Perfect fourth

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Perfect fourth Play (help*info) Perfect fourth on C.png
Perfect fourth Loudspeaker.svg Play  
perfect fourth
Inverse perfect fifth
Name
Other namesdiatessaron
AbbreviationP4
Size
Semitones 5
Interval class 5
Just interval 4:3
Cents
Equal temperament 500
Just intonation 498

A fourth is a musical interval encompassing four staff positions in the music notation of Western culture, and a perfect fourth ( Loudspeaker.svg Play  ) 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 fourths span the same number of staff positions, but consist of a different number of semitones (four and six, respectively).

Contents

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 cents ( Loudspeaker.svg 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. [1] Its most common occurrence is between the fifth and upper root of all major and minor triads and their extensions.

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 "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 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". [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, in the terminology used in popular music, 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. The 4:3 just perfect fourth arises in the C major scale between G and C. [3] Loudspeaker.svg Play  

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 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. [4]

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.

(Listen) with perfect (a), augmented (b) and diminished (c) fourths Notenbeispiel Quarten.gif
( Loudspeaker.svg 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:

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.

Fourths in Guillaume Du Fay's Antiphon Ave Maris Stella AveMarisStellaDufay.png
Fourths in Guillaume Du Fay's Antiphon Ave Maris Stella

For instance, in one "Alleluia" ( Loudspeaker.svg 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 ( Loudspeaker.svg Listen) by Guillaume Dufay, a master of Fauxbourdon.

Renaissance and Baroque

The development of tonality continued through the Renaissance until it was fully realized by composers of the Baroque era.

Conventional closing cadences Renaissance Kadenz for wikipedia.png
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 Orlando di Lasso and Palestrina show the fourth being resolved as a suspension. ( Loudspeaker.svg 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 (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 ( Loudspeaker.svg 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 ( Loudspeaker.svg 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 Tristan und Isolde .

Perfect fourth

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.

Measures 24 to 27 from Mussorgsky's The Hut on Fowl's Legs Baby Yaga for wikipedia.png
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. 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) ( Loudspeaker.svg 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 (Grey Clouds), La lugubre gondola (The Mournful Gondola), and other works).

In the 1897 work 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 and Ma Mère l'Oye (Mother Goose) would follow a few years later.

20th century music

Western classical music

Quartal harmony in "Laideronnette" from Ravel's Ma Mere l'Oye. The top line uses the pentatonic scale Play (help*info) Ravel Ma Mere l'Oye Laideronnette.PNG
Quartal harmony in "Laideronnette" from Ravel's Ma Mère l'Oye. The top line uses the pentatonic scale Loudspeaker.svg 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 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, 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 .

Bartok'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) or internal (C, E, F) minor second, as a common intervallic source in place of triadic harmonies. Bartok's fourths.png
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) or internal (C, E, F) minor second, as a common intervallic source in place of triadic harmonies.
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). Schoenberg's fourths.png
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).
Quartal chord from Schoenberg's String Quartet No. 1 Schoenberg string quartet quartal chord.png
Quartal chord from Schoenberg's String Quartet No. 1

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:

(Listen) The II-V-I cadence (Listen) The fourth-suspension or "sus"-chord II V I for wikipedia.png
( Loudspeaker.svg Listen) The II-V-I cadence ( Loudspeaker.svg Listen) The fourth-suspension or "sus"-chord
Fourths in Herbie Hancock's Maiden Voyage Maiden Voyage2.png
Fourths in Herbie Hancock's Maiden Voyage
Listen The brass section of Ray Barretto's version of Amor Artificial Barretto Amor Artificial.png
Loudspeaker.svg Listen The brass section of Ray Barretto's version of Amor Artificial
Listen Guitar break from Milton Nascimentos composition "Vera Cruz" Nascimento Vera Cruz.png
Loudspeaker.svg Listen Guitar break from Milton Nascimentos composition "Vera Cruz"

See also

Related Research Articles

Counterpoint Polyphonic music with separate melodies

In music, counterpoint is the relationship between two or more musical lines which are harmonically interdependent yet independent in rhythm and melodic contour. It has been most commonly identified in the European classical tradition, strongly developing during the Renaissance and in much of the common practice period, especially in the Baroque. The term originates from the Latin punctus contra punctum meaning "point against point", i.e. "note against note".

