Generator-offset property: Difference between revisions
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A scale satisfies the '''alternating generator property''', or the '''AG''' property for short, if it satisfies the following equivalent properties: | A scale satisfies the '''alternating generator property''', or the '''AG''' property for short, if it satisfies the following equivalent properties: | ||
* the scale can be built by stacking alternating generators | * the scale can be built by stacking alternating generators | ||
* 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. | ||
[[Diasem]] is an example of an AG scale. | [[Diasem]] is an example of an AG scale, because it is built by stacking alternating 7/6 and 8/7 (or 8/7 and 7/6 for the other [[chirality]]). | ||
More formally, a cyclic word ''S'' (representing a [[periodic scale]]) of size ''n'' is '''AG''' if it satisfies the following equivalent properties: | More formally, a cyclic word ''S'' (representing a [[periodic scale]]) of size ''n'' is '''AG''' if it satisfies the following equivalent properties: | ||