Generator-offset property: Difference between revisions
m Clarify "does not necessarily take up the same number of steps" |
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# The scale is generated by two chains of stacked copies of a ''generator''. | # The scale is generated by two chains of stacked copies of a ''generator''. | ||
# The two chains are separated by an ''offset'' (the difference between the first note of the second chain and the first note of the first chain). | # The two chains are separated by an ''offset'' (the difference between the first note of the second chain and the first note of the first chain). | ||
# The lengths of the chains differ by at most one. (1-3 can be restated as: The scale can be built by stacking two alternating generators (called ''alternants'') a<sub>1</sub> and a<sub>2</sub>. Note that a<sub>1</sub> does not need to [[subtend]] the same number of steps as a<sub>2</sub>.) | # The lengths of the chains differ by at most one. (1-3 can be restated as: The scale can be built by stacking two alternating generators (called ''alternants'') a<sub>1</sub> and a<sub>2</sub>. Note that a<sub>1</sub> does not need to [[subtend]], or occur as, the same number of steps as a<sub>2</sub>.) | ||
# The generator always occurs as the same number of steps. For example, the generator is never both a 2-step and a 3-step. | # The generator always occurs as the same number of steps. For example, the generator is never both a 2-step and a 3-step. | ||