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In musical notation, a key signature is a series of sharp or flat symbols placed on the staff, designating notes that are to be consistently played one semitone higher or lower than the equivalent natural notes unless otherwise altered with an accidental. Key signatures are generally written immediately after the clef at the beginning of a line of musical notation, although they can appear in other parts of a score, notably after a double bar.
Key signatures are generally used in a score to avoid the complication of having sharp or flat symbols on every instance of certain notes. Each major and minor key has an associated key signature that sharpens or flattens the notes which are used in its scale. However, it is not uncommon for a piece to be written with a key signature that does not match its key, for example, in some Baroque pieces, or in transcriptions of traditional modal folk tunes.
Conventions of common practice period
In principle, any piece can be written with any key signature, using accidentals to correct any notes where it shouldn't apply. The purpose of the key signature is to minimize the number of such accidentals required to notate the music. The sequence of sharps or flats in key signatures is generally rigid in music from the common practice period. For example, if a key signature has only one sharp, it must be an F sharp.
The effect of a key signature continues throughout a piece or movement, unless explicitly cancelled by another key signature. For example, if a five-sharp key signature is placed at the beginning of a piece, every A in the piece in any octave will be played as A sharp, unless preceded by an accidental (for instance, the A in the above scale — the next-to-last note — is played as an A♯ even though the A♯ in the key signature is written an octave lower).
In a score containing more than one instrument, all the instruments are usually written with the same key signature. Exceptions include:
The convention for the notation of key signatures follows the circle of fifths. Starting from C major (or equivalently A minor) which has no sharps or flats, successively raising the key by a fifth adds a sharp, going clockwise round the circle of fifths. The new sharp is placed on the new key's leading note (seventh degree) for major keys or supertonic (second degree) for minor keys. Thus G major (E minor) has one sharp which is on the F; then D major (B minor) has two sharps (on F and C) and so on.
Similarly successively lowering the key by fifth adds a flat, going counter-clockwise round the circle of fifths. The new flat is placed on the subdominant (fourth degree) for major keys or submediant (sixth degree) for minor keys. Thus F major (D minor) has one flat which is on the B; then B♭ major (G minor) has two flats (on B and E) and so on.
Put another way: for key signatures with sharps, the first sharp is placed on F line with subsequent sharps on C, G, D, A, E and B; for key signatures with flats, the first flat is placed on B with subsequent flats on E, A, D, G, C and F. There are thus 15 conventional key signatures, with up to seven sharps or flats and including the empty signature of C major (A minor).
The relative minor is a minor third down from the major, regardless of whether it is a flat or a sharp key signature.
The key signatures with seven flats and seven sharps are rarely used because they have simpler enharmonic equivalents. For example, the key of C♯ major (seven sharps) is more simply represented as D♭ major (five flats). For modern practical purposes these keys are (in twelve tone equal temperament) the same, because C♯ and D♭ are enharmonically the same note. Pieces are written in these extreme sharp or flat keys, however: for example, Bach's Prelude and Fugue No. 3 from Book 1 of The Well-Tempered Clavier BWV 848 is in C♯ major. The modern musical Seussical by Flaherty and Ahrens also has several songs written in these extreme keys.
Major scale structure
Except for C major, key signatures appear in two varieties, "sharp key signatures" ("sharp keys") and "flat key signatures" ("flat keys"), so called because they contain only one or other.
Scales with sharp key signatures
Sharp key signatures consist of a number of sharps between one and seven, applied in this order: F C G D A E B. A mnemonic device often used to remember this is "Father Charles Goes Down And Ends Battle". The key note or tonic of a piece in a major key is immediately above the last sharp in the signature. For example, one sharp (F♯) in the key signature of a piece in a major key indicates the key of G major, the next note above F♯. (Six sharps, the last one being E♯ (an enharmonic spelling of F♮) indicate the key of F♯ major, since F has already been sharped in the key signature.)
