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 and narrowing by one chromatic semitone the perfect fourth and fifth, respectively. 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.
Read more about this topic: Tri-tone
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