Mathematical aspects of musical scales and series
Musical scales may be interpreted as specific increasing sequences of real numbers. Periodic scales, i.e. musical scales whose pattern is periodic, feature in this article. Of special interest are regular scales of which are given seven properties in four theorems which are new results, engaging the concepts of: the period of scale, the length of period of scale, the pattern, being homomorphous, a transposition and having the same key. This paper considers the idea of musical scales in general,...