Perfect fifth
From Wikipedia, the free encyclopedia
| Inverse | perfect fourth | |
|---|---|---|
| Name | ||
| Other names | diapente | |
| Abbreviation | P5 | |
| Size | ||
| Semitones | 7 | |
| Interval class | 5 | |
| Just interval | 3:2 | |
| Cents | ||
| Equal temperament | 700 | |
| Just intonation | 702 | |
The perfect fifth is the musical interval between a note and the note seven semitones above it on the musical scale. For example, the note G lies a perfect fifth above C; D is a perfect fifth above G, C is a perfect fifth above F, and so on.
The term perfect identifies it as belonging to the group of perfect intervals (perfect fourth, perfect octave) so called because of their simple pitch relationships and their high degree of consonance.[1] There are two other kinds of fifths: the diminished fifth, which is one chromatic semitone smaller, and the augmented fifth, which is one chromatic semitone larger.
The perfect fifth is occasionally referred to as the diapente, and abbreviated P5. Its inversion is the perfect fourth.
The perfect fifth is an important interval in tonal music. It is more consonant, or stable, than any other interval except the unison and the octave. It is a valuable interval in chord structure, song development, and western tuning systems. It occurs on the root of all major and minor chords (triads) and their extensions. It was the first accepted harmony (besides the octave) in Gregorian chant, a very early formal style of musical composition.
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[edit] Hearing perfect fifths
There are various ways to train the ear to recognize a perfect fifth. One is to sing the first five notes of the major scale in solfege: do re mi fa sol; the first and last notes form a perfect fifth. Another is to sing the first four notes of the familiar tune Twinkle, Twinkle, Little Star, which likewise outline a perfect fifth. On a piano keyboard, a perfect fifth can be approximated by holding down two notes, one of which is the seventh note higher than the base note.[2]
[edit] The pitch ratio of a perfect fifth
The idealized pitch ratio of a perfect fifth is 3:2, meaning that the upper note makes three vibrations in the same amount of time that the lower note makes two. In the cent system of pitch measurement, the 3:2 ratio corresponds to approximately 702 cents. Something close to the idealized perfect fifth can be heard when a violin is tuned: if adjacent strings are adjusted to the exact ratio of 3:2, the result is a smooth and consonant sound, and the violin is felt to be "in tune". Idealized perfect fifths are employed in just intonation.
In keyboard instruments such as the piano, a slightly different version of the perfect fifth is normally used: in accordance with the principle of equal temperament, the perfect fifth must be slightly narrowed: seven semitones, or 700 cents. (The narrowing is necessary to enable the instrument to play in all keys.) Many people can hear the slight deviation from the idealized perfect fifth when they play the interval on a piano.
The following sound file illustrates the perfect fifth in equal temperament. In this recording, the interval displays quite noticeable "beats" (pulsations), which result from the 700-cent interval.
Perfect fifth (equal temperament)
[edit] Use in harmony
The perfect fifth is a basic element in the construction of major and minor triads, and because these chords occur frequently in much music, the perfect fifth interval occurs just as often. However, because many instruments contain a perfect fifth as an overtone, it is not unusual to omit the fifth of a chord (esp. in root position) since it is already present due to this overtone.
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.
One can also build chords 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 Trumpets, a Piccolo Trumpet, and one Horn play a five-tone B-Flat quintal chord.[3]
A bare fifth, open fifth or empty fifth is a chord containing only a perfect fifth with no third. The closing chord of the Kyrie in Mozart's Requiem and of the first movement of Bruckner's Ninth Symphony are both examples of pieces ending on an empty fifth, though these "chords" are common in Sacred Harp singing and throughout rock music, especially hard rock, metal, and punk music, where overdriven or distorted guitar can make thirds sound muddy, and fast chord-based passages are made easier to play by combining the four most common guitar hand shapes into one. Rock musicians refer to them as power chords and often include octave doubling (i.e. their bass note is doubled one octave higher, e.g. F3-C4-F4).
An empty fifth is sometimes used in traditional music, e.g. in some Andean music genres of pre-Columbian origin, such as k'antu, tarqueada and sikuri. The same melody is being led by parallel fifths and octaves during all the piece. Hear examples: K'antu, Pacha Siku.
[edit] Use in tuning and tonal systems
A perfect fifth in just intonation, a just fifth, corresponds to a frequency ratio of 3:2, while in 12-tone equal temperament, a perfect fifth is equal to seven semitones, or 700 cents, about two cents smaller than the just fifth.
The just perfect fifth, together with the octave, forms the basis of Pythagorean tuning. A flattened perfect fifth is likewise the basis for meantone tuning.
The circle of fifths is a model of pitch space for the chromatic scale (chromatic circle) which considers nearness not as adjacency but as the number of perfect fifths required to get from one note to another.
[edit] Notes
- ^ For instance, Piston and DeVoto's harmony text (1987, 15) classifies octaves, perfect intervals, thirds, and sixths as being "consonant intervals", but qualifies the thirds and sixths as "imperfect consonances".
- ^ However, since pianos are tuned with equal temperament, the interval sounded will be a tiny amount narrower than the mathematically pure 3:2 ratio of the ideal perfect fifth.
- ^ For more examples and discussion of quintal harmony, see Piston and DeVoto (1987, 503-505).
[edit] References
- Piston, Walter and Mak DeVoto (1987) Harmony. 5th ed. New York: Norton.
[edit] See also
- Musical tuning
- diminished fifth
- Power chord
- dominant — a perfect fifth above the tonic
- All fifths
- Circle of fifths
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