Generator-offset property: Difference between revisions
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# (''k'' − 1)''g''<sub>1</sub> + ''kg''<sub>2</sub> | # (''k'' − 1)''g''<sub>1</sub> + ''kg''<sub>2</sub> | ||
# (''k'' − 1)''g''<sub>1</sub> + (''k'' − 1) ''g''<sub>2</sub> + ''g''<sub>3</sub>, | # (''k'' − 1)''g''<sub>1</sub> + (''k'' − 1) ''g''<sub>2</sub> + ''g''<sub>3</sub>, | ||
if a step is an odd number of generators (since the scale size is odd, we can always ensure this by taking octave complements of all the generators). The first two sizes must occur the same number of times. | if a step is an odd number of generators (since the scale size is odd, we can always ensure this by taking octave complements of all the generators). The first two sizes must occur the same number of times. This proves (2). | ||
(The above holds for any odd ''n'' ≥ 3.) | (The above holds for any odd ''n'' ≥ 3.) | ||