User:VectorGraphics/Mapping

The operation of "tempering" can be thought of as establishing a relationship or equality between two intervals. This can be seen as a "flattening" from a higher-dimensional interval space (such as just intonation) down to a lower-dimensional space, called a regular temperament; while an interval in 5-limit just intonation requires 3 numbers to represent (see Monzo notation), an interval in meantone temperament requires only 2 numbers to represent. A mapping essentially tells you how to do that flattening, and can be seen as a list of monzos in the temperament telling you where to find each basis interval of the original interval space.

For example, for meantone temperament, the mapping is:

[math]\displaystyle{ 2.3.5 \left[ \begin{array}{rr} 1 & 0 & -4 \\ 0 & 1 & 4 \\ \end{array} \right] }[/math]