Tenney norm: Difference between revisions

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{{Wikipedia| James Tenney }}
{{Wikipedia| James Tenney }}


If ''n''/''d'' is a positive rational number reduced to its lowest terms, then the [[Benedetti height]] is the integer ''nd''. Often it is more convenient instead to take the logarithm, usually base 2 ([[log2]]), of the [[Benedetti height]], leading to '''Tenney height'''. In either form, it is widely used as a [[measure of inharmonicity]] and/or [[complexity]] for intervals. Alternative terms used include '''harmonic distance''' ('''HD''').
The '''Tenney height''', '''Tenney norm''', or otherwise known as '''harmonic distance''' ('''HD'''), is widely used as a [[measure of inharmonicity]] and/or [[complexity]] for [[interval]]s. If ''n''/''d'' is a positive rational number reduced to its lowest terms, then the [[Benedetti height]] is the integer ''nd''. Often it is more convenient instead to take the logarithm, usually base 2 ([[log2]]), of the Benedetti height, leading to the Tenney height.  


== Computation ==
== Computation ==
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== See also ==
== See also ==
* [[Generalized Tenney norms and Tp interval space]]
* [[Generalized Tenney norms and Tp interval space|Generalized Tenney norms and T<sub>''p''</sub> interval space]]


== Notes ==
== Notes ==