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Augmented fourth : ウィキペディア英語版
Tritone

In music theory, the tritone is strictly defined as a musical interval composed of three adjacent whole tones.〔Don Michael Randel (2003). The Harvard Dictionary of Music: Fourth Edition. Harvard University Press. (ISBN 0-674-01163-5 ).〕 For instance, the interval from F up 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. According to this definition, within a diatonic scale there is only one tritone for each octave. For instance, the above-mentioned interval F–B is the only tritone formed from the notes of the C major scale. A tritone is also commonly defined as an interval spanning six semitones. According to this definition, a diatonic scale contains two tritones for each octave. For instance, the above-mentioned C major scale contains the tritones F–B (from F to the B above it, also called augmented fourth) and B–F (from B to the F above it, also called diminished fifth, semidiapente, or semitritonus).〔E.g., Jacobus Leodiensis, ''Speculum musicae'', Liber secundus, in ''Jacobi Leodiensis Speculum musicae'', edited by Roger Bragard, Corpus Scriptorum de Musica 3/2 ((): 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 ((): American Institute of Musicology, 1973): 1-161, citations on 52 and 68; Johannes Torkesey, ''Declaratio et expositio'', London: British Library, Lansdowne 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.〕
In classical music, the tritone is a harmonic and melodic dissonance and is important in the study of musical harmony. The tritone can be used to avoid traditional tonality: "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."〔
〕 Contrarily, the tritone found in the dominant seventh chord helps establish the tonality of a composition. These contrasting uses exhibit the flexibility, ubiquity, and distinctness of the tritone in music.
The condition of having tritones is called tritonia; that of having no tritones is atritonia. A musical scale or chord containing tritones is called tritonic; one without tritones is atritonic.
== Augmented fourth and diminished fifth ==

Since a chromatic scale is formed by 12 pitches (each a semitone apart from its neighbors), it contains 12 distinct tritones, each starting from a different pitch and spanning six semitones. According to a complex but widely used naming convention, six of them are classified as ''augmented fourths'', and the other six as ''diminished fifths''.
Under that convention, a ''fourth'' is an interval encompassing four staff positions, while a ''fifth'' encompasses five staff positions (see interval number for more details).
The augmented fourth (''A4'') and diminished fifth (''d5'') are defined as the intervals produced by widening the perfect fourth and narrowing the perfect fifth by one chromatic semitone.〔Bruce Benward & Marilyn Nadine Saker (2003). ''Music: In Theory and Practice, Vol. I'', seventh edition (Boston: McGraw-Hill), p. 54. ISBN 978-0-07-294262-0.〕
They both span six semitones, and they are the inverse of each other, meaning that their sum is exactly equal to one perfect octave (A4 + d5 = P8).
In 12-tone equal temperament, the most commonly used tuning system, the A4 is equivalent to a d5, as both have the size of exactly half an octave. In most other tuning systems, they are not equivalent, and neither is exactly equal to half an octave.
Any augmented fourth can be decomposed into three whole tones. For instance, the interval F–B is an augmented fourth and can be decomposed into the three adjacent whole tones F–G, G–A, and A–B.
It is not possible to decompose a diminished fifth into three adjacent whole tones. The reason is that a whole tone is a major second, and according to a rule explained elsewhere, the composition of three seconds is always a fourth (for instance, an A4). To obtain a fifth (for instance, a d5), it is necessary to add another second. For instance, using the notes of the C major scale, the diminished fifth B–F can be decomposed into the four adjacent intervals
:B–C (minor second), C–D (major second), D–E (major second), and E–F (minor second).
Using the notes of a chromatic scale, B–F may be also decomposed into the four adjacent intervals
:B–C (major second), C–D (major second), D–E (major second), and E–F (diminished second).
Notice that the latter diminished second is formed by two enharmonically equivalent notes (E and F). On a piano keyboard, these notes are produced by the same key. However, in the above-mentioned naming convention, they are considered different notes, as they are written on different staff positions.

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