View source for User:Sonia/Perfect fourth

{{refimprove|date=September 2008}}
{{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 = 500|
       cents_just_intonation = 498
}}

[[Image:Perfect fourth on C.png|thumb|right|250px|Perfect fourth {{audio|Perfect fourth on C.mid|Play}}]]

The '''perfect fourth''' ( {{audio|Perfect fourth on C.mid|Play}})  is a [[musical interval]] which spans four [[diatonic scale|scale]] [[scale degree|degrees]].  It consists of the note and the note five [[semitones]] above it on the musical scale.  For example, the interval between a C and the next F above it is a perfect fourth; similarly the interval between a G and the next C above it, between an F and the B flat above it, and so on. 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 (such as thirds, which are either [[minor third|minor]] or [[major third|major]]) but perfect. "Perfect" distinguishes the perfect fourth from the [[augmented fourth]], which is one [[chromatic semitone]] larger. 

The perfect fourth is occasionally called the '''''diatessaron'''''.<ref>{{cite book | title = A Dictionary of Christian Antiquities | author = William Smith and Samuel Cheetham | publisher = London: John Murray | year = 1875 | url = http://books.google.com/books?id=1LIPFk6oFVkC&pg=PA550&dq=diatessaron+diapason+diapente+fourth+fifth&lr=&as_brr=3&ei=OVzHSNWIF4-4swP2iYnYDA }}</ref>  It is abbreviated '''P4'''.  The perfect fourth's [[inversion (music)|inversion]] is the [[perfect fifth]].

Its most common occurrence is between the [[fifth]] and upper [[root (chord)|root]] of all [[Major chord|major]] and [[Minor chord|minor triad]]s and their [[extended chords|extensions]]. 

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 [[semitone]]s, or 500 cents.

A helpful way to recognize a perfect fourth is to hum the starting of the "Bridal Chorus" from [[Wagner]]'s ''Lohengrin'' ("''Treulich gefuehrt''", the colloquially-titled "[[Bridal Chorus|Here Comes the Bride]]"). Other examples are the first two notes of the [[Christmas]] [[carol]]s "[[Hark! The Herald Angels Sing]]" and "[[Away in a Manger]]".

The perfect fourth is a perfect interval like the [[unison]], [[octave]], and [[perfect fifth]], and it is a sensory [[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 appears above the bass.<ref>{{cite paper  |author=Sean Ferguson and [[Richard Parncutt]]  |url=http://smc04.ircam.fr/scm04actes/P43.pdf  |format=PDF  |title=Composing in the Flesh: Perceptually-Informed Harmonic Syntax  |accessdate=2006-09-05}}</ref> If the bass note also happens to be the chord's root, the interval's upper note almost always temporarily displaces the [[third]] of any chord, and 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|unstopped]], as are all pairs but one of adjacent [[guitar]] strings under [[Standard_tuning#Plucked_strings|standard guitar tuning]].  Sets of [[Tom-tom drum|tom-tom]] drums are also commonly tuned in perfect fourths.

<!--{{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.}}-->

==Short history of the fourth==

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 and Renaissance]].  At this point the perfect fourth was heard as a ''consonance'' rather than as a ''dissonance'' (see the article [[Consonance and dissonance]]). The major and minor thirds were later added and these three interval types (3rd, 4th, 5th)—alongside the [[major second]] and [[minor second]]—were used freely to add an extra "part" to the texture which was often placed over a droning "tenor" part.   This style of writing slowly developed into the [[triad (music)|triadic]] polyphony found in the Renaissance.  At this stage, the "bare" third (ie no only those two notes are sounding) was felt to be more "pleasing" to the ear than bare seconds, fourths and fifths and the thirds were often use at points of repose; the perfect fourth was used at points of tension and went from being heard as a ''consonance'' to being heard as a ''dissonance''.  (Seconds have generally always been heard as dissonances because they are so small and occur high up on the [[Harmonic series (music)|harmonic series]] having complex ratios; the perfect fifth is generally always heard as a consonance because it occurs low down the harmonic series, having a simple ratio of 3-2.)  At the beginning of the 20th century, fourths played a strong role in contemporary music-styles, but in quite a different way: "Quartal harmony", the harmonic layering of fourths, imbued modern music with structural commonalities, creating parts more widely separated in space and/or time (because the fourth is a wider interval than the third), and allowing for a very different sound.  In a sense, these composers were re-evaluating the fourth as a ''consonance'' once again.

The ancient Greeks defined the group of "symphonia", the beautiful intervals, naming the fourth "syllabe" (Greek: fastened together) and later [[Diatessaron]] (Greek: by four, from four). This interval became the framework upon which the [[tetrachord]]s of Greek music theory were built.

