Perfect fourth

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Perfect fourth Playⓘ
perfect fourth
Inverse
perfect fifth
Name
Other namesdiatessaron
AbbreviationP4
Size
Semitones5
Interval class5
Just interval4:3
Cents
12-Tone equal temperament500
Just intonation498

A fourth is a

staff positions in the music notation of Western culture, and a perfect fourth (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).

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 (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.

extensions
.

An example of a perfect fourth is the beginning of the "Bridal Chorus" from

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

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.[3] Playⓘ

Perfect fourth (equal temperament)
The file plays
middle C
, followed by F (a tone 500 cents sharper than C), followed by both tones together.
Problems playing this file? See media help.

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

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 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

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

For instance, in one "Alleluia" (

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-

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

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

church modes
.

In the first third of the 18th century, ground-laying theoretical treatises on composition and

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

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 first chord heard in Richard Wagner's opera Tristan und Isolde.

{ \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 } >> >> }

The chord had been found in earlier works, notably

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

Fourth-based harmony became important in the work of Slavic and Scandinavian composers such as

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) (Listen
) the fourth always makes an "unvarnished" entrance.

The romantic composers

Nuages gris
(Grey Clouds), La lugubre gondola (The Mournful Gondola), and other works).

In the 1897 work

Ma Mère l'Oye
(Mother Goose) would follow a few years later.

20th century music

Western classical music

Main article: quartal and quintal harmony
Quartal harmony in "Laideronnette" from Ravel's Ma Mère l'Oye. The top line uses the pentatonic scale[5] 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

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
.

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.[6]
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).[7][8][failed verification]
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
Fourths in Herbie Hancock's Maiden Voyage[citation needed]
Listen The brass section of Ray Barretto's version of Amor Artificial
Listen Guitar break from Milton Nascimentos composition "Vera Cruz"

See also

References

  1. 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}}: 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. John Tyrrell
    (London: Macmilln Publishers).
  5. ISBN 978-0-07-294262-0
    .
  6. 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/. {{cite news}}: External link in |via= (help)
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