Generator-offset property: Difference between revisions
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Label the notes (1, ''k'') and (2, ''k''), 1 ≤ ''k'' ≤ ''m'' or ''m'' − 1, for notes in the upper and lower chain respectively. | Label the notes (1, ''k'') and (2, ''k''), 1 ≤ ''k'' ≤ ''m'' or ''m'' − 1, for notes in the upper and lower chain respectively. | ||
In case 1, let ''g''<sub>1</sub> = (2,1) − (1,1) and ''g''<sub>2</sub> = (1,2) − (2,1). We have the chain ''g''<sub>1</sub> ''g''<sub>2</sub> ''g''<sub>1</sub> ''g''<sub>2</sub> ... ''g''<sub>1</sub> ''g''<sub>3</sub>. | In case 1, let ''g''<sub>1</sub> = (2, 1) − (1, 1) and ''g''<sub>2</sub> = (1, 2) − (2, 1). We have the chain ''g''<sub>1</sub> ''g''<sub>2</sub> ''g''<sub>1</sub> ''g''<sub>2</sub> ... ''g''<sub>1</sub> ''g''<sub>3</sub>. | ||
Let ''r'' be odd and ''r'' ≥ 3. Consider the following abstract sizes for the interval class reached by stacking ''r'' generators: | Let ''r'' be odd and ''r'' ≥ 3. Consider the following abstract sizes for the interval class reached by stacking ''r'' generators: | ||