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== Conventions == The order in which sharps or flats appear in key signatures is illustrated in the diagram of the [[circle of fifths]]. Starting the major scale pattern (whole step, whole, half, whole, whole, whole, half) on C requires no sharps or flats. Proceeding clockwise in the diagram starts the scale a fifth higher, on G. Starting on G requires one sharp, F{{music|sharp}}, to form a major scale. Starting another fifth higher, on D, requires F{{music|sharp}} and C{{music|sharp}}. This pattern continues, raising the seventh scale degree of each successive key. As the scales become notated in flats, this is shown by eliminating one of the flats. This is strictly a function of notation—the seventh scale degree is still being raised by a semitone compared to the previous key in the sequence. Going counter-clockwise from C results in lowering the fourth scale degree with each successive key (starting on F requires a B{{music|flat}} to form a major scale). Each major key has a relative minor key that shares the same key signature. The relative minor is always a [[minor third]] lower than its relative major. The key signatures with seven flats and seven sharps are usually notated in their enharmonic equivalents. [[C-sharp major|C{{music|#}} major]] (seven sharps) is usually written as [[D-flat major|D{{music|b}} major]] (five flats) and [[C-flat major|C{{music|b}} major]] is usually written as [[B major]]. {{Image frame|content=<score> { \omit Score.TimeSignature << \new ChordNames \chordmode { ais1:m a:m } \new Staff \relative c' { \key ais \minor <ais cis eis ais>1 \bar "||" \key a \minor <a c e a>} >> } </score>|width=266|align=right|caption=Natural key signature: a key signature with seven [[Natural (music)|naturals]] ({{Music|natural}}) used to cancel the seven sharps ({{Music|sharp}}) of the previous signature.}} The key signature may be changed at any time in a piece by providing a new signature. If the new signature has no sharps or flats, a signature of naturals, as shown, is used to cancel the preceding signature. If a change in signature occurs at the start of a new line on the page, where a signature would normally appear, the new signature is customarily repeated at the end of the previous line to make the change more conspicuous. === Variations === {{unreferenced|section|date=May 2025}} In the past, when a key signature changes from sharps to flats or vice versa, the old key signature was cancelled with a matching set of naturals before the new key signature was shown. Newer music and newer editions of older music dispense with the naturals and simply insert the new signature, unless the new key signature has no sharps or flats (C major, A minor, or an open key signature), in which case the cancelling natural signs are necessary. Similarly, when a flat key changes to fewer flats, or a sharp key changes to fewer sharps, the convention was to use naturals to cancel the flats or sharps that are being subtracted before the new signature is written. Modern usage often simply shows the new signature without these naturals. As in the previous cases, the use of natural signs is required if the new key signature has no sharps or flats. When a flat key changes to more flats or a sharp key changes to more sharps, the new signature is simply written in without using naturals to cancel the old signature. This convention applies in both traditional and newer styles. At one time it was usual to precede the new signature with a [[barline|double barline]] even if it was not otherwise required, but it has become increasingly common to simply use a single barline. The courtesy signature that appears at the end of a line immediately before a change is usually preceded by an additional barline and the line at the very end of the staff is omitted. If both naturals and a new key signature appear at a key signature change, there are also modern variations about where a barline will be placed. In some scores by Debussy the barline is placed after the naturals but before the new key signature. Hitherto, it would have been usual to place all the symbols after the barline. The A{{music|sharp}} which