# Extension and restriction

An **extension** of a regular temperament on a JI subgroup *G* to a larger subgroup *G' * is a new temperament that contains the same intervals as the original temperament, and whose rank remains the same, with the same JI interpretations in the subgroup *G*, but gives them new JI interpretations not in the original subgroup (but are in the larger subgroup). The opposite of extension is **restriction**.

For example, septimal meantone and flattone are both extensions of 5-limit (2.3.5) meantone to the 7-limit (2.3.5.7), because C-E (4 fifths) represents 5/4 in both. They are different extensions, because in septimal meantone, 7/4 is C-A# (10 fifths), while in flattone, 7/4 is C-Bbb (-9 fifths).

A **strong extension** is an extension in which the generators are not split compared to the original temperament. The structure of a strong extension is not changed, and no new intervals are introduced. A **weak extension** is one in which the generators are split.

For example, both septimal meantone and flattone are strong extensions of 5-limit meantone since they all share the same period and generator. Godzilla is a weak extension of meantone but a strong extension of semaphore.

## See also

- Subgroup Temperament Families, Relationships, and Genes – formal definitions