As discussed repeatedly in this course, diatonic harmony and its progressions work because of the strength of the voice-leading. To prove this, let’s listen to the following standard progression. As you listen, pay special attention to the voice-leading. Do you consider this progression to have strong voice-leading? If so, what makes it strong? If not, what makes it weak and what could strengthen it?
Most students when presented with these questions determine that the strength of the progression comes from three things:
Between any two chords with roots separated by descending P5, there is one common tone and two voices that resolve by step. If we remove the bass voice, we can clearly see (and hear) the smooth voice-leading between these chords while still using complete chords. (The tenor voice has been written in treble clef to make it easier to see the voice-leading. Its octave is not altered.)
By quantifying this aspect of voice-leading–the “smoothness” between two chords–we can study how this aspect of voice-leading strengthens a progression. In the simplified progression above, count the half-steps necessary to move between each of the two chords. Which chords have the smoothest voice-leading? Which are the most disjunct? Does this line up with what you would have expected?
Counting the half-steps necessary for resolution in idealized voice-leading will be helpful to us as we explore more advanced harmonic concepts, because it gives us a tool to quantify something that is relatively subjective–what makes good voice-leading. We will call this process Idealized Voice-leading Intervals (IVI). You can do this between any two chords by:
When counting the half-steps in the the above progression, you hopefully found that the movement from ii to V was the “weakest” voice-leading and required four half-steps to resolve. The next strongest resolutions were vi to ii and V to I. Both of these resolutions require only three half-steps. But in a surprise twist, the winner of the smoothest voice-leading in the above progression, was not a standard function progression at all; it was the I chord moving to the vi chord to start the progression. This happens because it has two common tones rather than just the one associated with chords that have roots separated by P5.
Let’s take this one step further. Before reading on, take a moment to find the IVI between a C major triad and all triads that are diatonic to C major or C minor.* Rank them in order of smoothest voice-leading to least.
As you can see the smoothest voice-leading possible between a C major triad and a different triad is the one half-step necessary to create E minor, the mediant. In the next closest category (two half-steps), there are three chords: A minor (the submediant), A-flat major (the borrowed submediant), and F minor (the borrowed subdominant). Of the four smoothest chords, three are chords whose roots are separated by a third.
Anytime a progression has two chords whose roots are separated by a M3 or a m3, we call this mediant harmony. (Do not confuse this with tertian harmony; tertian harmony is any harmony that uses chords built by stacking thirds. This has nothing to do with the root movement within a progression.) Rather than the structured rules and tendency tones of standard diatonic harmony, mediant harmony relies on the smoothness of voice-leading between two chords to create interesting new colors and progressions within a somewhat tonal framework.
For any major or minor triad, there are eight possible mediant chords: one major and one minor chord for each of the four mediant pitches. For example, the four mediant pitches for C are E (mediant), E-flat (borrowed mediant), A (submediant), and A-flat (borrowed submediant). Each of these four pitches can have either a major or minor chord built off of it for a total of eight possible mediant chords.
Before looking at the completed chart below, find the IVI for each of the eight possible chords. After you group the mediants by IVI, also note how many common tones there are between the C major and each chord.
All mediant harmonies for a C major triad:
| Diatonic mediants | Chromatic mediant | Doubly chromatic mediants |
|---|---|---|
| E minor | E major | E-flat minor |
| A minor | A major | A-flat minor |
| – | E-flat major | – |
| – | A-flat major | – |
There are three categories of mediants. The following descriptions compare describe the relationship to any major or minor chord:
Diatonic mediants (2 possible chords)
Chromatic mediants (4 possible chords)
Doubly chromatic mediants (2 possible chords)
Listen to the following progression. It will not sound like a standard diatonic progression, but at the same time, it will likely sound like a convincing modulation from a C major chord to a B-flat major chord. You may even hear the last two chords as a cadence. Is it possible for you to analyze this using normal Roman numeral analysis?
In this progression, Roman numerals cease to have a meaningful role because the chords do not follow standard function. What good is using Roman numerals if a iii chord can function directly before the tonic chord? You could label this passage as beginning in C major and moving through I-bVI-iv, and you would then need to pivot on the F major chord to become the V chord in B-flat major. You could even analyze the D minor chord as just the arrival of the B-flat major triad with a retardation on the A.
But none of this truly explains why this works. In passages like these– those that rely more on an interesting pattern of voice-leading rather than standard function–I recommend writing Roman numerals under each chord in order to give an approximation of what key you are hearing, but also putting an IVI number between each pair of chords. I would analyze the above passage as:
| Key | Chord 1 | Chord 2 | Chord 3 | Chord 4 | Chord 5 | Chord 6 |
|---|---|---|---|---|---|---|
| C: | I [IVI:2] | bVI6 [IVI:2] | iv6/4 [IVI:1] | IV6/4 [IVI:2] | —– | —– |
| Bb: | —– | —– | —– | V6/4 [IVI:2] | iii [IVI:1] | I |
As with all tools, you must be careful with how you use Idealized Voice-leading Intervals and mediant harmony. For example, when looking at diatonic progressions, the order in which the chords appear matters as much as the smoothness of the voice-leading. If you try to resolve V to ii, you have created a regression that will likely sound displeasing to someone familiar with tonal harmony. Also, many would say that adding a seventh to a chord (e.g. V becoming V7) strengthens the progression, because we have added a second tendency tone and therefore more tonal gravity between the two chords. But if you were to only look at IVI, adding the seventh would weaken the progression because it adds an extra half-step of resolution. In general, IVI is most useful when looking at non-standard tonal progressions.