Editing Closely related key

{{Short description|Musical keys sharing many common tones}}
[[File:Circle of fifths deluxe 4.svg|thumb|right|upright=1.4|[[Circle of fifths]] showing [[major and minor]] keys.]]

In [[music]], a '''closely related key''' (or '''close key''') is one sharing many [[common tone (scale)|common tones]] with an original [[key (music)|key]], as opposed to a '''distantly related key''' (or '''distant key'''). In music [[harmony]], there are six of them: four of them share all the pitches except one with a key with which it is being compared, one of them shares all the pitches, and one shares the same [[Tonic (music)|tonic]].

Such keys are the most commonly used destinations or [[Transposition (music)|transpositions]] in a [[modulation (music)|modulation]],<ref name="Everything">Schonbrun, Marc (2006). ''The Everything Music Theory Book'', p.76. {{ISBN|1-59337-652-9}}.</ref> because of their strong structural links with the home key. Distant keys may be reached sequentially through closely related keys by [[chain modulation]], for example, C to G to D.<ref>George T. Jones (1994). ''HarperCollins College Outline Music Theory'', p.217. {{ISBN|0-06-467168-2}}.</ref> For example, "One principle that every composer of [[Joseph Haydn|Haydn]]'s day <nowiki>[</nowiki>[[Classical period (music)|Classical music era]]<nowiki>]</nowiki> kept in mind was over-all unity of [[tonality]]. No piece dared wander too far from its [[tonic (music)|tonic]] key, and no piece in a four-movement form dared to present a tonality not closely related to the key of the whole series."<ref>Ulrich, Homer (1966). ''Chamber Music'', p.175. {{ISBN|978-0-231-08617-2}}.</ref> For example, the first movement of Mozart's [[Piano Sonata No. 7 (Mozart)|Piano Sonata No. 7]], K. 309, modulates only to closely related keys (the dominant, supertonic, and submediant).<ref>Benward & Saker (2009). ''Music in Theory and Practice: Volume II'', p. 155. 8th ed. {{ISBN|978-0-07-310188-0}}.</ref>

Given a [[major scale|major key]] tonic (I), the related keys are: 
* ii ([[supertonic]],<ref name="B&S" /> the relative minor of the subdominant)
*iii ([[mediant]],<ref name="B&S" /> the relative minor of the dominant)
*IV ([[subdominant]]<ref name="Everything" /><ref name="Stone" /><ref name="Jones 35-36">Jones (1994), p.35-36.</ref><ref name="B&S" />): one less [[sharp (music)|sharp]] (or one more [[flat (music)|flat]]) around circle of fifths
*V ([[dominant (music)|dominant]]<ref name="Everything" /><ref name="Jones 35-36" /><ref name="B&S" />): one more sharp (or one fewer flat) around circle of fifths
*vi ([[submediant]] or relative minor<ref name="Everything" /><ref name="Stone">Barry, Barbara R. (2000). ''The Philosopher's Stone: Essays in the Transformation of Musical Structure'', p.19. {{ISBN|1-57647-010-5}}.</ref><ref name="B&S">Benward & Saker (2003). ''Music: In Theory and Practice''. Vol. I. p. 243. 7th ed. McGraw-Hill. {{ISBN|978-0-07-294262-0}}. "Most modulations occur between ''closely related keys'', which are those keys that differ by no more than one accidental in the key signature."</ref>): different tonic, same key signature
*i ([[Parallel key|parallel minor]]): same tonic, different key signature

[[File:Closely Related keys in C.png|alt=|center|thumb|upright=1.8|Closely related keys in C.]]
Specifically:

