exponent

A number written as a superscript following another number, which indicates how many times the first number is to be multiplied by itself.

For example: 25 = 5 * 5, which can also be written 5². Here, 2 is the exponent.

Exponents are important in my theory because they represent steps along each axis of a lattice-diagram, which thus shows information about the influence of each prime-factor in the tuning. My theories are based on the idea that the prime-series represents the ultimate basis to which our minds can reduce the mathematics of a tuning.

When a particular prime-series is known or given, the exponents can be written alone in a vector, thus simplifying the notation of a tuning without sacrificing any mathematical precision (which is what happens when cents-values or other logarithmic measurements are used).

For example, if the series of prime-factors is given as {2,3,5}, the "25" cited above would be written [0 0 2], which indicates a point in 3-dimensional ratio-space which lies along the origin of both the 2- and the 3-axes, and 2 steps in the positive direction along the 5-axis.

The ASCII (i.e., plain text) convention for indicating exponents (in an email, for example) is to use the caret sign "^" before the exponent; for example, 3² would be typed as 3^2.

[from Joe Monzo, JustMusic: A New Harmony]

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For many more diagrams and explanations of historical tunings, see my book. If you don't understand my theory or the terms I've used, start here

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