In the Middle Ages the fourth was considered to be a consonance, as were the [[unison]], octave, fifth, and later the third. After the 12th century, music theorists sometimes classified the fourth as a dissonance requiring resolution.

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. In the 15th century the fourth was considered dissonant, and removed from the group of concords.

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]] 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 has the ratio of 3:4. Ancient and medieval music theorists appear to be familiar with these ratios, see for example their experiments on the [[Monochord]].
[[Image:Notenbeispiel Quarten.gif|thumb|right|400px|([[Image:Loudspeaker.svg|11px]][[Media: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 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. It became very common in the 20th century for the fourth to be used as a structural element.

===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, fifth 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]][[Media: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]][[Media:AveMarisStellaDufay for wikipedia.mid|Listen]]) by [[Guillaume Dufay]], a master of Fauxbourdon.

In medieval thought, contemplation of the musical intervals was frequently expressed from theological perspectives. Pope [[John XXII]] issued a [[Papal bull|bull]] in 1324 forbidding most contrapuntal practice, but permitting on solemn occasions an enrichment of the plainchant by the concord of the octave which he described as a symbol for the perfect beauty and holiness of God, sounding out over earthly imperfection and infertility, along with the fifth and fourth which have a similar purity.

===Renaissance and Baroque===

The development of tonality continued through the [[Renaissance music|Renaissance]] until it was fully realized at last 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]][[Media: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'' (French: the theory of harmony reduced to its natural principles) in 1722 which supplemented his work of four years earlier, ''Nouveau Système de musique theoretique'' (French: 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]]'' (Latin: 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, 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]][[Media: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. 110]] ([[Image:Loudspeaker.svg|11px]][[Media: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]].

[[Image:TristanChord.svg|thumb|left|350px|{{Multi-listen item|filename=Wagner Tristan opening (orchestral).ogg|title=The "Tristan chord" in context}}]]
The ''Tristan chord'' is made up of the [[note]]s F{{music|natural}}, B{{music|natural}}, D{{music|sharp}} and G{{music|sharp}} and is the very first chord heard in [[Richard Wagner]]'s [[opera]] ''[[Tristan und Isolde]]''.  The bottom two notes make up an ''augmented fourth'' the upper two make up a ''perfect fourth''; this layering of fourths in this context has been seen as highly significant.  The chord had been found in earlier works (notably 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.  Beethoven usage is of short duration and resolves in the accepted manner; Wagner's usage lasts much longer and resolves in a highly unorthodox manner for the time.  Despite the layering of fourths, it is rare to find musicologists identifying this chord as "quartal harmony" or even as "proto-quartal harmony", since Wagner's musical language is still essentially built on thirds; this unusual chord is really a device to draw the listener in to the musical-dramatic argument that the composer is presenting us with.  However, fourths become important later in the opera, especially in the melodic development.

[[Image:Baby Yaga for wikipedia.png|thumb|right|400px|Measures 24 to 27 from Mussorgsky's ''The Hut on Fowl's Legs'']]
From 1850 to 1900 the application of tonality began to dissolve as evidenced in the works of composers of the Late Romantic such as Wagner, [[Anton Bruckner]], [[Gustav Mahler]] and [[Claude Debussy]], and as the 20th century began with tonality no longer a strong binding force, quartal harmony became one of the new means of expression.

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. 12 of 1893 used [[tremolo]] passages of near-[[quartal harmony]] in a way that was relatively hard and modern. Even in the example on the right 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]][[Media:Baba Yaga Quarten for wikipedia.mid|Listen]]) the fourth always makes an "unvarnished" entrance. Rudiments of quartal harmony appear in Janáček's [[Rhapsody (music)|Rhapsody]] ''[[Taras Bulba (rhapsody)|Taras Bulba]]'', his [[Opera]] ''[[The Makropulos Affair (opera)|Věc Makropulos]]'' (The Makropulos Affair) and ''[[From the House of the Dead|Z Mrtvého Domu]]'' (From the House of the Dead), and descending fourths and sevenths can be found dominating the writing.

===Impressionism===

The Romantic composers [[Frédéric Chopin]] and [[Franz Liszt]], had use the special "thinned out" sound of fourth-chord in late works for piano (''[[Nuages Gris|Nuages gris]]'' (Fr: Grey Clouds), ''La lugubre gondola'' (Fr: The Mournful Gondola), and other works).

The Impressionists would make much more use of chords built from fourths, even allowing them as a places of relaxation, altering our perception of them in the context of harmonic function and winning them their status as autonomous chords.

