Extension and restriction: Difference between revisions
mNo edit summary |
mNo edit summary |
||
| Line 1: | Line 1: | ||
An '''extension''' of a [[temperament]] on a [[JI subgroup]] ''G'' to a larger subgroup ''G' '' is a new temperament that contains the same intervals as the original temperament, with the same JI interpretations in the subgroup ''G'', but gives the same intervals new JI interpretations not in the original subgroup (but are in the larger subgroup). | An '''extension''' of a [[temperament]] on a [[JI subgroup]] ''G'' to a larger subgroup ''G' '' is a new temperament that contains the same intervals as the original temperament (in particular the [[rank]] remains the same), with the same JI interpretations in the subgroup ''G'', but gives the same intervals new JI interpretations 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), 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). | 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). | ||
[[Category:Terms]] | [[Category:Terms]] | ||