Closely related key

Circle of fifths showing major and minor keys.

In music, a closely related key is one sharing many common tones with an original key, as opposed to a distantly related key (or "close key" and "distant key"). In music harmony, such a key shares all, or all except one, pitches with a key with which it is being compared, and is adjacent to it on the circle of fifths and its relative majors or minors.

Such keys are the most commonly used destinations or transpositions in a modulation,^[1] because of their strong structural links with the home key. Distant keys may be reached sequentially through closely related keys by chain modulation, for example C to G to D or C to C minor to E♭ major.^[2] For example, "One principle that every composer of Haydn's day kept in mind was over-all unity of tonality. No piece dared wander too far from its tonic key, and no piece in a four-movement form dared to present a tonality not closely related to the key of the whole series."^[3]

Given a major key tonic (I), the related keys are:

• vi (submediant or relative minor^[1][4]): same key signature
• IV (subdominant^[1][4][5]): one less sharp (one more flat) around circle of fifths
• V (dominant^[1][5]): one more sharp (one less flat) around circle of fifths
• i (parallel minor^[1]): same tonic, different key signature

Closely related keys in C.

Specifically:

Major	Relative Minor	Subdominant and dominants
C	Am	F, G, Dm, Em
G	Em	C, D, Am, Bm
D	Bm	G, A, Em, F♯m
A	F♯m	D, E, Bm, C♯m
E	C♯m	A, B, F♯m, G♯m
B	G♯m	E, F♯, C♯m, D♯m
F♯	D♯m	B, C♯, G♯m, A♯m
G♭	E♭m	C♭, D♭, A♭m, B♭m
D♭	B♭m	G♭, A♭, E♭m, Fm
A♭	Fm	D♭, E♭, B♭m, Cm
E♭	Cm	A♭, B♭, Fm, Gm
B♭	Gm	E♭, F, Cm, Dm
F	Dm	B♭, C, Gm, Am

Closely related keys in C. Note the three parallel keys: C & a, F & d, and G & e.

Another view of closely related is that there are six closely related keys, based on the tonic and the remaining triads of the diatonic scale, excluding the dissonant leading-tone diminished triad.^[5] Four of which differ by one accidental, one with the same key signature, and the parallel modal form. In the key of C major these would be: D minor, E minor, F major, G major, A minor, and C minor.

In modern music, the closeness of a relation between any two keys or sets of pitches may be determined by the number of tones they share in common, which allows one to consider modulations not occurring in standard major-minor tonality. For example, in music based on the pentatonic scale containing pitches C, D, E, G, and A, modulating a fifth higher gives the collection of pitches G, A, B, D, and E, having four of five tones in common. However, modulating up a tritone would produce F♯, G♯, A♯, C♯, D♯, which shares no common tones with the original scale. Thus the scale a fifth higher is very closely related, while the scale a tritone higher is not. Other modulations may be placed in order from closest to most distant depending upon the number of common tones.

Another view in modern music, notably in Bartok, a common tonic produces closely related keys, the other scales being the six other modes. This usage can be found in several of the Mikrokosmos piano pieces.

When modulation causes the new key to traverse the bottom of the circle of fifths this may give rise to a theoretical key, containing eight (or more) sharps in its notated key signature; in such a case, notational conventions require re-casting the new section to its enharmonically equivalent key.

See also

• Chromatic mediant
• Pitch space

Sources

1. ^ ^{a b c d e} Schonbrun, Marc (2006). The Everything Music Theory Book, p.76. ISBN 1593376529.
2. ^ George T. Jones (1994). HarperCollins College Outline Music Theory, p.217. ISBN 0064671682.
3. ^ Ulrich, Homer (1966). Chamber Music, p.175. ISBN 9780231086172.
4. ^ ^{a b} Barry, Barbara R. (2000). The Philosopher's Stone: Essays in the Transformation of Musical Structure, p.19. ISBN 1576470105.
5. ^ ^{a b c} Jones (1994), p.35-36.

Further reading

• Howard Hanson, Harmonic Materials of Modern Music. Appleton-Century-Crofts, Inc, 1960.