As we leave strict diatonic function and begin to explore chromatic alterations, one of the most difficult challenges in analysis is discerning what tonic is implied at any given moment. Roman numeral analysis shows function–tonic, dominant, etc.,–but a chord’s function can only be defined by its relationship to tonic. Simply put, you cannot write a Roman numeral if you do not know your tonic.
Leadsheet notation solves this issue by providing a way to begin analyzing music that is independent of key or tonic. An F major chord could be a I chord in F major, a IV chord in C major, a III chord in D-flat major, and many others, but it will always be an F major chord. Leadsheet notation does not rely on any pre-existing knowledge of the piece, so I strongly urge you to begin analyzing music by writing the leadsheet symbols first. This will allow you to look for patterns within chord progressions rather than having to repeatedly re-examine every chord each time that you discover something new.
The simplest modulation is one that uses standard functional progressions and produces modulations through slight changes. Analyze the following excerpt from a Haydn piano sonata using leadsheet symbols. Even though there is only one altered note, it clearly ends in a different key than the key in which it starts. To begin understanding how this modulation works, ask these key questions:
Once you have answered these, create Roman numerals for both the beginning key and the ending key. (This will require secondary function chords.) When looking at the Roman numeral progressions, you can see where the progressions function diatonically and where they emphasize non-tonic chords such as the subdominant.
The example begins in the key of G major but ends in the key of D major. The first two bars clearly establish G major and end with an authentic cadence on beats 2, 3, and 4 of the second measure. The third measure also begins in G major, but beats 3 and 4 have a chromatic tone (C-sharp) as part of an A7 chord used to tonicize D major. This tonicization is then solidified through an authentic cadence in D major in measure 4, completing the modulation.
If you attempt to analyze this excerpt in only one of the two keys, you do not create a convincing explanation of either key. In G major, the second phrase requires many secondary dominants and results in a heavily tonicized V chord at the end. Conversely, if we try to analyze the first phrase in D major, we end up with a progression that looks as if it’s operating entirely in the key of IV.
When you look at the analyses in both keys on top of each like this however, their is one point at which the progression makes sense in both keys. At the beginning of the measure three, the listener will hear the G major triad as a continuation of the I chord from the previous cadence. This chord can also act as the diatonic IV chord in the key of D major. Therefore, this moment is both the conclusion of V-I in G major as well as the beginning of a IV-V-I progression in D major. This is an exemplar of a pivot chord.
A pivot chord is a chord that allows the composer to smoothly modulate between two keys. Any chord can be used to pivot between two keys, but this chord must be part of a functional progression in both keys to be considered a pivot chord. If a chord does not have an obvious function on both sides of the pivot, it is not a pivot modulation. We will discuss the other modulatory techniques in the next topic.
The smoothest pivot chords will be diatonic to both keys, although we will study some common non-diatonic chords in Unit 16c. In the example above, if you pivot anywhere other than the G major chord that bridges the first and second phrases, you must use a secondary dominant. By having a chord that is diatonic to both keys, the transition between the two keys is as smooth as possible. The less strong the pivot chord’s function in both keys, the more jarring the modulation will be.
When a modulation centers around a common chord between two keys, we call this a common chord pivot modulation. To better understand why closely-related keys create smoother modulations, it is helpful to look at the number of common chords between the two keys. In the following chart, I have listed each chord from C major and G major, but I have aligned them by root rather than by scale degree.
| C major | Chord | Chord | G major |
|---|---|---|---|
| I | C maj | C maj | IV |
| ii | D min | D maj | V |
| iii | E min | E min | vi |
| IV | F maj | F#o | viio |
| V | G maj | G maj | I |
| vi | A min | A min | ii |
| viio | Bo | B min | iii |
You can see that the two keys share four common chords (highlighted in bold), so writing a smooth progression in both keys is fairly easy because it can rely on multiple common chords. Try creating a table like this for distantly-related keys such as C major and E major. What about G major and F minor? You will find that closely related keys share many more common chords than distantly related keys.
As described above, the pivot chord of a pivot chord modulation is more than just a chord that is common to both keys. A pivot chord smoothly transitions from one key to another because it is part of a functional progression in both the old and the new keys. The simpler the pivot’s progression, the less-jarring the modulation.
In the previous topic, we listened to an excerpt from the third movement of the second movement of Tchaikovsky’s Symphony No. 5. Analyze this piece beginning with leadsheet symbols, then add Roman numerals from the beginning until you get to the modulation point – the place where you first hear the modulation.
Common chord pivots occur right before you hear the modulation point.
To show a modulation:
What makes this modulation work so well? More specifically, how strong is the progression before and after the pivot chord?