Generator-offset property: Difference between revisions
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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). | 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). | ||
== Related properties == | |||
* A strengthening of the AG property states that ''g''<sub>1</sub> and ''g''<sub>2</sub> can be taken to be the same number of scale steps. Only odd AG scales can satisfy this property. | |||
== Theorems == | == Theorems == | ||
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