A fourth is a
musical interval
In music theory, an interval is a difference in pitch between two sounds.
An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or ha ...
encompassing four
staff positions in the music notation of
Western culture
Leonardo da Vinci's ''Vitruvian Man''. Based on the correlations of ideal Body proportions">human proportions with geometry described by the ancient Roman architect Vitruvius in Book III of his treatise ''De architectura''.
image:Plato Pio-Cle ...
, and a perfect fourth () is the fourth spanning five
semitones (half steps, or half tones). For example, the ascending interval from C to the next F is a perfect fourth, because the note F is the fifth semitone above C, and there are four staff positions between C and F.
Diminished and
augmented fourth
Augment or augmentation may refer to:
Language
*Augment (Indo-European), a syllable added to the beginning of the word in certain Indo-European languages
*Augment (Bantu languages), a morpheme that is prefixed to the noun class prefix of nouns i ...
s span the same number of staff positions, but consist of a different number of semitones (four and six, respectively).
The perfect fourth may be derived from the
harmonic series as the interval between the third and fourth harmonics. The term ''perfect'' identifies this interval as belonging to the group of perfect intervals, so called because they are neither major nor minor.
A perfect fourth in
just intonation corresponds to a pitch ratio of 4:3, or about 498
cent
Cent may refer to:
Currency
* Cent (currency), a one-hundredth subdivision of several units of currency
* Penny (Canadian coin), a Canadian coin removed from circulation in 2013
* 1 cent (Dutch coin), a Dutch coin minted between 1941 and 1944
* ...
s (), while in
equal temperament
An equal temperament is a musical temperament or tuning system, which approximates just intervals by dividing an octave (or other interval) into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, ...
a perfect fourth is equal to five semitones, or 500 cents (see
additive synthesis
Additive synthesis is a sound synthesis technique that creates timbre by adding sine waves together.
The timbre of musical instruments can be considered in the light of Fourier theory to consist of multiple harmonic or inharmonic '' partials'' ...
).
Until the late 19th century, the perfect fourth was often called by its Greek name, ''diatessaron''. Its most common occurrence is between the
fifth and upper
root
In vascular plants, the roots are the organs of a plant that are modified to provide anchorage for the plant and take in water and nutrients into the plant body, which allows plants to grow taller and faster. They are most often below the su ...
of all
major
Major ( commandant in certain jurisdictions) is a military rank of commissioned officer status, with corresponding ranks existing in many military forces throughout the world. When used unhyphenated and in conjunction with no other indicato ...
and
minor triad
In music theory, a minor chord is a chord that has a root, a minor third, and a perfect fifth. When a chord comprises only these three notes, it is called a minor triad. For example, the minor triad built on C, called a C minor triad, has pitc ...
s and their
extensions
Extension, extend or extended may refer to:
Mathematics
Logic or set theory
* Axiom of extensionality
* Extensible cardinal
* Extension (model theory)
* Extension (predicate logic), the set of tuples of values that satisfy the predicate
* Ex ...
.
An example of a perfect fourth is the beginning of the "Bridal Chorus" from
Wagner's ''
Lohengrin'' ("''Treulich geführt''", the colloquially-titled "
Here Comes the Bride"). Other examples are the first two notes of the
Christmas carol
A Christmas carol is a carol (a song or hymn) on the theme of Christmas, traditionally sung at Christmas itself or during the surrounding Christmas holiday season. The term noel has sometimes been used, especially for carols of French or ...
"
Hark! The Herald Angels Sing" and "
El Cóndor Pasa", and, for a descending perfect fourth, the second and third notes of "
O Come All Ye Faithful
"O Come, All Ye Faithful" (originally written in Latin as "") is a Christmas carol that has been attributed to various authors, including John Francis Wade (1711–1786), John Reading (1645–1692), King John IV of Portugal (1604–1656), and ...
".
