Consonance and dissonance

In music, consonance and dissonance form a structural dichotomy in which the terms define each other by mutual exclusion: a consonance is what is not dissonant, and reciprocally. However, a finer consideration shows that the distinction forms a gradation, from the most consonant to the most dissonant. Consonance and dissonance define a level of sweetness / harshness, pleasantness / unpleasantness, acceptability / unacceptability, of the sounds or intervals under consideration. As Hindemith stressed, "The two concepts have never been completely explained, and for a thousand years the definitions have varied" (Hindemith 1942, p. 85).