"Ricardo M. Forno" wrote: snip
... the rules of harmony, which are simple and verifiable by anyone. A fifth, a major third, a fourth, a minor third, etc. are all consonant because the the frequencies ratios are fractions composed of small numbers and so they generate less interference sounds (it is more complex than that
\snip In fact the rules of harmony are quite mutable, and are largely a matter of taste, and what we are used to (try listening to Middle Eastern or Asian music sometime). The ancient Greeks, for instance, regarded the octave as the only acceptable harmony. In mediaeval times, the perfect fifth, then later the fourth, were allowed, and it's only quite recently that the major and minor thirds, major and minor sevenths, augmented and diminished fifths, etc, have been judged to be harmonic. Each time a musician tries harmonising with a new interval, it is at first regarded as dissonant, then finally accepted as a harmony and included in the relevant textbooks as a harmonic interval (thus becoming no longer quite so interesting). Regards, David