Generator-offset property: Difference between revisions

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== Other definitions ==

* A strengthening of the generator-offset property, tentatively named the ''split-generator-alternant property'' (SGA), states that ''g''1 and ''g''2 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 GO scales and xyxz can satisfy this property. 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 ''split-generator-alternant property'' (SGA), states that the alternants ''g''1 and ''g''2 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). Only odd GO scales and xyxz can satisfy this property. The Zarlino and diasem scales above are both SGA. [[Blackdye]] is GO but not SGA.

* 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. (This alludes to the term [[constant structure]].)

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 == Other definitions ==
-* A strengthening of the generator-offset property, tentatively named the ''split-generator-alternant property'' (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 GO scales and xyxz can satisfy this property. 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 ''split-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). Only odd GO scales and xyxz can satisfy this property. The Zarlino and diasem scales above are both SGA. [[Blackdye]] is GO but not SGA.
 * 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. (This alludes to the term [[constant structure]].)