Afourth is amusical interval encompassing fourstaff positions in the music notation ofWestern culture, and aperfect fourth (Play^ⓘ) is the fourth spanning fivesemitones (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 andaugmented fourths 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 theharmonic series as the interval between the third and fourth harmonics. The termperfect identifies this interval as belonging to the group of perfect intervals, so called because they are neither major nor minor.

A perfect fourth injust intonation corresponds to a pitch ratio of 4:3, or about 498cents (Play^ⓘ), while inequal temperament a perfect fourth is equal to five semitones, or 500 cents (seeadditive synthesis).

Until the late 19th century, the perfect fourth was often called by its Greek name,diatessaron.^[1] Its most common occurrence is between thefifth and upperroot of allmajor andminor triads and theirextensions.

An example of a perfect fourth is the beginning of the "Bridal Chorus" fromWagner'sLohengrin ("Treulich geführt", the colloquially-titled "Here Comes the Bride"). Another example is the beginning melody of theState Anthem of the Soviet Union. Other examples are the first two notes of theChristmas carol "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".^{[citation needed]}

The perfect fourth is a perfect interval like theunison,octave, andperfect fifth, and it is a sensoryconsonance. Incommon 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".^[2] If the bass note also happens to be the chord's root, the interval's upper note almost always temporarily displaces thethird of any chord, and, in the terminology used in popular music, is then called asuspended fourth.

Conventionally, adjacent strings of thedouble bass and of thebass guitar are a perfect fourth apart whenunstopped, as are all pairs but one of adjacentguitar strings understandard guitar tuning. Sets oftom-tom drums are also commonly tuned in perfect fourths. The 4:3 just perfect fourth arises in the Cmajor scale between F and C.^[3]Play^ⓘ

Perfect fourth (equal temperament)

The file playsmiddle C, followed by F (a tone 500 cents sharper than C), followed by both tones together.

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Problems playing this file? Seemedia help.

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 Europeanpolyphonic music of theMiddle Ages.

In the 13th century, the fourth and fifth together were theconcordantiae 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 byJohannes Tinctoris in hisTerminorum 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.^[4]

Modernacoustic 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' atA440 and a'' at 880 Hz, giving the ratio 880:440, or 2:1. The fifth has a ratio of 3:2, and itscomplement 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 themonochord.

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 asmeantone temperament,well temperament, andequal temperament were developed.

In early westernpolyphony, 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 forvoice 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 ofparallel octaves and fifths).

The music of the 20th century for the most part discards the rules of "classical" Western tonality. For instance, composers such asErik Satie borrowed stylistic elements from the Middle Ages, but some composers found more innovative uses for these intervals.

Inmedieval music, thetonality 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. TheMusica 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 theNotre Dame school may be considered the apex of a coherent harmony in this style.

For instance, in one "Alleluia" (Listen) byPérotin, the fourth is favoured. Elsewhere, in parallelorganum at the fourth, the upper line would be accompanied a fourth below. Also important was the practice ofFauxbourdon, which is a three-voice technique (not infrequentlyimprovisatory) 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 afirst 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 theFauxbourdon style. An example of this is the start of the Marian-AntiphonAve Maris Stella (Listen) byGuillaume Dufay, a master ofFauxbourdon.

The development of tonality continued through theRenaissance until it was fully realized by composers of theBaroque 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 byOrlando di Lasso andPalestrina show the fourth being resolved as a suspension. (Listen)

In the early Baroque music ofClaudio Monteverdi andGirolamo Frescobaldi triadic harmony was thoroughly utilized. Diatonic and chromatic passages strongly outlining the interval of a fourth appear in thelamento genre, and often inpassus duriusculus passages of chromatic descent. In themadrigals of Claudio Monteverdi andCarlo 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'sChromaticToccata of 1635 the outlined fourths overlap, bisecting variouschurch modes.

In the first third of the 18th century, ground-laying theoretical treatises on composition andharmony were written.Jean-Philippe Rameau completed his treatiseLe 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 modernmusic theory relating to consonance and harmony. The Austrian composerJohann Fux published in 1725 his powerful treatise on the composition ofcounterpoint in the style of Palestrina under the titleGradus ad Parnassum (The Steps toParnassus). He outlined various types of counterpoint (e.g.,note against note), and suggested a careful application of the fourth so as to avoid dissonance.

The blossoming of tonality and the establishment ofwell temperament in Bach's time both had a continuing influence up to the lateromantic period, and the tendencies towards quartal harmony were somewhat suppressed. An increasingly refinedcadence, 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-calledDissonance QuartetKV 465 (Listen) usedchromatic andwhole tone scales to outline fourths, and the subject of the fugue in the third movement ofBeethoven'sPiano sonata op. 110 (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 ofquartal and quintal harmony.

TheTristan chord is made up of thenotes F♮, B♮, D♯ and G♯ and is the first chord heard inRichard Wagner'soperaTristan und Isolde.

The chord had been found in earlier works, notablyBeethoven'sPiano Sonata No. 18, but Wagner's usage was significant, first because it is seen as moving away from traditionaltonal harmony and even towardsatonality, and second because with this chord Wagner actually provoked thesound or structure of musical harmony to become more predominant than itsfunction, 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 asModest Mussorgsky,Leoš Janáček, andJean Sibelius. These composers used this harmony in a pungent, uncovered, almost archaic way, often incorporating thefolk music of their particular homelands. Sibelius'Piano Sonata in F-Major op. 12 of 1893 usedtremolo passages of near-quartal harmony in a way that was relatively difficult and modern. Even in the example from Mussorgsky's piano-cyclePictures at an Exhibition(Избушка на курьих ножках (Баба-Яга) – The Hut on Fowl's Legs) (Listen) the fourth always makes an "unvarnished" entrance.

The romantic composersFrédéric Chopin andFranz Liszt, had used the special "thinned out" sound of fourth-chord in late works for piano (Nuages gris (Grey Clouds),La lugubre gondola (The Mournful Gondola), and other works).

In the 1897 workThe Sorcerer's Apprentice (L'Apprenti sorcier) byPaul 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'sSonatine andMa Mère l'Oye (Mother Goose) would follow a few years later.

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 withninth chords, thewhole tone scale, thepentatonic scale, andpolytonality 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 workLa Mer (The Sea) and in his piano works, in particularLa cathédrale engloutie (The Sunken Cathedral) from hisPréludes for piano,Pour les quartes (For Fourths) andPour les arpéges composées (For Composite Arpeggios) from hisEtudes.

Jazz uses quartal harmonies (usually calledvoicing in fourths).

Cadences are often "altered" to include unresolvedsuspended chords which include a fourth above the bass:

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