Generator-offset property: Difference between revisions
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m first para point 2): changed "the difference between [x] minus [y]" to "the difference between [x] and [y]" |
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A scale satisfies the '''generator-offset property''' (also '''GO''', '''alternating generator''' or '''AG''') if it satisfies the following properties: | A scale satisfies the '''generator-offset property''' (also '''GO''', '''alternating generator''' or '''AG''') if it satisfies the following properties: | ||
# 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 | # 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''), which do not necessarily take up the same number of steps.) | # 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''), which do not necessarily take up the same number of steps.) | ||
# 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. | ||