Tritone

6 semitones — exactly half an octave, maximum instability

Degree ♯4Solfège: triNotation: d5

The tritone is an interval of 6 semitones — exactly half an octave — also called the augmented 4th (♯4), diminished 5th (♭5), or "the devil's interval". It is the most dissonant of the simple intervals: restless and unstable, and the only interval that inverts to itself. It is the signature interval of lydian (♯4) and locrian (♭5), and the defining tension of the dominant 7th chord (between its 3rd and ♭7), which drives the V–I resolution underpinning much of Western harmony.

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The instrumentTap a note to hear it.
The tritone in the harmonic series
f2f3f4f5f5f completes 5 cycles in one period of the sum5 cycles6f7f7f completes 7 cycles in one period of the sum7 cycles8f9f10f11f12f13f14f15f16fsum7:5 — the higher note vibrates 7 times for every 5 of the lower: harmonics 7 and 5 of one fundamental7:517¢ — this pure ratio is 17 cents narrower than the equal-tempered tritone an instrument plays; a semitone is 100 cents−17¢♯4: the tritone — the interval's degree above the root, as the app writes it♯4The sum repeats every 5 cycles of 5f — the shorter this is, the more simply the two notes fit together, and the more consonant the intervalrepeats every 5 cycles16 cycles of 5f
Harmonic seriesEach row is one harmonic of the note — n times the fundamental's frequency, about 1/n of its strength — faster and fainter as it climbs. The rows in ink are where the chosen interval first arises. The bottom row is the one your ear actually receives: those rows added, a single wave. The shaded band is one repeat of it — the shorter that pattern, the sooner the ear settles on it as one sound. Harmonics 5 and 7 — the ratio 7:5: a tritone. Together they repeat every 5 cycles of the lower note — the shorter that pattern, the sooner your ear has heard it come round enough times to settle on one sound. Equal temperament tunes it 17¢ wider. 7:5 is the tritone of a dominant seventh chord — its 3rd against its ♭7th, harmonics 5 and 7 of the root — and the smoothest face the series has for it. The interval is its own upside down: six semitones up and six more make the octave, so neither note points at the other as home, and it sits one semitone from the fifth on one side and the fourth on the other. How harsh it sounds is therefore a question about the music around it, not about the pair — why the tritone is the ambiguous one →

Related

Contained byIntervalsRelatedSolfègeDominant 7thLydianLocrianDissonance