Parallel and counter parallel

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Tonic and tonic parallel in C major: CM and Am chords Play (help*info)
. Tonic parallel in C major.png
Tonic and tonic parallel in C major: CM and Am chords Loudspeaker.svg Play  .
Tonic and tonic parallel in C minor: Cm and EM chords Play (help*info)
. Tonic parallel in C minor.png
Tonic and tonic parallel in C minor: Cm and EM chords Loudspeaker.svg Play  .
Subdominant and subdominant parallel in C major (Sp): FM and Dm chords. Play (help*info) Subdominant parallel in C major.png
Subdominant and subdominant parallel in C major (Sp): FM and Dm chords. Loudspeaker.svg Play  
Subdominant and subdominant parallel in C minor (sP): Fm and AM chords Play (help*info)
. Subdominant parallel in C minor.png
Subdominant and subdominant parallel in C minor (sP): Fm and AM chords Loudspeaker.svg Play  .
Dominant and dominant parallel in C major: GM and Em chords Play (help*info)
. Dominant parallel in C major.png
Dominant and dominant parallel in C major: GM and Em chords Loudspeaker.svg Play  .
Dominant and dominant parallel in C minor: Gm and BM chords Play (help*info)
. Dominant parallel in C minor.png
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The similarity between the subdominant and supertonic chords is easily seen and heard through the supertonic seventh chord Play (help*info)
. Subdominant and supertonic similarity.png
The similarity between the subdominant and supertonic chords is easily seen and heard through the supertonic seventh chord Loudspeaker.svg Play  .

Parallel and counter parallel chords are terms derived from the German (Parallelklang, Gegenparallelklang) to denote what is more often called in English the "relative", and possibly the "counter relative" chords. In Hugo Riemann's theory, and in German theory more generally, these chords share the function of the chord to which they link: subdominant parallel, dominant parallel, and tonic parallel. [4] Riemann defines the relation in terms of the movement of one single note:

Contents

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 major thence arises an apparent A minor triad (Tp, the parallel triad of the tonic, or tonic parallel), D minor triad (Sp), and E minor triad (Dp).

Hugo Riemann, "Dissonance", Musik-Lexikon [5]

For example, the major Loudspeaker.svg tonic   and Loudspeaker.svg tonic parallel   and minor Loudspeaker.svg tonic   and Loudspeaker.svg tonic parallel  .

MajorMinor
ParallelNote letter in CNameParallelNote letter in CName
TpA minor [6] Submediant tPE major [6] Mediant
SpD minor [4] [6] Supertonic sPA major [6] Submediant
DpE minor [1] [4] [2] [3] [6] Mediant dPB major [1] [4] [6] Subtonic

Dp stands for Dominant-parallel. The word "parallel" in German has the meaning of "relative" in English. G major and E minor are called parallel keys. The G major chord and the E minor chord in the key of C major are called parallel chords in the Riemann system.

[7]

Tonic, subdominant, dominant, and their parallels.png

The tonic, subdominant, and dominant chords, in root position, each followed by its parallel. The parallel is formed by raising the fifth a whole tone.

Minor tonic, subdominant, dominant, and their parallels.png

The minor tonic, subdominant, dominant, and their parallels, created by lowering the fifth (German)/root (US) a whole tone.

The parallel chord (but not the counter parallel chord) of a major chord will always be the minor chord whose 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, 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.

Dr. Riemann...sets himself to demonstrate that every chord within the key-system has, and must have, either a Tonic, Dominant or Subdominant function or significance. For example, the 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,' into which the foreign note a is introduced. This, as we have seen, is the explanation which Helmholtz has given of this minor chord."

Shirlaw 2010 [8]

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

Counter parallel

Tonic and tonic counter parallel in C major: CM and Em chords Play (help*info)
. Tonic counter parallel in C major.png
Tonic and tonic counter parallel in C major: CM and Em chords Loudspeaker.svg Play  .
Tonic and tonic counter parallel in C minor: Cm and AM chords Play (help*info)
. Tonic counter parallel in C minor.png
Tonic and tonic counter parallel in C minor: Cm and AM chords Loudspeaker.svg Play  .
Contrast chord example Play (help*info)
: C major and E minor contrast through their respective notes C and B (in red and orange), each a half step apart or leading tones. The chords share two notes (in blue) however. Contrast chord example.png
Contrast chord example Loudspeaker.svg Play  : C major and E minor contrast through their respective notes 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 (German: parallel) diatonic functions 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 changing sounds"), sometimes called gegenklang or "contrast chord", abbreviated Tl in major and tL in minor, [6] or, in German literature, abbreviated Tg in major and tG in minor (standing for "Gegenklang" or "Gegenparallel")[ citation needed ]. 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.

