  The perception of consonance/dissonance of musical harmonies is strongly
correlated with their periodicity. This is shown in this article by
consistently applying recent results from psychophysics and neuroacoustics,
namely that the just noticeable difference between pitches for humans is about
1% for the musically important low frequency range and that periodicities of
complex chords can be detected in the human brain. Based thereon, the concepts
of relative and logarithmic periodicity with smoothing are introduced as
powerful measures of harmoniousness. The presented results correlate
significantly with empirical investigations on the perception of chords. Even
for scales, plausible results are obtained. For example, all classical church
modes appear in the front ranks of all theoretically possible seven-tone
scales.