C maj – 0 sharps G maj – 1 sharp – F♯ D maj – 2 sharps – F♯, C♯ A maj – 3 sharps – F♯, C♯, G♯ E maj – 4 sharps – F♯, C♯, G♯, D♯ B maj – 5 sharps – F♯, C♯, G♯, D♯, A♯ F♯ maj – 6 sharps – F♯, C♯, G♯, D♯, A♯, E♯ C♯ maj – 7 sharps – F♯, C♯, G♯, D♯, A♯, E♯, B♯
Scales with flat key signatures
"Flat key signatures" consist of one to seven flats, applied as: B E A D G C F (same as the order of sharps, but reversed.) The mnemonic device is then reversed for use in the flat keys: "Battle Ends And Down Goes Charles' Father". The major scale with one flat is F major. In all other "flat major scales", the tonic or key note of a piece in a major key is four notes below the last flat, which is the same as the second-to-last flat in the signature. In the major key with four flats (B♭ E♭ A♭ D♭), for example, the penultimate flat is A♭, indicating a key of A♭ major.
C maj – 0 flats F maj – 1 flat – B♭ B♭ maj – 2 flats – B♭, E♭ E♭ maj – 3 flats – B♭, E♭, A♭ A♭ maj – 4 flats – B♭, E♭, A♭, D♭ D♭ maj – 5 flats – B♭, E♭, A♭, D♭, G♭ G♭ maj – 6 flats – B♭, E♭, A♭, D♭, G♭, C♭ C♭ maj – 7 flats – B♭, E♭, A♭, D♭, G♭, C♭, F♭
In this case each new scale starts a fifth below (or a fourth above) the previous one.
Relationship between key signature and key
A key signature is not the same as a key; key signatures are merely notational devices. They are convenient principally for diatonic or tonal music. Some pieces that change key (modulate) insert a new key signature on the staff partway, while others use accidentals: natural signs to neutralize the key signature and other sharps or flats for the new key.
For a given musical mode the key signature defines the diatonic scale that a piece of music uses. Most scales require that some notes be consistently sharped or flatted. For example, the only sharp in the G major scale is F sharp, so the key signature associated with the G major key is the one-sharp key signature. However, the connection is not absolute; a piece with a one-sharp key signature is not necessarily in the key of G major, and likewise, a piece in G major may not always be written with a one-sharp key signature. This is particularly true of minor keys. Keys which are associated with the same key signature are called relative keys.
The Dorian Toccata and Fugue in D minor, BWV 538 by Bach has no key signature, which accords with its Dorian mode status (empty signature on D) in preference to its minor key status (which would have a single B♭ signature). The B♭s that occurs in the piece are written with accidentals.
Exceptions to common practice period use may be found in Klezmer scales, such as Freygish (Phrygian). In the 20th century, composers such as Bartók and Rzewski (see below) began experimenting with unusual key signatures that departed from the standard order.
In 15th-century scores, partial signatures are quite common, in which different voices will have different key signatures; however, this is derived from the different hexachords in which the parts were implicitly written, and the use of the term key signature can be misleading for music of this and earlier periods.
Because of the limitations of the traditional highland bagpipe scale, key signatures are often omitted from written pipe music, which otherwise would be written with two sharps, the usual F♯ and C♯.
The above key signatures only express diatonic scales and are therefore sometimes called standard key signatures. Other scales are written either with a standard key signature and use accidentals as required, or with a non-standard key signature. Examples of the latter include the E♭ (right hand) and F♭ & G♭ (left hand) used for the E♭ diminished (E♭ octatonic) scale in Bartók's Crossed Hands (no. 99, vol. 4, Mikrokosmos), or the B♭, E♭ & F♯ used for the D Phrygian dominant scale in Frederic Rzewski's God to a Hungry Child.
The use of a one-flat signature developed in the Medieval period, but signatures with more than one flat did not appear until the 16th century, and signatures with sharps not until the mid-17th century.
When signatures with multiple flats first came in, the order of the flats was not standardized, and often a flat appeared in two different octaves, as shown at right. In the late 15th and early 16th centuries, it was common for different voice parts in the same composition to have different signatures, a situation called a partial signature or conflicting signature. This was actually more common than complete signatures in the 15th century. The 16th-century motet Absolon fili mi attributed to Josquin des Prez features two voice parts with two flats, one part with three flats, and one part with four flats.
Baroque music written in minor keys often was written with a key signature with fewer flats than we now associate with their keys; for example, movements in C minor often had only two flats (because the A♭ would frequently have to be sharpened to A♮ in the ascending melodic minor scale, as would the B♭).
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