Closely related key

Last updated October 24, 2023

In music, a closely related key (or close key) is one sharing many common tones with an original key, as opposed to a distantly related key (or distant key). In music harmony, there are six of them: four of them share all the pitches except one with a key with which it is being compared, one of them share all the pitches, and one shares the same tonic.

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.^[2] For example, "One principle that every composer of Haydn's day [ Classical music era ] 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] For example, the first movement of Mozart's Piano Sonata No. 7, K. 309, modulates only to closely related keys (the dominant, supertonic, and submediant).^[4]

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

ii (supertonic,^[5] the relative minor of the subdominant)
iii (mediant,^[5] the relative minor of the dominant)
IV (subdominant ^[1]^[6]^[7]^[5]): one less sharp (or one more flat) around circle of fifths
V (dominant ^[1]^[7]^[5]): one more sharp (or one fewer flat) around circle of fifths
vi (submediant or relative minor^[1]^[6]^[5]): different tonic, same key signature
i (parallel minor): same tonic, different key signature

Specifically:

Original key (major)	Submediant (relative minor)	Subdominant, dominant, supertonic, and mediant	Subdominants	Dominants	Parallel minor
C	Am	F, G, Dm, Em	B♭, E♭, A♭, D♭	D, A, E, B	Cm
G	Em	C, D, Am, Bm	F, B♭, E♭, A♭	A, E, B, F♯	Gm
D/E	Bm/C♭m	G/A , A/B , Em/F♭m, F♯m/G♭m	C/D , F/G , B♭/C , E♭/F	E/F♭, B/C♭, F♯/G♭, C♯/D♭	Dm/E m
A/B	F♯m/G♭m	D/E , E/F♭, Bm/C♭m, C♯m/D♭m	G/A , C/D , F/G , B♭/C	B/C♭, F♯/G♭, C♯/D♭, G♯/A♭	Am/B m
E/F♭	C♯m/D♭m	A/B , B/C♭, F♯m/G♭m, G♯m/A♭m	D/E , G/A , C/D , F/G	F♯/G♭, C♯/D♭, G♯/A♭, D♯/E♭	Em/F♭m
B/C♭	G♯m/A♭m	E/F♭, F♯/G♭, C♯m/D♭m, D♯m/E♭m	A/B , D/E , G/A , C/D	C♯/D♭, G♯/A♭, D♯/E♭, A♯/B♭	Bm/C♭m
F♯/G♭	D♯m/E♭m	B/C♭, C♯/D♭, G♯m/A♭m, A♯m/B♭m	E/F♭, A/B , D/E , G/A	G♯/A♭, D♯/E♭, A♯/B♭, E♯/F	F♯m/G♭m
C♯/D♭	A♯m/B♭m	F♯/G♭, G♯/A♭, D♯m/E♭m, E♯m/Fm	B/C♭, E/F♭, A/B , D/E	D♯/E♭, A♯/B♭, E♯/F, B♯/C	C♯m/D♭m
G♯/A♭	E♯m/Fm	C♯/D♭, D♯/E♭, A♯m/B♭m, B♯m/Cm	F♯/G♭, B/C♭, E/F♭, A/B	A♯/B♭, E♯/F, B♯/C, F /G	G♯m/A♭m
D♯/E♭	B♯m/Cm	G♯/A♭, A♯/B♭, E♯m/Fm, F m/Gm	C♯/D♭, F♯/G♭, B/C♭, E/F♭	E♯/F, B♯/C, F /G, C /D	D♯m/E♭m
A♯/B♭	F m/Gm	D♯/E♭, E♯/F, B♯m/Cm, C m/Dm	G♯/A♭, C♯/D♭, F♯/G♭, B/C♭	B♯/C, F /G, C /D, G /A	A♯m/B♭m
F	Dm	B♭, C, Gm, Am	E♭, A♭, D♭, G♭	G, D, A, E	Fm

In a minor key, the closely related keys are the parallel major, mediant or relative major, the subdominant, the minor dominant, the submediant, and the subtonic. In the key of A minor, when we translate them to keys, we get:

A major (I)
C major (III)
D minor (iv)
E minor (v)
F major (VI)
G major (VII)

Another view of closely related keys is that there are six closely related keys, based on the tonic and the remaining triads of the diatonic scale, excluding the dissonant diminished triads.^[7] Four of the five differ by one accidental, one has the same key signature, and one uses 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. Despite being three sharps or flats away from the original key in the circle of fifths, parallel keys are also considered as closely related keys as the tonal center is the same, and this makes this key have an affinity with the original key.

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.

According to another view in modern music, notably in Bartók, 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 or flats in its notated key signature; in such a case, notational conventions require recasting the new section in its enharmonically equivalent key.

Andranik Tangian suggests 3D and 2D visualizations of key/chord proximity for both all major and all minor keys/chords by locating them along a single subdominant-dominant axis, which wraps a torus that is then unfolded.^[8]

Related Research Articles

The major scale is one of the most commonly used musical scales, especially in Western music. It is one of the diatonic scales. Like many musical scales, it is made up of seven notes: the eighth duplicates the first at double its frequency so that it is called a higher octave of the same note.

In music, the tonic is the first scale degree of the diatonic scale and the tonal center or final resolution tone that is commonly used in the final cadence in tonal classical music, popular music, and traditional music. In the movable do solfège system, the tonic note is sung as do. More generally, the tonic is the note upon which all other notes of a piece are hierarchically referenced. Scales are named after their tonics: for instance, the tonic of the C major scale is the note C.

