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Encyclopedia of Microtonal Music Theory

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[Chris Wittmann and Joe Monzo]

The basic realm used by musical tuning computations and modeling is a real space.

A real space is a linear or vector space that is restricted to the set of real numbers, i.e., it does not deal with imaginary or complex numbers.

Informally, the real space consists of a collection of objects called vectors, real numbers (scalars), and two operations which are required to have certain specific properties. The two operations are:

There are specific properties of a real space.

A specific use of real-space is tone-space, which is the space used by tuning theorists.

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