Root - Revision history

FloraC: +see also

2025-05-08T08:23:35Z

+see also

← Older revision		Revision as of 08:23, 8 May 2025
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	:''This page is about the root of a chord. For the ''n''th root of an interval, see [[Radical interval]]. For the tonic of a scale, occasionally called its 'root', see [[Tonic]].''		:''This page is about the root of a chord. For the ''n''-th root of an interval, see [[Radical interval]]. For the tonic of a scale, occasionally called its 'root', see [[Tonic]].''
	{{~~wikipedia~~\|Root (chord)}}		{{Wikipedia\|Root (chord)}}
	The '''root''' is a specific note that names and characterizes a given chord.		The '''root''' is a specific note that names and characterizes a given chord. Chords are often spoken about in terms of their root, their quality, and their extensions. The root of the chord often appears in the bass, although this is not always the case. When the chord is voiced such that the root is the lowest note, it is said to be in ''root position''.
	Chords are often spoken about in terms of their root, their quality, and their extensions.
	The root of the chord often appears in the bass, although this is not always the case.
	When the chord is voiced such that the root is the lowest note, it is said to be in ''root position''.

	== In tertian harmony ==		== In tertian harmony ==
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	== In other types types of harmony ==		== In other types types of harmony ==
	If a chord is not composed of thirds, the root can be ambiguous.		If a chord is not composed of thirds, the root can be ambiguous. The chord may still be given a root, although there is no established procedure for doing so.
	The chord may still be given a root, although there is no established procedure for doing so.

	{{~~stub~~}}		== See also ==
	{{~~todo~~\|add examples}}		* [[Rooted interval]]
			* [[Uprooted interval]]

			{{Stub}}
			{{Todo\| add examples }}

Sintel: Manually implement template instead of using it twice

2025-05-07T00:24:03Z

Manually implement template instead of using it twice

← Older revision		Revision as of 00:24, 7 May 2025
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	~~{{About\|~~the root of a chord\|the ''n''th root of an interval\|Radical interval}}		:''This page is about the root of a chord. For the ''n''th root of an interval, see [[Radical interval]]. For the tonic of a scale, occasionally called its 'root', see [[Tonic]].''
	~~{{About\|the root of a chord\|~~the tonic of a scale (occasionally called its 'root')\|Tonic}}
	{{wikipedia\|Root (chord)}}		{{wikipedia\|Root (chord)}}
	The '''root''' is a specific note that names and characterizes a given chord.		The '''root''' is a specific note that names and characterizes a given chord.

BudjarnLambeth at 23:49, 6 May 2025

2025-05-06T23:49:36Z

← Older revision		Revision as of 23:49, 6 May 2025
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	{{About\|the root of a chord\|the ''n''th root of an interval\|Radical interval}}		{{About\|the root of a chord\|the ''n''th root of an interval\|Radical interval}}
	{{About\|the root of a chord\|the tonic of a scale (occasionally called its 'root'\|Tonic}}		{{About\|the root of a chord\|the tonic of a scale (occasionally called its 'root')\|Tonic}}
	{{wikipedia\|Root (chord)}}		{{wikipedia\|Root (chord)}}
	The '''root''' is a specific note that names and characterizes a given chord.		The '''root''' is a specific note that names and characterizes a given chord.

BudjarnLambeth at 23:49, 6 May 2025

2025-05-06T23:49:28Z

← Older revision		Revision as of 23:49, 6 May 2025
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	{{About\|the root of a chord\|the ''n''th root of an interval\|Radical interval}}		{{About\|the root of a chord\|the ''n''th root of an interval\|Radical interval}}
			{{About\|the root of a chord\|the tonic of a scale (occasionally called its 'root'\|Tonic}}
	{{wikipedia\|Root (chord)}}		{{wikipedia\|Root (chord)}}
	The '''root''' is a specific note that names and characterizes a given chord.		The '''root''' is a specific note that names and characterizes a given chord.

Fredg999: Disambiguate nth root

2025-05-06T21:58:59Z

Disambiguate nth root

← Older revision		Revision as of 21:58, 6 May 2025
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			{{About\|the root of a chord\|the ''n''th root of an interval\|Radical interval}}
	{{wikipedia\|Root (chord)}}		{{wikipedia\|Root (chord)}}
	The '''root''' is a specific note that names and characterizes a given chord.		The '''root''' is a specific note that names and characterizes a given chord.

Sintel: basic information, mark stub

2025-05-06T16:16:55Z

basic information, mark stub

← Older revision		Revision as of 16:16, 6 May 2025
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	~~== Melodic root ==~~		{{wikipedia\|Root (chord)}}
	The ~~term~~ '''root''' is ~~sometimes used to refer to~~ the ~~central establishing pitch which all other pitches are perceived~~ in ~~relation to~~. It is ~~used interchangeably with "tonic"~~.		The '''root''' is a specific note that names and characterizes a given chord.
			Chords are often spoken about in terms of their root, their quality, and their extensions.
			The root of the chord often appears in the bass, although this is not always the case.
			When the chord is voiced such that the root is the lowest note, it is said to be in ''root position''.

