Cent: Difference between revisions

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| en = Cent

| de = Cent

| es = ~~Centésimas~~

| es = Cent

| ja = セント

| ko = 센트

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The '''cent''' (symbol: '''¢''') is a [[unit of interval size]] equal to exactly 1/~~100th~~ (or 1%) of a [[12edo]] [[semitone (interval size measure)|semitone]]. In other words, cents divide the half step (semitone) of 12edo into 100 equal parts. First proposed in the late 19th century by {{w|Alexander John Ellis|Alexander J. Ellis}}, the cent may also be defined as the {{w|logarithm}} base 1200th root of 2 of a ratio.

The '''cent''' (symbol: '''¢''') is a [[unit of interval size]] equal to exactly 1/100 (or 1%) of a [[12edo]] [[semitone (interval size measure)|semitone]]. In other words, cents divide the half step (semitone) of 12edo into 100 equal parts. First proposed in the late 19th century by {{w|Alexander John Ellis|Alexander J. Ellis}}, the cent may also be defined as the {{w|logarithm}} base 1200th root of 2 of a ratio.

Cents are often used to express the size of intervals in different tuning systems, sometimes to express the accuracy of the representation of a [[just intonation]] [[interval]] in a given system.

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== Conversion ==

=== Ratio to cents ===

To find the size ''s'' of an interval in cents from its ratio ''r'', calculate the [[log2|binary logarithm]] (log<sub>2</sub>) of its [[frequency ratio]], and multiply it by 1200.

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 | en = Cent
 | de = Cent
-| es = Centésimas
+| es = Cent
 | ja = セント
 | ko = 센트
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 }}
 {{Wikipedia|Cent (music)}}
-The '''cent''' (symbol: '''¢''') is a [[unit of interval size]] equal to exactly 1/100th (or 1%) of a [[12edo]] [[semitone (interval size measure)|semitone]]. In other words, cents divide the half step (semitone) of 12edo into 100 equal parts. First proposed in the late 19th century by {{w|Alexander John Ellis|Alexander J. Ellis}}, the cent may also be defined as the {{w|logarithm}} base 1200th root of 2 of a ratio.
+The '''cent''' (symbol: '''¢''') is a [[unit of interval size]] equal to exactly 1/100 (or 1%) of a [[12edo]] [[semitone (interval size measure)|semitone]]. In other words, cents divide the half step (semitone) of 12edo into 100 equal parts. First proposed in the late 19th century by {{w|Alexander John Ellis|Alexander J. Ellis}}, the cent may also be defined as the {{w|logarithm}} base 1200th root of 2 of a ratio.
 Cents are often used to express the size of intervals in different tuning systems, sometimes to express the accuracy of the representation of a [[just intonation]] [[interval]] in a given system.
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 == Conversion ==
+{{See also| Ratio #Conversion }}
 === Ratio to cents ===
 To find the size ''s'' of an interval in cents from its ratio ''r'', calculate the [[log2|binary logarithm]] (log<sub>2</sub>) of its [[frequency ratio]], and multiply it by 1200.