Tritone

Diabolus in musica

The tritone consists of three whole tones on top of each other. Because of its tense, unstable sound it was often avoided in the Middle Ages; the nickname “diabolus in musica”, the devil in music, is attested only from the 18th century. With the complex ratio 45:32 it lies almost in the middle of the octave (590 instead of 600 cents); only in equal temperament (√2) does it divide it exactly into two equal halves. Its inversion is again a tritone: 6 + 6 make 12 semitones. That makes it the only interval that is symmetrical with itself.

In equal temperament it is the ratio of the square root of two, and there is no common period of the two vibrations. That is why it stays floating and undecided.

The tension point of harmony

Its very tension makes it indispensable. In the dominant seventh chord, say G7 (G–B–D–F), the major third B and the minor seventh F form a tritone. This built-in tension point is the driving force of tonal music: it demands resolution into the tonic, the B pulls to C, the F to E. The article The leading tone explains this.

In jazz and in the music of the 20th century the tritone is used deliberately as a sound of tension.

On the guitar

Six frets apart: if you fret the high E string (329.63 Hz) at the 6th fret, B♭ sounds. The tritone cannot be produced as a simple natural harmonic; its ratio does not lie in the natural harmonic series. It counts as one of the most dissonant intervals and is in a certain sense an “artificial” interval that arises only through the construction of the scale.

Common mistakes

• Confusing the tritone with the fifth: Six instead of seven semitones.
• Dismissing it as mere discord: It is the engine of the cadence.
• Forgetting the name: Depending on the spelling it is called an augmented fourth or a diminished fifth.