Tuesday, February 4, 2014

The Parsimonious Major Tritone Progression

Around ten years ago, I started circulating an idea regarding the association between two major triads a tritone apart and depictions of outer space in recent Hollywood movies. It eventually ended up here. In the article, I noted that the major tritone progression, if voiced with a texture of complete triads and three voices, is tied for last place as the least parsimonious of all triadic progressions. For example, in this texture, one of the voices must leap -- that is, move by more than two semitones.

However, the typical number of voices in common-practice music is four, not three. Moreover, in such four-voice textures, the general preference is to double the root of consonant triads. In this more customary environment, the freakish major tritone progression makes a Disney-style comeback worthy of the most epic of space operas: it is the only progression in four voices in which 1) the chords are complete, 2) the roots are doubled, 3) no voice duplicates any other, and 4) all voices can move by no more than two semitones. For any other four-voice triadic progression that meets the first three conditions, the fourth condition will necessarily not be met.

Next month, I will show how this property relates to some music of Dvořák.