Tritone Explained

In music theory, a tritone is a musical interval spanning three whole tones.^[1] 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.^[2]

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."^[3]

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).^[4]

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.^[5] 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:

Notes and References

1. Web site: Drabkin . William . Tritone . . August 31, 2020 . 10.1093/gmo/9781561592630.article.28403 . 20 January 2001 . 978-1-56159-263-0 . limited.
2. https://books.google.com/books?id=02rFSecPhEsC&q=%22A+prominent+element%22 Randel (2003), p. 911
3. Book: Smith Brindle , Reginald . Reginald Smith Brindle. Serial Composition. Oxford University Press. 1966. 0-19-311906-4. 66 .
4. Bruce Benward & Marilyn Nadine Saker (2003). Music: In Theory and Practice, Vol. I, seventh edition (Boston: McGraw-Hill), p. 54. .
5. E.g., Jacobus_Leodiensis, Speculum musicae, Liber secundus, in Jacobi Leodiensis Speculum musicae, edited by Roger Bragard, Corpus Scriptorum de Musica 3/2 ([Rome]: American_Institute_of_Musicology, 1961): 128–31, citations on 192–96, 200, and 229; Jacobus Leodiensis, Speculum musicae, Liber sextus, in Jacobi Leodiensis Speculum musicae, edited by Roger Bragard, Corpus Scriptorum de Musica 3/6 ([Rome]: American_Institute_of_Musicology, 1973): 1–161, citations on 52 and 68; Johannes Torkesey, Declaratio et expositio, London: British Library, Lansdowne MS 763, ff.89v-94v, citations on f.92r,2–3; Prosdocimus_de_Beldemandis, Tractatus musice speculative, in D. Raffaello Baralli and Luigi Torri, "Il Trattato di Prosdocimo de' Beldomandi contro il Lucidario di Marchetto da Padova per la prima volta trascritto e illustrato", Rivista Musicale Italiana 20 (1913): 731–62, citations on 732–34.