Parallel and counter parallel: Difference between revisions

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{{Short description|Type of chord}}

{{See also|Parallel key|Parallel harmony|#Leittonwechselklänge}}

[[Image:Tonic parallel in C major.png|thumb|Tonic and tonic parallel in C  major: CMC{{sup|M}} and Am chords {{audio|Tonic parallel in C major.mid|Play}}.]]

[[Image:Tonic parallel in C minor.png|thumb|Tonic and tonic parallel in C  minor: CmC{{small|m}} and E{{sup|{{music|b}}M}} chords {{audio|Tonic parallel in C minor.mid|Play}}.]]

[[Image:Subdominant parallel in C major.png|thumb|Subdominant and subdominant parallel in C &nbsp;major (Sp): FMF{{sup|M}} and DmD{{small|m}} chords.<ref name="Material">[[{{cite book |author1-link=Percy Goetschius |last1=Goetschius, Percy]]|first1=P. and [[|author2-link=Immanuel Faisst |last2=Faisst, Immanuel]]|first2=I. (|year=1889). ''|title=The Material Used in Musical Composition'', p.|page=139. |publisher=[[G. Schirmer|G.&nbsp;Schirmer]] }}</ref><ref name="Kober">{{cite book |last=Kober, |first=Thorsten (|year=2003). ''|title=Guitar Works: A Comprehensivecomprehensive Guideguide to Playingplaying the Guitar'',guitar p.|page=136. |ISBN =978-0-634-03123-6. }}</ref><ref name="Kalamajski">{{cite book |first=Sebastian |last=Kalamajski (|year=2000). ''|title=All Aspects of Rock & Jazz'', p.|page=35. |ISBN =978-87-88619-68-3. }}</ref> {{audio|Subdominant parallel in C major.mid|Play}}]]

[[Image:Subdominant parallel in C minor.png|thumb|Subdominant and subdominant parallel in C &nbsp;minor (sP): FmF{{small|m}} and A{{sup|{{music|b}}M}} chords {{audio|Subdominant parallel in C minor.mid|Play}}.]]

[[Image:Dominant parallel in C major.png|thumb|Dominant and dominant parallel in C &nbsp;major: GMG{{sup|M}} and EmE{{small|m}} chords {{audio|Dominant parallel in C major.mid|Play}}.]]

[[Image:Dominant parallel in C minor.png|thumb|Dominant and dominant parallel in C &nbsp;minor: GmG{{small|m}} and B{{sup|{{music|b}}M}} chords {{audio|Dominant parallel in C minor.mid|Play}}.]]

[[Image:Subdominant and supertonic similarity.png|thumb|The similarity between the [[subdominant]] and [[supertonic]] chords is easily seen and heard through the supertonic seventh chord {{audio|Subdominant and supertonic similarity.mid|Play}}.]]

In [[music]], a '''parallel chordParallel''' (and '''relativecounter chordparallel''', chords are terms derived from the German: (''Parallelklang'', ''Gegenparallelklang'') to denote what is anmore auxiliaryoften chordcalled derivedin fromEnglish onethe of"relative", and possibly the "counter relative" chords. In [[primaryRiemannian triadtheory|Hugo Riemann's theory]]s, and sharingin itsGerman theory more generally, these chords share the [[diatonic function|function]] of the chord to which they link: '''subdominant parallel''', '''dominant parallel''', and '''tonic parallel'''.<ref name="Harmony">{{cite book |last=Haunschild, |first=Frank (|year=2000). ''|title=The New Harmony Book'', p.|page=47. |ISBN =978-3-927190-68-9. }}</ref> TheRiemann termdefines isthe derivedrelation fromin Germanterms theory andof the writingsmovement of [[Hugoone Riemann]]single (seenote: [[Riemannian theory]]).

