Download or read book Abstract Musical Intervals written by Ming Tsao and published by Lulu.com. This book was released on 2007 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to GIS (Generalized Interval Systems) theory that includes the major results of pitch-class theory. It provides mathematicians with applications of group theory to music and music theorists with the essential connections between GIS theory and pitch-class theory. Many of the results in pitch-class theory are not addressed by David Lewin (such as power functions or the Common Tone Theorem for inversions). The book states those results and generalizes them to conform with GIS theory. Finally, it addresses recent criticisms leveled at pitch-class theory and suggests how they can be addressed in GIS theory.