MajorMinor
ContrastNote letter in CNameContrastNote letter in CName
Tl (Tcp)E minor [6] MedianttL (tCp)A major [6] Submediant
Sl (Scp)A minor [6] SubmediantsL (sCp)D major [6] Neapolitan chord
Dl (Dcp)B minor [6] Leading-tonedL (dCp)E major [6] Mediant

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< = E minor, S< = A minor, D< = B minor[!]; in A minor: T> = F major, D> = C major, S> = B major [!].

Hugo Riemann, "Dissonance", Musik-Lexikon [5]

Major Leittonwechselklange.png

Major Leittonwechselklänge, formed by lowering the root a half step.

Minor Leittonwechselklange.png

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

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 (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 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    Em - Am - B - C
where C is located a major third below Em
   Ex.    T  - S  - D - tCp    F  - Bb - C - Db
where Db is located a major third below the minor tonic Fm

In four-part harmony, the Tcp usually has a doubled third to avoid 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.

Perfect authentic cadence: IV-V-I progression in C Play (help*info)
. Considered the strongest ending during the common practice period. Play sP-dP-T (help*info) IV-V-I in C.png
Perfect authentic cadence: IV–V–I progression in C Loudspeaker.svg Play  . Considered the strongest ending during the common practice period. Loudspeaker.svg Play sP-dP-T  

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, cadential schema. A sequence of A-major, B-major, and C-major chords, for example, could be neatly interpreted as a subdominant (sP) to dominant (dP) to tonic (T) progression in C-major, a reading...not without support in certain late-Romantic cadences.

Gjerdingen [6]

See also

Sources

  1. 1 2 3 Goetschius, Percy and Faisst, Immanuel (1889). The Material Used in Musical Composition, p.139. G. Schirmer.
  2. 1 2 Kober, Thorsten (2003). Guitar Works: A Comprehensive Guide to Playing the Guitar, p.136. ISBN   978-0-634-03123-6.
  3. 1 2 Sebastian Kalamajski (2000). All Aspects of Rock & Jazz, p.35. ISBN   978-87-88619-68-3.
  4. 1 2 3 4 Haunschild, Frank (2000). The New Harmony Book, p.47. ISBN   978-3-927190-68-9.
  5. 1 2 Gollin, Edward and Rehding, Alexander; eds. (2011). The Oxford Handbook of Neo-Riemannian Music Theories, p.105. Oxford. ISBN   9780195321333. The German text, in the 11th edition of Riemann's Musiklexikon, 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 dur entstehen so scheinbar der A moll-Akkord (Tp, d. h. Parallelklang der Tonika, Tonikaparallele), D moll-Akkord (SP) und Emoll-Akkord (DP). (literally: "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 major in this way arise the apparent A minor chord (Tp, that is the "parallel" chord of the tonic), D minor chord (Sp), and E minor chord (Dp).")
  6. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 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), p.xiii. Princeton University Press. ISBN   0-691-09135-8.
  7. Gail Boyd de Stwolinski Center for Music Theory Pedagogy (1993). Journal of Music Theory Pedagogy, Volumes 5-7, p.37, n.9. School of Music, The University of Oklahoma. What is meant here is that, in the key of C major, G major (the dominant) and E minor (the mediant, the relative of the dominant) are "parallel" (relative) to each other. The same could be said of C major and A minor (the tonic and its relative) and of F major and D minor (the subdominant and its relative).
  8. Shirlaw, Matthew (reprinted 2010). 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, p.401. ISBN   1-4510-1534-8. "Archived copy". Archived from the original on 2010-09-01. Retrieved 2010-12-15.CS1 maint: archived copy as title (link)

Related Research Articles

In music, the tonic is the first scale degree of the diatonic scale and the tonal center or final resolution tone that is commonly used in the final cadence in tonal classical music, popular music, and traditional music. In the movable do solfège system, the tonic note is sung as do. More generally, the tonic is the note upon which all other notes of a piece are hierarchically referenced. Scales are named after their tonics: for instance, the tonic of the C major scale is the note C.

In music, the subdominant is the fourth tonal degree of the diatonic scale. It is so called because it is the same distance below the tonic as the dominant is above the tonic – in other words, the tonic is the dominant of the subdominant. It also happens to be the note one step below the dominant. In the movable do solfège system, the subdominant note is sung as fa.

Chord (music)

A chord, in music, is any harmonic set of pitches/frequencies consisting of multiple notes that are heard as if sounding simultaneously. For many practical and theoretical purposes, arpeggios and broken chords, or sequences of chord tones, may also be considered as chords in the right musical context.

