Skip to main content
Try Wikispaces Classroom now.
Brand new from Wikispaces.
xenharmonic (microtonal wiki)
Pages and Files
XA Facebook Group
XA IRC Chat
Lists and Galleries
Backing up this wiki
Given a ratio of positive integers p/q, the
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
, 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. It can also be thought of as the quotient norm of Weil height, mod 2/1. Additionally, it can
be extended to tempered intervals using the quotient norm.
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
on pitches. The measure was proposed by
Kees van Prooijen
Kees tuning pages
7/4, 7/5, 7/6, 8/7
5/3, 8/5, 5/4, 6/5
help on how to format text
Contributions to http://xenharmonic.wikispaces.com/ are licensed under a
Creative Commons Attribution Share-Alike Non-Commercial 3.0 License
Portions not contributed by visitors are Copyright 2016 Tangient LLC
TES: The largest network of teachers in the world
Turn off "Getting Started"