20b Discussion - Mediant harmony and Simplified Voice-leading Intervals

Class discussion

Mediant Harmony and Idealized Voice Leading Intervals

How do we judge good voice leading?

  • Stepwise and static motion

  • The chordal thirds resolve how you expect

If you put chords in closed position voicing without the bass line there’s not much movement.

If you count the half steps it takes to move between two chords and take the total you have IVI, or Idealized Voice-Leading Intervals.

Which chords have the lowest IVI?

The ones that share two common tones.

Anytime we have harmonies whose roots relate by a 3rd those chords have smooth voice leading because they share two tones.

Mediant Harmony allows composers to have smooth voice leading while using interesting harmony.

Ex: G7 - D

  • GBDF to DF#A

  • G moves to F#, B moves to A, D stays the same, F moves to F#.

  • IVI:5

Voice-leading for IVI is not the same as writing for a chorale.

Bass lines don’t follow the rules of IVI for smooth voice-leading.

Ex: Bbm - Co7

  • BbDbF to CEbGbBbb

  • Bb moves to Bbb, Db moves to Eb and C, F moves to Gb.

  • IVI:5

Ex: G - Fmaj7

  • GBD to FACE

  • G moves to F and A, B moves to C, D moves to E.

  • IVI:7

IVI In C Major and Parallel Minor

  1. C to Dm - IVI:5

  2. C to Do - IVI:4

  3. C to Eb - IVI:3

  4. C to Em - IVI:1

  5. C to Fm - IVI:2

  6. C to F - IVI:3

  7. C to Gm - IVI:4

  8. C to G - IVI:3

  9. C to Ab - IVI:2

  10. C to Am - IVI:2

  11. C to Bb - IVI:5

  12. C to Bo - IVI:4

Which chords have the smallest IVI?

Mediant Harmony

The mediant harmony: or any harmony whose root starts a 3rd away.

These chords are the mediant and borrowed mediant, and the submediant and borrowed submediant.

We are left with (in C) Eb, Em, Ab, Am.

We have 4 more mediant harmony chords, and they come from changing the quality of the previous chords.

  • Ebm, E, Abm, A.

In total we have 4 chromatic mediant chords (Ebm, Eb, Em, E) and 4 chromatic submediant chords (Abm, Ab, Am, A).

Diatonic mediants: the two mediants that are in the key.

  • In C major, Em and Am.

  • your diatonic mediants always have 2 common tones and opposite chord qualities.

Chromatic mediants: the 4 mediants that are borrowed from the parallel minor and the opposite chord quality of the diatonic mediants.

  • In C major, Eb, Ab, E, and A.

  • Eb and Ab are from the parallel minor while the E and A are opposite chord qualities of diatonic mediants.

Doubly chromatic mediants: the 2 mediants that are not in the key, but are the opposite chord qualities of the parallel minor mediants.

  • In C major, Ebm and Abm.

You find the first 4 mediants by using the diatonic and chromatic mediants (the 2 from major and 2 from the parallel minor).