Linear step scale: Difference between revisions

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A '''linear step scale'''{{idiosyncratic}} is a possible generalization of [[equal temperament]]s other than [[MOS scale]]s. 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-~~335~~ cents and the intervals as 285-580-885-1200 cents. All linear step scales are logically [[harmonotonic tuning]]s (decreasing step sizes for negative slope and increasing step sizes for positive slope).

A '''linear step scale'''{{idiosyncratic}} is a possible generalization of [[equal temperament]]s other than [[MOS scale]]s. 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 tuning]]s (decreasing step sizes for negative slope and increasing step sizes for positive slope).

The term "linear step scale" was proposed by [[User:CompactStar|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.

[[Category:Scale]]

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-A '''linear step scale'''{{idiosyncratic}} is a possible generalization of [[equal temperament]]s other than [[MOS scale]]s. 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 285-295-305-335 cents and the intervals as 285-580-885-1200 cents. All linear step scales are logically [[harmonotonic tuning]]s (decreasing step sizes for negative slope and increasing step sizes for positive slope).
+A '''linear step scale'''{{idiosyncratic}} is a possible generalization of [[equal temperament]]s other than [[MOS scale]]s. 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 tuning]]s (decreasing step sizes for negative slope and increasing step sizes for positive slope).
 The term "linear step scale" was proposed by [[User:CompactStar|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.
 [[Category:Scale]]
-{{Stub}}
+{{Todo|inline=1|link|expand}}
+[[Category:Scale]]