Perfect fifth
Encyclopedia
Classical music
Classical music is the art music produced in, or rooted in, the traditions of Western liturgical and secular music, encompassing a broad period from roughly the 11th century to present times...
from Western culture
Western culture
Western culture, sometimes equated with Western civilization or European civilization, refers to cultures of European origin and is used very broadly to refer to a heritage of social norms, ethical values, traditional customs, religious beliefs, political systems, and specific artifacts and...
, a fifth is a musical interval encompassing five staff positions (see Interval (music)#Number for more details), and the perfect fifth is a fifth spanning seven semitone
Semitone
A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically....
s, or in meantone
Meantone temperament
Meantone temperament is a musical temperament, which is a system of musical tuning. In general, a meantone is constructed the same way as Pythagorean tuning, as a stack of perfect fifths, but in meantone, each fifth is narrow compared to the ratio 27/12:1 in 12 equal temperament, the opposite of...
, four diatonic semitones and three chromatic semitones. For example, the interval from C to G is a perfect fifth, as the note G lies seven semitones above C, and there are five staff positions from C to G. Diminished and augmented fifth
Augmented fifth
In classical music from Western culture, an augmented fifth is an interval produced by widening a perfect fifth by a chromatic semitone. For instance, the interval from C to G is a perfect fifth, seven semitones wide, and both the intervals from C to G, and from C to G are augmented fifths,...
s span the same number of staff positions, but consist of a different number of semitones (six and eight).
The perfect fifth may be derived from the harmonic series
Harmonic series (music)
Pitched musical instruments are often based on an approximate harmonic oscillator such as a string or a column of air, which oscillates at numerous frequencies simultaneously. At these resonant frequencies, waves travel in both directions along the string or air column, reinforcing and canceling...
as the interval between the second and third harmonics. In a diatonic scale
Diatonic scale
In music theory, a diatonic scale is a seven note, octave-repeating musical scale comprising five whole steps and two half steps for each octave, in which the two half steps are separated from each other by either two or three whole steps...
, the dominant
Dominant (music)
In music, the dominant is the fifth scale degree of the diatonic scale, called "dominant" because it is next in importance to the tonic,and a dominant chord is any chord built upon that pitch, using the notes of the same diatonic scale...
note is a perfect fifth above the tonic
Tonic (music)
In music, the tonic is the first scale degree of the diatonic scale and the tonal center or final resolution tone. The triad formed on the tonic note, the tonic chord, is thus the most significant chord...
note.
The perfect fifth is more consonant
Consonance and dissonance
In music, a consonance is a harmony, chord, or interval considered stable, as opposed to a dissonance , which is considered to be unstable...
, or stable, than any other interval except the unison
Unison
In music, the word unison can be applied in more than one way. In general terms, it may refer to two notes sounding the same pitch, often but not always at the same time; or to the same musical voice being sounded by several voices or instruments together, either at the same pitch or at a distance...
and the octave
Octave
In music, an octave is the interval between one musical pitch and another with half or double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems"...
. It occurs above the root
Root (chord)
In music theory, the root of a chord is the note or pitch upon which a triadic chord is built. For example, the root of the major triad C-E-G is C....
of all major
Major chord
In music theory, a major chord is a chord having a root, a major third, and a perfect fifth. When a chord has these three notes alone, it is called a major triad...
and minor
Minor chord
In music theory, a minor chord is a chord having a root, a minor third, and a perfect fifth.When a chord has these three notes alone, it is called a minor triad....
chords (triads) and their extensions. Up until the late 19th century it was often referred to by its Greek name, diapente, and abbreviated P5. Its inversion
Inversion (music)
In music theory, the word inversion has several meanings. There are inverted chords, inverted melodies, inverted intervals, and inverted voices...
is the perfect fourth
Perfect fourth
In classical music from Western culture, a fourth is a musical interval encompassing four staff positions , and the perfect fourth is a fourth spanning five semitones. For example, the ascending interval from C to the next F is a perfect fourth, as the note F lies five semitones above C, and there...
.
