editing disabled

Given a ratio of positive integers p/q, the Kees height is found by first removing factors of two and all common factors from p/q, producing a ratio a/b of relatively prime odd positive integers. Then kees(p/q) = kees(a/b) = max(a, b). The Kees "expressibility" is then the logarithm base two of the Kees height. Expressibility can be extended to all vectors in interval space, by means of the formula KE(|m2 m3 m5... mp>) = (|m3 + m5+ ... +mp| + |m3| + |m5| + ... + |mp|)/2, where "KE" denotes Kees expressibility and |m2 m3 m5 ... mp> is a vector with weighted coordinates in interval space.

The set of JI intervals with Kees height less than or equal to an odd integer q comprises the q odd limit

The point of Kees height is to serve as a metric/height on JI pitch classes corresponding to Benedetti height on pitches. The measure was proposed by Kees van Prooijen.

Kees tuning pages

Examples

interval
kees height
5/3
5
4/3
3
2/1
1