Perfect fourth

From Wikipedia for FEVERv2
Jump to navigation Jump to search

Perfect fourth_table_infobox_0

perfect fourthPerfect fourth_table_caption_0
InversePerfect fourth_header_cell_0_0_0 perfect fifthPerfect fourth_cell_0_0_1
NamePerfect fourth_header_cell_0_1_0
Other namesPerfect fourth_header_cell_0_2_0 diatessaronPerfect fourth_cell_0_2_1
AbbreviationPerfect fourth_header_cell_0_3_0 P4Perfect fourth_cell_0_3_1
SizePerfect fourth_header_cell_0_4_0
SemitonesPerfect fourth_header_cell_0_5_0 5Perfect fourth_cell_0_5_1
Interval classPerfect fourth_header_cell_0_6_0 5Perfect fourth_cell_0_6_1
Just intervalPerfect fourth_header_cell_0_7_0 4:3Perfect fourth_cell_0_7_1
CentsPerfect fourth_header_cell_0_8_0
Equal temperamentPerfect fourth_header_cell_0_9_0 500Perfect fourth_cell_0_9_1
Just intonationPerfect fourth_header_cell_0_10_0 498Perfect fourth_cell_0_10_1

A fourth is a musical interval encompassing four staff positions in the music notation of Western culture, and a perfect fourth (Play (help·)) is the fourth spanning five semitones (half steps, or half tones). Perfect fourth_sentence_0

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). Perfect fourth_sentence_1

The perfect fourth may be derived from the harmonic series as the interval between the third and fourth harmonics. Perfect fourth_sentence_2

The term perfect identifies this interval as belonging to the group of perfect intervals, so called because they are neither major nor minor. Perfect fourth_sentence_3

A perfect fourth in just intonation corresponds to a pitch ratio of 4:3, or about 498 cents (Play (help·)), while in equal temperament a perfect fourth is equal to five semitones, or 500 cents (see additive synthesis). Perfect fourth_sentence_4

Until the late 19th century, the perfect fourth was often called by its Greek name, diatessaron. Perfect fourth_sentence_5

Its most common occurrence is between the fifth and upper root of all major and minor triads and their extensions. Perfect fourth_sentence_6

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"). Perfect fourth_sentence_7

Other examples are the first two notes of the Christmas carol "Hark! Perfect fourth_sentence_8 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". Perfect fourth_sentence_9

The perfect fourth is a perfect interval like the unison, octave, and perfect fifth, and it is a sensory consonance. Perfect fourth_sentence_10

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". Perfect fourth_sentence_11

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. Perfect fourth_sentence_12

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. Perfect fourth_sentence_13

Sets of tom-tom drums are also commonly tuned in perfect fourths. Perfect fourth_sentence_14

The 4:3 just perfect fourth arises in the C major scale between G and C. Play (help·) Perfect fourth_sentence_15

History Perfect fourth_section_0

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. Perfect fourth_sentence_16

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. Perfect fourth_sentence_17

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). Perfect fourth_sentence_18

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. Perfect fourth_sentence_19

Modern acoustic theory supports the medieval interpretation insofar as the intervals of unison, octave, fifth and fourth have particularly simple frequency ratios. Perfect fourth_sentence_20

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. Perfect fourth_sentence_21

The fifth has a ratio of 3:2, and its complement has the ratio of 3:4. Perfect fourth_sentence_22

Ancient and medieval music theorists appear to have been familiar with these ratios, see for example their experiments on the monochord. Perfect fourth_sentence_23

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. Perfect fourth_sentence_24

In early western polyphony, these simpler intervals (unison, octave, fifth and fourth) were generally preferred. Perfect fourth_sentence_25

However, in its development between the 12th and 16th centuries: Perfect fourth_sentence_26

Perfect fourth_unordered_list_0

  • In the earliest stages, these simple intervals occur so frequently that they appear to be the favourite sound of composers.Perfect fourth_item_0_0
  • Later, the more "complex" intervals (thirds, sixths, and tritones) move gradually from the margins to the centre of musical interest.Perfect fourth_item_0_1
  • 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).Perfect fourth_item_0_2

The music of the 20th century for the most part discards the rules of "classical" Western tonality. Perfect fourth_sentence_27

For instance, composers such as Erik Satie borrowed stylistic elements from the Middle Ages, but some composers found more innovative uses for these intervals. Perfect fourth_sentence_28

Middle Ages Perfect fourth_section_1

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. Perfect fourth_sentence_29

The Musica enchiriadis of the mid-10th century, a guidebook for musical practice of the time, described singing in parallel fourths, fifths, and octaves. Perfect fourth_sentence_30

