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== In scale building == | == In scale building == | ||
Building a scale out of 7 of [[21edo]]'s sharp fifths (of about 742.857 cents) gives a scale that can be interpreted as a [[diatonic]] scale with large steps of size 5 and small steps of size -2 (note that this means "ascending" small steps are actually descending). When attempting to make an [[antidiatonic|antidiatonic scale]] with the same relative step sizes, it always lands on the unison (as there are 2 large steps and 5 small steps, 5 × 2 + (-2) × 5 = 0), and as such, the sizes of the steps go to infinity – the [[generator]] for this scale is, in fact, 1/0, and the scale is represented by [[0edo]]. | Building a scale out of 7 of [[21edo]]'s sharp fifths (of about 742.857 cents) gives a scale that can be interpreted as a [[diatonic]] scale with large steps of size 5 and small steps of size -2 (note that this means "ascending" small steps are actually descending). When attempting to make an [[antidiatonic|antidiatonic scale]] with the same relative step sizes, it always lands on the unison (as there are 2 large steps and 5 small steps, 5 × 2 + (-2) × 5 = 0), and as such, the sizes of the steps go to infinity – the [[generator]] for this scale is, in fact, 1/0, and the scale is represented by [[0edo]]. | ||
== Temperaments == | |||
If 1/0 is taken as a comma to be tempered out, it leads to the [[singularity]] temperament. | |||
== Practical application == | == Practical application == | ||