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In music theory, a perfect fifth is the musical interval corresponding to a pair of pitches with a frequency ratio of 3:2, or very nearly so.
In classical music from Western culture, a fifth is the interval from the first to the last of the first five consecutive Musical note in a diatonic scale.Don Michael Randel (2003), "Interval", Harvard Dictionary of Music, fourth edition (Cambridge, Massachusetts: Harvard University Press): p. 413. The perfect fifth (often abbreviated P5) spans seven , while the Tritone spans six and the augmented fifth spans eight semitones. For example, the interval from C to G is a perfect fifth, as the note G lies seven semitones above C.
The perfect fifth may be derived from the harmonic series as the interval between the second and third harmonics. In a diatonic scale, the dominant note is a perfect fifth above the tonic note.
The perfect fifth is more consonant, or stable, than any other interval except the unison and the octave. It occurs above the root of all Major chord and Minor chord chords (triads) and their extended chords. Until the late 19th century, it was often referred to by one of its Greek names, diapente. Its inversion is the perfect fourth. The octave of the fifth is the twelfth.
A perfect fifth is at the start of "Twinkle, Twinkle, Little Star"; the pitch of the first "twinkle" is the root note and the pitch of the second "twinkle" is a perfect fifth above it.
Perfect intervals are also defined as those natural intervals whose inversions are also natural, where natural, as opposed to altered, designates those intervals between a base note and another note in the major diatonic scale starting at that base note (for example, the intervals from C to C, D, E, F, G, A, B, C, with no sharps or flats); this definition leads to the perfect intervals being only the unison, perfect fourth, fifth, and octave, without appealing to degrees of consonance.
The term perfect has also been used as a synonym of just interval, to distinguish intervals tuned to ratios of small integers from those that are "tempered" or "imperfect" in various other tuning systems, such as equal temperament. The perfect unison has a interval ratio 1:1, the perfect octave 2:1, the perfect fourth 4:3, and the perfect fifth 3:2.
Within this definition, other intervals may also be called perfect, for example a perfect third (5:4) or a perfect major sixth (5:3).
Keyboard instruments such as the piano normally use an equal-tempered version of the perfect fifth, enabling the instrument to play in all keys. In 12-tone equal temperament, the frequencies of the tempered perfect fifth are in the ratio or approximately 1.498307. An equally tempered perfect fifth, defined as 700 cents, is about two cents narrower than a just perfect fifth, which is approximately 701.955 cents.
Johannes Kepler explored musical tuning in terms of integer ratios, and defined a "lower imperfect fifth" as a 40:27 pitch ratio, and a "greater imperfect fifth" as a 243:160 pitch ratio. His lower perfect fifth ratio of 1.48148 (680 cents) is much more "imperfect" than the equal temperament tuning (700 cents) of 1.4983 (relative to the ideal 1.50). Hermann von Helmholtz uses the ratio 301:200 (708 cents) as an example of an imperfect fifth; he contrasts the ratio of a fifth in equal temperament (700 cents) with a "perfect fifth" (3:2), and discusses the audibility of the beats that result from such an "imperfect" tuning.
The perfect fifth is a basic element in the construction of major and minor triads, and their extended chords. Because these chords occur frequently in much music, the perfect fifth occurs just as often. However, since many instruments contain a perfect fifth as an overtone, it is not unusual to omit the fifth of a chord (especially in root position).
The perfect fifth is also present in seventh chords as well as "tall tertian" harmonies (harmonies consisting of more than four tones stacked in thirds above the root). The presence of a perfect fifth can in fact soften the dissonant intervals of these chords, as in the major seventh chord in which the dissonance of a major seventh is softened by the presence of two perfect fifths.
Chords can also be built by stacking fifths, yielding quintal harmonies. Such harmonies are present in more modern music, such as the music of Paul Hindemith. This harmony also appears in Stravinsky's The Rite of Spring in the "Dance of the Adolescents" where four C , a piccolo trumpet, and one French horn play a five-tone B-flat quintal chord.
An empty fifth is sometimes used in traditional music, e.g., in Asian music and in some Andean music genres of pre-Columbian origin, such as k'antu and sikuri. The same melody is being led by parallel fifths and octaves during all the piece.
Western composers may use the interval to give a passage an exotic flavor.Scott Miller, " Inside The King and I", New Line Theatre, accessed December 28, 2012 Empty fifths are also sometimes used to give a cadence an ambiguous quality, as the bare fifth does not indicate a major or minor tonality.
The circle of fifths is a model of pitch space for the chromatic scale (chromatic circle), which considers nearness as the number of perfect fifths required to get from one note to another, rather than chromatic adjacency.
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