Generator-offset property: Difference between revisions
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== Other definitions == | == Other definitions == | ||
* A strengthening of the generator-offset property, tentatively named ''split-generator-alternant'' (SGA), states that ''g''<sub>1</sub> and ''g''<sub>2</sub> can be taken to be 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). Only odd AG scales and xyxz can satisfy this property. The Zarlino and diasem scales above are both SGA. [[Blackdye]] is AG but not SGA. | * A strengthening of the generator-offset property, tentatively named ''split-generator-alternant'' (SGA), states that ''g''<sub>1</sub> and ''g''<sub>2</sub> can be taken to be 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). Only odd AG scales and xyxz can satisfy this property. The Zarlino and diasem scales above are both SGA. [[Blackdye]] is AG but not SGA. | ||
* We say that a particular interval size ''is constantly subtended'' if the interval size always occurs as the same number of steps. | * We say that a particular interval size in a scale ''is constantly subtended'' if the interval size always occurs as the same number of steps. | ||
== Theorems == | == Theorems == | ||