Distance principle
Tone organization from equal-sized intervals, such as whole-tone or minor-third sequences.
What it means
The distance principle is the formation of scales and sonorities from equal-sized intervals. In place of the uneven diatonic order, in which whole tones and semitones alternate in a definite sequence, there is a regular pattern that divides the octave evenly or proceeds in a fixed alternation of two distances. The principle has little in common with modal scales in the sense of the church modes, for it stands precisely opposed to modal and tonal thinking.
Musical use
The simplest examples are known from other entries. The whole-tone scale divides the octave into six equal steps, the augmented triad into three, the diminished seventh chord into four, the tritone into two. In addition come scales that alternate two distances regularly, for instance the sequence of semitone and whole tone, which yields eight notes and is in use in the music of the twentieth century as in jazz.
Common to all distance formations is that they repeat after a few transpositions and single out no note over the others. They therefore lack the gradient on which the tonal cadence rests. From this arises their double use: as a floating tone colour that suspends tonal references, and as a hinge for modulations, because a symmetrical sonority can be resolved in several directions.
In the music of the nineteenth century such formations appear at first as passages within tonal contexts; around 1900 they become independent bases of composition.
In analysis the principle is applied especially to the music of Liszt, Debussy, Bartók, and Messiaen. Messiaen's modes of limited transposition likewise follow the distance principle. Characteristic is that such sonorities have no unambiguous root and therefore seem to float.
Performance practice
Play distance scales evenly and without emphasizing individual notes — any emphasis creates a centre that the scale does not have. Use the repeating pattern for the fingering. And, with symmetrical chords, watch the spelling in the score; it shows in which direction the sonority is to be resolved.