The perfect fourth is a perfect interval like the
unison,
octave, and
perfect fifth, and it is a sensory
consonance. In
common practice harmony, however, it is considered a stylistic dissonance in certain contexts, namely in two-voice textures and whenever it occurs "above the bass in chords with three or more notes". If the bass note also happens to be the chord's root, the interval's upper note almost always temporarily displaces the
third
Third or 3rd may refer to:
Numbers
* 3rd, the ordinal form of the cardinal number 3
* , a fraction of one third
* 1⁄60 of a ''second'', or 1⁄3600 of a ''minute''
Places
* 3rd Street (disambiguation)
* Third Avenue (disambiguation)
* Hi ...
of any chord, and, in the terminology used in popular music, is then called a ''
suspended fourth
A chord, in music, is any harmonic set of pitches/frequencies consisting of multiple notes (also called "pitches") that are heard as if sounding simultaneously. For many practical and theoretical purposes, arpeggios and broken chords (in whi ...
''.
Conventionally, adjacent strings of the
double bass
The double bass (), also known simply as the bass () (or #Terminology, by other names), is the largest and lowest-pitched Bow (music), bowed (or plucked) string instrument in the modern orchestra, symphony orchestra (excluding unorthodox addit ...
and of the
bass guitar
The bass guitar, electric bass or simply bass (), is the lowest-pitched member of the string family. It is a plucked string instrument similar in appearance and construction to an electric or an acoustic guitar, but with a longer neck and ...
are a perfect fourth apart when
unstopped, as are all pairs but one of adjacent
guitar
The guitar is a fretted musical instrument that typically has six strings. It is usually held flat against the player's body and played by strumming or plucking the strings with the dominant hand, while simultaneously pressing selected string ...
strings under
standard guitar tuning. Sets of
tom-tom drums are also commonly tuned in perfect fourths. The 4:3 just perfect fourth arises in the C
major scale
The major scale (or Ionian mode) is one of the most commonly used musical scales, especially in Western music. It is one of the diatonic scales. Like many musical scales, it is made up of seven notes: the eighth duplicates the first at doub ...
between G and C.
History
The use of perfect fourths and fifths to sound in parallel with and to "thicken" the melodic line was prevalent in music prior to the European
polyphonic music of the
Middle Ages
In the history of Europe, the Middle Ages or medieval period lasted approximately from the late 5th to the late 15th centuries, similar to the post-classical period of global history. It began with the fall of the Western Roman Empire ...
.
In the 13th century, the fourth and fifth together were the ''concordantiae mediae'' (middle consonances) after the unison and octave, and before the thirds and sixths. The fourth came in the 15th century to be regarded as dissonant on its own, and was first classed as a dissonance by
Johannes Tinctoris in his ''Terminorum musicae diffinitorium'' (1473). In practice, however, it continued to be used as a consonance when supported by the interval of a third or fifth in a lower voice.
[William Drabkin (2001), "Fourth", ''The New Grove Dictionary of Music and Musicians'', second edition, edited by ]Stanley Sadie
Stanley John Sadie (; 30 October 1930 – 21 March 2005) was an influential and prolific British musicologist, music critic, and editor. He was editor of the sixth edition of the '' Grove Dictionary of Music and Musicians'' (1980), which was pub ...
and John Tyrrell (London: Macmilln Publishers).
Modern
acoustic theory supports the medieval interpretation insofar as the intervals of unison, octave, fifth and fourth have particularly simple frequency ratios. The octave has the ratio of 2:1, for example the interval between a' at
A440 and a
'' at 880 Hz, giving the ratio 880:440, or 2:1. The fifth has a ratio of 3:2, and its
complement has the ratio of 3:4. Ancient and medieval music theorists appear to have been familiar with these ratios, see for example their experiments on the
monochord.
In the years that followed, the frequency ratios of these intervals on keyboards and other fixed-tuning instruments would change slightly as different systems of tuning, such as
meantone temperament,
well temperament, and
equal temperament
An equal temperament is a musical temperament or tuning system, which approximates just intervals by dividing an octave (or other interval) into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, ...
were developed.
In early western
polyphony
Polyphony ( ) is a type of musical texture consisting of two or more simultaneous lines of independent melody, as opposed to a musical texture with just one voice, monophony, or a texture with one dominant melodic voice accompanied by chords, ...
