This section will give a brief overview of the rest of the thesis.
After introducing some typographical conventions of this document, the rest of this introductory chapter will be devoted to a review of key background topics in Western music theory, acoustics, and mathematics.
Chapter 2 reviews work that is related to this thesis. The related work falls into two major categories: related theories of tuning and related dynamic intonation software or instruments.
Chapter 3 presents a theory of tuning. The theory is of general applicability but is oriented towards application to dynamic intonation. This theory begins with the presentation of several mathematical models of tunings, one of which is chosen to be the primary model used in this work. A mathematical formalization of pitch notation is presented. The criteria of just perfect fifths and major thirds are introduced as a way to evaluate tunings. Several types of diatonic tunings are discussed in the context of the formalisms previously developed. The chapter concludes with a discussion of triadic tunings and their theory, which are particularly applicable to just intonation.
Chapter 4 describes Helm, the dynamic intonation software suite developed as part of this thesis research. It presents the language in which scores are described, which includes facilities for intonation annotation. It then presents the two main things that can be done with such score descriptions. The first is the creation of Standard MIDI File realizations of the score. The second is the creation of an instrument that follows along in the score, retuning notes it receives from a MIDI keyboard in real-time.
Chapter 5 presents some conclusions about the theory and software of this work. It also presents some experiments in just intonation that were conducted using the theory and software developed in this work.
Chapter 6 suggests some future directions that this work could take. These include extensions to the theory, extensions to the software, and new synthesis techniques related to tuning.