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familiar tune

Perfect fifth

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, octave) so called because of their simple pitch relationships and their high degree of consonance. Perfect intervals are also defined as those natural intervals whose inversions are also natural intervals, where natural, as opposed to altered, designates those intervals between a base note and the major diatonic scale starting at that 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, fourth, fifth, and octave, without appealing to degrees of consonance.

In addition to perfect, 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. In terms of semitones, these are equivalent to the tritone (or augmented fourth), and the minor sixth, respectively.

The perfect fifth is occasionally referred to as the diapente, and abbreviated P5. Its inversion is the perfect fourth.

The term perfect has also been used to distinguish intervals tuned to ratios of small integers from those that are "tempered" or "imperfect" in various other tunings such as equal temperament. The perfect unison is 1:1, the perfect octave is 2:1, the perfect fourth is 4:3, and the perfect fifth is 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).

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.

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. Additionally, the opening of Richard Strauss's Also Sprach Zarathustra (used in Stanley Kubrick's 2001: A Space Odyssey) and the Wicked Witch of the West's Soldiers' March (Oh-Ee-Oh-Yo-Oh-Yo!) in Harold Arlen's The Wizard of Oz prominently feature the interval. On a piano keyboard, a perfect fifth of equal temperament can be sounded by holding down two notes, one of which is the seventh note higher than the base note.

The pitch ratio of a 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, or 2% of a semitone sharper than seven semitones. 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.

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 1.4815 (680 cents) is much more "imperfect" than the equal temperament tuning (700 cents) of 1.498 (relative to the ideal 1.50). 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.

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.

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.

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: , .

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.

Notes

References

  • Piston, Walter and Mak DeVoto (1987) Harmony. 5th ed. New York: Norton.

See also

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