Linear step scale

A linear step scale^{[idiosyncratic term]} is a possible generalization of equal temperaments other than MOS scales. The size of the step after a note increases linearly in the form ax+b where x is the index of the note (starting from 0). For example, a 3-tone octave-repeating scale with the step size determined as 10x+285 in cents would have the step sizes between intervals as 285-295-305-315 cents and the intervals as 285-580-885-1200 cents. All linear step scales are logically harmonotonic tunings (decreasing step sizes for negative slope and increasing step sizes for positive slope).

The term "linear step scale" was proposed by CompactStar.

Most such scales are nonoctave. The scales which have octaves can have the a in "ax+b" determined by only b and the number of tones:

a = (-2bn + 2b + 2400)/(n^2 - 3n + 2)

Where n represents the number of tones, and all pitches are given in cents.

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