	~~This wiki's article about that concept~~ is~~: [[Tonic]]~~.		== In tertian harmony ==
			If the chord can be voiced as a stack of thirds, then the root is typically the lowest note in the stack.

	== ~~Arithmetical root~~ ==		== In other types types of harmony ==
	~~{{Wikipedia\|Nth~~ root~~}} The arithmetical concept of '''roots''' is often encountered in discussions about tuning~~. The ~~remainder of this page discusses that type of~~ root.		If a chord is not composed of thirds, the root can be ambiguous.
			The chord may still be given a root, although there is no established procedure for doing so.

	~~=== How are roots related to equal divisions? ===~~		{{stub}}
	~~To divide an interval ''a'' into ''b'' equal parts, that is, to calculate the size of the interval that, when repeated ''b'' times, would~~ add ~~up to ''a'', calculate the ''b''-th root of ''a''. The equivalent expression is to take ''a'' to the (1/''b'')th power.~~		{{todo\|add examples}}

	~~Why roots and powers? Because intervals are proportions, which you must multiply in order to "add".~~

	Take a simple example: what is half of an [[octave]]? Well, an octave means "twice the frequency" or "2 times whatever you have" or "2 to 1" or simply "2". (The 2 itself has no units, because they cancel out: to calculate that octave between A220 and A440, we divide 440 Hertz by 220 Hertz and get… plain ol' 2.) If an octave means "twice", then what is half of "twice"?

	~~It is not once… because two onces is just another once!~~

	~~It is the square ''root'' of 2! Try it: The √2 ''multiplied'' twice is √2·√2 = 2. (Note that √2 ''added'' twice would be 2√2.)~~

	~~[[Category:Elementary math]]~~

BudjarnLambeth: Add section specifying this is not "root" as in "tonic" and directing readers to there if that’s what they were after

2024-12-24T06:40:33Z

Add section specifying this is not "root" as in "tonic" and directing readers to there if that’s what they were after

← Older revision		Revision as of 06:40, 24 December 2024
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	~~{{Wikipedia\|Nth~~ root}}		== Melodic root ==
			The term '''root''' is sometimes used to refer to the central establishing pitch which all other pitches are perceived in relation to. It is used interchangeably with "tonic".

	~~The arithmetical~~ concept ~~of '''roots'''~~ is ~~often encountered in discussions about tuning~~.		This wiki's article about that concept is: [[Tonic]].

	== ~~How are roots related to equal divisions?~~ ==		== Arithmetical root ==
			{{Wikipedia\|Nth root}} The arithmetical concept of '''roots''' is often encountered in discussions about tuning. The remainder of this page discusses that type of root.

			=== How are roots related to equal divisions? ===
	To divide an interval ''a'' into ''b'' equal parts, that is, to calculate the size of the interval that, when repeated ''b'' times, would add up to ''a'', calculate the ''b''-th root of ''a''. The equivalent expression is to take ''a'' to the (1/''b'')th power.		To divide an interval ''a'' into ''b'' equal parts, that is, to calculate the size of the interval that, when repeated ''b'' times, would add up to ''a'', calculate the ''b''-th root of ''a''. The equivalent expression is to take ''a'' to the (1/''b'')th power.

FloraC: Cleanup

2023-10-13T05:06:24Z

Cleanup

← Older revision		Revision as of 05:06, 13 October 2023
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	~~The arithmetical concept of ''[http://en.wikipedia.org/wiki/Nth_root roots]'' is often encountered in discussions about tuning.~~		{{Wikipedia\|Nth root}}

	~~==How are~~ roots ~~related to equal divisions?==~~		The arithmetical concept of '''roots''' is often encountered in discussions about tuning.

	~~To divide an interval ''a'' into ''b''~~ equal parts, that is, to calculate the size of the interval that, when repeated ''b'' times, would add up to ''a'', calculate the ''bth root of a''. The equivalent expression is to take ''a'' to the ''(1/b)th power''.		== How are roots related to equal divisions? ==

	~~Why roots and powers? Because intervals are proportions~~, ~~which you must multiply in order~~ to "add".		To divide an interval ''a'' into ''b'' equal parts, that is, to calculate the size of the interval that, when repeated ''b'' times, would add up to ''a'', calculate the ''b''-th root of ''a''. The equivalent expression is to take ''a'' to the (1/''b'')th power.

	~~Take a simple example: what's half of an octave~~? ~~Well~~, ~~an octave means "twice the frequency" or "2 times whatever~~ you ~~have" or "2~~ to 1" ~~or simply~~ "~~2". (The 2 itself has no units, because they cancel out: to calculate that octave between A-220 and A-440, we divide 440 Hertz by 220 Hertz and get..~~. ~~plain ol' 2.) If an octave means "twice", then what's half of "twice"?~~		Why roots and powers? Because intervals are proportions, which you must multiply in order to "add".

