A numerical exercise in musical scales Available to Purchase

This paper investigates why the 12‐note scale, having equal intervals, seems to be the best representation of scales constructed from purely harmonic intervals. Is it possible that other equal temperament scales with more or less than 12 notes would serve just as well? The investigation is done by displaying the difference between a set of harmonic notes and scales with equal intervals having n notes per octave. The difference is small when n is equal to 12, but also when n equals 19 and 29. The number density of notes per unit frequency intervals is also investigated.