Extension and restriction

An extension of a temperament on a JI subgroup G to a larger subgroup G' is a new temperament that contains all the intervals of the original temperament, with the same JI interpretations in the subgroup G, but adds JI interpretations (and possibly new intervals if necessary) not in the original subgroup (but are in the larger subgroup).

For example septimal meantone and flattone are both extensions of 5-limit (2.3.5) meantone to the 7-limit (2.3.5.7).