The Key Signature :: In the previous lesson we touched upon a method for reducing the number of sharp and flat signs when writing music in a particular key. Examine the row of notes in the key of A major. C, F and G are 'sharpened'. If the notes are written with no key signature every 'sharpened' note must be marked with a 'sharp' sign. If we write the A major key signature (three sharps), at the beginning of the stave, one no longer needs to place 'sharp' signs in front of these notes. The key signature applies to all the relevant notes in every octave. As well as simplifying the notation, the key signature tells us the key of the piece of music. The key signature appear on every line of music immediately after the clef sign. The time signature is written only on the first line, placed after the clef sign and key signature. The bars have been numbered 'line by line'. This part is written for an oboe. On the first line the instrument name is written in full, while on the other line(s) it is abbreviated. As an aside, it is worth remembering that the concept of key signatures as we know it today developed in the latter part of the 18th century. Music from Baroque and earlier periods may be written with key signatures containing fewer sharps or flats than we might expect. This is found particularly when the music is written in a minor key. One explanation is the association between 'key signatures' and the use of 'major' and 'minor' keys. Before the end of the 18th century, composers still thought musically in terms of modes which would, for a particular key note, tend to have different number of sharps or flats associated with them than with our modern major and minor scales. Modes may contain intervals that are not pleasing to the ear. e.g. an augmented 4th between F and B. The singers would alter these by flattening the B. Alterations such as these, were never written in the music but are an example of musica ficta which means, literally, "feigned music". Reference What is Musica Ficta? - part of an article entitled Hexachords, solmization, and musica ficta The Circle of Fifths :: We now need to determine the key signature for each of the major keys. Of course, we could work out the note row for each major key and so identify the number of sharps or flats in each key. There is, however, a shorthand way of remembering the relationship between the key and the key signature using the circle of fifths illustrated below. Place the note C in the twelve o'clock position on a clock face. Moving clockwise, place the fifth degree of the C major scale, the note G, in the one o'clock position. Again moving clockwise, place the fifth degree of the G major scale, the note D, in the two o'clock position. Having done this the necessary number of times you will have produced the sequence C, G, D, A, E, B, F sharp and C sharp. The key signature for each key has one sharp more than the key preceding it in the sequence. We have marked the number of sharps for the first two sharp keys Place the note C in the twelve o'clock position on a clock face. Moving anti-clockwise, place the fourth degree of the C major scale, the note F, in the eleven o'clock position. Again moving anti-clockwise, place the fourth degree of the F major scale, the note B flat, in the ten o'clock position. Having done this the necessary number of times you will have produced the sequence C, F, B flat, E flat, A flat, D flat , G flat and C flat. The key signature for each key has one flat more than the key preceding it in the sequence. We have marked the number of flats for the first two flat keys. You may be wondering why, if we use a circle of fifths, the flat keys are found by taking the fourth degree of the major scale. In fact, the fourth degree of the scale is the same note as you would get by moving a 'fifth' down the major scale. We illustrate below the sequence of key signatures that the circle of fifths produces in each case - moving clockwise for the sharp keys or anti-clockwise for the flat keys. The key name is confirmed by the minim appearing after each signature. The order of the sharps or flats remains unchanged in each signature and each stave in a line of music will have the same key signature adjusted for that line's particular clef. You may be wondering also why 'circle of fifths' - why not 'circle of fourths' or 'circle of thirds'. You may remember that in lesson 8 we introduced the Greek tetrachord, a row of four notes based on the interval sequence tone-tone-semitone. The major scale of C is just two consecutive tetrachords: C - tone - D - tone - E - semitone - F : the first tetrachord G - tone - A - tone - B - semitone - C : the second tetrachord Note that the first note in the first tetrachord is exactly one octave below the fourth note of the second tetrachord. The second scale, starting on the key note G, starts from the first note of the second tetrachord of the C major scale, that is, from the fifth degree. The two tetrachords for the G major scale are: G - tone - A - tone - B - semitone - C : the first tetrachord D - tone - E - tone - F sharp - semitone - G : the second tetrachord The flat keys are 'constructed' by treating the first tetrachord of the present scale as the second tetrachord of the key flatter by one accidental to it. The C tetrachords are: C - tone - D - tone - E - semitone - F : the first tetrachord G - tone - A - tone - B - semitone - C : the second tetrachord So for the major scale of F major C - tone - D - tone - E - semitone - F is the the second tetrachord and, remembering that the last note of the second tetrachord is the first note of the first, F - tone - G - tone - A - semitone - B flat is the first tetrachord The Order of Sharps & Flats in The Key Signature :: If you look at the sequence of steadily 'sharper' keys as one progresses clockwise around the circle of fifths, starting with G major, then D major and so on, you will find that the order of the sharps, read left to right in the key signature, preserves the order in which the sharp signs first appear; first F sharp (in G major), then C sharp (in D major), then G sharp (in A major) and so on. Again, the order of the flats, again read from left to right in the key signature, as they appear in the steadily 'flatter' keys as one moves anti-clockwise around the circle of fifths, preserves the order in which the flat signs first appear; first B flat (in F major), then E flat (in B flat major), then A flat (in E flat major) and so on. The advantage of a preserved order is that the last sharp or flat on the right of the key signature, itself uniquely identifies the key of the work. The performer does not need to confirm this by reading the other signs in the key signature. In the case of the sharp keys, the key, if it is a major key, is a semitone above the last sharp in the key signature (e.g. if the last sharp is F sharp, the key is G major); otherwise it is the relative minor, E minor. For flat keys, the key, if it is a major key, is the last but one flat in the key-signature (e.g. if the last but one flat is B flat, the key is B flat major); otherwise it is its relative minor, G minor. Obviously, in the case of one flat you just remember that this, if it is in a major key, is F major; otherwise it is its relative minor, D minor. If there is no sharp or flat in the key-signature, the key, if it is in a major key, is C major; otherwise it is the relative minor, A minor. For more on relative minor keys see lesson 10: Relative & Parallel Major & Minor. Enharmonics :: We have already seen that note names may not be unique; for example, D flat and C sharp. The problem is even greater than that. If you look again at the keyboard below you will appreciate that 'sharpening' and 'flattening' leads to other double named notes. For example, B is also C flat, F is also E sharp. If you refer back to the circle of fifths diagram above you will see that the five, six and seven o'clock positions each has two key names. If you play the two scales on the keyboard, the sequence of sounds will be the same for each pair of keys - the key pairs are enharmonic. Similarly with note names, E flat is enharmonic to D sharp, A sharp is enharmonic to B flat. C D E F G A B * C D E F G A B C D E F G A B You may be wondering why, if enharmonic keys are identical when played on a keyboard, composers don't just chose the key with the fewer sharps or flats. It is only with the modern tuning system we call 'equal temperament' that the pairs of enharmonic notes have the same pitch. In other tuning systems these two notes are actually different. C sharp, for example, is slightly flatter than D flat. Lesson 27 considers these matters in much greater detail. We set out the enharmonic notes in the table below using the (sharp), (double sharp), (flat), (double flat) or (natural) signs. In any column all the notes are the same pitch. In any column the notes are one semitone sharper than those in the column to the left and one semitone flatter than those in the column to the right. the numbers are in units of one semitone (e.g. C + 5 = C plus 5 semitones = F) C + 0 C + 1 C + 2 C + 3 C + 4 C + 5 C + 6 C + 7 C + 8 C + 9 C + 10 C + 11 B B C C C D D D D D E E E E E F F F F F G G G G G A A A A A B B B C C We can display the enharmonic relationships on a piano keyboard. This is shown below. Using Accidentals :: We have assumed, until now, that pieces of music are written in various keys and that, once the right key signature has been chosen, we never need to write sharp or flat signs. Actually, this could not be further from the truth. The introduction of notes from the chromatic scale that are not part of the major scale, or modulation, when the key changes, both add 'spice' to a musical line and produce a change of 'mood'. Generally, music starts and finishes in the same key and generally it is that key that will be indicated by the key signature. However, the key signature never 'determines' the key of a piece of music. In the sixteenth century, minor keys with key signatures made up of flats and where the sixth and seventh