Explain the concept of modal interchange and demonstrate how it can be used to create harmonic variety and color within a tonal composition, giving specific examples with chord symbols and analysis.

Modal interchange, also known as mode mixture or borrowed chords, is a harmonic technique used in tonal music where chords are "borrowed" from a parallel key or mode to add color, variety, and expressive depth to a composition. It involves using chords that are not diatonic to the primary key of the piece, but instead derive from related modes like the parallel minor, the Lydian mode, or the Phrygian mode. The key here is that the root remains the same, but its quality changes based on the other modes. By introducing these borrowed chords, composers can create moments of unexpected harmonic shifts, darker or brighter tonal color, or a sense of nostalgia or exoticism.

The most common form of modal interchange involves borrowing chords from the parallel minor key. For instance, in C major, the parallel minor is C minor. From C minor, we might borrow the submediant (♭VI), which would be A♭ major (Ab major). This chord is not diatonic to C major, where the submediant is A minor. Another very common borrowed chord from the parallel minor is the subdominant (iv), which would be F minor in C major. In the major key, the subdominant is F major.

Here are some examples of modal interchange in practice:

1. Borrowed ♭VI (Submediant from Minor): In a piece in C major, a typical progression might be I - vi - IV - V - I (Cmaj - Amin - Fmaj - Gmaj - Cmaj). By using the borrowed submediant (♭VI) from C minor, the progression could become I - ♭VI - IV - V - I (Cmaj - Abmaj - Fmaj - Gmaj - Cmaj). This creates a darker and more dramatic sound due to the major chord with the lowered root. The A♭ major chord here provides a moment of surprise and contrasts with the typical C major harmony. This creates a moment of tension before it resolves back to the tonic. In chord analysis, a borrowed chord is often indicated by its degree in the borrowed key, followed by the notation indicating that it's "borrowed" for example, ♭VI/i indicates borrowed submediant from the parallel minor.

2. Borrowed iv (Subdominant from Minor): Another frequent example occurs in major key progressions. Consider a progression in G major: I - IV - V - I (Gmaj - Cmaj - Dmaj - Gmaj). By borrowing the iv from G minor, we might get I - iv - V - I (Gmaj - Cmin - Dmaj - Gmaj). The C minor chord provides an immediate shift to a darker sound, contrasting with the bright G major. This is a common substitution and can often add a sense of yearning or melancholy to the music.

3. Borrowed ♭iii (Mediant from Minor): Another possible borrowing is the ♭iii. In A major, using the parallel minor, A minor, we have the iii chord as C# minor. The ♭iii from A minor would be C major. Thus a progression in A major like I - vi - ii - V -I (Amaj - F#min - Bmin - Emaj -Amaj) may become I - ♭iii - ii - V- I (Amaj - Cmaj - Bmin - Emaj - Amaj). This example again shows a shift to a darker color and is less direct than the usual progression.

4. Borrowed chords from Phrygian: The Phrygian mode features a lowered second degree, which creates a distinctive exotic sound. A common chord borrowed from the Phrygian mode is the lowered supertonic (♭ii). In C major using the Phrygian mode, we can borrow the supertonic that would normally be d minor, and use Db major (♭II). A progression like I - V - vi (C - G - A minor), could be changed to I - ♭II - V (C - Db - G).

Modal interchange isn’t just limited to single chord substitutions. It can also be used to create entire passages or sections that temporarily evoke a different modal character. For instance, a piece in a major key might incorporate a short section that uses chords predominantly borrowed from the parallel minor, creating a dramatic or contrasting mood before returning to the main key. The goal of modal interchange is not to abandon tonality but to enrich it. Modal interchange allows composers to expand their expressive palette while still remaining within a tonal framework. The borrowed chords add color and depth, create a sense of surprise, and enhance the overall musical experience, making the music more emotive and nuanced. By carefully employing these techniques, composers can create sophisticated and emotionally compelling music.