{{quote|:The substitution of the major sixth for the perfect fifth above in the major triad and below in the minor triad results in the parallel of a given triad. In C &nbsp;major thence arises an apparent A &nbsp;minor triad (Tp, the parallel triad of the tonic, or tonic parallel), D &nbsp;minor triad (Sp), and E &nbsp;minor triad (Dp).|Hugo Riemann|"Dissonance", ''Musik-Lexikon''<ref name="Oxford">{{cite book |editor1-last=Gollin, |editor1-first=Edward and |editor2-last=Rehding, |editor2-first=Alexander; eds. (|year=2011). ''|title=The Oxford Handbook of Neo-Riemannian Music Theories'', p.|page=105. |publisher=Oxford U.P. |ISBN =9780195321333.}}</ref>}}{{efn|

The German text, in the 11th&nbsp;edition of Riemann's ''Musiklexikon''{{rp|style=ama|p=407}} reads:

:

''die Sexte des Durakkords und die Untersexte des Moll-akkordes bei fehlender Quinte (für diese eintretend), ergibt den für den betreffenden Klang innerhalb der Tonart stellvertretenden Parallelklang. In C&nbsp;dur entstehen so scheinbar der A&nbsp;moll-Akkord (Tp, d. h. Parallelklang der Tonika, Tonikaparallele), D&nbsp;moll-Akkord (SP) und Emoll-Akkord (DP).''

:

[literal translation] "The sixth of the major chord and the inferior sixth of the minor chord, substituting for the fifth when it is absent, produce the substituting ''Parallelklang'' for the corresponding chord in the tonality. In C&nbsp;major in this way arise the apparent A&nbsp;minor chord (Tp, that is the "parallel" chord of the tonic), D&nbsp;minor chord (Sp), and E&nbsp;minor chord (Dp).")<ref name=Oxford/>

}}

For example, the major {{audio|C majorMajor triad on C.mid|tonic}} and {{audio|Minor chord on A.mid|tonic parallel}} and minor {{audio|Minor chord on C.mid|tonic}} and {{audio|Eb major triad.mid|tonic parallel}}.

{| class="wikitable"

|!colspan=3| '''Major'''

|!colspan=3| '''Minor'''

|-

| ''Parallel''

| ''Note letter in &nbsp;C''

| ''Name''

| ''Parallel''

| ''Note letter in &nbsp;C''

| ''Name''

|-

| {{center|Tp}}

|Tp

| A&nbsp;minor<ref name=Gjerdingen>{{cite book |last=Gjerdingen |first=Robert O. |year=1990 |title=A Guide to the Terminology of German Harmony |series=Studies in the Origin of Harmonic Tonality |editor-last=Dahlhaus |editor-first=Carl |translator-last=Gjerdingen |page={{mvar|xiii}} |publisher=Princeton University Press |ISBN=0-691-09135-8 }}</ref>

|A minor

| [[Submediant]]

| {{center|tP}}

|tP

| {{nobr|E{{sup|{{music|flatb}}}} major<ref name=Gjerdingen/>}}

| Mediant

|-

| {{center|Sp}}

|Sp

|D D&nbsp;minor<ref name="Harmony"/><ref name=Gjerdingen/>

| [[Supertonic]]

| {{center|sP}}

|sP

| {{nobr|A{{sup|{{music|flatb}}}} major<ref name=Gjerdingen/>}}

| Submediant

|-

| {{center|Dp}}

|Dp

|E E&nbsp;minor<ref name="Material"/><ref name="Harmony"/><ref name="Kober"/><ref name="Kalamajski"/><ref name=Gjerdingen/>

| [[Mediant]]

| {{center|dP}}

|dP

| {{nobr|B{{sup|{{music|flatb}}}} major<ref name="Material"/>}}<ref name="Harmony"/><ref name=Gjerdingen/>

| [[Subtonic]]

|}

{{quote|: Dp stands for ''Dominant-parallel''. The word ''"parallel"'' in German {{grey|[musical vocabulary]}} has the meaning{{grey|[same ofconnotation as]}} ''"relative"'' in English. G &nbsp;major and E &nbsp;minor are called ''parallel keys''. The G &nbsp;major chord and the E &nbsp;minor chord in the key of C &nbsp;major are called ''parallel chords'' in the Riemann system.|<ref name=GailBoyd-1993>{{cite journal |first=Gail |last=Boyd |title=de &nbsp;Stwolinski Center for Music Theory Pedagogy (|year=1993). ''|journal=[[Journal of Music Theory Pedagogy]], Volumes |volume=5-7'', p.|page=37, n.|issue=9. |publisher=[[The University of Oklahoma]] |series=School of Music |place=Tulsa, TheOK University of Oklahoma.}}</ref>}}{{efn|