Alternative definitions
The term perfect identifies the perfect fifth as belonging to the group of perfect intervals (including the unisonUnison
In music, the word unison can be applied in more than one way. In general terms, it may refer to two notes sounding the same pitch, often but not always at the same time; or to the same musical voice being sounded by several voices or instruments together, either at the same pitch or at a distance...
, perfect fourth
Perfect fourth
In classical music from Western culture, a fourth is a musical interval encompassing four staff positions , and the perfect fourth is a fourth spanning five semitones. For example, the ascending interval from C to the next F is a perfect fourth, as the note F lies five semitones above C, and there...
and octave
Octave
In music, an octave is the interval between one musical pitch and another with half or double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems"...
), so called because of their simple pitch relationships and their high degree of consonance
Consonance and dissonance
In music, a consonance is a harmony, chord, or interval considered stable, as opposed to a dissonance , which is considered to be unstable...
. Note that this interpretation of the term is not in all contexts compatible with the definition of perfect fifth given in the introduction. In fact, when an instrument is tuned using Pythagorean tuning
Pythagorean tuning
Pythagorean tuning is a system of musical tuning in which the frequency relationships of all intervals are based on the ratio 3:2. This interval is chosen because it is one of the most consonant...
or meantone temperament
Meantone temperament
Meantone temperament is a musical temperament, which is a system of musical tuning. In general, a meantone is constructed the same way as Pythagorean tuning, as a stack of perfect fifths, but in meantone, each fifth is narrow compared to the ratio 27/12:1 in 12 equal temperament, the opposite of...
, one of the twelve fifths (the wolf fifth
Wolf interval
In music theory, the wolf fifth is a particularly dissonant musical interval spanning seven semitones. Strictly, the term refers to an interval produced by a specific tuning system, widely used in the sixteenth and seventeenth centuries: the quarter-comma meantone temperament...
) sounds severely dissonant and can hardly be qualified as "perfect", if this term is interpreted as "highly consonant". However, when using correct enharmonic
Enharmonic
In modern musical notation and tuning, an enharmonic equivalent is a note , interval , or key signature which is equivalent to some other note, interval, or key signature, but "spelled", or named, differently...
spelling, the wolf fifth in Pythagorean tuning or meantone temperament is actually not a perfect fifth but a diminished sixth
Diminished sixth
In classical music from Western culture, a diminished sixth is an interval produced by narrowing a minor sixth by a chromatic semitone. For example, the interval from A to F is a minor sixth, eight semitones wide, and both the intervals from A to F, and from A to F are diminished sixths, spanning...
(for instance G–E).
Perfect intervals are also defined as those natural intervals whose inversions
Inversion (music)
In music theory, the word inversion has several meanings. There are inverted chords, inverted melodies, inverted intervals, and inverted voices...
are also perfect, 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
Unison
In music, the word unison can be applied in more than one way. In general terms, it may refer to two notes sounding the same pitch, often but not always at the same time; or to the same musical voice being sounded by several voices or instruments together, either at the same pitch or at a distance...
, fourth
Perfect fourth
In classical music from Western culture, a fourth is a musical interval encompassing four staff positions , and the perfect fourth is a fourth spanning five semitones. For example, the ascending interval from C to the next F is a perfect fourth, as the note F lies five semitones above C, and there...
, fifth, and octave
Octave
In music, an octave is the interval between one musical pitch and another with half or double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems"...
, without appealing to degrees of consonance.
The term perfect has also been used as a synonym of just, 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
Equal temperament
An equal temperament is a musical temperament, or a system of tuning, in which every pair of adjacent notes has an identical frequency ratio. As pitch is perceived roughly as the logarithm of frequency, this means that the perceived "distance" from every note to its nearest neighbor is the same for...
. The perfect unison has a pitch ratio
Interval ratio
In music, an interval ratio is a ratio of the frequencies of the pitches in a musical interval. For example, a just perfect fifth is 3:2 , 1.5, and may be approximated by an equal tempered perfect fifth which is 27/12, 1.498...
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
Major sixth
In classical music from Western culture, a sixth is a musical interval encompassing six staff positions , and the major sixth is one of two commonly occurring sixths. It is qualified as major because it is the largest of the two...
