Interval Dichotomies as an Expression of Contrast

Summary

For contrapuntal composition and theory, consonant and dissonant intervals are a dichotomic concept. We present the mathematical restatement and fundamental properties of the basic concept of an interval dichotomy. For the classification of dichotomies, a strong condition on unique symmetries of polarity between the two halves of dichotomies is added. It reveals a distinguished role of the consonance/dissonance dichotomy of classical counterpoint and of the major dichotomy (associated with the major scale).We discuss evidence of the consonance/dissonance dichotomy from theoretical and empirical points of view and open the discourse to an intercultural perspective guided by the classification of dichotomies, as investigated by Jens Hichert [466].

enim vero sicut vitium mala virtus a nullo umquam morali philosopho dictum fuit, ita nec musicus umquam litteratus discordiantiam malam concordantiam nuncupavit.

Johannes Tinctoris [1053, p.90]