In the

theory A theory is a systematic and rational form of abstract thinking about a phenomenon, or the conclusions derived from such thinking. It involves contemplative and logical reasoning, often supported by processes such as observation, experimentation, ...

and practice of

music Music is the arrangement of sound to create some combination of Musical form, form, harmony, melody, rhythm, or otherwise Musical expression, expressive content. Music is generally agreed to be a cultural universal that is present in all hum ...

, a fifth interval is an

ordered pair In mathematics, an ordered pair, denoted (''a'', ''b''), is a pair of objects in which their order is significant. The ordered pair (''a'', ''b'') is different from the ordered pair (''b'', ''a''), unless ''a'' = ''b''. In contrast, the '' unord ...

note Note, notes, or NOTE may refer to: Music and entertainment * Musical note, a pitched sound (or a symbol for a sound) in music * ''Notes'' (album), a 1987 album by Paul Bley and Paul Motian * ''Notes'', a common (yet unofficial) shortened versi ...

s that are separated by an interval of 6–8

semitone A semitone, also called a minor second, half step, or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically. It is defined as the interval between ...

s. There are three types of fifth intervals, namely * ''perfect'' fifths (7 semitones), * ''diminished'' fifth (6 semitones), and *

augmented fifth In Western classical music, an augmented fifth () is an interval produced by widening a perfect fifth by a chromatic semitone.Benward & Saker (2003). ''Music: In Theory and Practice, Vol. I'', p.54. . For instance, the interval from C to G i ...

(8 semitones). After the

unison Unison (stylised as UNISON) is a Great Britain, British trade union. Along with Unite the Union, Unite, Unison is one of the two largest trade unions in the United Kingdom, with over 1.2 million members who work predominantly in public servic ...

and

octave In music, an octave (: eighth) or perfect octave (sometimes called the diapason) is an interval between two notes, one having twice the frequency of vibration of the other. The octave relationship is a natural phenomenon that has been referr ...

intervals, the ''perfect fifth'' is the most important interval in tonal harmony. It is highly

consonant In articulatory phonetics, a consonant is a speech sound that is articulated with complete or partial closure of the vocal tract, except for the h sound, which is pronounced without any stricture in the vocal tract. Examples are and pronou ...

. Its implementation in equal temperament tuning is highly accurate, unlike the

major third In music theory, a third is a Interval (music), musical interval encompassing three staff positions (see Interval (music)#Number, Interval number for more details), and the major third () is a third spanning four Semitone, half steps or two ...

interval, for example. As explained below, it is used to generate the chromatic circle and the cycle of fifths, and it is used for tuning string-instruments. It is a constituent interval for the fundamental chords of tonal harmony.

Tonal harmony

The fundamental chords of

tonal music Tonality is the arrangement of pitches and / or chords of a musical work in a hierarchy of perceived ''relations'', ''stabilities'', ''attractions'', and ''directionality''. In this hierarchy, the single pitch or the root of a triad with t ...

—

major Major most commonly refers to: * Major (rank), a military rank * Academic major, an academic discipline to which an undergraduate student formally commits * People named Major, including given names, surnames, nicknames * Major and minor in musi ...

and

minor triad In music theory, a minor chord is a chord that has a root, a minor third, and a perfect fifth. When a chord comprises only these three notes, it is called a minor triad. For example, the minor triad built on A, called an A minor triad, has pit ...

s and also

seventh chord A seventh chord is a chord (music), chord consisting of a triad (music), triad plus a note forming an interval (music), interval of a Interval (music), seventh above the chord's root (chord), root. When not otherwise specified, a "seventh chord" ...

s—all contain fifth intervals. *''Perfect'' fifths are contained in major and minor triads and in particular seventh chords (especially major-minor sevenths with dominant function,

major seventh In music from Western culture, a seventh is a interval (music), musical interval encompassing seven staff positions (see Interval (music)#Number, Interval number for more details), and the major seventh is one of two commonly occurring sevenths. ...

s, and

minor seventh In music theory, a minor seventh is one of two musical intervals that span seven staff positions. It is ''minor'' because it is the smaller of the two sevenths, spanning ten semitones. The major seventh spans eleven. For example, the interval ...

s). *''Diminished'' fifths are contained in

diminished triad In music theory, a diminished triad is a triad (music), triad consisting of two minor thirds above the root (chord), root. It is a Minor chord, minor triad with a lowered (flat (music), flattened) Fifth (chord), fifth. When using Chord names and ...

s and in

half-diminished seventh In music theory, the half-diminished seventh chord (also known as a half-diminished chord or a minor seventh flat five chord) is a seventh chord composed of a Root (chord), root note, together with a minor third, a tritone, diminished fifth, and ...

s and fully diminished seventh chords. Fifths are stacked to form chords in quintal harmony.

Cycle of fifths

Concatenating the perfect fifths ((F, C), (C, G), (G, D), (D, A), (A, E), (E, B),...) generates the sequence of fifths (F, C, G, D, A, E, B, F, ...); this

sequence In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is cal ...

of fifths displays all twelve notes of the chromatic circle.

Harmonization of scales in fifths

Major scale on C

All but one of the intervals are perfect fifths. The (b, f) interval is a diminished fifth.

Tuning of instruments

'' All-fifths tuning'' refers to the set of tunings for

string instrument In musical instrument classification, string instruments, or chordophones, are musical instruments that produce sound from vibrating strings when a performer strums, plucks, strikes or sounds the strings in varying manners. Musicians play some ...

s in which each interval between consecutive open strings is a perfect fifth. All-fifths tuning is the standard tuning for

mandolin A mandolin (, ; literally "small mandola") is a Chordophone, stringed musical instrument in the lute family and is generally Plucked string instrument, plucked with a plectrum, pick. It most commonly has four Course (music), courses of doubled St ...

and

violin The violin, sometimes referred to as a fiddle, is a wooden chordophone, and is the smallest, and thus highest-pitched instrument (soprano) in regular use in the violin family. Smaller violin-type instruments exist, including the violino picc ...

and it is an alternative tuning for guitars. All-fifths tuning is also called ''fifths'', ''perfect fifths'', or ''mandoguitar'' tuning.

References

Notes Bibliography * * * * {{cite book , last=Persichetti , first=Vincent , author-link=Vincent Persichetti , title=Twentieth-century harmony: Creative aspects and practice , year=1961 , publisher=W. W. Norton , location=New York , isbn=0-393-09539-8 , oclc=398434 , url-access=registration , url=https://archive.org/details/isbn_9780393095395 Fifths (music)