Scales and Temperament from the Mathematical Viewpoint

Year: 2016 Authors: Steven A. Bleiler; Ewan Kummel

Core claim

Equal-tempered scales can approximate just and Pythagorean intervals well enough to balance harmonic purity against practical musical flexibility.

Topics

equal temperament, just intonation, Pythagorean comma, scale construction

Domains

number theory, ratio approximation, continued fractions, lattice structures, music theory, instrument design, performance practice, tuning systems

Methods

interval analysis, historical comparison, computational exploration, GeoGebra applet

Media

fretted lute, diddley bow, equal-temperament diagrams, Java applet

Source status

This page publishes metadata and extracted analytical signals only. Raw PDF and full OCR text are kept local for now.