Distance principle
The distance principle (German Distanzprinzip) denotes the formation of scales and chords from equal-sized intervals. In place of the uneven diatonic order a regular pattern appears that divides the octave evenly or uses two distances in a fixed alternation.
- Principle
- equal distances instead of alternating whole tones and semitones
- Even division of the octave
- 6 (whole tone), 4 (minor third), 3 (major third), 2 (tritone)
- Alternation of two distances
- semitone–whole tone: eight-step scale
- Result
- no centre, no gradient
Equal distances
The diatonic scale, major or minor, lives from the alternation of whole tones and semitones. That makes some notes more important than others: the tonic, the fifth, the leading tone. The distance principle goes the opposite way. You choose a distance and build from it. The results have no centre and no gradient.
Octave in 6 parts: the whole-tone scale
Six equal steps of a whole tone.
Octave in 4 parts: the diminished seventh chord
Three minor thirds on top of each other, the fourth closes back to the octave. On the left C–E♭–F♯–A, on the right E♭–F♯–A–C: the notes are the same, only the lowest changes. The chord repeats after a shift by a minor third.
Octave in 3 parts: the augmented triad
Two major thirds on top of each other, the third closes back to the octave. Here too both chords are rearrangements of the same chord.
Octave in 2 parts: the tritone
Two equal halves. The tritone is the only interval that is its own inversion.
Two distances in alternation: semitone–whole tone
Eight notes per octave, called the octatonic scale in theory. The sequence semitone–whole tone–semitone–whole tone … repeats four times within the octave, each time shifted by a minor third.
In the glossary: Whole-tone scale · Augmented triad · Tritone
Overview
| Formation | Step | Number per octave | Example on C |
|---|---|---|---|
| Whole-tone scale | whole tone | 6 | C D E F♯ G♯ A♯ |
| Diminished seventh chord | minor third | 4 | C E♭ F♯ A |
| Augmented triad | major third | 3 | C E G♯ |
| Tritone | augmented fourth | 2 | C F♯ |
| Half-whole scale | ½ and 1 alternating | 8 notes | C D♭ E♭ E F♯ G A B♭ |
What all distance formations share is that they repeat after a few shifts. There are only two forms of the whole-tone scale, three of the diminished seventh chord, four of the augmented triad. In addition they lack the gradient on which the tonal cadence rests. From this follows their double use: as a floating tone colour that suspends tonal relations, and as a hinge for modulations, because a symmetrical chord can resolve in several directions (see Harmonic ambiguity).
A basis in its own right since 1900
In the 19th century such formations appear at first as a passing event within tonal contexts. Around 1900 they become independent foundations 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: they consist of symmetrical groups and can be transposed only a few times before they repeat. The half-whole scale is also widespread in jazz.
The principle has little in common with the church modes: it is directly opposed to modal and tonal thinking.
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Related terms
Whole-tone scaleAugmented triadDiminished seventh chordTritoneHarmonic ambiguityImpressionismScale
Editor: Maik Krohm · reviewed on 3 October 2026
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