.
+; [[just intonation]] (JI) : The set of intervals expressible as rational numbers.
-'''generators''' - A set of intervals that generate a larger set through linear combination. e.g. the primes {2, 3} generate the Pythogorean scale.
+; [[generator]]s : A set of intervals that generate a larger set through linear combination. e.g. the primes {2, 3} generate the Pythogorean scale.
-'''just intonation subgroup''' - The set of JI ratios obtainable by stacking (finitely many) copies of a finite set of 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.
+; [[just intonation subgroup]] : The set of JI ratios obtainable by stacking (finitely many) copies of a finite set of 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 [[just intonation subgroup]] to a set of intervals with fewer generators. expressible as a [[Intro_to_Mappings|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 [[Vals_and_Tuning_Space|vals]].
+; [[temperament]] : A mapping from a [[just intonation subgroup]] to a set of intervals with fewer generators. expressible as a [[Intro_to_Mappings|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 [[Vals_and_Tuning_Space|vals]].
-'''comma''' - A rational number that maps to 1/1 in a given temperament.
+; [[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 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}.
+; [[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]].
+; [[equal temperament]] : A rank-1 temperament. The temperament-agnostic term is [[equal-step tuning]].
-'''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.
+; [[tuning system|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]].
+; 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]].
-'''subtend''' - Of an interval size, to occur as a certain number of steps in a given scale.
+; subtend : Of an interval size, to occur as a certain number of steps in a given scale.
-:''In the diatonic scale, the perfect fifth always subtends 4 steps.''
+: ''In the diatonic scale, the perfect fifth always subtends 4 steps.''
 [[Category:terminology]]
 [[Category:Terms]]