Root: Difference between revisions

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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]].''

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''.

~~The arithmetical concept~~ of ~~'''roots'''~~ is ~~often encountered~~ in ~~discussions about tuning~~.

== 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.

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

== In other types types of harmony ==

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.

~~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.~~

== See also ==

* [[Rooted interval]]

* [[Uprooted interval]]

~~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]]~~

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-{{Wikipedia|Nth root}}
+:''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)}}
+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''.
-The arithmetical concept of '''roots''' is often encountered in discussions about tuning.
+== 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.
-== How are roots related to equal divisions? ==
+== In other types types of harmony ==
+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.
-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.
+== See also ==
+* [[Rooted interval]]
+* [[Uprooted interval]]
-Why roots and powers? Because intervals are proportions, which you must multiply in order to "add".
+{{Stub}}
+{{Todo| add examples }}
-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]]