In the theory and practice of music, a fifth interval is an

ordered pair In mathematics, an ordered pair (''a'', ''b'') is a pair of objects. The order in which the objects appear in the pair is significant: the ordered pair (''a'', ''b'') is different from the ordered pair (''b'', ''a'') unless ''a'' = ''b''. (In con ...

of notes that are separated by an interval of 6–8 semitones. There are three types of fifth intervals, namely * ''perfect'' fifths (7 semitones), * ''diminished'' fifth (6 semitones), and * augmented fifth (8 semitones). After the unison and

octave In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been refer ...

intervals, the ''perfect fifth'' is the most important interval in tonal harmony. It is highly consonant. Its implementation in equal temperament tuning is highly accurate, unlike the major third 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—

major Major (commandant in certain jurisdictions) is a military rank of commissioned officer status, with corresponding ranks existing in many military forces throughout the world. When used unhyphenated and in conjunction with no other indicators ...

and minor triads and also seventh chords—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 sevenths, and minor sevenths). *''Diminished'' fifths are contained in diminished triads and in half-diminished sevenths and fully diminished seventh chords. Fifths are stacked to form chords in

quintal harmony In music, quartal harmony is the building of harmonic structures built from the intervals of the perfect fourth, the augmented fourth and the diminished fourth. For instance, a three-note quartal chord on C can be built by stacking perfect fourths ...

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 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 String instruments, stringed instruments, or chordophones are musical instruments that produce sound from vibrating strings when a performer plays or sounds the strings in some manner. Musicians play some string instruments by plucking the ...

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

mandolin A mandolin ( it, mandolino ; literally "small mandola") is a stringed musical instrument in the lute family and is generally plucked with a pick. It most commonly has four courses of doubled strings tuned in unison, thus giving a total of 8 ...

and violin and it is an

alternative tuning Guitar tunings are the assignment of pitches to the open strings of guitars, including acoustic guitars, electric guitars, and classical guitars. Tunings are described by the particular pitches that are made by notes in Western music. By ...

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)