Generator-offset property: Difference between revisions
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* the scale is generated by two chains of generators separated by a fixed interval, and the lengths of the chains differ by at most one. | * the scale is generated by two chains of generators separated by a fixed interval, and the lengths of the chains differ by at most one. | ||
The [[Zarlino]] (3L 2M 2S) JI scale is an example of an alt-gen scale, because it is built by stacking alternating 5/4 and 6/5 generators. [[ | The [[Zarlino]] (3L 2M 2S) JI scale is an example of an alt-gen scale, because it is built by stacking alternating 5/4 and 6/5 generators. 7-limit [[diasem]] (5L 2M 2S) is another example, with generators 7/6 and 8/7. | ||
More formally, a cyclic word ''S'' (representing a [[periodic scale]]) of size ''n'' is '''alt-gen''' if it satisfies the following equivalent properties: | More formally, a cyclic word ''S'' (representing a [[periodic scale]]) of size ''n'' is '''alt-gen''' if it satisfies the following equivalent properties: | ||