Cent: Difference between revisions
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== Examples == | == Examples == | ||
The 12edo perfect fifth is exactly 700 cents, and the 12edo major third is exactly 400 cents. In contrast, the just perfect fifth, which corresponds to two notes in a frequency ratio of [[3/2]], is approximately 702 cents, and the just major third of [[5/4]] is about 386 cents. The [[24edo]] neutral third is exactly 350 cents. The [[22edo]] approximation to 3/2 is approximately 709 cents. | The 12edo perfect fifth is exactly 700 cents, and the 12edo major third is exactly 400 cents. In contrast, the just perfect fifth, which corresponds to two notes in a frequency ratio of [[3/2]], is approximately 702 cents, and the just major third of [[5/4]] is about 386 cents. The [[24edo]] neutral third is exactly 350 cents. The [[22edo]] approximation to 3/2 is approximately 709 cents. | ||
== Conversion == | == Conversion == | ||
=== Ratio to cents === | === Ratio to cents === | ||
To find the size ''s'' of an interval in cents from its ratio ''c'', you have to calculate the [[log2|binary logarithm]] (log<sub>2</sub>) of its [[frequency ratio]], and multiply this by 1200. | To find the size ''s'' of an interval in cents from its ratio ''c'', you have to calculate the [[log2|binary logarithm]] (log<sub>2</sub>) of its [[frequency ratio]], and multiply this by 1200. | ||
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== Other interval size units == | == Other interval size units == | ||
The cent is commonly used because of its ease in communicating information about intervals to a 12edo-savvy audience. However, some have suggested that the cent be deprecated, as other than societal convention there's no reason to give 12edo inherent importance over any other decent tuning. In contrast, others have suggested that cents are a useful unit of interval measure for purely mathematical reasons, even despite of 12edo's current status as the dominant tuning in Western society. | The cent is commonly used because of its ease in communicating information about intervals to a 12edo-savvy audience. However, some have suggested that the cent be deprecated, as other than societal convention there's no reason to give 12edo inherent importance over any other decent tuning. In contrast, others have suggested that cents are a useful unit of interval measure for purely mathematical reasons, even despite of 12edo's current status as the dominant tuning in Western society. | ||
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== See also == | == See also == | ||
* [[Relative cent]] – a useful generalization for the cent measure to ''any'' [[equal]] tuning | * [[Relative cent]] – a useful generalization for the cent measure to ''any'' [[equal]] tuning | ||
* [[Millioctave]] – one prominent alternative interval measure | * [[Millioctave]] – one prominent alternative interval measure | ||
* [[Interval size measure]] – overview | * [[Interval size measure]] – overview | ||
== External links == | |||
* [http://tonalsoft.com/enc/c/cent.aspx cent, ¢, 1200-ed2] on [[Tonalsoft Encyclopedia]] | |||
[[Category:Interval size measures]] | [[Category:Interval size measures]] | ||