ABSTRACT
In this chapter, the authors utilize group actions to investigate questions regarding symmetry in Western music. Western musicians divide octaves into 12 distinct equally spaced notes, each separated from its nearest neighbors by a semitone. The authors deal with a discussion of pitch class segments, a mathematical tool used by music theorists to study structural properties of music. They discuss major and minor diatonic scales. This will include a discussion of the circle of fifths, which is used by music theorists to visualize relationships between scales. The authors also discuss major and minor triads, called consonant triads since they are pleasant sounding. Consonant triads are defined in terms of the musical intervals of the perfect fifth, the major third, and the minor third. They show how MATLAB can be used to find the cycle index for the rotations of the musical clock.
