An alternative approach to generalized Pythagorean scales.

What is it about?

Well-formed scales are studied by following a constructive procedure by pointing out the links to other approaches, namely the continued fractions, combinatorics of words, Farey sums, and the Stern-Brocot tree.

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Why is it important?

New proofs of several scale properties are derived from the generating procedure. The paper provides new and alternative viewpoints to obtain the main characterizations of well-formed scales, such as those related to the best comma, the chromatic length of the generator, Myhill’s property, the spectrum width, etc.