{{Short description|none}} In the theory and practice of music, a '''fifth interval''' is an ordered pair 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 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 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.
===Cycle of fifths=== [[Image:Pitch class space star.svg|thumb|right|The circle of fifths drawn within the chromatic circle as a regular star dodecagon<ref>{{harvtxt|McCartin|1998|p=364}}: {{cite journal|title=Prelude to musical geometry|first=Brian J.|last=McCartin|journal=The College Mathematics Journal|volume=29|number=5|date=November 1998|pages=354–370|doi=10.1080/07468342.1998.11973971 |url=http://www.maa.org/pubs/cmj_Nov98.html|jstor=2687250|url-access=subscription }}</ref>]]
Concatenating the perfect fifths <big>(</big>(F, C), (C, G), (G, D), (D, A), (A, E), (E, B),...<big>)</big> generates the sequence of fifths (F, C, G, D, A, E, B, F{{music|sharp}}, ...); this sequence of fifths displays all twelve notes of the chromatic circle.<ref>This sequence of fifths features the diminished fifth (b, f), which replaces the perfect fifth (b, f{{music|sharp}}) containing the chromatic note f{{music|sharp}}, which is not a member of the C major key.
The note f (of the C major scale) is replaced by the note f{{music|sharp}} in the Lydian chromatic scale {{harv|Russell|2001|loc="The fundamental harmonic structure of the Lydian scale", Example 1:7, "The C Lydian scale", p. 5}}. {{cite book|last=Russell|first=George|author-link=George Russell (composer)|title=George Russell's Lydian chromatic concept of tonal organization|edition=Fourth (Second printing, corrected, 2008) |year=2001|orig-year=1953|volume=One: The art and science of tonal gravity|publisher=Concept Publishing Company|location=Brookline, Massachusetts|isbn=0-9703739-0-2|chapter=Chapter 1 The Lydian scale: The seminal source of the principal of tonal gravity|pages=1–9}}</ref>
===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. <score vorbis="1"> { <c' g'> <d' a'> <e' b'> <f' c''> <g' d''> <a' e''> <b' f''> <c'' g''> }</score>
===Tuning of instruments=== thumb|right|All-fifths tuning
''All-fifths tuning'' refers to the set of tunings 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 and it is an alternative tuning for guitars. All-fifths tuning is also called ''fifths'', ''perfect fifths'', or ''mandoguitar'' tuning.<ref>{{cite book |chapter=Regular tunings |title=Alternate tuning guide |first=Bill |last=Sethares |author-link=William Sethares |year=2001 |pages=52–67 |url=http://sethares.engr.wisc.edu/alternatetunings/regulartunings.pdf |publisher=University of Wisconsin; Department of Electrical Engineering|location=Madison, Wisconsin |access-date=19 May 2012 |id=[http://sethares.engr.wisc.edu/alternatetunings/alltunings.pdf 2010 ''Alternate tuning guide'', including a revised chapter on regular tunings]}}</ref>
==References== '''Notes''' {{Reflist}}
'''Bibliography''' * {{cite book|last1=Clendinning|first1=Jane Piper|last2=Marvin|first2=Elizabeth West|title=The musician's guide to theory and analysis|year=2005|publisher=W. W. Norton and Company|location=New York|isbn=0-393-97652-1|edition=First}} *{{cite book|last=Duckworth|first=William|author-link=William Duckworth (composer)|title=A creative approach to music fundamentals: Includes keyboard and guitar insert|pages=[https://archive.org/details/creativeapproach00will/page/1 1–384]|publisher=Thomson Schirmer|edition=ninth|year=2007|isbn=978-0-495-09093-9|location=2005928009|url-access=registration|url=https://archive.org/details/creativeapproach00will/page/1}} * {{cite book |last1=Kostka|first1=Stefan|first2=Dorothy|last2=Payne|first3=Byron|last3=Almén |title=Tonal harmony with an introduction to twentieth-century music |edition=seventh|year=2013|location=New York|publisher=McGraw-Hill |isbn=978-0-07-131828-0}} * {{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 }}
Category:Fifths (music)