Generator-offset property: Difference between revisions
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# ''S'' is generated by two chains of generators separated by a fixed interval; either both chains are of size ''n''/2, or one chain has size (''n'' + 1)/2 and the second has size (''n'' − 1)/2. | # ''S'' is generated by two chains of generators separated by a fixed interval; either both chains are of size ''n''/2, or one chain has size (''n'' + 1)/2 and the second has size (''n'' − 1)/2. | ||
These are equivalent, since the separating interval can be taken to be ''g''<sub>1</sub> and the generator of each chain = ''g''<sub>1</sub> + ''g''<sub>2</sub>. This doesn't imply that ''g''<sub>1</sub> and ''g''<sub>2</sub> are the same number of scale steps. | These are equivalent, since the separating interval can be taken to be ''g''<sub>1</sub> and the generator of each chain = ''g''<sub>1</sub> + ''g''<sub>2</sub>. This doesn't imply that ''g''<sub>1</sub> and ''g''<sub>2</sub> are the same number of scale steps. For example, 5-limit [[blackdye]] has ''g''<sub>1</sub> = 9/5 (a 9-step) and ''g''<sub>2</sub> = 5/3 (a 7-step). | ||
== Theorems == | == Theorems == | ||