Root mean square: Difference between revisions
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In mathematics and tuning, the '''root mean square''' of two frequencies <math>f_1</math> and <math>f_2</math> is equal to <math> | {{Wikipedia}} | ||
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 the context of tuning schemes such as [[TOP-RMS]] and [[miniRMS]], as well as [[RMS temperament measures]]. | |||
== Examples == | |||
The root mean square of [[1/1]] (0{{cent}}) and [[3/2]] (≈ 701.955{{cent}}) is <math>\operatorname {RMS}(\frac{1}{1}, \frac{3}{2}) = \sqrt{\frac{13}{8}}</math> (≈ 420.264{{cent}}). | |||
The root mean square of [[5/4]] (≈ 386.314{{cent}}) and [[6/5]] (≈ 315.641{{cent}}) is <math>\operatorname {RMS}(\frac{5}{4}, \frac{6}{5}) = \sqrt{\frac{1201}{800}}</math> (≈ 351.699{{cent}}). | |||
The root mean square of [[9/8]] (≈ 203.910{{cent}}) and [[10/9]] (≈ 182.404{{cent}}) is <math>\operatorname {RMS}(\frac{9}{8}, \frac{10}{9}) = \sqrt{\frac{12961}{10368}}</math> (≈ 193.224{{cent}}). | |||
== See also == | |||
* [[Pythagorean means]] | |||
** [[Arithmetic mean]] | |||
** [[Geometric mean]] | |||
** [[Inverse-arithmetic mean]] | |||
* [[Mediant]] | |||
[[Category:Means]] | |||
[[Category:Elementary math]] | |||
[[Category:Terms]] | |||