[[Image:Ravel Ma Mere l'Oye Laideronnette.PNG|thumb|right|550px|Quartal harmony in "Laideronnette" from Ravel's Ma Mère l'Oye]]
Fourth-chords became consolidated with [[Ninth chord]]s, the [[Whole tone scale]], the [[Pentatonic]] scale, and [[polytonality]] as part of the language of Impressionism, 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]]'' (Fr: The Sea) and in his piano works, in particular ''La cathédrale engloutie'' (Fr: The Sunken Cathedral) from his ''[[Préludes (Debussy)|Préludes]]'' for piano, ''Pour les quartes'' (Fr: For Fourths) and ''Pour les arpéges composées'' (Fr: For Composite Arpeggios) from his ''[[Études (Debussy)|Etudes]]''.

In the 1897 work ''[[The Sorcerer's Apprentice]] (L'Apprenti sorcier)'' by Debussy's colleague composer [[Paul Dukas]], we hear a rising repetition in fourths, as 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]]'' (Fr: Mother Goose) would follow a few years later.

===20th century music===

====Western classical music====

{{main|quartal and quintal harmony}}

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.  [[Arnold Schoenberg]] and the [[Second Viennese School]], [[Béla Bartók]], [[Charles Ives]], [[Paul Hindemith]] and [[Igor Stravinsky]] all wrote works using this type of harmonic structuring.
<!--
{|
|[[Image:Bartok's fourths.png|thumb|300px|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">Morgan, Robert P. (1991). ''Twentieth-Century Music'', p.179-80. ISBN 978-0-393-95272-8.</ref>]]
|[[Image:Schoenberg's fourths.png|thumb|300px|During Schoenberg's middle period he favoured a chord composed of two fourths, one perfect and one augmented ('''C''', '''''F''''', ''B'' or ''C'', '''''F#''''', '''B''').<ref>Morgan (1991), p.71. "no doubt for its 'nontonal' quality"</ref>]]
|[[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 abve the bass:

[[Image:II V I for wikipedia.png|thumb|none|275px|([[Image:Loudspeaker.svg|11px]][[Media:II V9 I.MID|Listen]]) The II-V-I Cadence ([[Image:Loudspeaker.svg|11px]][[Media:II V9sus I.MID|Listen]]) The Fourth-suspension or "Sus"-Chord]]

Quartal harmony was also explored as a possibility under new experimental [[Scale (music)|scale]] models as they were "discovered" by Jazz. Musicians began to work extensively with the so-called [[Mode (music)|church modes]] of old European music, and they became firmly situated in their compositional process; Jazz was well suited to incorporate the medieval usage of fourths to thicken lines into its improvisation. The pianists [[Herbie Hancock]], and [[Chick Corea]] are two musicians well known for their modal experimentation. At this time a phenomenon known as [[Free Jazz]] also came into being, in which quartal harmony had extensive usage due to the wandering nature of its harmony.

[[Image:Maiden Voyage2.png|thumb|center|750px|Fourths in Herbie Hancock's ''Maiden Voyage'']]

====Rock music====

In Rock Music fourth-based harmony became part of the compositional framework, especially in [[Riff]]s and [[Power chord]]s which often use fifths and fourths instead of triadic harmony.  This preference for fourths in Rock stems directly from the chosen "high instrument of Rock Music", the guitar, on which they are very simple to play because the strings are mainly tuned a fourth apart.

====Latin-American music====

In the ''[[Música Popular Brasileira]]'' of Brazil, the guitar has a central role as the harmonic instrument similar to the instrument's role in Rock. As a result, the quartal oriented playing of the guitar was borrowed and the unique rhythmic tradition adapted to fit (as in ''[[Tropicalismo]]''). Even earlier, however, the notable Brazilian composer [[Heitor Villa-Lobos]] (1887-1959) wrote pioneering works in the first half of the 20th century combining elements of folk music and the popular music of his homeland with the quartal-harmonic experiments of European and North American classical music.

{|
|[[Image:Barretto Amor Artificial.png|thumb|right|345px|[[Image:Loudspeaker.svg|11px]] [[Media: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]] [[Media:Nascimento Vera Cruz.mid|Listen]] Guitar [[Break (music)|break]] from ''[[Milton Nascimento]]s'' composition "Vera Cruz"]]
|}

==See also==
* [[tritone|augmented fourth]]
* [[All fifths]]
* [[List of intervals]]
* [[list of meantone intervals]]
* [[eleventh]]
* [[chromatic fourth]]

{{Diatonic intervals}}

==References==
<!-- See [[Wikipedia:Footnotes]] for instructions -->
<references />

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