Editing Perfect fourth

[[Image:Perfect fourth on C.png|thumb|right|Perfect fourth {{audio|Perfect fourth on C.mid|Play}}]]
{{Infobox Interval| 
       main_interval_name = perfect fourth|
       inverse = [[perfect fifth]]|
       complement = [[perfect fifth]]|
       other_names = diatessaron| 
       abbreviation = P4 |
       semitones = 5 | 
       interval_class = 5 | 
       just_interval = 4:3| 
       cents_equal_temperament = 500|
       cents_24T_equal_temperament = |
       cents_just_intonation = 498
}}

A '''fourth''' is a [[interval (music)|musical interval]] encompassing four [[staff position]]s in the music notation of [[Western culture]], and a '''perfect fourth''' ({{audio|Perfect fourth on C.mid|Play}}) is the fourth spanning five [[semitone]]s (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 fourth|Diminished]] and [[Tritone|augmented fourth]]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 (music)|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 (music)|cent]]s ({{audio|Just perfect fourth on C.mid|Play}}), while in [[equal temperament]] a perfect fourth is equal to five semitones, or 500 cents (see [[additive synthesis]]).

Until the late 19th century, the perfect fourth was often called by its Greek name, ''diatessaron''.<ref>{{cite book  |author=William Smith and Samuel Cheetham |title=A Dictionary of Christian Antiquities |year=1875 |publisher=John Murray |location=London |isbn=9780790582290 |url=https://books.google.com/books?id=1LIPFk6oFVkC&q=diatessaron+diapason+diapente+fourth+fifth&pg=PA550}}</ref> Its most common occurrence is between the [[Fifth (chord)|fifth]] and upper [[root (chord)|root]] of all [[Major chord|major]] and [[Minor chord|minor triad]]s and their [[extended chords|extensions]].

An example of a perfect fourth is the beginning of the "Bridal Chorus" from [[Wagner]]'s ''[[Lohengrin (opera)|Lohengrin]]'' ("''Treulich geführt''", the colloquially-titled "[[Bridal Chorus|Here Comes the Bride]]"). Another example is the beginning melody of the [[State Anthem of the Soviet Union]]. Other examples are the first two notes of the [[Christmas carol]] "[[Hark! The Herald Angels Sing]]" and "[[El Cóndor Pasa (song)|El Cóndor Pasa]]", and, for a descending perfect fourth, the second and third notes of "[[O Come All Ye Faithful]]".{{citation needed|date=May 2014}}

The perfect fourth is a perfect interval like the [[unison]], [[octave]], and [[perfect fifth]], and it is a sensory [[consonance and dissonance|consonance]]. In [[common practice period|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".<ref>{{cite journal |author=Sean Ferguson and [[Richard Parncutt]] |url=http://smc04.ircam.fr/scm04actes/P43.pdf |title=Composing in the Flesh: Perceptually-Informed Harmonic Syntax |access-date=2006-09-05 |archive-url=https://web.archive.org/web/20051013015208/http://smc04.ircam.fr/scm04actes/P43.pdf |archive-date=2005-10-13}}</ref> If the bass note also happens to be the chord's root, the interval's upper note almost always temporarily displaces the [[Third (chord)|third]] of any chord, and, in the terminology used in popular music, is then called a ''[[suspended chord|suspended fourth]]''.

Conventionally, adjacent strings of the [[double bass]] and of the [[bass guitar]] are a perfect fourth apart when [[open string (music)|unstopped]], as are all pairs but one of adjacent [[guitar]] strings under [[Standard tuning#Guitar family|standard guitar tuning]]. Sets of [[Tom-tom drum|tom-tom]] drums are also commonly tuned in perfect fourths. The 4:3 just perfect fourth arises in the C [[major scale]] between F and C.<ref>Paul, Oscar (1885). ''[https://archive.org/details/bub_gb_4WEJAQAAMAAJ <!-- quote=musical interval "pythagorean major third". --> A manual of harmony for use in music-schools and seminaries and for self-instruction]'', p.165. Theodore Baker, trans. G. Schirmer.</ref> {{audio|Just perfect fourth in scale.mid|Play}}

{{Listen|filename=Fourth_ET.ogg|title=Perfect fourth (equal temperament)|description=The file plays [[middle C]], followed by F (a tone 500 cents sharper than C), followed by both tones together.}}

==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 [[Polyphony|polyphonic]] music of the [[early music|Middle Ages]].