What is meant here is that, in the key of C&nbsp;major, G&nbsp;major (the dominant) and E&nbsp;minor (the [[mediant]], the relative of the [[dominant (music)|dominant]]) are "parallel" [''relative''] to each other. The same could be said of C&nbsp;major and A&nbsp;minor (the tonic and its relative) and of F&nbsp;major and D&nbsp;minor (the [[subdominant]] and its relative).<ref name=GailBoyd-1993/>

}}

[[Image:Tonic, subdominant, dominant, and their parallels.png|550px|Major T, S, D, and parallels]]

: The '''[[tonic (music)|tonic]]''', '''[[subdominant]]''', and {{nobr|'''[[dominant (music)|dominant]]''' chords,}} in [[root (chord)|root]] position, each followed by its parallel. The parallel is formed by raising the [[fifth (chord)|fifth]] a [[whole tone]].

[[Image:Minor tonic, subdominant, dominant, and their parallels.png|550px|Minor T, S, D, and parallel]]

: The [[Minor chord|minor]] [[tonic (music)|tonic]], [[subdominant]], [[Dominant (music)|dominant]], and their parallels, created by lowering the fifth (German) / root (USEnglish) a whole tone.

The parallel [[chord (music)|chord]] (but ''not'' the [[#Counter parallel|counter parallel]] chord) of a major chord will always be the minor chord whose [[root (chord)|root]] is a [[minor third]] ''down'' from the major chord's root, inversely the parallel chord of a minor chord will be the major chord whose root is a minor third ''up'' from the root of the minor chord. Thus, in a major [[key (music)|key]], where the dominant is a major chord, the dominant parallel will be the minor chord a minor third below the dominant. In a minor key, where the dominant may be a minor chord, the dominant parallel will be the major chord a minor third above the (minor) dominant.

{{quoteblockquote|Dr. &nbsp;Riemann ... sets himself to demonstrate that every chord within the key-system has, and must have, either a Tonic, [[Dominant (music)|Dominant]] or [[Subdominant]] function or significance. For example, the [[primary triad|secondary triad]] on the sixth degree [submediant] of the scale of C major, ''a-c-e'', or rather ''c-e-a'', is a Tonic 'parallel,' and has a Tonic significance, because the chord represents the C major '[[klang (music)|klang]],' into which the foreign note ''a'' is introduced. This, as we have seen, is the explanation which [[Hermann von Helmholtz|Helmholtz]] has given of this minor chord."|Shirlaw 2010<ref>{{cite book |last=Shirlaw, |first=Matthew (reprinted|edition=reprint |year=2010). ''|title=The Theory of Harmony: An Inquiryinquiry Intointo the Naturalnatural Principlesprinciples of Harmonyharmony, Withwith an Examinationexamination of the Chiefchief Systemssystems of Harmonyharmony from Rameau to the Presentpresent Day'',day p.|page=401. |ISBN =1-4510-1534-8. [http://www.forgottenbooks.org/info/9781451015348]</ref>}}

: Online source:

{{cite web |title=The Theory of Harmony: An inquiry into the natural principles of harmony, with an examination of the chief systems of harmony from Rameau to the present day |url=http://www.forgottenbooks.org/info/9781451015348 |access-date=2010-12-15 |url-status=dead |archive-url=https://web.archive.org/web/20100901191118/http://www.forgottenbooks.org/info/9781451015348 |archive-date=2010-09-01 }}</ref>}}

The name "parallel chord" comes from the [[German language|German]] musical theory, where "Paralleltonart" means not "parallel key" but "relative key", and "parallel key" is "Varianttonart".