(5:3).
Other qualities of fifth
In addition to perfect, there are two other kinds, or qualities, of fifths: the diminished fifth, which is one chromatic semitoneSemitone
A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically....
smaller, and the augmented fifth
Augmented fifth
In classical music from Western culture, an augmented fifth is an interval produced by widening a perfect fifth by a chromatic semitone. For instance, the interval from C to G is a perfect fifth, seven semitones wide, and both the intervals from C to G, and from C to G are augmented fifths,...
, which is one chromatic semitone larger. In terms of semitones, these are equivalent to the tritone
Tritone
In classical music from Western culture, the tritone |tone]]) is traditionally defined as a musical interval composed of three whole tones. In a chromatic scale, each whole tone can be further divided into two semitones...
(or augmented fourth), and the minor sixth
Minor sixth
-Subminor sixth:In music, a subminor sixth or septimal sixth is an interval that is noticeably narrower than a minor sixth but noticeably wider than a diminished sixth.The sub-minor sixth is an interval of a 14:9 ratio or alternately 11:7....
, respectively.
The pitch ratio of a fifth
The idealized pitch ratioInterval ratio
In music, an interval ratio is a ratio of the frequencies of the pitches in a musical interval. For example, a just perfect fifth is 3:2 , 1.5, and may be approximated by an equal tempered perfect fifth which is 27/12, 1.498...
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
Cent (music)
The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each...
system of pitch measurement, the 3:2 ratio corresponds to approximately 702 cents, or 2% of a semitone wider than seven semitones. Something close to the idealized perfect fifth can be heard when a violin
Violin
The violin is a string instrument, usually with four strings tuned in perfect fifths. It is the smallest, highest-pitched member of the violin family of string instruments, which includes the viola and cello....
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
Just intonation
In music, just intonation is any musical tuning in which the frequencies of notes are related by ratios of small whole numbers. Any interval tuned in this way is called a just interval. The two notes in any just interval are members of the same harmonic series...
.
Kepler explored musical tuning
Musical tuning
In music, there are two common meanings for tuning:* Tuning practice, the act of tuning an instrument or voice.* Tuning systems, the various systems of pitches used to tune an instrument, and their theoretical bases.-Tuning practice:...
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
Beat (acoustics)
In acoustics, a beat is an interference between two sounds of slightly different frequencies, perceived as periodic variations in volume whose rate is the difference between the two frequencies....
that result from such an "imperfect" tuning.
In keyboard instruments such as the piano
Piano
The piano is a musical instrument played by means of a keyboard. It is one of the most popular instruments in the world. Widely used in classical and jazz music for solo performances, ensemble use, chamber music and accompaniment, the piano is also very popular as an aid to composing and rehearsal...
, a slightly different version of the perfect fifth is normally used: in accordance with the principle of equal temperament
Equal temperament
An equal temperament is a musical temperament, or a system of tuning, in which every pair of adjacent notes has an identical frequency ratio. As pitch is perceived roughly as the logarithm of frequency, this means that the perceived "distance" from every note to its nearest neighbor is the same for...
, the perfect fifth is slightly narrowed to exactly 700 cents (seven semitones). (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.
Use in harmony
It was the first accepted harmony (besides the octave) in Gregorian chantGregorian chant
Gregorian chant is the central tradition of Western plainchant, a form of monophonic liturgical music within Western Christianity that accompanied the celebration of Mass and other ritual services...
, a very early formal style of musical composition. Moritz Hauptmann
Moritz Hauptmann
Moritz Hauptmann , was a German music theorist, teacher and composer.Hauptmann was born in Dresden, and studied violin under Scholz, piano under Franz Lanska, composition under Grosse and Francesco Morlacchi,...
describes the octave as a higher unity appearing as such within the triad, produced from the prime unity of first the octave, then fifth, then third, "which is the union of the former". Hermann von Helmholtz argues that some intervals, namely the perfect fourth, fifth, and octave, "are found in all the musical scales known." though his editor notes the fourth and fifth may be interchangeable or indeterminate.
