Pivot chord modulation, and the chord that is two at once
A chord read in two keys at the same time, serving as a hinge between them; how to find it, how to write it with two Roman numerals, and why it is the gentlest way into a new key.
The gentlest way to change key is to pass through a chord belonging to both. The ear hears it as a degree of the old key; what comes next reinterprets it as a degree of the new one; and by the time a cadence confirms the new centre, the border is already behind you with nobody having noticed. That chord is the pivot, and finding it is the central skill of modulating naturally.
Where the fields cross
Two neighbouring keys share chords. C major and G major have in common C major, E minor, G major and A minor: any of them serves as a pivot. C major and A minor, the relative, share the whole field, which is why the passage between them is the gentlest of all.
A minor is the vi of C and the ii of G. In a phrase in C, arrive at the A minor; carry on with D seventh, the dominant of G; resolve to G and stay: you have modulated. The A minor was heard first as vi and then, in retrospect, as ii.
The procedure
To modulate from one key to another by pivot:
- Write out the harmonic fields of both keys.
- Find the common chords. Prefer those that, in the new key, are the subdominant or the second degree, because they prepare the dominant.
- Arrive at the pivot by the old key's normal route.
- From the pivot, go to the new key's dominant and resolve.
- Confirm with a cadence in the new key; without one, it was a secondary dominant, not a modulation.
From C to G, with A minor as the pivot, D seventh, G, and a cadence in G to confirm.
Two numerals for one chord
Analysis writes the pivot with two readings, one under the other: the old key's and the new key's. From it onwards, the second line takes over. In C major modulating to G: I, IV, vi on the C line; and, under the same A minor, ii on the G line, followed by V7, I. The notation says exactly where the hinge is, and that the chord was heard two ways.
Pivots that are not diatonic
The common chord can come from outside both fields. A modal borrowing in the old key that is diatonic in the new one is a pivot: in C major, the borrowed A flat major is the IV of E flat major, and it serves as a door to a distant key. And the diminished chord, with its four readings, is the universal pivot: the same sound resolves to four tonics, depending on the name you give it.
In the first case, A flat is the ♭VI of C and the IV of E flat, and the music went from C to E flat in three chords. In the second, the diminished chord on B reappears spelled on D flat and resolves to D major, a tone higher, with no common diatonic chord existing between the two keys at all.
What to take from here
The pivot chord belongs to the old key and the new one, is heard as a degree of each, and is the hinge between them; neighbouring fields share several, the relative shares all of them, and borrowings and diminished chords serve as pivots to distant keys. It is written with two Roman numerals, one per key, and the modulation is only made when a cadence confirms the new centre.