Parallel keys are the major and minor using the same tonic, for example C major and C minor are parallel keys.
Sometimes parallel keys use enharmonic equivalents, to simplify the key signature. For example, Ab major and Ab minor are parallel keys, but Ab minor would need a key signature with seven flats. G# minor is the enharmonic equivalent of Ab minor, and only(!) uses 5 sharps, so is more often used than Ab minor.
Parallel keys share a dominant chord, e.g. both C major and C minor use G major as the dominant chord (V). They also share the leading note chord e.g. B diminished (vii°).
Parallel keys are sometimes visited when music modulates.
Some composers have written sets of pieces in parallel keys, the most famous example being Bach’s two sets of books entitled Das wohltemperierte Klavier (“The Well-Tempered Keyboard”). Each book contains a prelude and fugue in each of the twelve major and minor keys.
Borrowed chords are chords that are not part of the key the music is in, but instead they exist in the parallel key. For example, if the music is in C major, a chord could be borrowed from C minor. Borrowed chords are used as chromatic chords, without causing a change of key.
Borrowed chords are more often minor-key chords used in the major key, rather than the other way round.
Here are the chords which exist diatonically in C major, and in C minor (harmonic minor scale).
|C minor H
So, if the music is in C major, we might find a borrowed chord of C minor, D diminished, F minor or Ab major used as chromatic chords.
Here are the chords in C minor, built from the alternative melodic minor scale notes.
|C minor M
In C major, the borrowed chords of Eb major, G minor are relatively common. Bb major is rarer. A diminished is not commonly used.
When the music is in a minor key, the only commonly used borrowed chord is the major tonic chord. This is often found at cadences, where it is called the Tierce de Picardie.
Naming Borrowed Chords
In the extended Roman numeral system (which uses capitals for major and augmented chords, and lower-case letters for minor and diminished chords), use the correct capitalisation for the borrowed chord. For example, in C major, a borrowed chord of F minor is written as iv (lower-case).
In addition, if the root of the chord has been altered chromatically, use flat or sharp signs to show whether the note has been raised or lowered. For example, a chord of Ab major used in the key of C major is chord ♭VI (major chord built on a flattened 6th degree of the scale).
As with all chromatic chords, borrowed chords are mostly approached and quit by semitone steps in the parts where these are available. Notice the chromatic steps here of G-Ab-G, and E-Eb-E.
Chord iv (Borrowed)
In a major key, minor chord iv is a fairly common chromatic, borrowed chord.
For example, if the key is C major, then minor chord iv is borrowed from the parallel key of C minor. The root of the chord is the same as in the major key, but the third is lowered by a semitone to make the chord minor.
Minor chord iv can be used in most places where a normal major chord IV would work. The chromatic note will normally resolve downwards by a semitone step, which will be G in this case. The most typical progressions are iv-I or iv-V.
Here is an example in an extract from a piano piece by Tchaikovsky (op.39, no.9). The key is Bb major.
In bars 50 and 52, Tchaikovsky uses minor chord iv (Eb minor), which then moves to chord I, (Bb major). Tchaikovsky lets the lowered third, Gb, rise by an augmented 2nd to A, instead of using the more typical voice-leading, which lends a Russian feel to the harmony.
Chord ♭VI (Borrowed)
Another fairly common borrowed chord in major keys is bVI – the major triad built on the lowered submediant. In the key of C major, the submediant is A. Lower this to Ab, then build a major triad: Ab-C-Eb.
An example can be seen in this extract from a song by Schubert, “Gondelfahrer”, D808. The key is C major. In bar 2, he uses chord bVI (Ab major), moving between I and bVI as an introduction to the song. (Schubert was particularly fond of using bVI. It was not used very much in music before around 1800 however.)
Chord ii° (Borrowed)
Sometimes, the supertonic chord from the parallel minor key is used as a chromatic chord within a major key. This is a diminished chord, for example D° in the key of C major.
In C minor, the 6th note in the harmonic minor scale is Ab, so the borrowed supertonic is D-F-Ab (D diminished).
The borrowed diminished supertonic sounds very similar to the borrowed diminished 7th chord, as three of the notes are common to both chords.
As with other diminished chords, ii° is most often found in first inversion (although root position is also possible), and the best note to double is the third.
Here is a borrowed ii° in G major. Notice how the alto part moves chromatically (E-Eb-D) in smooth steps. Chord ii° is used as a substitute for minor chord ii.