Conclusion

In summary then the Steadman representation of harmonic space is very powerful for musical reasoning. It provides a method of manipulating music geometrically, in addition to the traditional symbolic forms. It also explains the meaning behind the rules of traditional music theory.

In this report I have presented some ideas as to how the M.I.M. could be constructed. In practice the Sparc computer system that I used as a platform for the program presented in the appendices suffers under real-time conditions due to the restrictions imposed by the operating system (SunOs/Solaris Unix). Consequently I was unable to experiment with the mechanism much past the interpretation stage. Ideally a single user operating system or a bare architecture with minimal operating system resources, such as a Pentium system running in protected mode, would much better suit further exploration.

Constructing the M.I.M. cannot be considered a trivial task, but I feel that exploring these avenues could open the door to some very useful tools for musical manipulation.

Here are a few example application ideas that could be constructed using the Steadman representation as a foundation:

• Harmonic Tutor Package.

  The Steadman representation, if presented graphically on a computer screen, provides a direct correlation between auditory and visual cues. A program could therefore be written to teach harmony to music students by sounding chord sequences, showing their standard musical representation in sheet music form and also displaying the patterns they form in Steadman space. Using the program that is part of this report to "see" MIDI files in Steadman space as well as hearing them it is apparent that this is a very useful technique. Even people who little or no musical background seemed to find it easy to gain a basic understanding of chord sequences after a very short time of experimenting with a keyboard and the program.

• Mean Tone Temperament Keyboard.

  If the key of a piece that is being played on a keyboard can be reliably followed during a performance then it is feasible that this information could be used to re-tune the notes of the keyboard as it is being played. The new tuning could be derived from the key centre that the performance is currently using. This would amount to an intelligent instrument. Would it sound more harmonious than the default equally tempered sound that we're used to?

• Higher abstraction MIDI sequencer.

  A MIDI sequencer is a program that behaves like a multi-track tape recorder, but instead of recording musical sound it records event information against time, for example:

  • Time: 00:00:00 Note On: C Attack Velocity: 60
  • Time: 00:00:01 Note On: E Attack Velocity: 63
  • Time: 00:01:00 Note Off: C Release Velocity: 50

  Once this information is in memory it can be manipulated in various ways, for instance the tempo can be changed without changing the pitch and visa versa. The data can be represented on screen in any format, in sheet music notation for instance, and individual events modified independently. Using a representation like Steadman space however it would be possible to "get away from the dots" and manipulate the music from a higher level of abstraction. This could open up completely new avenues of musical creation.