Root mean square: Difference between revisions
CompactStar (talk | contribs) No edit summary |
Cmloegcmluin (talk | contribs) correct tuning scheme name, and include a reference to the more basic family of RMS-based tunings |
||
| (3 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
{{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 [[ | 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 == | == 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>\operatorname {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>\operatorname {RMS}(\frac{5}{4}, \frac{6}{5}) = \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>\operatorname {RMS}(\frac{9}{8}, \frac{10}{9}) = \sqrt{\frac{12961}{10368}}</math> (≈ 193.224{{cent}}). | ||
== See also == | == See also == | ||
| Line 19: | Line 19: | ||
[[Category:Means]] | [[Category:Means]] | ||
[[Category:Elementary math]] | |||
[[Category:Terms]] | [[Category:Terms]] | ||
Latest revision as of 16:34, 21 March 2023
In mathematics and tuning, the root mean square (RMS) 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 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 ¢) and 3/2 (≈ 701.955 ¢) is [math]\displaystyle{ \operatorname {RMS}(\frac{1}{1}, \frac{3}{2}) = \sqrt{\frac{13}{8}} }[/math] (≈ 420.264 ¢).
The root mean square of 5/4 (≈ 386.314 ¢) and 6/5 (≈ 315.641 ¢) is [math]\displaystyle{ \operatorname {RMS}(\frac{5}{4}, \frac{6}{5}) = \sqrt{\frac{1201}{800}} }[/math] (≈ 351.699 ¢).
The root mean square of 9/8 (≈ 203.910 ¢) and 10/9 (≈ 182.404 ¢) is [math]\displaystyle{ \operatorname {RMS}(\frac{9}{8}, \frac{10}{9}) = \sqrt{\frac{12961}{10368}} }[/math] (≈ 193.224 ¢).