Results in mathematics and music: visualization of roughness in musical consonance
Florian Sobieczky · 2002
The definition of consonance as the ability to resolve a sound into the pitch categories is introduced. For a vector space of chords a norm is used to evaluate the consonance linearly in dependence of the instrument used. It is shown that in the corresponding Hilbert space the chords which usually appear together in a conventional musical piece are recognized in terms of "closeness".