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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''. |
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| 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. |
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| == 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. |
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| === How are roots related to equal divisions? ===
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| 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}} |
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| Why roots and powers? Because intervals are proportions, which you must multiply in order to "add".
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| 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"?
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| It is not once… because two onces is just another once!
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| 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.)
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| [[Category:Elementary math]]
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