Line 64 ⟶ 75:

==Counter parallel==

{{anchor|Counter parallel chord|Contrast chord|Gegenklang|Leittonwechselklange|Leittonwechselklänge|Leading-tone contrast chord}}

{{refmore improvecitations needed section|date=May 2008}}

[[Image:Tonic counter parallel in C major.png|thumb|Tonic and tonic counter parallel in C &nbsp;major: CMC{{sup|M}} and EmE{{small|m}} chords {{audio|Tonic counter parallel in C major.mid|Play}}.]]

[[Image:Tonic counter parallel in C minor.png|thumb|Tonic and tonic counter parallel in C &nbsp;minor: CmC{{small|m}} and {{nobr|A{{sup|{{music|b}}M}} chords}} {{audio|Tonic counter parallel in C minor.mid|Play}}.]]

[[Image:Contrast chord example.png|thumb|Contrast chord example {{audio|Contrast chord example.mid|Play}}: C major and E minor contrast through their respective notes &nbsp;C and B (in red and orange), each a half step apart or leading tones. The chords share two notes (in blue) however.]]

The "'''counter parallel'''" or "'''contrast chord'''" is terminology used in German theory derived mainly from Hugo Riemann to refer to (US:) [[relative (music)|relative]] (German: parallel) [[diatonic function]]s and is abbreviated Tcp in major and tCp in minor (Tkp respectively tKp in Riemann's diction). The chord can be seen as the "tonic parallel reversed" and is in a major key the same chord as the dominant parallel (Dp) and in a minor key equal to the subdominant parallel (sP); yet, it has another function. According to Riemann the chord is derived through '''''Leittonwechselklänge''''' (German, literally: "[[leading-tone]] contrastchanging chordssounds"), sometimes called ''gegenklang'' or "contrast chord", abbreviated Tl in major and tL in minor,<ref name=Gjerdingen/> or, in German literature, abbreviated Tg in major and tG in minor (standing for "Gegenklang" or "Gegenparallel"){{citation needed|date=February 2020}}. If chords may be formed by raising (major) or lowering (minor) the fifth a whole step ["parallel" or relative chords], they may also be formed by lowering (major) or raising (minor) the root a [[half-step]] to ''wechsel'', the [[leading tone]] or ''leitton''.

{{quote|The substitution of the leading tone for the prime (from below [<] in major, from above [>] in minor) likewise results...in the leading-tone change (in C major: T< <nowiki>=</nowiki> E minor, S< <nowiki>=</nowiki> A minor, D< <nowiki>=</nowiki> B minor[!]; in A minor: T> <nowiki>=</nowiki> F major, D> <nowiki>=</nowiki> C major, S> <nowiki>=</nowiki> B major [!].|Hugo Riemann|"Dissonance", ''Musik-Lexikon''<ref name="Oxford"/>}}

{| class="wikitable"

|colspan=3| '''Major'''

|colspan=3| '''Minor'''

|-

| ''Contrast''

| ''Note letter in &nbsp;C''

| ''Name''

| ''Contrast''

| ''Note letter in &nbsp;C''

| ''Name''

|-

| Tl (Tcp)

| {{nobr|E minor<ref name=Gjerdingen/>}}

|E minor

| [[Mediant]]

| tL (tCp)

| {{nobr|A{{sup|{{music|flatb}}}} major<ref name=Gjerdingen/>}}

| [[Submediant]]

|-

| Sl (Scp)

| {{nobr|A minor<ref name=Gjerdingen/>}}

|A minor

| [[Submediant]]

| sL (sCp)

| {{nobr|D{{sup|{{music|flatb}}}} major<ref name=Gjerdingen/>}}

| [[Neapolitan chord]]

|Supertonic

|-

| Dl (Dcp)

| {{nobr|B minor<ref name=Gjerdingen/>}}

|B minor

| Leading-tone

| dL (dCp)

| {{nobr|E{{sup|{{music|flatb}}}} major<ref name=Gjerdingen/>}}

| [[Mediant]]