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.<ref>William Drabkin (2001), "Fourth", ''The New Grove Dictionary of Music and Musicians'', second edition, edited by [[Stanley Sadie]] and [[John Tyrrell (professor of music)|John Tyrrell]] (London: Macmilln Publishers).</ref>

Modern [[Acoustics|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 (pitch standard)|A440]] and a<nowiki>''</nowiki> at 880&nbsp;Hz, giving the ratio 880:440, or 2:1. The fifth has a ratio of 3:2, and its [[complement (music)|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]].
[[Image:Notenbeispiel Quarten.gif|thumb|right|400px|([[Image:Loudspeaker.svg|11px]][//upload.wikimedia.org/wikipedia/commons/a/aa/R_U_V_Quarten_for_wikipedia.mid Listen]) with perfect (a), augmented (b) and diminished (c) fourths]]

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]] were developed.

In early western [[polyphony]], 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 [[Consecutive fifths|parallel]] 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]] 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.

[[Image:AveMarisStellaDufay.png|thumb|left|400px|Fourths in Guillaume Du Fay's Antiphon ''Ave Maris Stella'']]
For instance, in one "Alleluia" ([[Image:Loudspeaker.svg|11px]][//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 [[Improvisation (music)|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'' ([[Image:Loudspeaker.svg|11px]][//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 music|Renaissance]] until it was fully realized by composers of the [[Baroque]] era.

[[Image:Renaissance Kadenz for wikipedia.png|thumb|left|200px|Conventional closing cadences]]
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 [[Orlande de Lassus|Orlando di Lasso]] and [[Giovanni Pierluigi da Palestrina|Palestrina]] show the fourth being resolved as a suspension. ([[Image:Loudspeaker.svg|11px]][//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]]'' genre, and often in ''passus duriusculus'' passages of chromatic descent. In the [[Madrigal (music)|madrigals]] of Claudio Monteverdi and [[Carlo Gesualdo]] 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|Gradus ad Parnassum]]'' (The Steps to [[Mount Parnassus#Parnassus as metaphor|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 music|romantic]] period, and the tendencies towards quartal harmony were somewhat suppressed. An increasingly refined [[cadence (music)|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.  [[Wolfgang Amadeus Mozart|Mozart]] in his so-called ''[[String Quartet No. 19 (Mozart)|Dissonance Quartet]]'' [[Köchel-Verzeichnis|KV]] 465 ([[Image:Loudspeaker.svg|11px]][//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 [[Ludwig van Beethoven|Beethoven's]] ''[[Piano Sonata No. 31 (Beethoven)|Piano sonata op.&nbsp;110]]'' ([[Image:Loudspeaker.svg|11px]][//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 [[Musical note|note]]s F{{music|natural}}, B{{music|natural}}, D{{music|sharp}} and G{{music|sharp}} and is the first chord heard in [[Richard Wagner]]'s [[opera]] ''[[Tristan und Isolde]]''.

: <score lang="lilypond" override_ogg="Wagner Tristan opening (orchestral).ogg">
    {
      \new PianoStaff <<
        \new Staff <<
            \new Voice \relative c'' {
                \clef treble \key a \minor \time 6/8
                \voiceOne \partial8 r8 R2. \once \override NoteHead.color = #red gis4.->(~ gis4 a8 ais8-> b4~ b8) r r
                }
            \new Voice \relative c' {
                \override DynamicLineSpanner.staff-padding = #4.5
                \once \override DynamicText.X-offset = #-5
                \voiceTwo \partial8 a\pp( f'4.~\< f4 e8 \once \override NoteHead.color = #red dis2.)(\> d!4.)~\p d8 r r
                }
            >>
        \new Staff <<
            \relative c {
                \clef bass \key a \minor \time 6/8
                \partial8 r8 R2. \once \override NoteHead.color = #red <f b>2.( <e gis>4.)~ <e gis>8 r r
                }
            >>
    >> }
</score>

The chord had been found in earlier works, notably [[Ludwig van Beethoven|Beethoven]]'s [[Piano Sonata No. 18 (Beethoven)|Piano Sonata No. 18]], but Wagner's usage was significant, first because it is seen as moving away from traditional [[tonal harmony]] 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.

[[Image:Baby Yaga for wikipedia.png|thumb|right|400px|Measures 24 to 27 from Mussorgsky's ''The Hut on Fowl's Legs'']]

Fourth-based harmony became important in the work of Slavic and Scandinavian composers such as [[Modest Mussorgsky]], [[Leoš Janáček]], and [[Jean Sibelius]]. These composers used this harmony in a pungent, uncovered, almost archaic way, often incorporating the [[folk music]] of their particular homelands. Sibelius' ''Piano Sonata in F-Major op.&nbsp;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)'' ([[Image:Loudspeaker.svg|11px]][//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]] and [[Franz Liszt]], had used the special "thinned out" sound of fourth-chord in late works for piano (''[[Nuages Gris|Nuages gris]]'' (Grey Clouds), ''La lugubre gondola'' (The Mournful Gondola), and other works).

In the 1897 work ''[[The Sorcerer's Apprentice (Dukas)|The Sorcerer's Apprentice]] (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 (Ravel)|Sonatine]]'' and ''[[Ma Mère l'Oye]]'' (Mother Goose) would follow a few years later.