{| class="wikitable"
!Original key (major)
!Submediant (relative minor)
!Subdominant, dominant, supertonic, and mediant
!Subdominants
!Dominants
!Parallel minor
|-
|C
|Am
|F, G, Dm, Em
|B{{music|flat}}, E{{music|flat}}, A{{music|flat}}, D{{music|flat}}
|D, A, E, B
|Cm
|-
|G
|Em
|C, D, Am, Bm
|F, B{{music|flat}}, E{{music|flat}}, A{{music|flat}}
|A, E, B, F{{music|sharp}}
|Gm
|-
|D/E{{music|double flat}}
|Bm/C{{music|flat}}m
|G/A{{music|double flat}}, A/B{{music|double flat}}, Em/F{{music|flat}}m, F{{music|sharp}}m/G{{music|flat}}m
|C/D{{music|double flat}}, F/G{{music|double flat}}, B{{music|flat}}/C{{music|double flat}}, E{{music|flat}}/F{{music|double flat}}
|E/F{{music|flat}}, B/C{{music|flat}}, F{{music|sharp}}/G{{music|flat}}, C{{music|sharp}}/D{{music|flat}}
|Dm/E{{music|double flat}}m
|-
|A/B{{music|double flat}}
|F{{music|sharp}}m/G{{music|flat}}m
|D/E{{music|double flat}}, E/F{{music|flat}}, Bm/C{{music|flat}}m, C{{music|sharp}}m/D{{music|flat}}m
|G/A{{music|double flat}}, C/D{{music|double flat}}, F/G{{music|double flat}}, B{{music|flat}}/C{{music|double flat}}
|B/C{{music|flat}}, F{{music|sharp}}/G{{music|flat}}, C{{music|sharp}}/D{{music|flat}}, G{{music|sharp}}/A{{music|flat}}
|Am/B{{music|double flat}}m
|-
|E/F{{music|flat}}
|C{{music|sharp}}m/D{{music|flat}}m
|A/B{{music|double flat}}, B/C{{music|flat}}, F{{music|sharp}}m/G{{music|flat}}m, G{{music|sharp}}m/A{{music|flat}}m
|D/E{{music|double flat}}, G/A{{music|double flat}}, C/D{{music|double flat}}, F/G{{music|double flat}}
|F{{music|sharp}}/G{{music|flat}}, C{{music|sharp}}/D{{music|flat}}, G{{music|sharp}}/A{{music|flat}}, D{{music|sharp}}/E{{music|flat}}
|Em/F{{music|flat}}m
|-
|B/C{{music|flat}}
|G{{music|sharp}}m/A{{music|flat}}m
|E/F{{music|flat}}, F{{music|sharp}}/G{{music|flat}}, C{{music|sharp}}m/D{{music|flat}}m, D{{music|sharp}}m/E{{music|flat}}m
|A/B{{music|double flat}}, D/E{{music|double flat}}, G/A{{music|double flat}}, C/D{{music|double flat}}
|C{{music|sharp}}/D{{music|flat}}, G{{music|sharp}}/A{{music|flat}}, D{{music|sharp}}/E{{music|flat}}, A{{music|sharp}}/B{{music|flat}}
|Bm/C{{music|flat}}m
|-
|F{{music|sharp}}/G{{music|flat}}
|D{{music|sharp}}m/E{{music|flat}}m
|B/C{{music|flat}}, C{{music|sharp}}/D{{music|flat}}, G{{music|sharp}}m/A{{music|flat}}m, A{{music|sharp}}m/B{{music|flat}}m
|E/F{{music|flat}}, A/B{{music|double flat}}, D/E{{music|double flat}}, G/A{{music|double flat}}
|G{{music|sharp}}/A{{music|flat}}, D{{music|sharp}}/E{{music|flat}}, A{{music|sharp}}/B{{music|flat}}, E{{music|sharp}}/F
|F{{music|sharp}}m/G{{music|flat}}m
|-
|C{{music|sharp}}/D{{music|flat}}
|A{{music|sharp}}m/B{{music|flat}}m
|F{{music|sharp}}/G{{music|flat}}, G{{music|sharp}}/A{{music|flat}}, D{{music|sharp}}m/E{{music|flat}}m, E{{music|sharp}}m/Fm
|B/C{{music|flat}}, E/F{{music|flat}}, A/B{{music|double flat}}, D/E{{music|double flat}}
|D{{music|sharp}}/E{{music|flat}}, A{{music|sharp}}/B{{music|flat}}, E{{music|sharp}}/F, B{{music|sharp}}/C
|C{{music|sharp}}m/D{{music|flat}}m
|-
|G{{music|sharp}}/A{{music|flat}}
|E{{music|sharp}}m/Fm
|C{{music|sharp}}/D{{music|flat}}, D{{music|sharp}}/E{{music|flat}}, A{{music|sharp}}m/B{{music|flat}}m, B{{music|sharp}}m/Cm
|F{{music|sharp}}/G{{music|flat}}, B/C{{music|flat}}, E/F{{music|flat}}, A/B{{music|double flat}}
|A{{music|sharp}}/B{{music|flat}}, E{{music|sharp}}/F, B{{music|sharp}}/C, F{{music|double sharp}}/G
|G{{music|sharp}}m/A{{music|flat}}m
|-
|D{{music|sharp}}/E{{music|flat}}
|B{{music|sharp}}m/Cm
|G{{music|sharp}}/A{{music|flat}}, A{{music|sharp}}/B{{music|flat}}, E{{music|sharp}}m/Fm, F{{music|double sharp}}m/Gm
|C{{music|sharp}}/D{{music|flat}}, F{{music|sharp}}/G{{music|flat}}, B/C{{music|flat}}, E/F{{music|flat}}
|E{{music|sharp}}/F, B{{music|sharp}}/C, F{{music|double sharp}}/G, C{{music|double sharp}}/D
|D{{music|sharp}}m/E{{music|flat}}m
|-
|A{{music|sharp}}/B{{music|flat}}
|F{{music|double sharp}}m/Gm
|D{{music|sharp}}/E{{music|flat}}, E{{music|sharp}}/F, B{{music|sharp}}m/Cm, C{{music|double sharp}}m/Dm
|G{{music|sharp}}/A{{music|flat}}, C{{music|sharp}}/D{{music|flat}}, F{{music|sharp}}/G{{music|flat}}, B/C{{music|flat}}
|B{{music|sharp}}/C, F{{music|double sharp}}/G, C{{music|double sharp}}/D, G{{music|double sharp}}/A
|A{{music|sharp}}m/B{{music|flat}}m
|-
|F
|Dm
|B{{music|flat}}, C, Gm, Am
|E{{music|flat}}, A{{music|flat}}, D{{music|flat}}, G{{music|flat}}
|G, D, A, E
|Fm
|-
|}

