Generator-offset property: Difference between revisions
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The [[Zarlino]] (3L 2M 2S) JI scale is an example of a generator-offset scale, because it is built by stacking alternating 5/4 and 6/5 generators. The 7-limit version of [[diasem]] (5L 2M 2S) is another example, with generators 7/6 and 8/7. | The [[Zarlino]] (3L 2M 2S) JI scale is an example of a generator-offset scale, because it is built by stacking alternating 5/4 and 6/5 generators. The 7-limit version of [[diasem]] (5L 2M 2S) is another example, with generators 7/6 and 8/7. | ||
Generator-offset is a conception developed by [[User:ks26|ground fault]], and generalizes the notion of [[dipentatonic scale|dipentatonic]] and [[diheptatonic scale|diheptatonic]] scales to scales of all sizes. A related notion is [[alternating generator sequence]]. Generator-offset scales can be seen as a result of an alternating generator sequence of length 2, but the generator-offset conception views the "aggregrate generator" of the AGS as the "canonical" generator, and the alternants as rather being offsets. While a well-formed alternating generator sequence requires each alternant in the AGS and the "imperfect" alternant to subtend the same number of steps, the generator-offset only requires each generator to subtend the same number of steps. | |||
== Mathematical definition == | == Mathematical definition == | ||