If p/q is a positive rational number reduced to its lowest terms, then the Benedetti height is the integer pq. 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.
The Tenney height of a monzo is given by
|| |e2 e3 ... ep> || = |e2| + log2(3)|e3| + ... + log2(p)|ep| = log2(2^|e2| * 3^|e3| * ... * p^|ep|)
|Interval name||Ratio (p/q)||Monzo||Tenney height||log2(p*q)|
|just perfect fifth||3/2||[-1 1⟩||2.585||log2(6)|
|just major third||5/4||[-2 0 1⟩||4.322||log2(20)|
|harmonic seventh||7/4||[-2 0 0 1⟩||4.807||log2(28)|