Home > Mathematics, Statistics > Vol 12 No 1 June 2024 Abstract 3
Mathematics of Countour Classes
Ilhan M. Izmirli

Abstract
Regardless of their degree of musical sophistication and their cultural differences, all who listen to music have an innate feel for proximity (distance between consecutive notes, or what note is expected to follow the other), and direction (whether the melody is ascending or descending). In [7], I had looked into the mathematics of pitch spaces where proximity was the distinguishing characteristic. In this paper, I will investigate the properties of pitch spaces where only the direction counts, that is, spaces where we are not interested in the distance between the pitches, but only in whether a pitch is higher than, lower than, or the same as another pitch. The resulting constructs, the so called contour classes, are used as sequences in fugues, as leitmotifs in operas, and as changes of mode from major to minor in variations.

Full Text: PDF     DOI: 10.15640/arms.v12n1a3