Definitions of tuning terms © 1998 by Joseph L. Monzo All definitions by Joe Monzo unless otherwise cited

prime

a number which has as its factors only itself and 1.

The prime series is infinite, and as yet no one has discovered a pattern in its progression. Primes are are important in number theory because of the Fundamental Theorem of Arithmetic.

The first fourteen primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41 and 43.

Some theorists attach special importance to the prime numbers as they seem to each produce a unique affect in music, at least for the lower primes. Much is still unclear about this idea, but it has been explored by Harry Partch, Ben Johnston, Alain Daniélou, La Monte Young, Scott Makeig, and myself, among others.

My own feeling is that, although there are many aspects of sound that are involved in the feelings and perceptions we have of music, the primes seem to be a kind of cognitive archtype or template that helps us to grasp or understand the harmonic relationships we are hearing in music, and that the more sophisticated use the performer/ composer makes of subtle prime relationships, and the better the listener understands those relationships, whether intellectually, intuitively, or viscerally, the more rewarding the experience for both performer and listener.

There is much debate about this, in particular, where the boundaries of our perception of these affects/effects lie within the primes and within the exponents of the primes, and to what extent ratios which have greatly differentiated prime-factors but which lie very close to each other in pitch resemble or differ from each other.

But it is undeniable that simultaneous notes bear harmonic proportional frequency relationships, and that the human cognitive apparatus will perceive those relationships in the simplest way it knows. I hold the opinion that prime-factorization is the ultimate simplification of rational numerical musical relationships.

In my model of this process, two important concepts are involved, which I have named finity and bridging.

An important aspect of my theory is the use of prime-factor notation.

[from Joe Monzo, JustMusic: A New Harmony]