The perfect fifth is a basic element in the construction of major and minor triad
Triad (music)
In music and music theory, a triad is a three-note chord that can be stacked in thirds. Its members, when actually stacked in thirds, from lowest pitched tone to highest, are called:* the Root...
s, and their extensions. 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
Overtone
An overtone is any frequency higher than the fundamental frequency of a sound. The fundamental and the overtones together are called partials. Harmonics are partials whose frequencies are whole number multiples of the fundamental These overlapping terms are variously used when discussing the...
, 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
Consonance and dissonance
In music, a consonance is a harmony, chord, or interval considered stable, as opposed to a dissonance , which is considered to be unstable...
intervals of these chords, as in the major seventh chord
Major seventh chord
In music, a major seventh chord is any nondominant seventh chord where the "third" note is a major third above the root.Most typically, major seventh chord refers to where the "seventh" note is a major seventh above the root . This is more precisely known as the major/major seventh chord, and it...
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
Paul Hindemith
Paul Hindemith was a German composer, violist, violinist, teacher, music theorist and conductor.- Biography :Born in Hanau, near Frankfurt, Hindemith was taught the violin as a child...
. This harmony also appears in Stravinsky's The Rite of Spring
The Rite of Spring
The Rite of Spring, original French title Le sacre du printemps , is a ballet with music by Igor Stravinsky; choreography by Vaslav Nijinsky; and concept, set design and costumes by Nicholas Roerich...
in the Dance of the Adolescents where four C Trumpet
Trumpet
The trumpet is the musical instrument with the highest register in the brass family. Trumpets are among the oldest musical instruments, dating back to at least 1500 BCE. They are played by blowing air through closed lips, producing a "buzzing" sound which starts a standing wave vibration in the air...
s, a Piccolo Trumpet
Piccolo trumpet
The smallest of the trumpet family is the piccolo trumpet, pitched one octave higher than the standard B trumpet. Most piccolo trumpets are built to play in either B or A, using a separate leadpipe for each key. The tubing in the B piccolo trumpet is one-half the length of that in a standard B...
, and one Horn
Horn (instrument)
The horn is a brass instrument consisting of about of tubing wrapped into a coil with a flared bell. A musician who plays the horn is called a horn player ....
play a five-tone B-flat quintal chord.
Bare fifth, open fifth, or empty fifth
A bare fifth, open fifth or empty fifth is a chord containing only a perfect fifth with no third. The closing chord of the KyrieKyrie
Kyrie, a transliteration of Greek κύριε , vocative case of κύριος , meaning "Lord", is the common name of an important prayer of Christian liturgy, which is also called the Kýrie, eléison ....
in Mozart
Wolfgang Amadeus Mozart
Wolfgang Amadeus Mozart , baptismal name Johannes Chrysostomus Wolfgangus Theophilus Mozart , was a prolific and influential composer of the Classical era. He composed over 600 works, many acknowledged as pinnacles of symphonic, concertante, chamber, piano, operatic, and choral music...
's Requiem
Requiem (Mozart)
The Requiem Mass in D minor by Wolfgang Amadeus Mozart was composed in Vienna in 1791 and left unfinished at the composer's death. A completion by Franz Xaver Süssmayr was delivered to Count Franz von Walsegg, who had anonymously commissioned the piece for a requiem Mass to commemorate the...
and of the first movement of Bruckner
Anton Bruckner
Anton Bruckner was an Austrian composer known for his symphonies, masses, and motets. The first are considered emblematic of the final stage of Austro-German Romanticism because of their rich harmonic language, complex polyphony, and considerable length...
's Ninth Symphony
Symphony No. 9 (Bruckner)
Anton Bruckner's Symphony No. 9 in D minor is the last Symphony upon which he worked, leaving the last movement incomplete at the time of his death in 1896. The symphony was premiered under Ferdinand Löwe in Vienna in 1903, after Bruckner's death...
are both examples of pieces ending on an empty fifth. These "chords" are common in Sacred Harp
Sacred Harp
Sacred Harp singing is a tradition of sacred choral music that took root in the Southern region of the United States. It is part of the larger tradition of shape note music.- The music and its notation :...
singing and throughout rock music
Rock music
Rock music is a genre of popular music that developed during and after the 1960s, particularly in the United Kingdom and the United States. It has its roots in 1940s and 1950s rock and roll, itself heavily influenced by rhythm and blues and country music...