This development continued, and the music of the Notre Dame school may be considered the apex of a coherent harmony in this style. Perfect fourth_sentence_31

For instance, in one "Alleluia" () by Pérotin, the fourth is favoured. Perfect fourth_sentence_32

Elsewhere, in parallel organum at the fourth, the upper line would be accompanied a fourth below. Perfect fourth_sentence_33

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. Perfect fourth_sentence_34

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. Perfect fourth_sentence_35

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. Perfect fourth_sentence_36

An example of this is the start of the Marian-Antiphon Ave Maris Stella () by Guillaume Dufay, a master of Fauxbourdon. Perfect fourth_sentence_37

Renaissance and Baroque Perfect fourth_section_2

The development of tonality continued through the Renaissance until it was fully realized by composers of the Baroque era. Perfect fourth_sentence_38

As time progressed through the late Renaissance and early Baroque, the fourth became more understood as an interval that needed resolution. Perfect fourth_sentence_39

Increasingly the harmonies of fifths and fourths yielded to uses of thirds and sixths. Perfect fourth_sentence_40

In the example, cadence forms from works by Orlando di Lasso and Palestrina show the fourth being resolved as a suspension. Perfect fourth_sentence_41

() Perfect fourth_sentence_42

In the early Baroque music of Claudio Monteverdi and Girolamo Frescobaldi triadic harmony was thoroughly utilized. Perfect fourth_sentence_43

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. Perfect fourth_sentence_44

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. Perfect fourth_sentence_45

Also, in Frescobaldi's Chromatic Toccata of 1635 the outlined fourths overlap, bisecting various church modes. Perfect fourth_sentence_46

In the first third of the 18th century, ground-laying theoretical treatises on composition and harmony were written. Perfect fourth_sentence_47

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. Perfect fourth_sentence_48

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). Perfect fourth_sentence_49

He outlined various types of counterpoint (e.g., note against note), and suggested a careful application of the fourth so as to avoid dissonance. Perfect fourth_sentence_50

Classical and romantic Perfect fourth_section_3

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. Perfect fourth_sentence_51

An increasingly refined cadence, and triadic harmony defined the musical work of this era. Perfect fourth_sentence_52

Counterpoint was simplified to favour an upper line with a clear accompanying harmony. Perfect fourth_sentence_53

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. Perfect fourth_sentence_54

Mozart in his so-called Dissonance Quartet KV 465 () 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 () opens with three ascending fourths. Perfect fourth_sentence_55

These are all melodic examples, however, and the underlying harmony is built on thirds. Perfect fourth_sentence_56

Composers started to reassess the quality of the fourth as a consonance rather than a dissonance. Perfect fourth_sentence_57

This would later influence the development of quartal and quintal harmony. Perfect fourth_sentence_58

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_sentence_59

Perfect fourth_description_list_1

The chord had been found in earlier works, notably Beethoven's Piano Sonata No. Perfect fourth_sentence_60 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. Perfect fourth_sentence_61

Fourth-based harmony became important in the work of Slavic and Scandinavian composers such as Modest Mussorgsky, Leoš Janáček, and Jean Sibelius. Perfect fourth_sentence_62

These composers used this harmony in a pungent, uncovered, almost archaic way, often incorporating the folk music of their particular homelands. Perfect fourth_sentence_63

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. Perfect fourth_sentence_64

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) () the fourth always makes an "unvarnished" entrance. Perfect fourth_sentence_65

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). Perfect fourth_sentence_66

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". Perfect fourth_sentence_67

Quartal harmony in Ravel's Sonatine and Ma Mère l'Oye (Mother Goose) would follow a few years later. Perfect fourth_sentence_68

20th century music Perfect fourth_section_4

Western classical music Perfect fourth_section_5

Main article: quartal and quintal harmony Perfect fourth_sentence_69

In the 20th century, harmony explicitly built on fourths and fifths became important. Perfect fourth_sentence_70

This became known as quartal harmony for chords based on fourths and quintal harmony for chords based on fifths. Perfect fourth_sentence_71

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. Perfect fourth_sentence_72

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. Perfect fourth_sentence_73

Jazz Perfect fourth_section_6

Jazz uses quartal harmonies (usually called voicing in fourths). Perfect fourth_sentence_74

Cadences are often "altered" to include unresolved suspended chords which include a fourth above the bass: Perfect fourth_sentence_75

See also Perfect fourth_section_7

Perfect fourth_unordered_list_2

Credits to the contents of this page go to the authors of the corresponding Wikipedia page: fourth.