Root mean square
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 ¢).
|
Todo: review |
The root mean square of 5/4 and 6/5 is √(1201/800).
The root mean square of 9/8 and 10/9 is √(12961/10368).