The Euclidean algorithm (which comes down to us from Euclid's Elements) computes the
greatest common divisor of two given integers. It is shown here that the structure of the …

The theory of musical scales involves mathematical ratios, harmonic resonators, beats, and
human perception and provides an interesting application of the physics of waves and …

An intuitive model of classical guitar intonation is presented that includes the effects of the
resonant length of the fretted string, linear mass density, tension, and bending stiffness. An …

Convex (concave) interaction weighting functions are combined with circular configurations
of black and white sites to determine configurations that have minimum (maximum) weight …

Classical algorithms for principal and intermediate continued fraction convergents provide
convenient ways of obtaining information about musical scales. It is shown that the principal …

Een woord van dank aan de mensen die er aan bijgedragen hebben dat dit proefschrift nu is
zoals het is. Ik wil graag mijn promotor en begeleider Rens Bod bedanken, allereerst voor …

Numbers called quality modifiers are used to identify interval qualities: 0 numerically
represents perfect, 1/2 represents major,–1/2 represents minor, and so on. These modifiers …

Jack Douthett (douthett@ unm. edu) holds two Master of Music degrees, one in performance
and the other in theory and composition, and received his Doctorate of Mathematics from the …

This contribution gives a brief overview of a mathematical and physical interpretation of
musical consonance and dissonance. In addition to the traditionally accepted Pythagorean …

A dissonância sensorial é um conceito que restringe a noção da dissonância à sua
dimensão psicofísica, por meio do fenômeno psicoacústico conhecido como rugosidade …