	~~It isn~~'~~t once.~~.~~.because two onces~~ is ~~just another once!~~		Take a simple example: what is half of an [[octave]]? Well, an octave means "twice the frequency" or "2 times whatever you have" or "2 to 1" or simply "2". (The 2 itself has no units, because they cancel out: to calculate that octave between A220 and A440, we divide 440 Hertz by 220 Hertz and get… plain ol' 2.) If an octave means "twice", then what is half of "twice"?

	It's the square ''root'' of 2! Try it: The √2 multiplied twice is ~~√2√2~~ = 2. (Note that √2 added* twice would be 2√2.)		It is not once… because two onces is just another once!
	~~[[Category:concept]]~~
	[[Category:math]]		It is the square ''root'' of 2! Try it: The √2 ''multiplied'' twice is √2·√2 = 2. (Note that √2 ''added'' twice would be 2√2.)
	~~[[Category:root]]~~
	~~[[Category:tuning~~]]		[[Category:Elementary math]]

Xenwolf: Xenwolf moved page Roots to Root: changed lemma to singular form

2018-10-28T11:52:36Z

Xenwolf moved page Roots to Root: changed lemma to singular form

← Older revision	Revision as of 11:52, 28 October 2018
(No difference)

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

← Older revision		Revision as of 00:00, 17 July 2018
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	~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~		The arithmetical concept of ''[http://en.wikipedia.org/wiki/Nth_root roots]'' is often encountered in discussions about tuning.
	~~This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>~~
	~~: This revision was by author [[User:xenjacob\|xenjacob]] and made on <tt>2008-08-29 00:20:05 UTC</tt>.<br>~~
	~~: The original revision id was <tt>36370601</tt>.<br>~~
	~~: The revision comment was: <tt></tt><br>~~
	~~The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>~~
	~~<h4>Original Wikitext content:</h4>~~
	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html"> The arithmetical concept of ~~//[~~[http://en.wikipedia.org/wiki/Nth_root\|roots]~~]//~~ is often encountered in discussions about tuning.

	==How are roots related to equal divisions?==		==How are roots related to equal divisions?==

	To divide an interval //a// into //b// equal parts, that is, to calculate the size of the interval that, when repeated //b// times, would add up to //a//, calculate the //bth root of a//. The equivalent expression is to take //a// to the //(1/b)th power//.		To divide an interval ''a'' into ''b'' equal parts, that is, to calculate the size of the interval that, when repeated ''b'' times, would add up to ''a'', calculate the ''bth root of a''. The equivalent expression is to take ''a'' to the ''(1/b)th power''.

	Why roots and powers? Because intervals are proportions, which you must multiply in order to "add".		Why roots and powers? Because intervals are proportions, which you must multiply in order to "add".
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	It isn't once...because two onces is just another once!		It isn't once...because two onces is just another once!

	It's the square //root// of 2! Try it: The √2 multiplied twice is √2√2 = 2. (Note that √2 added* twice would be 2√2.)		It's the square ''root'' of 2! Try it: The √2 multiplied twice is √2√2 = 2. (Note that √2 added* twice would be 2√2.)
	~~</pre></div>~~		[[Category:concept]]
	~~<h4>Original HTML content~~:~~</h4>~~		[[Category:math]]
	~~<div style="width:100%; max-height:400pt; overflow:auto; background-color~~:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>roots</title></head><body> The arithmetical concept of <em><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Nth_root" rel="nofollow">roots</a></em> is often encountered in discussions about tuning.<br />		[[Category:root]]
	~~<br />~~		[[Category:tuning]]
	~~<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-How are roots related to equal divisions?"></a><!-- ws:end:WikiTextHeadingRule~~:~~0 -->How are roots related to equal divisions?</h2>~~
	~~<br />~~
	To divide an interval <em>a</em> into <em>b</em> equal parts, that is, to calculate the size of the interval that, when repeated <em>b</em> times, would add up to <em>a</em>, calculate the <em>bth root ~~of a</em>. The equivalent expression is to take <em>a</em> to the <em>(1/b)th power</em>.<br />~~
	~~<br />~~
	~~Why roots and powers? Because intervals are proportions, which you must multiply in order to &quot;add&quot;.<br />~~
	~~<br />~~
	~~Take a simple example~~: what's half of an octave? Well, an octave means &quot;twice the frequency&quot; or &quot;2 times whatever you have&quot; or &quot;2 to 1&quot; or simply &quot;2&quot;. (The 2 itself has no units, because they cancel out: to calculate that octave between A-220 and A-440, we divide 440 Hertz by 220 Hertz and get... plain ol' 2.) If an octave means &quot;twice&quot;, then what's half of &quot;twice&quot;? <br />
	~~<br />~~
	~~It isn't once...because two onces is just another once!<br />~~
	~~<br />~~
	~~It's the square <em>root</em> of 2! Try it: The √2 multiplied twice is √2√2 = 2. (Note that √2 added* twice would be 2√2.)</body></html></pre></div>~~