Benedetti height: Difference between revisions
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The '''Benedetti height''' of a positive rational number N/D reduced to lowest terms (no common factor between N and D) is equal to N*D, the product of the numerator and denominator. | The '''Benedetti height''' of a positive rational number N/D reduced to lowest terms (no common factor between N and D) is equal to N*D, the product of the numerator and denominator. | ||
The [[logarithm]] | The [[logarithm base two]] of the Benedetti height is the [[Tenney height]], or Tenney norm. | ||
The name is based on the fact that the scientist, mathematician and music theorist [http://www.webcitation.org/6076Lm8r4 Giovanni Battista Benedetti] first proposed it as a [[measure | The name is based on the fact that the scientist, mathematician and music theorist [http://www.webcitation.org/6076Lm8r4 Giovanni Battista Benedetti] first proposed it as a [[measure of inharmonicity]]. It may be the first number-theoretic [[height]] function ever defined for any purpose. | ||
== Examples == | == Examples == | ||