# Benedetti height

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 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 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.

See also Kees Height.

# Examples

Interval | Benedetti height | Tenney height |
---|---|---|

3/2 | 6 | 2.585 |

6/5 | 30 | 4.907 |

9/7 | 63 | 5.977 |

13/11 | 143 | 7.160 |