. In hard rock
Hard rock
Hard rock is a loosely defined genre of rock music which has its earliest roots in mid-1960s garage rock, blues rock and psychedelic rock...
, metal
Heavy metal music
Heavy metal is a genre of rock music that developed in the late 1960s and early 1970s, largely in the Midlands of the United Kingdom and the United States...
, and punk music, overdriven or distorted guitar can make thirds sound muddy while the bare fifth remains crisp. In addition, 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 chord
Power chord
In music, a power chord is a chord consisting of only the root note of the chord and the fifth interval, usually played on electric guitar, and typically through an amplification process that imparts distortion...
s 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
Traditional music
Traditional music is the term increasingly used for folk music that is not contemporary folk music. More on this is at the terminology section of the World music article...
, e.g., in some Andean music
Andean music
Andean music comes from the general area inhabited by Quechuas, Aymaras and other peoples that lived roughly in the area of the Inca Empire prior to European contact. It includes folklore music of parts of Argentina, Bolivia, Ecuador, Chile, Colombia, Peru and Venezuela...
genres of pre-Columbian origin, such as k'antu and sikuri
Sikuri
Sikuri is a musical style from Peru and Bolivia, the kind of huayño, consisting of siku players and drum accompaniment. There are usually around twenty siku players. As each siku cannot play all the notes of a scale, the siku players use an interlocking technique to play the entire melody...
. 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 intonationJust intonation
In music, just intonation is any musical tuning in which the frequencies of notes are related by ratios of small whole numbers. Any interval tuned in this way is called a just interval. The two notes in any just interval are members of the same harmonic series...
, a just fifth, corresponds to a frequency ratio of 3:2 (702 cents
Cent (music)
The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each...
); while in 12-tone equal temperament
Equal temperament
An equal temperament is a musical temperament, or a system of tuning, in which every pair of adjacent notes has an identical frequency ratio. As pitch is perceived roughly as the logarithm of frequency, this means that the perceived "distance" from every note to its nearest neighbor is the same for...
, where each semitone spans 100 cents, a perfect fifth is equal to 700 cents, about two cents smaller than the just fifth.
The just perfect fifth, together with the octave
Octave
In music, an octave is the interval between one musical pitch and another with half or double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems"...
, forms the basis of Pythagorean tuning
Pythagorean tuning
Pythagorean tuning is a system of musical tuning in which the frequency relationships of all intervals are based on the ratio 3:2. This interval is chosen because it is one of the most consonant...
. A flattened perfect fifth is likewise the basis for meantone
Meantone temperament
Meantone temperament is a musical temperament, which is a system of musical tuning. In general, a meantone is constructed the same way as Pythagorean tuning, as a stack of perfect fifths, but in meantone, each fifth is narrow compared to the ratio 27/12:1 in 12 equal temperament, the opposite of...
tuning.
The circle of fifths
Circle of fifths
In music theory, the circle of fifths shows the relationships among the 12 tones of the chromatic scale, their corresponding key signatures, and the associated major and minor keys...
is a model of pitch space
Pitch space
In music theory, pitch spaces model relationships between pitches. These models typically use distance to model the degree of relatedness, with closely related pitches placed near one another, and less closely related pitches placed farther apart. Depending on the complexity of the relationships...
for the chromatic scale
Chromatic scale
The chromatic scale is a musical scale with twelve pitches, each a semitone apart. On a modern piano or other equal-tempered instrument, all the half steps are the same size...
(chromatic circle) which considers nearness not as adjacency but as the number of perfect fifths required to get from one note to another.
See also
- All fifthsAll fifthsAll fifths is a tuning for guitar, in which the interval between each string is a perfect fifth. The conventional "standard tuning" consists of perfect fourths and a single major third between the G and B strings...
- Circle of fifthsCircle of fifthsIn music theory, the circle of fifths shows the relationships among the 12 tones of the chromatic scale, their corresponding key signatures, and the associated major and minor keys...