Root mean square: Difference between revisions

(7 intermediate revisions by 3 users not shown)

Line 1:

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 tuning schemes such as [[TOP-RMS]] and [[miniRMS]], as well as [[RMS temperament measures]].

== Examples ==

The root mean square of [[1/1]] and [[3/2]] is <math>\sqrt{\frac{13}{8}}</math> (~~approx.~~ 420.3{{cent}}).

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}}).

~~{{todo|review|inline=1}}~~

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 [[5/4]] and [[6/5]] is √(1201/~~800~~).

The root mean square of [[9/8]] and [[10/9]] is √(12961/~~10368~~).

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 ==

Line 20:

Line 19:

[[Category:Means]]

[[Category:Elementary math]]

[[Category:Terms]]

~~[[Category:Stub]]~~

@@ Line 1: / Line 1: @@
 {{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 tuning schemes such as [[TOP-RMS]] and [[miniRMS]], as well as [[RMS temperament measures]].
 == Examples ==
-The root mean square of [[1/1]] and [[3/2]] is <math>\sqrt{\frac{13}{8}}</math> (approx. 420.3{{cent}}).
+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}}).
-{{todo|review|inline=1}}
+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 [[5/4]] and [[6/5]] is √(1201/800).
-The root mean square of [[9/8]] and [[10/9]] is √(12961/10368).
+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 ==
@@ Line 20: / Line 19: @@
 [[Category:Means]]
+[[Category:Elementary math]]
 [[Category:Terms]]
-[[Category:Stub]]