There is a physicist friend who would dispute that many of these scales, including the common Western equal-temperered scale, are in fact "musical" - many of the intervals involved are dissonant. My mentor Suzanne Haik-Vantoura, writing as a classical composer, pointed out the same while pointing out the fundamental (and therefore in that sense, universal) quality of diatonicism. But in any case, largely built on dissonances or not, the various scales have a fundamental mathematical property in common.
Here are some hints from the ScienceDaily article and the paper, respectively.
- John Wheeler (יוחנן רכב)