Augmented fourth and diminished fifth
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. (January 2017)
Full ascending and descending chromatic scale on C, with tritone above each pitch. Pairs of tritones that are inversions
of each other are marked below.
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.
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 twelve-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 and have different diatonic functions within music theory.