Generator-offset property: Difference between revisions
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== Other definitions == | == Other definitions == | ||
* A ''scale'' or ''scale word'' is a circular word with a chosen size for its equave. As we're not working with scales with distinct equaves simultaneously, all three terms are effectively synonymous for our purposes. | * A ''scale'' or ''scale word'' is a circular word with a chosen size for its equave. As we're not working with scales with distinct equaves simultaneously, all three terms are effectively synonymous for our purposes. | ||
* A scale is ''primitive'' if its period is the equave. | |||
* An ''n''-''ary'' scale is a scale with ''n'' different step sizes. ''Binary'' and ''ternary'' are used when ''n'' = 2 and 3 respectively. | * An ''n''-''ary'' scale is a scale with ''n'' different step sizes. ''Binary'' and ''ternary'' are used when ''n'' = 2 and 3 respectively. | ||
* A strengthening of the generator-offset property, tentatively named the ''swung-generator-alternant property'' (SGA), states that the alternants g<sub>1</sub> and g<sub>2</sub> can be taken to always subtend the same number of scale steps, thus both representing "detemperings" of a generator of a single-period [[mos]] scale (otherwise known as a well-formed scale). All odd GO scales are SGA, and aside from odd GO scales, the only ternary scales to satisfy SGA are (xy)<sup>''r''</sup>xz, ''r'' ≥ 1. The Zarlino and diasem scales above are both SGA. [[Blackdye]] is GO but not SGA. | * A strengthening of the generator-offset property, tentatively named the ''swung-generator-alternant property'' (SGA), states that the alternants g<sub>1</sub> and g<sub>2</sub> can be taken to always subtend the same number of scale steps, thus both representing "detemperings" of a generator of a single-period [[mos]] scale (otherwise known as a well-formed scale). All odd GO scales are SGA, and aside from odd GO scales, the only ternary scales to satisfy SGA are (xy)<sup>''r''</sup>xz, ''r'' ≥ 1. The Zarlino and diasem scales above are both SGA. [[Blackdye]] is GO but not SGA. | ||