, these simpler intervals (unison, octave, fifth and fourth) were generally preferred. However, in its development between the 12th and 16th centuries:
*In the earliest stages, these simple intervals occur so frequently that they appear to be the favourite sound of composers.
*Later, the more "complex" intervals (thirds, sixths, and tritones) move gradually from the margins to the centre of musical interest.
*By the end of the Middle Ages, new rules for
voice leading had been laid, re-evaluating the importance of unison, octave, fifth and fourth and handling them in a more restricted fashion (for instance, the later forbidding of
parallel
Parallel is a geometric term of location which may refer to:
Computing
* Parallel algorithm
* Parallel computing
* Parallel metaheuristic
* Parallel (software), a UNIX utility for running programs in parallel
* Parallel Sysplex, a cluster o ...
octaves and fifths).
The music of the 20th century for the most part discards the rules of "classical" Western tonality. For instance, composers such as
Erik Satie borrowed stylistic elements from the Middle Ages, but some composers found more innovative uses for these intervals.
Middle Ages
In
medieval music, the
tonality
Tonality is the arrangement of pitches and/or chords of a musical work in a hierarchy of perceived relations, stabilities, attractions and directionality. In this hierarchy, the single pitch or triadic chord with the greatest stability is ca ...
of the common practice period had not yet developed, and many examples may be found with harmonic structures that are built on fourths and fifths. The ''
Musica enchiriadis'' of the mid-10th century, a guidebook for musical practice of the time, described singing in parallel fourths, fifths, and octaves. This development continued, and the music of the
Notre Dame school may be considered the apex of a coherent harmony in this style.
For instance, in one "Alleluia" (
/upload.wikimedia.org/wikipedia/commons/3/34/Perotin_Alleluya_Quarten_for_wikipedia.mid Listen by
Pérotin, the fourth is favoured. Elsewhere, in parallel ''
organum'' at the fourth, the upper line would be accompanied a fourth below. Also important was the practice of ''
Fauxbourdon'', which is a three voice technique (not infrequently
improvisatory) in which the two lower voices proceed parallel to the upper voice at a fourth and sixth below. ''Fauxbourdon'', while making extensive use of fourths, is also an important step towards the later triadic harmony of tonality, as it may be seen as a
first inversion (or 6/3) triad.
This parallel 6/3 triad was incorporated into the contrapuntal style at the time, in which parallel fourths were sometimes considered problematic, and written around with ornaments or other modifications to the ''Fauxbourdon'' style. An example of this is the start of the Marian-
Antiphon ''Ave Maris Stella'' (
/upload.wikimedia.org/wikipedia/commons/3/3d/AveMarisStellaDufay_for_wikipedia.mid Listen by
Guillaume Dufay, a master of ''Fauxbourdon''.
Renaissance and Baroque
The development of tonality continued through the
Renaissance
The Renaissance ( , ) , from , with the same meanings. is a period in European history marking the transition from the Middle Ages to modernity and covering the 15th and 16th centuries, characterized by an effort to revive and surpass ide ...
until it was fully realized by composers of the
Baroque
The Baroque (, ; ) is a style of architecture, music, dance, painting, sculpture, poetry, and other arts that flourished in Europe from the early 17th century until the 1750s. In the territories of the Spanish and Portuguese empires including ...
era.
As time progressed through the late Renaissance and early Baroque, the fourth became more understood as an interval that needed resolution. Increasingly the harmonies of fifths and fourths yielded to uses of thirds and sixths. In the example, cadence forms from works by
Orlando di Lasso
Orlande de Lassus ( various other names; probably – 14 June 1594) was a composer of the late Renaissance. The chief representative of the mature polyphonic style in the Franco-Flemish school, Lassus stands with Giovanni Pierluigi da Pale ...
and
Palestrina show the fourth being resolved as a suspension. (
/upload.wikimedia.org/wikipedia/commons/5/59/Palestrina_Lasso_Schlusskadenz_for_wikipedia.mid Listen
In the early Baroque music of
Claudio Monteverdi and
Girolamo Frescobaldi triadic harmony was thoroughly utilized. Diatonic and chromatic passages strongly outlining the interval of a fourth appear in the ''
lamento
''Lamento'' (English: "Lament") is a song by Peruvian singer-songwriter Gian Marco released by Sony Music Latin and Crescent Moon Records in 2003 as the third single of his sixth studio album A Tiempo.