Musical tuning Terms for tuning an instrument and a systems of pitches

In music, there are two common meanings for tuning:

Harmony Aspect of music

In music, harmony is the process by which the composition of individual sounds, or superpositions of sounds, is analysed by hearing. Usually, this means simultaneously occurring frequencies, pitches, or chords.

Pythagorean tuning

Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are based on the ratio 3:2. This ratio, also known as the "pure" perfect fifth, is chosen because it is one of the most consonant and easiest to tune by ear and because of importance attributed to the integer 3. As Novalis put it, "The musical proportions seem to me to be particularly correct natural proportions." Alternatively, it can be described as the tuning of the syntonic temperament in which the generator is the ratio 3:2, which is ≈702 cents wide.

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 harmonic if it pertains to simultaneously sounding tones, such as in a chord.

In music theory, the tritone is defined as a musical interval composed of three adjacent whole tones. For instance, the interval from F up to the B above it is a tritone as it can be decomposed into the three adjacent whole tones F–G, G–A, and A–B. According to this definition, within a diatonic scale there is only one tritone for each octave. For instance, the above-mentioned interval F–B is the only tritone formed from the notes of the C major scale. A tritone is also commonly defined as an interval spanning six semitones. According to this definition, a diatonic scale contains two tritones for each octave. For instance, the above-mentioned C major scale contains the tritones F–B and B–F. In twelve-equal temperament, the tritone divides the octave exactly in half as 6 of 12 semitones or 600 of 1200 cents.

Perfect fifth musical interval

In music theory, a perfect fifth is the musical interval corresponding to a pair of pitches with a frequency ratio of 3:2, or very nearly so.

A seventh chord is a chord consisting of a triad plus a note forming an interval of a seventh above the chord's root. When not otherwise specified, a "seventh chord" usually means a dominant seventh chord: a major triad together with a minor seventh. However, a variety of sevenths may be added to a variety of triads, resulting in many different types of seventh chords.

Semitone musical interval

A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically. It is defined as the interval between two adjacent notes in a 12-tone scale. For example, C is adjacent to C; the interval between them is a semitone.

Major third musical interval

In classical music, a third is a musical interval encompassing three staff positions, and the major third is a third spanning four semitones. Along with the minor third, the major third is one of two commonly occurring thirds. It is qualified as major because it is the larger of the two: the major third spans four semitones, the minor third three. For example, the interval from C to E is a major third, as the note E lies four semitones above C, and there are three staff positions from C to E. Diminished and augmented thirds span the same number of staff positions, but consist of a different number of semitones.

The intervals from the tonic (keynote) in an upward direction to the second, to the third, to the sixth, and to the seventh scale degrees of a major scale are called major.

Minor third musical interval

In music theory a minor third is a musical interval that encompasses three half steps, or semitones. Staff notation represents the minor third as encompassing three staff positions. The minor third is one of two commonly occurring thirds. It is called minor because it is the smaller of the two: the major third spans an additional semitone. For example, the interval from A to C is a minor third, as the note C lies three semitones above A. Coincidentally, there are three staff positions from A to C. Diminished and augmented thirds span the same number of staff positions, but consist of a different number of semitones. The minor third is a skip melodically.

Major sixth musical interval

In music from Western culture, a sixth is a musical interval encompassing six note letter names or staff positions, and the major sixth is one of two commonly occurring sixths. It is qualified as major because it is the larger of the two. The major sixth spans nine semitones. Its smaller counterpart, the minor sixth, spans eight semitones. For example, the interval from C up to the nearest A is a major sixth. It is a sixth because it encompasses six note letter names and six staff positions. It is a major sixth, not a minor sixth, because the note A lies nine semitones above C. Diminished and augmented sixths span the same number of note letter names and staff positions, but consist of a different number of semitones.

The intervals from the tonic (keynote) in an upward direction to the second, to the third, to the sixth, and to the seventh scale degrees (of a major scale are called major.

