Root mean square - Revision history

Cmloegcmluin: correct tuning scheme name, and include a reference to the more basic family of RMS-based tunings

2023-03-21T16:34:46Z

correct tuning scheme name, and include a reference to the more basic family of RMS-based tunings

← Older revision		Revision as of 16:34, 21 March 2023
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	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 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 [[~~RMS tuning~~]] and [[RMS temperament measures]].		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 ==

FloraC: /* Examples */ math formatting ("RMS" is an operator, not variables)

2023-03-21T10:57:22Z

Examples: math formatting ("RMS" is an operator, not variables)

← Older revision		Revision as of 10:57, 21 March 2023
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	== Examples ==		== Examples ==
	The root mean square of [[1/1]] (0{{cent}}) and [[3/2]] (~~≈701~~.955{{cent}}) is <math>RMS(\frac{1}{1}, \frac{3}{2}) = \sqrt{\frac{13}{8}}</math> (~~≈420~~.264{{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}}).

	The root mean square of [[5/4]] (~~≈386~~.314{{cent}}) and [[6/5]] (~~≈315~~.641{{cent}}) is <math>RMS(\frac{5}{4}, \frac{6}{5}) = \sqrt{\frac{1201}{800}}</math> (~~≈351~~.699{{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>RMS(\frac{9}{8}, \frac{10}{9}) = \sqrt{\frac{12961}{10368}}</math> (~~≈193~~.224{{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 ==		== See also ==

Fredg999: I forgot to finish what I was doing...

2023-03-21T02:23:07Z

I forgot to finish what I was doing...

← Older revision		Revision as of 02:23, 21 March 2023
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	The root mean square of [[1/1]] (0{{cent}}) and [[3/2]] (≈701.955{{cent}}) is <math>RMS(\frac{1}{1}, \frac{3}{2}) = \sqrt{\frac{13}{8}}</math> (≈420.264{{cent}}).		The root mean square of [[1/1]] (0{{cent}}) and [[3/2]] (≈701.955{{cent}}) is <math>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>\sqrt{\frac{1201}{800}}</math> (≈351.699{{cent}}).		The root mean square of [[5/4]] (≈386.314{{cent}}) and [[6/5]] (≈315.641{{cent}}) is <math>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>\sqrt{\frac{12961}{10368}}</math> (≈193.224{{cent}}).		The root mean square of [[9/8]] (≈203.910{{cent}}) and [[10/9]] (≈182.404{{cent}}) is <math>RMS(\frac{9}{8}, \frac{10}{9}) = \sqrt{\frac{12961}{10368}}</math> (≈193.224{{cent}}).

	== See also ==		== See also ==

Fredg999: Improved examples, misc. edits, categories

2023-03-21T02:22:25Z

Improved examples, misc. edits, categories

← Older revision		Revision as of 02:22, 21 March 2023
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	{{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 [[RMS tuning]].		In [[regular temperament theory]], it is used in the context of [[RMS tuning]] and [[RMS temperament measures]].

	== Examples ==		== 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>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>\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>\sqrt{\frac{12961}{10368}}</math> (≈193.224{{cent}}).

	== See also ==		== See also ==
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	[[Category:Means]]		[[Category:Means]]
			[[Category:Elementary math]]
	[[Category:Terms]]		[[Category:Terms]]
	~~[[Category:Stub]]~~
	~~{{todo\|review\|inline=1}}~~

CompactStar at 23:12, 20 March 2023

2023-03-20T23:12:08Z

← Older revision		Revision as of 23:12, 20 March 2023
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	== Examples ==		== 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]] and [[3/2]] is <math>\sqrt{\frac{13}{8}}</math> (approx. 420.3{{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]] and [[6/5]] is <math>\sqrt{\frac{1201}{800}}</math>.

CompactStar at 23:11, 20 March 2023

2023-03-20T23:11:58Z

← Older revision		Revision as of 23:11, 20 March 2023
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	== Examples ==		== 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]] and [[3/2]] is <math>\sqrt{\frac{13}{8}}</math> (approx. 420.3{{cent}}).

	~~{{todo\|review\|inline=1}}~~
	The root mean square of [[5/4]] and [[6/5]] is <math>\sqrt{\frac{1201}{800}}</math>.		The root mean square of [[5/4]] and [[6/5]] is <math>\sqrt{\frac{1201}{800}}</math>.

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	[[Category:Terms]]		[[Category:Terms]]
	[[Category:Stub]]		[[Category:Stub]]
			{{todo\|review\|inline=1}}

CompactStar at 23:11, 20 March 2023

2023-03-20T23:11:49Z

← Older revision		Revision as of 23:11, 20 March 2023
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	The root mean square of [[5/4]] and [[6/5]] is <math>\sqrt{\frac{1201}{800}}</math>.		The root mean square of [[5/4]] and [[6/5]] is <math>\sqrt{\frac{1201}{800}}</math>.

	The root mean square of [[9/8]] and [[10/9]] is <math>\sqrt{\frac{12961}{10368}}<math>.		The root mean square of [[9/8]] and [[10/9]] is <math>\sqrt{\frac{12961}{10368}}</math>.

	== See also ==		== See also ==

CompactStar at 23:11, 20 March 2023

2023-03-20T23:11:42Z

← Older revision		Revision as of 23:11, 20 March 2023
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	{{todo\|review\|inline=1}}		{{todo\|review\|inline=1}}
	The root mean square of [[5/4]] and [[6/5]] is √(1201/~~800)~~.		The root mean square of [[5/4]] and [[6/5]] is <math>\sqrt{\frac{1201}{800}}</math>.

	The root mean square of [[9/8]] and [[10/9]] is √(12961/10368).		The root mean square of [[9/8]] and [[10/9]] is <math>\sqrt{\frac{12961}{10368}}<math>.

	== See also ==		== See also ==

CompactStar: Replace quadratic mean with RMS

2023-03-20T23:06:11Z

Replace quadratic mean with RMS

← Older revision		Revision as of 23:06, 20 March 2023
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	== Examples ==		== Examples ==
	The ~~quadratic~~ mean of [[1/1]] and [[3/2]] is <math>\sqrt{\frac{13}{8}}</math> (approx. 420.3{{cent}}).		The root mean square of [[1/1]] and [[3/2]] is <math>\sqrt{\frac{13}{8}}</math> (approx. 420.3{{cent}}).

	{{todo\|review\|inline=1}}		{{todo\|review\|inline=1}}
	The ~~quadratic~~ mean of [[5/4]] and [[6/5]] is √(1201/800).		The root mean square of [[5/4]] and [[6/5]] is √(1201/800).

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

	== See also ==		== See also ==

Fredg999: Add Wikipedia box, new page title, relation to RTT, fixed 1 example (others to be reviewed soon)

2023-03-20T21:59:15Z

Add Wikipedia box, new page title, relation to RTT, fixed 1 example (others to be reviewed soon)

← Older revision		Revision as of 21:59, 20 March 2023
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	In mathematics and tuning, the '''~~quadratic~~ mean''' 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>.		{{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'''.

	~~==Examples==~~		In [[regular temperament theory]], it is used in [[RMS tuning]].
	~~The quadratic mean of~~ [[~~1/1]] and [[3/2~~]] is √([[~~13/4~~]]).

			== 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]]