Generator-offset property: Difference between revisions

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 These are equivalent, since the offset can be taken to be ''g''<sub>1</sub> and the generator then equals ''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).
-More generally, we say that a scale is ''m'''''-GO''' if the scale consists of ''m'' + 1 chains of generator ''g'' (implying ''m'' offsets δ<sub>1</sub>, ...,δ<sub>''m''</sub> from a fixed chain), each chain having either ''k'' or ''k'' + 1 notes. (Thus 1-GO is the same thing as GO.)
+More generally, we say that a scale is ''m'''''-GO''' if the scale consists of ''m'' + 1 chains of generator ''g'' (implying ''m'' offsets δ<sub>1</sub>, ...,δ<sub>''m''</sub> from a fixed chain), each chain having either ''k'' or ''k'' + 1 notes. (Thus 1-GO is the same thing as GO.) An ''m''-GO scale can be interpreted as a scale in a rank-(''m'' + 2) [[regular temperament]].
 == Other definitions ==