Minor chord

In music theory, a minor chord is a chord that has a root, a minor third, and a perfect fifth. When a chord has these three notes alone, it is called a minor triad. For example, the minor triad built on C, called a C minor triad, has pitches C–E–G:

In music, quartal harmony is the building of harmonic structures built from the intervals of the perfect fourth, the augmented fourth and the diminished fourth. For instance, a three-note quartal chord on C can be built by stacking perfect fourths, C–F–B.

In Western music, the adjectives major and minor may describe a chord, scale, or key. As such, a composition, movement, section, or phrase may be referred to by its key, including whether that key is major or minor.

Guitar chord

In music, a guitar chord is a set of notes played on a guitar. A chord's notes are often played simultaneously, but they can be played sequentially in an arpeggio. The implementation of guitar chords depends on the guitar tuning. Most guitars used in popular music have six strings with the "standard" tuning of the Spanish classical guitar, namely E-A-D-G-B-E' ; in standard tuning, the intervals present among adjacent strings are perfect fourths except for the major third (G,B). Standard tuning requires four chord-shapes for the major triads.

Consecutive fifths

In music, consecutive fifths, or parallel fifths, are progressions in which the interval of a perfect fifth is followed by a different perfect fifth between the same two musical parts : for example, from C to D in one part along with G to A in a higher part. Octave displacement is irrelevant to this aspect of musical grammar; for example, parallel twelfths are equivalent to parallel fifths.

Consonance and dissonance Categorizations of simultaneous or successive sounds

In music, consonance and dissonance are categorizations of simultaneous or successive sounds. Within the Western tradition, some listeners associate consonance with sweetness, pleasantness, and acceptability, and dissonance with harshness, unpleasantness, or unacceptability, although there is broad acknowledgement that this depends also on familiarity and musical expertise. The terms form a structural dichotomy in which they define each other by mutual exclusion: a consonance is what is not dissonant, and a dissonance is what is not consonant. However, a finer consideration shows that the distinction forms a gradation, from the most consonant to the most dissonant. In casual discourse, as Hindemith stressed, "The two concepts have never been completely explained, and for a thousand years the definitions have varied". The term sonance has been proposed to encompass or refer indistinctly to the terms consonance and dissonance.

Music and mathematics Relationships between music and mathematics

Music theory has no axiomatic foundation in modern mathematics, although some interesting work has recently been done in this direction, yet the basis of musical sound can be described mathematically and exhibits "a remarkable array of number properties". Elements of music such as its form, rhythm and metre, the pitches of its notes and the tempo of its pulse can be related to the measurement of time and frequency, offering ready analogies in geometry.

Diatonic and chromatic Terms in music theory to characterize scales

Diatonic and chromatic are terms in music theory that are most often used to characterize scales, and are also applied to musical instruments, intervals, chords, notes, musical styles, and kinds of harmony. They are very often used as a pair, especially when applied to contrasting features of the common practice music of the period 1600–1900.

References

  1. William Smith and Samuel Cheetham (1875). A Dictionary of Christian Antiquities. London: John Murray. ISBN   9780790582290.
  2. Sean Ferguson and Richard Parncutt. "Composing in the Flesh: Perceptually-Informed Harmonic Syntax" (PDF). Archived from the original (PDF) on 2005-10-13. Retrieved 2006-09-05.Cite journal requires |journal= (help)
  3. Paul, Oscar (1885). A manual of harmony for use in music-schools and seminaries and for self-instruction , p.165. Theodore Baker, trans. G. Schirmer.
  4. William Drabkin (2001), "Fourth", The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell (London: Macmilln Publishers).
  5. Bruce Benward and Marilyn Nadine Saker (2003). Music: In Theory and Practice, Vol. I, seventh edition (Boston: McGraw-Hill): p. 37. ISBN   978-0-07-294262-0.
  6. 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. 179–80. ISBN   978-0-393-95272-8.
  7. Morgan (1991), p. 71. "no doubt for its 'nontonal' quality"
  8. Floirat, Bernard (2015). "Introduction aux accords de quartes chez Arnold Schoenberg". p. 19 via https://www.academia.edu/.