The understanding of the musical techniques of composition can not be reduced to a handbook of simplified rules. Music is complex and ever changing. It is the purpose of this book to trace the path of musical growth from the late Romantic period to the serial techniques of the contemporary composer. Through the detailed analysis of the musical characteristics that dominate a specific style of writing, a graduated plan is organized and presented here in the form of explanations and exercises. A new analytical method substitutes for the diatonic figured bass and makes exercises and the analysis of non-diatonic literature more manageable. The explanations describing each technique are thorough. They are designed to help the teacher and the student see the many extenuating circumstances that affect a particular analytical decision. More important than a dogmatic decision on a particular key center or a root tone, for example, is the understanding of why such an underdeterminate condition may exist.