|}

{{blockquote|

{{quote|The substitution of the leading tone for the prime (from below [<] in major, from above [>] in minor) likewise results ... in the leading-tone change (in C &nbsp;major: T< <nowiki>=</nowiki> E &nbsp;minor, S< <nowiki>=</nowiki> A &nbsp;minor, D< <nowiki>=</nowiki> B &nbsp;minor[!]; in A &nbsp;minor: T> <nowiki>=</nowiki> F &nbsp;major, D> <nowiki>=</nowiki> C &nbsp;major, S> <nowiki>=</nowiki> B &nbsp;major [!].|Hugo Riemann|"Dissonance", ''Musik-Lexikon''<ref name="Oxford"/>}}

|Hugo Riemann|"Dissonance", ''Musik-Lexikon''<ref name=Oxford/>

}}

[[Image:Major Leittonwechselklänge.png|400px|Major Leittonwechselklänge]]

: Major Leittonwechselklänge, formed by lowering the [[root (chord)|root]] a half step.

[[Image:Minor Leittonwechselklänge.png|400px|Minor Leittonwechselklänge]]

: Minor Leittonwechselklänge, formed by raising the root (US) / fifth (German) a half step.

For example, AmA{{small|m}} is the tonic parallel of C, thus, EmE{{small|m}} is the counter parallel of C. The usual parallel chord in a major key is a minor third below the root and the counter parallel is a major third above. In a minor key the intervals are reversed: the tonic parallel (e.g. EbE{{sup|{{music|b}}}} in CmC{{small|m}}) is a minor third above, and the counter parallel (e.g. AbA{{sup|{{music|b}}}} in CmC{{small|m}}) is a major third below. Both the parallel and the counter parallel have two notes in common with the [[Tonic (music)|tonic]] (AmA{{small|m}} and C share C & E; EmE{{small|m}} and C share E & G).

If chords may be formed by raising (major) or lowering (minor) the fifth a whole step [ [[parallel chord|parallel]] or relative chords], they may also be formed by lowering (major) or raising (minor) the root a [[half-step]] to ''wechsel'', the [[leading tone]] or ''leitton''. These chords are ''Leittonwechselklänge'' (literally: "leading-tone changing sounds"), sometimes called '''''gegenklang''''' or "contrast chord". <ref name="Gjerdingen">Gjerdingen, Robert O. (1990). "A Guide to the Terminology of German Harmony", Studies in the Origin of Harmonic Tonality by Dahlhaus, Carl, trans. Gjerdingen (1990). Princeton University Press. ISBN 0-691-09135-8.</ref>

For example, Am is the tonic parallel of C, thus, Em is the counter parallel of C. The usual parallel chord in a major key is a minor third below the root and the counter parallel is a major third above. In a minor key the intervals are reversed: the tonic parallel (e.g. Eb in Cm) is a minor third above, and the counter parallel (e.g. Ab in Cm) is a major third below. Both the parallel and the counter parallel have two notes in common with the [[Tonic (music)|tonic]] (Am and C share C & E; Em and C share E & G).

A chord should be analysed as a Tcp rather than Dp or sP particularly at cadential points, for example at an [[Cadence (music)|interrupted cadence]], where it substitutes the tonic. It is most easily recognised in a minor key since it creates an ascending [[semitone]] step at the end of the cadence by moving from the major dominant chord to the minor counter parallel:

:{|

Ex.

|-

t - s - D - tCp

| '''Example'''

Em - Am - B - C<br />

|-

where C is located a major third below Em

| t - s - D - tCp

| &emsp; E{{small|m}} - A{{small|m}} - B - C

Ex.

| &emsp; where C is located a major third below EmE{{small|m}}

T - S - D - tCp

|-

F - Bb - C - Db<br />

| '''Example'''

where Db is located a major third below the minor tonic Fm

|-

| T - S - D - tCp

| &emsp; F - B{{sup|{{music|b}}}} - C - D{{sup|{{music|b}}}}

| &emsp; where DbD{{sup|{{music|b}}}} is located a major third below the minor tonic FmF{{small|m}}

|}

In [[four-part harmony]], the Tcp usually has a doubled third to avoid [[consecutive fifths|consecutive fifths or octaves]]. This further emphasises its coherency with the tonic, since the third of the minor key counter parallel is the same as the tonic root which thus is doubled.

