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[DRAFT] Non-octave / generalized (?) overtone scale
TODO: research if a generalized form like this already exists
Non-octave overtone scales are an approach to describe overtone scales without the need of the octave as the period.
Therefore, they are non-octave-repeating scales based on a generating sequence which itself is a subset of the harmonic series.
They can also be viewed as a form of generator sequence.
Non-octave overtone scales are described by the form n...p:s
where
n ... root to which the following integers in the scale are relative to
p ... the period of the scale
s ... the step size, how many of the integers in the scale are skipped
n...p describes the integer sequence from including n to including p, for example, 4...7 gives: [4, 5, 6, 7]
for example, the scale 4...9:1 describes this 5-tone scale
4/4 - 5/4 - 6/4 - 7/4 - 8/4 - 9/4
the :1 indicates that every integer in the sequence is visited (step size of 1)
Contrast this to 4...9:2 which generates the following 3-tone scale
4/4 - 6/4 - 8/4 - 9/4
note that the :2 indicates that every other integer in the sequence from n ... p is visited (step size of 2)
Contrast this to 4...9:3 which generates the following 2-tone scale
4/4 - 7/4 - 9/4
etc.