is the fifth sharp in the sharp signatures may occasionally be notated on the top line of the bass staff, whereas it is more usually found in the lowest space on that staff. An example of this can be seen in the full score of [[Ottorino Respighi]]'s ''[[Pines of Rome]]'', in the third section, "Pines of the Janiculum" (which is in [[B major]]), in the bass-clef instrumental parts. In the case of seven-flat key signatures, the final F{{music|flat}} may occasionally be seen on the second-top line of the bass staff, whereas it would more usually appear on the space below the staff. An example of this can be seen in [[Isaac Albéniz]]'s ''[[Iberia (Albéniz)|Iberia]]'': first movement, "Evocación", which is in [[A-flat minor|A{{music|flat}}]] minor. === Double flats and sharps === [[Key signatures]] can extend into [[double flat]]s or [[double sharp]]s, but this is extremely rare. For example, the key of [[G sharp major|G{{music|#}} major]] would have eight sharps, requiring an F double-sharp (F{{music|x}}) and six single sharps. The key of [[A flat major|A{{music|b}} major]], with four flats, is [[Enharmonic equivalence|enharmonically equivalent]] and would generally be used instead. Although this system of notation could theoretically continue to be extended beyond single flats or sharps, a key signature with more than one or two double flats or sharps would be exceedingly hard to read and would be replaced by the enharmonically equivalent key signature. {| class="wikitable" ![[Major key|Major]] !Key signature ![[Minor key|Minor]] |- |[[F-flat major|F{{Music|flat}} major]] ([[E major]]) |8 flats (4 sharps) |[[D-flat minor|D{{Music|flat}} minor]] ([[C-sharp minor|C{{Music|sharp}} minor]]) |- |B{{Music|doubleflat}} major ([[A major]]) |9 flats (3 sharps) |G{{Music|flat}} minor ([[F-sharp minor|F{{Music|sharp}} minor]]) |- |E{{Music|doubleflat}} major ([[D major]]) |10 flats (2 sharps) |C{{Music|flat}} minor ([[B minor]]) |- |A{{Music|doubleflat}} major ([[G major]]) |11 flats (1 sharp) |F{{Music|flat}} minor ([[E minor]]) |- |D{{Music|doubleflat}} major ([[C major]]) |12 flats (no flats or sharps) |B{{Music|doubleflat}} minor ([[A minor]]) |- |G{{Music|doubleflat}} major ([[F major]]) |13 flats (1 flat) |E{{Music|doubleflat}} minor ([[D minor]]) |- |C{{Music|doubleflat}} major ([[B-flat major|B{{Music|flat}} major]]) |14 flats (2 flats) |A{{Music|doubleflat}} minor ([[G minor]]) |- |[[G-sharp major|G{{Music|sharp}} major]] ([[A-flat major|A{{Music|flat}} major]]) |8 sharps (4 flats) |[[E-sharp minor|E{{Music|sharp}} minor]] ([[F minor]]) |- |D{{Music|sharp}} major ([[E-flat major|E{{Music|flat}} major]]) |9 sharps (3 flats) |B-sharp minor|B{{Music|sharp}} minor ([[C minor]]) |- |A{{Music|sharp}} major ([[B-flat major|B{{Music|flat}} major]]) |10 sharps (2 flats) |F{{Music|doublesharp}} minor ([[G minor]]) |- |E{{Music|sharp}} major ([[F major]]) |11 sharps (1 flat) |C{{Music|doublesharp}} minor ([[D minor]]) |- |B{{Music|sharp}} major ([[C major]]) |12 sharps (no flats or sharps) |G{{Music|doublesharp}} minor ([[A minor]]) |- |F{{Music|doublesharp}} major ([[G major]]) |13 sharps (1 sharp) |D{{Music|doublesharp}} minor ([[E minor]]) |- |C{{Music|doublesharp}} major ([[D major]]) |14 sharps (2 sharps) |A{{Music|doublesharp}} minor ([[B minor]]) |} A piece in a major key might modulate up a [[Perfect fifth|fifth]] to the [[Dominant (music)|dominant]] (a common occurrence in Western music), resulting in a new key signature with an additional sharp. If the original key was C-sharp, such a [[Modulation (music)|modulation]] would lead to the key of G-sharp major (with eight sharps) requiring an F{{Music|x}} in place of the F{{Music|#}}. This section could be written using the enharmonically equivalent key signature of A-flat major instead. [[Claude Debussy]]'s ''[[Suite bergamasque]]'' does this: in the third movement "Clair de lune" the key shifts from D-flat major to D-flat minor (eight flats) for a few measures but the passage is notated in C-sharp minor (four sharps); the same happens in the final movement, "Passepied", in which a G-sharp major section is written as A-flat major. Such passages may instead be notated with the use