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Parallel and counter parallel

Parallel and counter parallel chords are terms derived from the German 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. Riemann defines the relation in terms of the movement of one single note: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, D minor triad (Sp), and E minor triad (Dp).

Counter parallel
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, or, in German literature, abbreviated Tg in major and tG in minor (standing for "Gegenklang" or "Gegenparallel"). 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. : Major Leittonwechselklänge, formed by lowering the root a half step. : Minor Leittonwechselklänge, formed by raising the root (US) / fifth (German) a half step. For example, A is the tonic parallel of C, thus, E 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. E in C) is a minor third above, and the counter parallel (e.g. A in C) is a major third below. Both the parallel and the counter parallel have two notes in common with the tonic (A and C share C & E; E 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: : 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. : IV–V–I progression in C . Considered the strongest ending during the common practice period. ==Footnotes==
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