Philosophical and Logical Aspects of Harmony in Music
Harmony in music can be characterized by fitting / joining together of chords or their agreement, concord etc. I will deal with harmony which is internal with respect to our well-known chromatic scale represented by an infinite line of integers. Internal harmony is nothing more than the pure interrelatedness of two or more chords. From a logical point of view we try to develop a formal theory of all the possibilities combining chords. From a philosophical point of view we look for a holistic understanding of harmony which cannot be based on any theoretical approach. In the first case we have to indicate invariant chord patterns and to formulate exact rules to modify them. In the second case we try to understand concrete patterns in the specific context of compositions created by composers. There are cases of harmony which we can describe as activities of following rules without any philosophical hope to make an underlying codex (a set of fixed rules) explicit. During the talk I will play and use some musical examples.
The first thesis of my presentation is that a concrete logic of harmony is possible. The second thesis is that a formal theory of harmony can neither be extended to a philosophy of harmony in the sense of grasping all the characteristic individual cases of harmony in musical compositions. Is there any chance to unify the logical and the philosophical approaches to harmony? The philosophical answer of the late Wittgenstein is: family resemblances. This is an approach to overcome the dichotomy between logical and misguided philosophical investigations.