Modulation

The circle of fifths as a road map

The page Circle of fifths says: neighbouring keys on the circle share six of seven notes, which is why modulations between them sound so natural and smooth. A jump from C major to G major sounds more familiar than one to F♯ major, because C and G lie only a fifth apart. Keys that lie far apart have only a few notes in common and need careful preparation.

Very remote modulations, say from C major to F♯ major, are so unusual for exactly that reason: the two keys lie directly opposite each other on the circle and have hardly any notes in common. The page names Schubert and Wagner as composers who used this distance for dramatic, almost otherworldly effects.

Three techniques

The Circle of Fifths page names three common ways of changing key:

The example of the pivot chord is there too: from C major to G major the chord Am is the sixth degree in C and the second degree in G. It belongs to both keys, which is why you hardly notice the change. Try it with the listening example.

The chord Am does not change, only its function: first it is diatonic chord vi of C major, then ii of G major. The following two chords D and G confirm the new key, as in a cadence.

Other ways into a new key

The articles on Maikstrings contain two further means:

• The diminished seventh chord: The article The diminished seventh chord calls it the quickest modulation bridge that harmony knows. It fits into any key and leads from there into several others, because each of its four notes can be read as a leading tone.
• Switching the third: Because the major and minor triads on the same degree share two notes, one can, according to Major and minor: the third as a switch, change from one to the other without a break. From there you are in a different key, although only one note has moved.

Modulation in the score

Carcassi's Study No. 7 shows a change of key in the sheet. The chord symbols make it readable: there are Am chords above the first eight bars, then in bar 9, after a double barline, a section begins with the chords C, Dm, G and C. From bar 16 E and Am lead back to A minor.

Guitar

• Etüde Nr. 7 Matteo Carcassi, op. 60 No. 7 · guitar · 2 pages

  Bars 1, 3 and 6 carry the chord symbol Am, in bar 2 a G♯ appears. In bar 9 a new section begins with a repeat sign and the chord symbols C, Dm, G, C. From bar 16 the chords E and Am follow: the study returns from C major to A minor.

Modulation and tuning

The article Equal, meantone, just: why your piano is slightly out of tune describes a practical consequence: in just intonation every single key sounds flawless. But if you modulate, it becomes unbearable, because individual intervals go wrong by more than 20 cents. Choirs singing a cappella nevertheless often aim for just intonation, because singers can adjust the pitch continually. Equal temperament is a compromise that makes all keys playable, as the page on Enharmonic Matching describes.

Common mistakes

• Confusing modulation with a secondary dominant: In a modulation the new key stays; a secondary dominant touches another degree only briefly.
• Looking only for the new key signature: A change of key need not begin with a new key signature. In Carcassi's study the key signature does not change; the change shows in the chords and accidentals.
• Taking the pivot chord for a chance product: The chord is chosen because it has a function in both keys.