User:Sonia/Perfect fourth

**perfect fourth**
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The perfect fourth ( Play (help·info)) is a musical interval which spans four scale 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 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 or 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.^[1] It is abbreviated P4. The perfect fourth's inversion is the perfect fifth.

Its most common occurrence is between the fifth and upper root of all major and minor triads and their extensions.

A perfect fourth in just intonation corresponds to a pitch ratio of 4:3, or about 498 cents (Play (help·info)), while in equal temperament a perfect fourth is equal to five semitones, 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 "Here Comes the Bride"). Other examples are the first two notes of the Christmas carols "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 harmony, however, it is considered a stylistic dissonance in certain contexts, namely in two-voice textures and whenever it appears above the bass.^[2] 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 fourth.

Conventionally, adjacent strings of the double bass and of the bass guitar are a perfect fourth apart when unstopped, as are all pairs but one of adjacent guitar strings under standard guitar tuning. Sets of tom-tom drums are also commonly tuned in perfect fourths.

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 polyphonic music of the 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 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 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 tetrachords 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 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 be familiar with these ratios, see for example their experiments on the Monochord.

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 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.

For instance, in one Alleluia (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 (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 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 until it was fully realized at last by composers of the Baroque 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 and Palestrina show the fourth being resolved as a suspension. (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 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 ad Parnassum (Latin: 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 (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 (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 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) 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.

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) (Listen) the fourth always makes an "unvarnished" entrance. Rudiments of quartal harmony appear in Janáček's Rhapsody Taras Bulba, his Opera Věc Makropulos (The Makropulos Affair) and 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 (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.

Quartal harmony in "Laideronnette" from Ravel's Ma Mère l'Oye

Fourth-chords became consolidated with Ninth chords, 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 (Fr: The Sea) and in his piano works, in particular La cathédrale engloutie (Fr: The Sunken Cathedral) from his Préludes for piano, Pour les quartes (Fr: For Fourths) and Pour les arpéges composées (Fr: For Composite Arpeggios) from his 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 and Ma Mère l'Oye (Fr: 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. 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.

Jazz

Jazz uses quartal harmonies (usually called voicing in fourths).

Cadences are often "altered" to include unresolved suspended chords which include a fourth abve the bass:

Quartal harmony was also explored as a possibility under new experimental scale models as they were "discovered" by Jazz. Musicians began to work extensively with the so-called 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.

Rock music

In Rock Music fourth-based harmony became part of the compositional framework, especially in Riffs and Power chords 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.

References

↑ William Smith and Samuel Cheetham (1875). A Dictionary of Christian Antiquities. London: John Murray.
↑ Sean Ferguson and Richard Parncutt. "Composing in the Flesh: Perceptually-Informed Harmonic Syntax" (PDF). Retrieved on 5 September 2006.

[1] William Smith and Samuel Cheetham (1875). A Dictionary of Christian Antiquities. London: John Murray.

[2] Sean Ferguson and Richard Parncutt. "Composing in the Flesh: Perceptually-Informed Harmonic Syntax" (PDF). Retrieved on 5 September 2006.

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**perfect fourth**
Inverse	perfect fifth
Name
Other names	diatessaron
Abbreviation	P4
Size
Semitones	5