Closely related keys

Most pieces begin in a main key, pass through others and return to the main key to end (Lacerda 1966, ch. XXVI). The question is: through which? From C major a piece can go to any other key, but some sit right next door and others take a journey. The ones next door have a name.

Closely related keys are the keys that have the same signature as the main key, or differ from it by one accidental more or fewer (Med 1996, ch. XXIV). Every key has five of them.

The five neighbours

Med divides them into three direct and two indirect neighbours (Med 1996, ch. XXIV):

Kind	Which it is	From C major	From A minor
direct	the relative	A minor	C major
direct	the key of the same mode a fifth above, on the dominant	G major	E minor
direct	the key of the same mode a fifth below, on the subdominant	F major	D minor
indirect	the relative of the dominant key	E minor	G major
indirect	the relative of the subdominant key	D minor	F major

By signature the count is simple. C major has no accidentals; neither does A minor; G major and E minor have one sharp; F major and D minor have one flat. The five neighbours of C major are all the keys with zero or one accidental, except C major itself.

Why these five

One accidental of difference in the signature means one note of difference in the scale. C major and G major share six notes and differ only in F, which is sharp in G major. C major and A minor, being relatives, share all seven.

Med calls this comparison tonal affinity: comparing two keys, one separates the common notes, found in both, from the differential notes, found in only one. The number of differential notes comes straight from the signatures: G major, with one sharp, and B major, with five, have four differential notes and three common ones (Med 1996, ch. XXIV).

The more notes in common, the smoother the move from one key to the other, because the music changes few notes to get there. That is why the neighbours are the first destinations of a modulation.

The degrees that become tonics

There is a way to find the neighbours without thinking about signatures. In a major key every scale degree except the seventh is the tonic of a neighbouring key; in a minor key, every degree except the second (Med 1996, ch. XXIV).

In C major, the triads on every degree except the seventh are the tonic chords of the neighbours:

CITonicDiatonicDmiiSubdominantDiatonicEmiiiTonicDiatonicFIVSubdominantDiatonicGVDominantDiatonicAmviTonicDiatonic

Hear the progression

D minor, E minor, F major, G major and A minor: the five neighbours, each with its tonic already inside C major. The seventh degree is left out because its triad, B, D, F, is diminished, and a diminished chord cannot serve as a tonic. In A minor it is the second degree that is left out, for the same reason.

The parallel key, close without being a neighbour

C minor has three flats. By the signature rule it is far from C major, which has none. And yet any ear hears that the two are close: they have the same tonic, the same dominant, and the music moves from one to the other without leaving its place.

Med solves this with a category of its own. The parallel key, three accidentals away, is a near key, because of the great affinity between their notes (Med 1996, ch. XXIV). The signature measures distance by the notes of the scale; the ear also measures it by the tonic, and by the tonic the parallel key is the closest neighbour of all.

Distant keys

All the other keys, outside the neighbours, are distant keys: they differ from the main key by two accidentals or more. C major and D major, with two sharps, are already distant (Med 1996, ch. XXIV). Reaching a distant key is not forbidden, but it takes more road: a chain of dominants, a chord that serves as a bridge, or a stop at a neighbour on the way.

Where pieces go

The books' examples confirm the preference for neighbours. The passage Lacerda uses to show a modulation starts in D minor and moves to F major, its relative (Lacerda 1966, ch. XXVI). And in sonata form, the most common form for the fast movements of Classical sonatas and symphonies, the exposition presents the first theme in the tonic and modulates to the dominant key, or to the relative major when the main key is minor, where the second theme appears (Blatter 2007, part 5, art. 4). Dominant and relative: two direct neighbours.

What comes next

Knowing which keys are neighbours tells you where a modulation usually goes. How it gets there, through a chord the two keys share or through the dominant of the new key, is the business of modulation.