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
Famous quotes containing the words augmented, fourth and/or diminished:
“Another success is the post-office, with its educating energy augmented by cheapness and guarded by a certain religious sentiment in mankind; so that the power of a wafer or a drop of wax or gluten to guard a letter, as it flies over sea over land and comes to its address as if a battalion of artillery brought it, I look upon as a fine meter of civilization.”
—Ralph Waldo Emerson (1803–1882)
“‘Tis said of love that it sometimes goes, sometimes flies; runs with one, walks gravely with another; turns a third into ice, and sets a fourth in a flame: it wounds one, another it kills: like lightning it begins and ends in the same moment: it makes that fort yield at night which it besieged but in the morning; for there is no force able to resist it.”
—Miguel De Cervantes (1547–1616)
“As I went forth early on a still and frosty morning, the trees looked like airy creatures of darkness caught napping; on this side huddled together, with their gray hairs streaming, in a secluded valley which the sun had not penetrated; on that, hurrying off in Indian file along some watercourse, while the shrubs and grasses, like elves and fairies of the night, sought to hide their diminished heads in the snow.”
—Henry David Thoreau (1817–1862)