In the

theory A theory is a rational type of abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with such processes as observational study or research. Theories may be ...

and practice of

music Music is generally defined as the art of arranging sound to create some combination of form, harmony, melody, rhythm or otherwise expressive content. Exact definitions of music vary considerably around the world, though it is an aspe ...

, a fifth interval is an ordered pair of

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 version ...

s that are separated by an interval of 6–8

semitone A semitone, also called a 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 two adjacent no ...

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

augmented fifth In classical music from Western culture, 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 f ...

(8 semitones). After the

unison In music, unison is two or more musical parts that sound either the same pitch or pitches separated by intervals of one or more octaves, usually at the same time. ''Rhythmic unison'' is another term for homorhythm. Definition Unison or per ...

and octave 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. Examples are and pronounced with the lips; and pronounced with the front of the tongue; and pronounced wi ...

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

major third In classical music, 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 semitones.Allen Forte, ...

interval, for example. As explained below, it is used to generate the

chromatic circle The chromatic circle is a clock diagram for displaying relationships among the 12 equal-tempered pitch classes making up the familiar chromatic scale on a circle. Explanation If one starts on any equal-tempered pitch and repeatedly ascends by ...

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 triadic chord with the greatest stability is cal ...

— major 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 C, called a C minor triad, has pitch ...

s and also

seventh chord A seventh chord is a chord consisting of a triad plus a note forming an interval of a seventh above the chord's root. When not otherwise specified, a "seventh chord" usually means a dominant seventh chord: a major triad together with a mi ...

s—all contain fifth intervals. *''Perfect'' fifths are contained in major and minor triads and in particular seventh chords (especially

major-minor seventh A seventh chord is a chord consisting of a triad plus a note forming an interval of a seventh above the chord's root. When not otherwise specified, a "seventh chord" usually means a dominant seventh chord: a major triad together with a minor ...

s with

dominant function In music, the dominant is the fifth scale degree () of the diatonic scale. It is called the ''dominant'' because it is second in importance to the first scale degree, the tonic. In the movable do solfège system, the dominant note is sung as "So ...

major seventh In music from Western culture, a seventh is a musical interval encompassing seven staff positions (see Interval number for more details), and the major seventh is one of two commonly occurring sevenths. It is qualified as ''major'' because it i ...

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 fr ...

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

diminished triad In music theory, a diminished triad (also known as the minor flatted fifth) is a triad consisting of two minor thirds above the root. It is a minor triad with a lowered ( flattened) fifth. When using chord symbols, it may be indicated by the s ...

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 note, together with a minor third, a diminished fifth, and a minor seventh (1, ...

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 calle ...

of fifths displays all twelve notes of the

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 Among guitar tunings, all-fifths tuning refers to the set of tunings in which each interval between consecutive open strings is a perfect fifth. All-fifths tuning is also called fifths, perfect fifths, or mandoguitar. The conventional ...

'' refers to the set of

tuning Tuning can refer to: Common uses * Tuning, the process of tuning a tuned amplifier or other electronic component * Musical tuning, musical systems of tuning, and the act of tuning an instrument or voice ** Guitar tunings ** Piano tuning, adjusti ...

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

violin The violin, sometimes known as a '' fiddle'', is a wooden chordophone ( string instrument) in the violin family. Most violins have a hollow wooden body. It is the smallest and thus highest-pitched instrument ( soprano) in the family in regu ...

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)