[[File:IV-V-I in C.png|thumb|[[Perfect authentic cadence]]: IV–V–I progression in C {{audio|IV-V-I in C.mid|Play}}. Considered the strongest ending during the [[common practice period]]. {{audio|sP-dP-T cadence in C.mid|Play sP-dP-T}}]]

{{Blockquote|This is clearly not a simple system. Three functional categories can appear in any one of three chordal guises in either of two modes, eighteen possibilities in all: T, Tp, Tl, t, tP, tL, S, Sp, Sl, s, sP, sL, D, Dp, Dl, d, dP, dL. Why all this complexity? Perhaps the central reason is that this ingenious, occasionally convoluted system enabled Riemann to ... [interpret] ostensibly remote triads ... through the traditional terms of the I-IV-V-I, or now T-S-D-T, [[cadence|cadential]] schema. A sequence of {{nobr|A{{sup|{{music|b}}}} major,}} {{nobr|B{{music|b}} major,}} and C&nbsp;major chords, for example, could be neatly interpreted as a subdominant (sP) to dominant (dP) to tonic (T) progression in C&nbsp;major, a reading ... not without support in certain late-Romantic cadences.

|Gjerdingen<ref name=Gjerdingen/>

}}

==Footnotes==

{{notelist}}

==See also==

{{div col begin|colwidth=15em}}

*[[Borrowed chord]]

*[[Chord substitution]]

Line 140 ⟶ 167:

*[[Subsidiary chord]]

*[[Voice leading]]

{{div col end}}

==SourcesReferences==

{{reflist|25em}}

==External links==

*"[ {{cite web |title=Chord functions |website=NiklasAndreasson.se |url=http://www.niklasandreasson.se/write/chordfunctions.html Chord|url-status=dead Functions]",<!-- ''NiklasAndreassonpresumed --> |archive-url=https://archive.today/20130418074357/http://www.niklasandreasson.se''/write/chordfunctions.html |archive-date=2013-04-18 }}

* {{cite report |first=Robert |last=Gjerdingen |year=1990 |section=A guide to the terminology of German harmony |title=Studies on the Origin of Harmonic Tonality |pages={{mvar|xi–xv}} |place=Princeton, NJ |publisher=Princeton Univ. Press |section-url=http://faculty-web.at.northwestern.edu/music/gjerdingen/Papers/PubPapers/GermanHarmony.pdf |archive-date=2011-06-12 |access-date=2017-02-09 |archive-url=https://web.archive.org/web/20110612205054/http://faculty-web.at.northwestern.edu/music/gjerdingen/Papers/PubPapers/GermanHarmony.pdf |url-status=dead }} {{cite web |title=Robert Gjerdingen published papers |website=faculty-web.at.northwestern.edu |series=School of Music |publisher=[[Northwestern University]] |url=http://faculty-web.at.northwestern.edu/music/gjerdingen/Papers/PubPapers/index.htm |access-date=2017-02-09 |archive-date=2010-06-08 |archive-url=https://web.archive.org/web/20100608115147/http://faculty-web.at.northwestern.edu/music/gjerdingen/Papers/PubPapers/index.htm |url-status=dead }}

*[http://faculty-web.at.northwestern.edu/music/gjerdingen/Papers/PubPapers/GermanHarmony.pdf “A Guide to the Terminology of German Harmony”], in ''Studies on the Origin of Harmonic Tonality'', pp. xi–xv (Princeton: Princeton Univ. Press, 1990). [http://faculty-web.at.northwestern.edu/music/gjerdingen/Papers/PubPapers/index.htm "Published Papers"], ''Robert Gjerdingen''.

{{Chords}}

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[[Category:Riemannian theory]]

[[de:GegenklangParallelklang]]

[[pt:Notas relativas]]

[[de:Parallelklang]]

[[sv:Funktionsanalys (musik)#Parallellackord]]