of double-sharp or double-flat accidentals, as in this example from [[Johann Sebastian Bach]]'s ''[[Well-Tempered Clavier]]'', which has this passage in G-sharp major in measures 10-12. [[File:G-sharp major example 2.png]] While these keys are sometimes notated with accidentals as in this example, the use of a key signature containing double flats or sharps is very rare. The final pages of [[John Foulds]]' ''[[A World Requiem]]'' are written in [[G-sharp major|G♯ major]] (with F{{music|x}} in the key signature), No. 18 of [[Anton Reicha]]'s ''Practische Beispiele'' is written in B{{music|#}} major, and the third movement of [[Victor Ewald]]'s [[Brass quintet|Brass Quintet]] Op. 8 is written in [[F♭ major]] (with B{{music|bb}} in the key signature).<ref name=":0">{{IMSLP|work=Practische Beispiele (Reicha, Anton)|cname=Anton Reicha: ''Practische Beispiele'', pp. 52-53.}}</ref><ref>{{cite web |author=<!--Staff writer(s); no by-line.--> |title=Ewald, Victor: Quintet No 4 in A{{music|b}}, op 8 |url=http://www.enspub.com/pages/93/93503.htm |access-date=14 February 2023 |publisher=imslp}}</ref> Examples of such key signatures are pictured below:<score> \relative c' { \omit Staff.TimeSignature \omit Staff.KeyCancellation \key gis \major <gis' bis dis><eis gis bis>_\markup \halign #0.2 \center-column { "G♯ maj" "E♯ min" } \bar "||" \key dis \major <dis fisis ais><bis dis fisis>_\markup \halign #0.2 \center-column { "D♯ maj" "B♯ min" } \bar "||" \key fes \major <fes' as ces><des fes as>_\markup \halign #0.2 \center-column { "F♭ maj" "D♭ min" } \bar "||" \key beses \major <beses' des fes><ges beses des>_\markup \halign #0.2 \center-column { "B♭♭ maj" "G♭ min" } } </score>There does not appear to be a standard on how to notate these key signatures: * The default behaviour of [[LilyPond]] (pictured above) writes all single sharps or flats in the circle-of-fifths order before showing the double signs. This is the format used in [[John Foulds]]' ''[[A World Requiem]]'', Op. 60, which uses the key signature of G♯ major as displayed above.<ref>{{IMSLP|work=A World Requiem, Op.60 (Foulds, John)|cname=John Foulds: ''A World Requiem'', pp. 153ff.}}</ref> The sharps in the key signature of [[G-sharp major|G♯ major]] proceed C♯, G♯, D♯, A♯, E♯, B♯, F{{music|x}}. * The single signs at the beginning are sometimes repeated as a courtesy, e.g. [[Max Reger]]'s ''Supplement to the Theory of Modulation'', which contains [[D♭ minor]] key signatures on pp. 42–45.<ref>{{cite book |author=Max Reger |title=Supplement to the Theory of Modulation |publisher=C. F. Kahnt Nachfolger |year=1904 |location=Leipzig |pages=[https://archive.org/details/supplementtotheo00rege/page/42/mode/2up 42–45] |translator=John Bernhoff}}</ref> These have a B♭ at the start and also a B{{music|bb}} at the end (with a double-flat symbol), going B♭, E♭, A♭, D♭, G♭, C♭, F♭, B{{music|bb}}. * Sometimes the double signs are written at the beginning of the key signature, followed by the single signs. For example, F♭ would be notated as B{{music|bb}}, E♭, A♭, D♭, G♭, C♭, F♭. This convention is used by Victor Ewald<ref>[https://www.hickeys.com/music/brass/brass_ensembles/brass_quintets/products/sku035994-ewald-victor-quintet-no-4-in-ab-op-8.php "Ewald, Victor: Quintet No 4 in A{{music|b}}, op 8"], Hickey's Music Center</ref> and by some theoretical works. * No. 18 of Anton Reicha's ''Practische Beispiele'' in B♯ major<ref name=":0" /> shows B♯, E♯, A{{music|x}}, D{{music|x}}, G{{music|x}}, C{{music|x}}, F{{music|x}}. In [[tuning system]]s where the number of notes per octave is not a multiple of 12, notes such as G{{music|#}} and A{{music|b}} are not enharmonically equivalent, nor are the corresponding key signatures. These tunings can produce keys with no analogue in 12-tone equal temperament, which can require double sharps, double flats, or [[microtonal music|microtonal alterations]] in key signatures. For example, the key of G♯ major, with eight sharps, is equivalent to A{{music|b}} major in 12-tone equal temperament, but in [[19 equal temperament|19-tone equal temperament]], it is equivalent to A{{Music|bb}} major instead, with 11 flats.
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