In a minor key, the closely related keys are the parallel major, mediant or relative major, the subdominant, the minor dominant, the submediant, and the [[subtonic]]. In the key of [[A minor]], when we translate them to keys, we get:
* [[A major]] (I)
* [[C major]] (III)
* [[D minor]] (iv)
* [[E minor]] (v)
* [[F major]] (VI)
* [[G major]] (VII)

Another view of closely related keys is that there are six closely related keys, based on the tonic and the remaining triads of the [[diatonic scale]], excluding the [[Consonance and dissonance|dissonant]] diminished triads.<ref name="Jones 35-36" /> Four of the six differ by one accidental, one has the same key signature, and one uses the parallel modal form. In the key of [[C major]], these would be: [[D minor]], [[E minor]], [[F major]], [[G major]], [[A minor]], and [[C minor]]. Despite being three sharps or flats away from the original key in the circle of fifths, parallel keys are also considered as closely related keys as the tonal center is the same, and this makes this key have an affinity with the original key. 

In modern music, the closeness of a relation between any two keys or sets of pitches may be determined by the number of tones they share in common, which allows one to consider modulations not occurring in standard major-minor tonality. For example, in music based on the [[pentatonic scale]] containing pitches C, D, E, G, and A, modulating a fifth higher gives the collection of pitches G, A, B, D, and E, having four of five tones in common. However, modulating up a [[tritone]] would produce F{{music|sharp}}, G{{music|sharp}}, A{{music|sharp}}, C{{music|sharp}}, D{{music|sharp}}, which shares no common tones with the original scale. Thus the scale a fifth higher is very closely related, while the scale a tritone higher is not. Other modulations may be placed in order from closest to most distant depending upon the number of common tones.

According to another view in modern music, notably in [[Béla Bartók|Bartók]], a common tonic produces closely related keys, the other scales being the six other modes. This usage can be found in several of the ''[[Mikrokosmos (Bartók)|Mikrokosmos]]'' piano pieces.

When modulation causes the new key to traverse the bottom of the circle of fifths this may give rise to a [[theoretical key]], containing eight (or more) sharps or flats in its notated key signature; in such a case, notational conventions require recasting the new section in its [[enharmonic|enharmonically equivalent]] key.

[[Andranik Tangian]] suggests 3D and 2D visualizations of key/chord proximity for both all major and all minor keys/chords by locating them along a single subdominant-dominant axis, which wraps a torus that is then unfolded.<ref name="Tangian2021ProximityMapsForMajorAndMinor">{{Cite book
|last=Tangian |first=Andranik 
|date=2021
|title= 2D and 3D proximity maps for major and minor keys and chords.
|series=KIT Scientific Working Papers |volume=171
|publisher=Karlsruhe Institute of Technology (KIT)
|location=Karlsruhe
|issn = 2194-1629
|url=https://publikationen.bibliothek.kit.edu/1000135520
|doi=10.5445/IR/1000135520}}</ref>

==See also==
* [[Chromatic mediant]]
* [[Common chord (music)]]
* [[Monotonality]]
* [[Parallel and counter parallel]]
* [[Pitch space]]

==References==
<references/>

==Further reading==
* Howard Hanson, ''Harmonic Materials of Modern Music''. Appleton-Century-Crofts, Inc, 1960.

{{Key (music)}}

{{DEFAULTSORT:Closely Related Key}}
[[Category:Musical keys]]