**One-dimensional Tone Factory**

The One-dimensional Tone Factory works to the specification:

where *f*ref is the reference frequency, and **a** and **b** are positive or negative integers. The value of **b** is sufficient in this instance to determine the position of a tone along the single dimension. The value of **a** has been fixed in order to give **f** a value between 1 and 2.
Disabling the octave dimension (powers of 2) by this means allows us to map this space to one rather than two dimensions.

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