Glossary: Difference between revisions

Line 1:

A concise list of essential terms in xenharmonic music theory

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

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

; [[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.

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

Line 25:

; [[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 [[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.

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

Line 35:

; [[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.

; 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. [[~~POTE_tuning|~~POTE tuning]].

; 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. [[POTE tuning]].

; 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.''

[[Category:~~terminology~~]]

== See also ==

* [[Acronyms]]

[[Category:Terminology]]

[[Category:Terms]]

[[Category:Overview]]

@@ Line 1: / Line 1: @@
 A concise list of essential terms in xenharmonic music theory
-; [[wikipedia:Hertz|Hertz]] (Hz) : A unit of frequency defined as one cycle per second.
+; [[wikipedia: Hertz|Hertz]] (Hz) : A unit of frequency defined as one cycle per second.
-; [[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.
+; [[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 [[Interval size measure|unit of measure of intervals]]. For a ratio R, 1200 · log<sub>2</sub>(R).
@@ Line 25: / Line 25: @@
 ; [[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 [[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.
 ; [[comma]] : A rational number that maps to 1/1 in a given temperament.
@@ Line 35: / Line 35: @@
 ; [[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.
-; 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. [[POTE_tuning|POTE tuning]].
+; 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. [[POTE tuning]].
 ; 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.''
-[[Category:terminology]]
+== See also ==
+* [[Acronyms]]
+[[Category:Terminology]]
 [[Category:Terms]]
+[[Category:Overview]]