Tritone
Six semitones, an augmented fourth.
What it means
The tritone comprises six semitones, that is, three whole tones — hence the name. It divides the octave exactly in half and is thereby the only interval that stays identical with itself when inverted. Depending on context it is written as an augmented fourth or as a diminished fifth; on tempered instruments both sound the same, but they differ in how they continue.
Musical use
In the diatonic scale it arises between the fourth and the seventh degree. In modal music it was regarded as something to be avoided, and the practice of musica ficta served, among other things, to avoid it; the drastic designation as diabolus in musica comes from the teaching tradition and is to be understood as a mnemonic saying, not as an ecclesiastical prohibition.
With major-minor tonality the problem interval became the motor of harmony. In the dominant seventh chord (D7) the tritone lies between the third and the seventh, and its resolution carries the cadence: the third, as the leading tone, rises to the root, the seventh falls to the third of the tonic. Without it, the dominant would have no unambiguous goal.
Its symmetrical nature makes it ambiguous at the same time. Since it divides the octave evenly, the same sonority can be interpreted differently — remote modulations rest on this, and in jazz the tritone substitution, in which two dominant seventh chords a tritone apart stand in for one another, because they contain the same tritone.
Other names
Diabolus in musica is a historical designation of the tritone. It reflects the difficulty this interval caused in medieval theory. That the tritone was ecclesiastically forbidden is a widespread simplification; in fact it was avoided in composition and circumvented through musica ficta.
Performance practice
Lead the two notes consistently onward — apart in the case of the augmented fourth, together in the case of the diminished fifth; the effect lives on this. When singing, derive the interval from a dominant seventh chord, or think of it as a fourth plus a semitone. And take the leading tone close to its goal.