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Perfect fourth
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Perfect fourth : ウィキペディア英語版
Perfect fourth

In classical music from Western culture, a fourth is a musical interval encompassing four staff positions (see Interval number for more details), and the perfect fourth () is a fourth spanning five semitones (half steps, or half tones). For example, the ascending interval from C to the next F is a perfect fourth, as the note F lies five semitones above C, and there are four staff positions from C to F. Diminished and augmented fourths span the same number of staff positions, but consist of a different number of semitones (four and six).
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 (unlike thirds, which are either minor or major) but perfect.
Up until the late 19th century, the perfect fourth was often called by its Greek name, ''diatessaron''.
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 (), 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 geführt''", the colloquially-titled "Here Comes the Bride"). Other examples are the first two notes of the Christmas carol "Hark! The Herald Angels Sing" or "El Cóndor Pasa", and, for a descending perfect fourth, the second and third notes of "O Come All Ye Faithful".
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. 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.〔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.〕
==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. In the 15th century the fourth came 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.〔William Drabkin (2001), "Fourth", ''The New Grove Dictionary of Music and Musicians'', second edition, edited by Stanley Sadie and John Tyrrell (London: Macmilln Publishers).〕
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.

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