Digital electronic instruments allow the expressive possibilities of intonation to be explored in a manner more accurate and more convenient than ever before. Like the violin or voice, they are capable of producing a continuous range of frequencies and therefore do not have to conform to a tuning. Unlike acoustic instruments with continuous frequency, their frequency can be controlled extremely accurately and consistently. Perhaps most importantly, digital electronic instruments can be controlled by a computer. This enables them to have at least two modes of operation that would be impossible with acoustic instruments. In the first mode of operation, an entire piece, along with intonation annotations, can be specified in a digital score and then played by the computer on an instrument with a MIDI interface.
In the second mode of operation, the computer does not replace the
performer but rather extends his intonation capabilities. The computer
``listens'' to the performance data from a MIDI keyboard, retunes it
according to some algorithm or score, and re-transmits it to a MIDI
instrument, all in real-time. This creates a new instrument in which
the performer is not burdened with the responsibility of controlling
intonation, but his performance can still have arbitrarily complex
intonation. Not only does this make dynamic intonation possible, it
also makes any static intonation possible. Normally, a keyboard can
only be used to realize the most restricted subset of static
intonations, those that tune all pitches separated by a diminished
second (like G
and A
) to the same frequency.
This thesis presents a software suite called Helm that unleashes the intonation capabilities of MIDI instruments. These tools allow intonation-annotated scores to be played by the computer or used as instructions for the real-time retuning of a performer's keyboard input. In addition, this thesis presents a theory of intonation that can be applied to the use of Helm. This theory, like most intonation theories, focuses on the role of intonation in maximizing harmonic consonance and treats dynamic intonation mainly with respect to just intonation. Within this conventionally narrow focus, it overcomes many other theories' weaknesses by introducing some new ideas and synthesizing the ideas of various theorists in new ways.