Modulation (music)

In music, modulation is the change from one tonality to another. This may or may not be accompanied by a change in key signature. Modulations articulate or create the structure or form of many pieces, as well as add interest. Treatment of a chord as the tonic for less than a phrase is considered tonicization.

Modulation is the essential part of the art. Without it there is little music, for a piece derives its true beauty not from the large number of fixed modes which it embraces but rather from the subtle fabric of its modulation.

A secondary chord is an analytical label for a specific harmonic device that is prevalent in the tonal idiom of Western music beginning in the common practice period: the use of diatonic functions for tonicization.

In music, the mediant is the third scale degree of a diatonic scale, being the note halfway between the tonic and the dominant. In the movable do solfège system, the mediant note is sung as mi. While the fifth scale degree is almost always a perfect fifth, the mediant can be a major or minor third.

In music, the submediant is the sixth degree of the diatonic scale, the lower mediant—halfway between the tonic and the subdominant. In the movable do solfège system, the submediant note is sung as la in major, as fa in minor. It is occasionally called superdominant, as the degree above the dominant. This is its normal name (sus-dominante) in French.

Supertonic

In music, the supertonic is the second degree of a diatonic scale, one step above the tonic. In the movable do solfège system, the supertonic note is sung as re.

In music, the subtonic is the flattened seventh scale degree of the diatonic scale, that is, the lowered or minor seventh degree of the scale, a whole step below the tonic. In the movable do solfège system, the subtonic note is sung as te. It appears in the natural minor and descending melodic minor scales but not in the major scale. In major keys, the subtonic sometimes appears in borrowed chords.

Eleventh chord

In music theory, an eleventh chord is a chord that contains the tertian extension of the eleventh. Typically found in jazz, an eleventh chord also usually includes the seventh and ninth, and elements of the basic triad structure. Variants include the dominant eleventh, minor eleventh, and the major eleventh chord. Symbols include: Caug11, C9aug11, C9+11, C9alt11, Cm9(11), C−9(11). The eleventh in an eleventh chord is, "almost always sharpened, especially in jazz," at least in reference to the third, with CM11 (major eleventh): C–E–G–B–D–F, Cm11 (minor eleventh): C–E–G–B–D–F, and C11 (dominant eleventh): C–E–G–B–D–F.

In music, function is a term used to denote the relationship of a chord or a scale degree to a tonal centre. Two main theories of tonal functions exist today:

In music theory, a dominant seventh chord, or major minor seventh chord, is a seventh chord, usually built on the fifth degree of the major scale, and composed of a root, major third, perfect fifth, and minor seventh. Thus it is a major triad together with a minor seventh, denoted by the letter name of the chord root and a superscript "7". An example is the dominant seventh chord built on G, written as G7, having pitches G–B–D–F:

In music theory, a Neapolitan chord is a major chord built on the lowered (flatted) second (supertonic) scale degree. In Schenkerian analysis, it is known as a Phrygian II, since in minor scales the chord is built on the notes of the corresponding Phrygian mode.

Closely related key

In music, a closely related key is one sharing many common tones with an original key, as opposed to a distantly related key. In music harmony, there are five of them: they share all, or all except one, pitches with a key with which it is being compared, and is adjacent to it on the circle of fifths and its relative major or minor.

In Western music, the adjectives major and minor may describe an interval, chord, scale, or key. As such, a composition, movement, section, or phrase may be referred to by its key, including whether that key is major or minor.

Chord substitution

In music theory, chord substitution is the technique of using a chord in place of another in a progression of chords, or a chord progression. Much of the European classical repertoire and the vast majority of blues, jazz and rock music songs are based on chord progressions. "A chord substitution occurs when a chord is replaced by another that is made to function like the original. Usually substituted chords possess two pitches in common with the triad that they are replacing."

Primary triad

In music, a primary triad is one of the three triads, or three-note chords built from major or minor thirds, most important in tonal and diatonic music, as opposed to an auxiliary triad or secondary triad.

Chromatic mediant

In music, chromatic mediants are "altered mediant and submediant chords." A chromatic mediant relationship defined conservatively is a relationship between two sections and/or chords whose roots are related by a major third or minor third, and contain one common tone. For example, in the key of C major the diatonic mediant and submediant are E minor and A minor respectively. Their parallel majors are E major and A major. The mediants of the parallel minor of C major are E major and A major. Thus, by this conservative definition, C major has four chromatic mediants: E major, A major, E major, and A major.

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

Terzschritt

In music theory, Terzschritt is the progression from one major chord to another major chord, or a minor chord to another minor chord by major third root movement. Additionally, and more specifically, it is a dualistic major third relationship, in which the ascending progression from a major tonic triad to major mediant triad is equivalent to the descending one between a major tonic triad and a flat subdominant minor triad. The major chord on the mediant is itself the Terzklang.