Parallel and counter parallel

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.

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).

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].

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.

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.

Tonic and tonic parallel in C major: CM and Am chords Play ⓘ .
Tonic and tonic parallel in C minor: Cm and E ♭ M chords Play ⓘ .
Subdominant and subdominant parallel in C major (Sp): FM and Dm chords. [ 1 ] [ 2 ] [ 3 ] Play ⓘ
Subdominant and subdominant parallel in C minor (sP): Fm and A ♭ M chords Play ⓘ .
Dominant and dominant parallel in C major: GM and Em chords Play ⓘ .
Dominant and dominant parallel in C minor: Gm and B ♭ M chords Play ⓘ .
The similarity between the subdominant and supertonic chords is easily seen and heard through the supertonic seventh chord Play ⓘ .
Tonic and tonic counter parallel in C major: CM and Em chords Play ⓘ .
Tonic and tonic counter parallel in C minor: Cm and A ♭ M chords Play ⓘ .
Contrast chord example 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.
Perfect authentic cadence : IV–V–I progression in C Play ⓘ . Considered the strongest ending during the common practice period . Play sP-dP-T ⓘ