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. 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. 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 's Antiphon
Ave Maris Stella 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. For instance, in one "Alleluia" ([//upload.wikimedia.org/wikipedia/commons/3/34/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
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 ([//upload.wikimedia.org/wikipedia/commons/3/3d/AveMarisStellaDufay_for_wikipedia.mid 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. 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. ([//upload.wikimedia.org/wikipedia/commons/5/59/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
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 ([//upload.wikimedia.org/wikipedia/commons/a/ab/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
Beethoven's Piano sonata op. 110 ([//upload.wikimedia.org/wikipedia/commons/8/84/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. 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 (~ 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.~\ d!4.)~\p d8 r r } >> \new Staff 2.( 4.)~ 8 r r } >> >> } 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. '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 ([//upload.wikimedia.org/wikipedia/commons/2/29/Baba_Yaga_Quarten_for_wikipedia.mid 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 's ''
Ma Mère l'Oye''. The top line uses the
pentatonic scale 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" from his
Préludes for piano as well as "Pour les quartes," and "Pour les arpéges composées from his
Etudes.
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: [//upload.wikimedia.org/wikipedia/commons/b/b1/II_V9_I.MID Listen]) The II-V-I cadence ([//upload.wikimedia.org/wikipedia/commons/6/6d/II_V9sus_I.MID Listen]) The fourth-suspension or "sus"-chord 's
Maiden Voyage ==See also==