===20th century music===

====Western classical music====
{{Main|quartal and quintal harmony}}

[[Image:Ravel Ma Mere l'Oye Laideronnette.PNG|thumb|right|400px|Quartal harmony in "Laideronnette" from Ravel's Ma Mère l'Oye. The top line uses the [[pentatonic scale]]<ref>Bruce Benward and Marilyn Nadine Saker (2003). ''Music: In Theory and Practice, Vol. I'', seventh edition (Boston: McGraw-Hill): p.&nbsp;37. {{ISBN|978-0-07-294262-0}}.</ref> {{audio|Ravel Ma Mere l'Oye Laideronnette.mid|Play}}]]
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 chord]]s, 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]], and others.  Examples are found in Debussy's orchestral work ''[[La Mer (Debussy)|La Mer]]'' (The Sea) and in his piano works, in particular ''La cathédrale engloutie'' (The Sunken Cathedral) from his ''[[Préludes (Debussy)|Préludes]]'' for piano, ''Pour les quartes'' (For Fourths) and ''Pour les arpéges composées'' (For Composite Arpeggios) from his ''[[Études (Debussy)|Etudes]]''.

{|
|[[Image:Bartok's fourths.png|thumb|275px|center|Bartók's music, such as the ''String Quartet No. 2'', often makes use of a three-note basic cell, a perfect fourth associated with an external (C, F, G{{music|flat}}) or internal (C, E, F) minor second, as a common intervallic source in place of triadic harmonies.<ref name="Morgan">Robert P. Morgan (1991). ''Twentieth-Century Music: A History of Musical Style in Modern Europe and America'', The Norton Introduction to Music History (New York: W. W. Norton), pp.&nbsp;179–80. {{ISBN|978-0-393-95272-8}}.</ref>]]
|[[Image:Schoenberg's fourths.png|thumb|center|During Schoenberg's middle period he favoured a chord composed of two fourths, one perfect and one augmented (C, F, B or C, F{{music|sharp}}, B).<ref>Morgan (1991), p.&nbsp;71. "no doubt for its 'nontonal' quality"</ref><ref>{{Cite news|url=https://www.academia.edu/12232101|title=Introduction aux accords de quartes chez Arnold Schoenberg|last=Floirat|first=Bernard|year=2015|pages=19|website=www.academia.edu}}</ref>{{Failed verification|date=March 2016}}<!--This page contains only the last portion of a quotation in French translation from Schoenberg's Style and Idea. It says nothing at all about Schoenberg's middle period, or what sort of chord in fourths he favoured at that time.-->]]
|[[Image:Schoenberg string quartet quartal chord.png|thumb|150px|center|Quartal chord from Schoenberg's ''String Quartet No. 1'']]
|}

====Jazz====
Jazz uses quartal harmonies (usually called ''[[Voicing (music)|voicing]] in fourths'').

[[Cadence (music)|Cadences]] are often "altered" to include unresolved [[suspended chord]]s which include a fourth above the bass:

[[Image:II V I for wikipedia.png|thumb|none|275px|([[Image:Loudspeaker.svg|11px]][//upload.wikimedia.org/wikipedia/commons/b/b1/II_V9_I.MID Listen]) The II-V-I cadence ([[Image:Loudspeaker.svg|11px]][//upload.wikimedia.org/wikipedia/commons/6/6d/II_V9sus_I.MID Listen]) The fourth-suspension or "sus"-chord]]

[[Image:Maiden Voyage2.png|thumb|center|400px|Fourths in [[Herbie Hancock]]'s ''[[Maiden Voyage (composition)|Maiden Voyage]]''{{citation needed|date=January 2011}}]]

{|
|[[Image:Barretto Amor Artificial.png|thumb|right|345px|[[Image:Loudspeaker.svg|11px]] [//upload.wikimedia.org/wikipedia/commons/f/f4/Barretto_Amor_Artificial.mid Listen] The brass section of [[Ray Barretto]]'s version of ''Amor Artificial'']]
|[[Image:Nascimento Vera Cruz.png|thumb|right|345px|[[Image:Loudspeaker.svg|11px]] [//upload.wikimedia.org/wikipedia/commons/a/a3/Nascimento_Vera_Cruz.mid Listen] Guitar [[Break (music)|break]] from [[Milton Nascimento]]s composition "Vera Cruz"]]
|}

==See also==
* [[All fifths]]
* [[Lists of intervals]]
* [[List of meantone intervals]]
* [[Eleventh]]

==References==
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{{Reflist}}

{{Intervals}}
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[[Category:Fourths (music)]]
[[Category:Perfect intervals]]
[[Category:3-limit tuning and intervals]]

[[fr:Quarte (musique)#Quarte juste]]