Root mean square: Difference between revisions
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{{Wikipedia}} | {{Wikipedia}} | ||
In mathematics and tuning, the '''root mean square''' of two frequencies <math>f_1</math> and <math>f_2</math> is equal to <math>\sqrt{\frac{f_1^{2} + f_2^{2}}{2}}</math>. The RMS is also known as the '''quadratic mean'''. | In mathematics and tuning, the '''root mean square''' ('''RMS''') of two frequencies <math>f_1</math> and <math>f_2</math> is equal to <math>\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]]. | In [[regular temperament theory]], it is used in the context of [[RMS tuning]] and [[RMS temperament measures]]. | ||
== Examples == | == Examples == | ||
The root mean square of [[1/1]] and [[3/2]] is <math>\sqrt{\frac{13}{8}}</math> ( | The root mean square of [[1/1]] (0{{cent}}) and [[3/2]] (≈701.955{{cent}}) is <math>RMS(\frac{1}{1}, \frac{3}{2}) = \sqrt{\frac{13}{8}}</math> (≈420.264{{cent}}). | ||
The root mean square of [[5/4]] and [[6/5]] is <math>\sqrt{\frac{1201}{800}}</math>. | The root mean square of [[5/4]] (≈386.314{{cent}}) and [[6/5]] (≈315.641{{cent}}) is <math>\sqrt{\frac{1201}{800}}</math> (≈351.699{{cent}}). | ||
The root mean square of [[9/8]] and [[10/9]] is <math>\sqrt{\frac{12961}{10368}}</math>. | The root mean square of [[9/8]] (≈203.910{{cent}}) and [[10/9]] (≈182.404{{cent}}) is <math>\sqrt{\frac{12961}{10368}}</math> (≈193.224{{cent}}). | ||
== See also == | == See also == | ||
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[[Category:Means]] | [[Category:Means]] | ||
[[Category:Elementary math]] | |||
[[Category:Terms]] | [[Category:Terms]] | ||