prime-space

A term coined by Chris Wittmann (in private communication to the author) to indicate the "numerical universe" within which a tuning system may be represented mathematically.

Prime-space refers specifically to the objectification of the pitch-continuum in multi-dimensional space as a series of axes, each of which represents simultaneously one unique prime-factor and one unique dimension of space, and along each of which are equally-spaced points representing the exponents of those prime-factors. This convention is then used in graphing specific pitches onto a lattice-diagram.

The use of prime-space may be conscious or unconscious, and in my theory, plays an important role (probably the most important) in determining the finity of a tuning system.

According to my theory, a composer, performer, or listener already has in mind (consciously or unconsciously) a prime-space before encountering a piece of music. Often during the course of the piece, a harmonic or melodic event will force the subject to make a change in his conception of that particular prime-space.

The dimensions used in any prime-factor notation are determined directly by the choice of prime-space.


[from Joe Monzo, JustMusic: A New Harmony]

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