Background and release
The song is a slow ...
'' genre, and often in ''passus duriusculus'' passages of chromatic descent. In the
madrigals of Claudio Monteverdi and
Carlo Gesualdo
Carlo Gesualdo da Venosa ( – 8 September 1613) was Prince of Venosa and Count of Conza. As a composer he is known for writing madrigals and pieces of sacred music that use a chromatic language not heard again until the late 19th century ...
the intensive interpretation of the text (
word painting) frequently highlights the shape of a fourth as an extremely delayed resolution of a fourth suspension. Also, in Frescobaldi's ''Chromatic
Toccata'' of 1635 the outlined fourths overlap, bisecting various
church modes.
In the first third of the 18th century, ground-laying theoretical treatises on composition and
harmony were written.
Jean-Philippe Rameau completed his treatise ''Le Traité de l'harmonie réduite à ses principes naturels'' (the theory of harmony reduced to its natural principles) in 1722 which supplemented his work of four years earlier, ''Nouveau Système de musique theoretique'' (new system of music theory); these together may be considered the cornerstone of modern
music theory relating to consonance and harmony. The Austrian composer
Johann Fux published in 1725 his powerful treatise on the composition of
counterpoint in the style of Palestrina under the title ''
Gradus ad Parnassum'' (The Steps to
Parnassus). He outlined various types of counterpoint (e.g., ''note against note''), and suggested a careful application of the fourth so as to avoid dissonance.
Classical and romantic
The blossoming of tonality and the establishment of
well temperament in Bach's time both had a continuing influence up to the late
romantic period, and the tendencies towards quartal harmony were somewhat suppressed. An increasingly refined
cadence, and triadic harmony defined the musical work of this era. Counterpoint was simplified to favour an upper line with a clear accompanying harmony. Still, there are many examples of dense counterpoint utilizing fourths in this style, commonly as part of the background urging the harmonic expression in a passage along to a climax.
Mozart in his so-called ''
Dissonance Quartet''
KV 465 (
/upload.wikimedia.org/wikipedia/commons/a/ab/Mozart_KV_465_1_Quarten_for_wikipedia.mid Listen used
chromatic and
whole tone scales to outline fourths, and the subject of the fugue in the third movement of
Beethoven's ''
Piano sonata op. 110'' (
/upload.wikimedia.org/wikipedia/commons/8/84/Beethoven_110_4_Quarten_for_wikipedia.mid Listen opens with three ascending fourths. These are all melodic examples, however, and the underlying harmony is built on thirds.
Composers started to reassess the quality of the fourth as a consonance rather than a dissonance. This would later influence the development of
quartal and quintal harmony.
The ''Tristan chord'' is made up of the
notes F, B, D and G and is the first chord heard in
Richard Wagner's
opera
Opera is a form of theatre in which music is a fundamental component and dramatic roles are taken by singers. Such a "work" (the literal translation of the Italian word "opera") is typically a collaboration between a composer and a libr ...
''
Tristan und Isolde''.
:
The chord had been found in earlier works, notably
Beethoven
Ludwig van Beethoven (baptised 17 December 177026 March 1827) was a German composer and pianist. Beethoven remains one of the most admired composers in the history of Western music; his works rank amongst the most performed of the classic ...
's
Piano Sonata No. 18, but Wagner's usage was significant, first because it is seen as moving away from traditional
tonal harmony
Tonality is the arrangement of pitches and/or chords of a musical work in a hierarchy of perceived relations, stabilities, attractions and directionality. In this hierarchy, the single pitch or triadic chord with the greatest stability is cal ...
and even towards
atonality, and second because with this chord Wagner actually provoked the ''sound'' or structure of musical harmony to become more predominant than its ''function'', a notion which was soon after to be explored by Debussy and others.
