Root mean square: Difference between revisions
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The root mean square of [[5/4]] and [[6/5]] is <math>\sqrt{\frac{1201}{800}}</math>. | The root mean square of [[5/4]] and [[6/5]] is <math>\sqrt{\frac{1201}{800}}</math>. | ||
The root mean square of [[9/8]] and [[10/9]] is <math>\sqrt{\frac{12961}{10368}}<math>. | The root mean square of [[9/8]] and [[10/9]] is <math>\sqrt{\frac{12961}{10368}}</math>. | ||
== See also == | == See also == | ||
Revision as of 23:11, 20 March 2023
In mathematics and tuning, the root mean square of two frequencies [math]\displaystyle{ f_1 }[/math] and [math]\displaystyle{ f_2 }[/math] is equal to [math]\displaystyle{ \sqrt{\frac{f_1^{2} + f_2^{2}}{2}} }[/math]. The RMS is also known as the quadratic mean.
In regular temperament theory, it is used in RMS tuning.
Examples
The root mean square of 1/1 and 3/2 is [math]\displaystyle{ \sqrt{\frac{13}{8}} }[/math] (approx. 420.3 ¢).
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The root mean square of 5/4 and 6/5 is [math]\displaystyle{ \sqrt{\frac{1201}{800}} }[/math].
The root mean square of 9/8 and 10/9 is [math]\displaystyle{ \sqrt{\frac{12961}{10368}} }[/math].