Tenney norm: Difference between revisions
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{{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. It is also known as ''log product complexity''. | 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. It is also known as ''log product complexity''. | ||
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where W is the Tenney weighter such that, for the prime basis Q = {{val| 2 3 5 … ''p'' }}, | where W is the Tenney weighter such that, for the prime basis Q = {{val| 2 3 5 … ''p'' }}, | ||
<math>W = \operatorname {diag} (1/log_2 (Q))</math> | <math>W = \operatorname {diag} (1/\log_2 (Q))</math> | ||
== Examples == | == Examples == | ||
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[[Category:Regular temperament theory]] | |||
[[Category:Psychoacoustics]] | |||
[[Category:Harmonic entropy]] | |||
[[Category:Tenney]] | [[Category:Tenney]] | ||
[[Category:Benedetti]] | [[Category:Benedetti]] | ||
[[Category:Consonance]] | [[Category:Consonance]] | ||
[[Category:Dissonance]] | [[Category:Dissonance]] | ||
[[Category:Height]] | [[Category:Height]] | ||
[[Category:Measure]] | [[Category:Measure]] | ||