Fourth-based harmony became important in the work of Slavic and Scandinavian composers such as
Modest Mussorgsky,
Leoš Janáček, and
Jean Sibelius
Jean Sibelius ( ; ; born Johan Julius Christian Sibelius; 8 December 186520 September 1957) was a Finnish composer of the late Romantic and early-modern periods. He is widely regarded as his country's greatest composer, and his music is often ...
. These composers used this harmony in a pungent, uncovered, almost archaic way, often incorporating the
folk music
Folk music is a music genre that includes traditional folk music and the contemporary genre that evolved from the former during the 20th-century folk revival. Some types of folk music may be called world music. Traditional folk music has ...
of their particular homelands. Sibelius' ''Piano Sonata in F-Major op. 12'' of 1893 used
tremolo passages of near-
quartal harmony in a way that was relatively difficult and modern. Even in the example from Mussorgsky's piano-cycle ''
Pictures at an Exhibition'' ''(Избушка на курьих ножках (Баба-Яга) – The Hut on Fowl's Legs)'' (
/upload.wikimedia.org/wikipedia/commons/2/29/Baba_Yaga_Quarten_for_wikipedia.mid Listen the fourth always makes an "unvarnished" entrance.
The romantic composers
Frédéric Chopin
Frédéric François Chopin (born Fryderyk Franciszek Chopin; 1 March 181017 October 1849) was a Polish composer and virtuoso pianist of the Romantic period, who wrote primarily for solo piano. He has maintained worldwide renown as a leadin ...
and
Franz Liszt
Franz Liszt, in modern usage ''Liszt Ferenc'' . Liszt's Hungarian passport spelled his given name as "Ferencz". An orthographic reform of the Hungarian language in 1922 (which was 36 years after Liszt's death) changed the letter "cz" to simpl ...
, had used the special "thinned out" sound of fourth-chord in late works for piano (''
Nuages gris
''Nuages gris'' (; French, lit. ''Grey Clouds''), S.199 or ''Trübe Wolken'', is a work for piano solo composed by Franz Liszt on August 24, 1881. It is one of Liszt's most haunting and at the same time one of his most experimental works, repres ...
'' (Grey Clouds), ''La lugubre gondola'' (The Mournful Gondola), and other works).
In the 1897 work ''
The Sorcerer's Apprentice
"The Sorcerer's Apprentice" (german: "Der Zauberlehrling", link=no, italic=no) is a poem by Johann Wolfgang von Goethe written in 1797. The poem is a ballad in 14 stanzas.
Story
The poem begins as an old sorcerer departs his workshop, leaving ...
(L'Apprenti sorcier)'' by
Paul Dukas, the repetition of rising fourths is a musical representation of the tireless work of out-of-control walking brooms causes the water level in the house to "rise and rise". Quartal harmony in Ravel's ''
Sonatine'' and ''
Ma Mère l'Oye'' (Mother Goose) would follow a few years later.
20th century music
Western classical music
In the 20th century, harmony explicitly built on fourths and fifths became important. This became known as quartal harmony for chords based on fourths and quintal harmony for chords based on fifths.
In the music of composers of early 20th century France, fourth chords became consolidated with
ninth chords, the
whole tone scale, the
pentatonic scale, and
polytonality as part of their language, and quartal harmony became an important means of expression in music by Debussy,
Maurice Ravel
Joseph Maurice Ravel (7 March 1875 – 28 December 1937) was a French composer, pianist and conductor. He is often associated with Impressionism along with his elder contemporary Claude Debussy, although both composers rejected the term. In ...
, and others. Examples are found in Debussy's orchestral work ''
La Mer'' (The Sea) and in his piano works, in particular ''La cathédrale engloutie'' (The Sunken Cathedral) from his ''
Préludes'' for piano, ''Pour les quartes'' (For Fourths) and ''Pour les arpéges composées'' (For Composite Arpeggios) from his ''
Etudes''.
Jazz
Jazz uses quartal harmonies (usually called ''
voicing in fourths'').
Cadences are often "altered" to include unresolved
suspended chords which include a fourth above the bass:
See also
*
All fifths
*
Lists of intervals
*
List of meantone intervals
*
Eleventh
References
{{Authority control
Fourths (music)
Perfect intervals
3-limit tuning and intervals
fr:Quarte (musique)#Quarte juste