Generator-offset property: Difference between revisions
m Ground didn't discover this (the MV page had had a statement of the classification thm using this), but just investigated musically using scales with the property. |
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A scale satisfies the '''generator-offset property''' if it satisfies the following properties: | A scale satisfies the '''generator-offset property''' if it satisfies the following properties: | ||
# The scale is generated by two chains of stacked copies of an interval called ''generator''. | # The scale is generated by two chains of stacked copies of an interval called the ''generator''. | ||
# The two chains are separated by a different interval called the ''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 a different interval called the ''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]], i.e. occur as, 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]], i.e. occur as, the same number of steps as a<sub>2</sub>.) | ||