Root mean square: Difference between revisions
Jump to navigation
Jump to search
m Fredg999 moved page Quadratic mean to Root mean square over redirect: RTT articles already use RMS |
Add Wikipedia box, new page title, relation to RTT, fixed 1 example (others to be reviewed soon) |
||
| Line 1: | Line 1: | ||
In mathematics and tuning, the ''' | {{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 [[regular temperament theory]], it is used in [[RMS tuning]]. | |||
== Examples == | |||
The quadratic mean of [[1/1]] and [[3/2]] is <math>\sqrt{\frac{13}{8}}</math> (approx. 420.3{{cent}}). | |||
{{todo|review|inline=1}} | |||
The quadratic mean of [[5/4]] and [[6/5]] is √(1201/800). | The quadratic mean of [[5/4]] and [[6/5]] is √(1201/800). | ||
The quadratic mean of [[9/8]] and [[10/9]] is √(12961/10368). | The quadratic mean of [[9/8]] and [[10/9]] is √(12961/10368). | ||
==See also== | == See also == | ||
* [[Pythagorean means]] | * [[Pythagorean means]] | ||
** [[Arithmetic mean]] | ** [[Arithmetic mean]] | ||
Revision as of 21:59, 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 quadratic mean of 1/1 and 3/2 is [math]\displaystyle{ \sqrt{\frac{13}{8}} }[/math] (approx. 420.3 ¢).
|
Todo: review |
The quadratic mean of 5/4 and 6/5 is √(1201/800).
The quadratic mean of 9/8 and 10/9 is √(12961/10368).