In music, modulation is the change from one tonality to another. This may or may not be accompanied by a change in key signature. Modulations articulate or create the structure or form of many pieces, as well as add interest. Treatment of a chord as the tonic for less than a phrase is considered tonicization.

Modulation is the essential part of the art. Without it there is little music, for a piece derives its true beauty not from the large number of fixed modes which it embraces but rather from the subtle fabric of its modulation.

A secondary chord is an analytical label for a specific harmonic device that is prevalent in the tonal idiom of Western music beginning in the common practice period: the use of diatonic functions for tonicization.

In music, relative keys are the major and minor scales that have the same key signatures, meaning that they share all the same notes but are arranged in a different order of whole steps and half steps. A pair of major and minor scales sharing the same key signature are said to be in a relative relationship. The relative minor of a particular major key, or the relative major of a minor key, is the key which has the same key signature but a different tonic.

In music, the mediant is the third scale degree of a diatonic scale, being the note halfway between the tonic and the dominant. In the movable do solfège system, the mediant note is sung as mi. While the fifth scale degree is almost always a perfect fifth, the mediant can be a major or minor third.

In music, the submediant is the sixth degree of a diatonic scale. The submediant is named thus because it is halfway between the tonic and the subdominant or because its position below the tonic is symmetrical to that of the mediant above.

In music, the supertonic is the second degree of a diatonic scale, one whole step above the tonic. In the movable do solfège system, the supertonic note is sung as re.

In music theory, the scale degree is the position of a particular note on a scale relative to the tonic—the first and main note of the scale from which each octave is assumed to begin. Degrees are useful for indicating the size of intervals and chords and whether an interval is major or minor.

The diminished seventh chord is a four-note chord composed of a root note, together with a minor third, a diminished fifth, and a diminished seventh above the root:. For example, the diminished seventh chord built on B, commonly written as B^o⁷, has pitches B-D-F-A♭:

In music, a minor seventh chord is a seventh chord composed of a root note, together with a minor third, a perfect fifth, and a minor seventh.

F-sharp major is a major scale based on F♯, consisting of the pitches F♯, G♯, A♯, B, C♯, D♯, and E♯. Its key signature has six sharps.

C-sharp major is a major scale based on C♯, consisting of the pitches C♯, D♯, E♯, F♯, G♯, A♯, and B♯. It is enharmonically equivalent to D-flat major. Its key signature has seven sharps.

G-sharp minor is a minor scale based on G♯, consisting of the pitches G♯, A♯, B, C♯, D♯, E, and F♯. Its key signature has five sharps.

A-sharp minor is a minor musical scale based on A♯, consisting of the pitches A♯, B♯, C♯, D♯, E♯, F♯, and G♯. Its key signature has seven sharps.

F minor is a minor scale based on F, consisting of the pitches F, G, A♭, B♭, C, D♭, and E♭. Its key signature consists of four flats. Its relative major is A-flat major and its parallel major is F major. Its enharmonic equivalent, E-sharp minor, has six sharps and the double sharp F, which makes it impractical to use.

In music, the axis system is a system of analysis originating in the work of Ernő Lendvai, which he developed in his analysis of the music of Béla Bartók.

G-sharp major is a theoretical key based on the musical note G♯, consisting of the pitches G♯, A♯, B♯, C♯, D♯, E♯, and F. Its key signature has one double sharp and six sharps.

In music, chromatic mediants are "altered mediant and submediant chords." A chromatic mediant relationship defined conservatively is a relationship between two sections and/or chords whose roots are related by a major third or minor third, and contain one common tone. For example, in the key of C major the diatonic mediant and submediant are E minor and A minor respectively. Their parallel majors are E major and A major. The mediants of the parallel minor of C major are E♭ major and A♭ major. Thus, by this conservative definition, C major has four chromatic mediants: E major, A major, E♭ major, and A♭ major.

Parallel and counter parallel chords are terms derived from the German to denote what is more often called in English the "relative", and possibly the "counter relative" chords. In Hugo Riemann's theory, and in German theory more generally, these chords share the function of the chord to which they link: subdominant parallel, dominant parallel, and tonic parallel. Riemann defines the relation in terms of the movement of one single note:

The substitution of the major sixth for the perfect fifth above in the major triad and below in the minor triad results in the parallel of a given triad. In C major thence arises an apparent A minor triad, D minor triad (Sp), and E minor triad (Dp).

References

1 2 3 4 Schonbrun, Marc (2006). The Everything Music Theory Book, p.76. ISBN 1-59337-652-9.
↑ George T. Jones (1994). HarperCollins College Outline Music Theory, p.217. ISBN 0-06-467168-2.
↑ Ulrich, Homer (1966). Chamber Music, p.175. ISBN 978-0-231-08617-2.
↑ Benward & Saker (2009). Music in Theory and Practice: Volume II, p. 155. 8th ed. ISBN 978-0-07-310188-0.
1 2 3 4 5 Benward & Saker (2003). Music: In Theory and Practice. Vol. I. p. 243. 7th ed. McGraw-Hill. ISBN 978-0-07-294262-0. "Most modulations occur between closely related keys, which are those keys that differ by no more than one accidental in the key signature."
1 2 Barry, Barbara R. (2000). The Philosopher's Stone: Essays in the Transformation of Musical Structure, p.19. ISBN 1-57647-010-5.
1 2 3 Jones (1994), p.35-36.
↑ Tangian, Andranik (2021). 2D and 3D proximity maps for major and minor keys and chords. KIT Scientific Working Papers. Vol. 171. Karlsruhe: Karlsruhe Institute of Technology (KIT). doi:10.5445/IR/1000135520. ISSN 2194-1629.

Closely related key

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