Music theory online

Since musical systems are generally limited to a discrete number of points in both the frequency and time domains, music theorists have properly concentrated on techniques for modeling discrete transformations of musical objects. However, a number of contemporary composers have explored continuous transformations of musical objects in the frequency, time, and other domains. Such processes include continuous transformations of pitch simultaneities, rhythmic patterns, and tempos. This paper discusses techniques for modeling in?nitesimal motions in continuous musical spaces (as well as discrete motion in atypical spaces such as non-tempered microtonal progressions) with analytic application to works by Kaija Saariaho, Conlon Nancarrow, and Gy�orgy Ligeti.