Editing Perfect fifth (section)

==Use in harmony==

W. E. Heathcote describes the octave as representing the prime unity within the triad, a higher unity produced from the successive process: "first Octave, then Fifth, then Third, which is the union of the two former".<ref>W. E. Heathcote (1888), "Introductory Essay", in [[Moritz Hauptmann]], [https://archive.org/details/bub_gb_a8o5AAAAIAAJ <!-- quote="first octave" "then fifth". --> ''The Nature of Harmony and Metre''], translated and edited by W. E. Heathcote (London: Swan Sonnenschein), p. xx.</ref> Hermann von Helmholtz argues that some intervals, namely the perfect fourth, fifth, and octave, "are found in all the musical scales known", though the editor of the English translation of his book notes the fourth and fifth may be interchangeable or indeterminate.<ref>{{cite book | title = On the Sensations of Tone as a Physiological Basis for the Theory of Music | publisher = Longmans, Green |author=[[Hermann von Helmholtz]]| year = 1912 | url = https://archive.org/details/onsensationston01helmgoog | quote = perfect fifth imperfect fifth Helmholtz tempered| page = [https://archive.org/details/onsensationston01helmgoog/page/n274 253]| isbn = 9781419178931 }}</ref>

The perfect fifth is a basic element in the construction of major and minor [[triad (music)|triad]]s, and their [[extended chords|extensions]]. Because these chords occur frequently in much music, the perfect fifth occurs just as often. However, since many instruments contain a perfect fifth as an [[overtone]], it is not unusual to omit the fifth of a chord (especially in root position).

The perfect fifth is also present in [[seventh chords]] as well as "tall tertian" harmonies (harmonies consisting of more than four tones stacked in thirds above the root). The presence of a perfect fifth can in fact soften the [[Consonance and dissonance|dissonant]] intervals of these chords, as in the [[major seventh chord]] in which the dissonance of a major seventh is softened by the presence of two perfect fifths.

Chords can also be built by stacking fifths, yielding quintal harmonies. Such harmonies are present in more modern music, such as the music of [[Paul Hindemith]]. This harmony also appears in [[Stravinsky]]'s ''[[The Rite of Spring]]'' in the "Dance of the Adolescents" where four C [[trumpet]]s, a [[piccolo trumpet]], and one [[French horn|horn]] play a five-tone B-flat quintal chord.{{sfn|Piston|DeVoto|1987|pp=503–505}}