In music theory, a tritone is a musical interval spanning three whole tones. For instance, the interval from F to the B above it (in short, F–B) is a tritone as it can be decomposed into the three adjacent whole tones F–G, G–A, and A–B.
In 12-tone-equal temperament, the tritone divides the octave (which is 12 semitones or 1200 cents) exactly in half, making it six semitones, or 600 cents. In traditional functional harmony, the tritone is a harmonic and melodic dissonance and tritones in chords push toward resolution. For instance, the tritone(s) found in diminished triads as well as the dominant, half-diminished, and fully diminished seventh chords push toward resolution to the tonic. On the other hand, the tritone can also be used to avoid tonality altogether, as composer Reginald Smith Brindle explains: "Any tendency for a tonality to emerge may be avoided by introducing a note three whole tones distant from the key note of that tonality."
Definition A tritone is composed of three whole tones. There are two possible interpretations of this, a narrow definition and a broad definition. Under the narrow definition, only augmented fourths (often abbreviated as A4) are considered tritones, while under the broad definition, augmented fourths and diminished fifths (d5)—as well as rarer intervals like doubly augmented thirds and a doubly diminished sixths—are all considered tritones. The augmented fourth is the interval produced by widening the perfect fourth by one semitone (without changing either letter name), while the diminished fifth is produced by narrowing the perfect fifth by one semitone (without changing either letter name). Under the narrow definition, each of the three whole tones that compose a tritone must be a diatonic step, so only the interval of an augmented fourth is considered a tritone. By this definition, within a diatonic scale (such as a major scale) there is only one tritone per octave. For instance, in the C major scale, the augmented fourth F–B is the only tritone because it is composed of three major seconds (F–G, G–A, and A–B), while its inversion, the diminished fifth B–F, is not considered a tritone because three major seconds above B is E♯, not F.
Under the broad definition, however, a tritone may include any interval spanning six semitones, regardless of scale degree. According to this definition, a diatonic scale contains two tritones for each octave. For instance, the C major scale contains the tritones, F–B and B–F. With this broad definition, a tritone can typically be classified as either an augmented fourth or a diminished fifth, though far rarer spellings of the notes in a tritone may be classified as a doubly augmented third, a doubly diminished sixth, etc.
Dissonance and expressiveness Ján Haluska wrote: The unstable character of the tritone sets it apart, as discussed in [Paul Hindemith. The Craft of Musical Composition, Book I. Associated Music Publishers, New York, 1945]. It can be expressed as a ratio by compounding suitable superparticular ratios. Whether it is assigned the ratio 64/45 or 45/32, depending on the musical context, or indeed some other ratio, it is not superparticular, which is in keeping with its unique role in music. Harry Partch has written:
Although this ratio [45/32] is composed of numbers which are multiples of 5 or under, they are excessively large for a 5-limit scale, and are sufficient justification, either in this form or as the tempered "tritone", for the epithet "diabolic", which has been used to characterize the interval. This is a case where, because of the largeness of the numbers, none but a temperament-perverted ear could possibly prefer 45/32 to a small-number interval of about the same width.
In the Pythagorean ratio 81/64 both numbers are multiples of 3 or under, yet because of their excessive largeness the ear certainly prefers 5/4 for this approximate degree, even though it involves a prime number higher than 3. In the case of the 45/32 "tritone" our theorists have gone around their elbows to reach their thumbs, which could have been reached simply and directly and non-"diabolically" via the number 7....
In tonal music
In major and minor scales In major scales, there is an augmented fourth between the fourth and seventh scale degrees (e.g., F–B in C major).
In natural minor scales, there is a diminished fifth between the second and sixth scale degrees (e.g., D–A♭ in C minor).
In harmonic minor scales, there is a diminished fifth between the second and sixth scale degrees and an augmented fourth between the fourth and seventh scale degrees (e.g., D–A♭ and F–B, respectively, in C minor).
Melodic minor scales, having two forms, contain tritones in different places when ascending and descending. When ascending, there are augmented fourths between the third and sixth scale degrees and between the fourth and seventh scale degrees (e.g., E♭–A and F–B, respectively, in C minor). When descending, there is a diminished fifth between the second and sixth scale degrees (e.g., D–A♭ in C minor).
Supertonic chords using the notes from the natural minor mode thus contain a tritone, regardless of inversion. Containing tritones, these scales are referred to as tritonic. A scale without tritones is called atritonic.
In tonal harmony Dominant seventh chords contain a diminished fifth (tritone) between their third and seventh chord factors. Diminished triads also contains a tritone in their construction between their root and fifth. Half-diminished seventh chords contain the same tritone, while fully diminished seventh chords are composed of two superposed tritones a minor third apart. Other chords built on these, such as ninth chords, often include tritones as diminished fifths. In addition, augmented sixth chords contain tritones spelled as augmented fourths. The Italian and German sixth chords each contain one augmented fourth, while the French sixth chord is composed of two superposed augmented fourths a major second apart. In traditional functional harmony, the tritone(s) in all of the chords described above push towards resolution, generally resolving by step in contrary motion. This determines the resolution of chords containing tritones; that is, augmented fourths resolve outward to a minor or major sixth (the first measure below), while diminished fifths resolve inward to a major or minor third (the second measure below).
Historical uses
Classical music
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