degrees were frequently inflected (i.e. raised by a semitone), were often written with key signatures one flat too few (i.e. without the flat for the sixth degree). As the sixth degree required a sharp or a natural, the composer would then notate this in the score. The signature was then and remains only a notational convenience that reduces the number of sharp and flat signs in the body of the score by placing them in the key signature at the beginning of the line. Notes that do not lie in the scale of the key are called accidentals and these are marked in the score by using the signs we have met already, the natural, sharp and flat signs as well as the double-sharp and double-flat signs. The rules for applying accidentals are simple to state today, but hundreds of years ago, the rules varied from composer to composer, from country to country and could be said to be 'confused'. Modern editions of mediaeval and renaissance music can disagree in their 'realisation' of accidentals, a situation made more difficult because the concept of key was changing from older modes to newer major and minor keys. So what now are the rules for using 'accidentals'? The sign is placed in front of the note. In some editions of early music, accidentals may appear above notes. In this case, the accidental is an editorial suggestion or correction The note-accidental combination 'names' the note to be played: so, F sharp means play F sharp, B natural means play B natural and E flat means play E flat whatever the key signature. When there is no accidental written, the actual note to be played depends on the key signature. The sign applies only to the line or space where it first appears; if the same note appears in another octave, or, in the case of multi-staves scores on another staff, the accidental must be restated (see the high B natural). Contrast this with the rule for signs appearing in the key signature which apply to all relevant notes in any octave on the stave. When used, the accidental applies only to the end of that particular bar, or until another accidental appears later in the same bar on the same note on the same line or space. The first two B's are both B naturals, the third B is marked B flat. There is one exception to the 'bar-line cancels the accidental' rule. If the note bearing the accidental is tied into the next bar, the accidental persists for that note only; any note after the end of the tie would have to be marked again. Both the C's in the second bar are C natural. Where there might be any doubt, precautionary marks (sometimes called 'courtesy accidentals') may be used - accidentals, sometimes within brackets, that confirm the status of the note. The C in the second bar would be C sharp because the previous bar-line ends the effect of the natural sign. Even so, a precautionary sharp sign has been used for the C sharp in the second bar. During the twentieth-century the traditional convention for applying accidentals, the convention we have described above, was extended. There are now four general approaches: Traditional accidentals apply for the duration of the bar Second Viennese School accidentals are used on every pitch except for repeated notes Modernist accidentals apply only to the pitch to which they are attached and any immediately repeated pitches. Naturals are not used except for clarification Salzedo accidentals only apply to the pitch to which they are attached, but not to any repetitions of the same pitch. Naturals are never used Changing Key :: There will be occasions when it is makes more sense to change the key signature than to rely only on accidentals. A new key signature is applied from the beginning of a bar. If the new bar-line is at the beginning of the line, a cautionary sign, may appear at the end of the previous line, after the last bar-line. We offer a trivial example to demonstrate both situations. The first two bars are in G major, the second two are in C major and the last four bars return to G major. Because the key signature for C major is normally 'empty' of sharp or flat signs, the 'change' of key is marked with a pattern of natural signs that matches the pattern of sharps or flats in the previous key signature - in this case, one natural where before there was the single sharp sign for G major. The application of the (sharp), (double sharp), (flat), (double flat) or (natural) sign to a note is called an inflection. There are two special signs used to indicate the cancellation of only one of a pair of sharps (double sharp) or flats (double flat). The two signs are and respectively. The table below sets out the names of the inflections in various languages. Notes and Keys in Various Languages :: English/US Italian French German Dutch Danish Swedish Finnish Spanish (Catalan) c double flat do doppio bemolle ut double-bémol Ceses ceses ceses ceses ceses do doble bemol (do doble bemoll) c flat do bemolle ut bémol Ces ces ces ces ces do bemol (do bemoll) c do ut C c c c c do (do) c sharp do diesis ut dièse Cis cis cis cis cis do sostenido (do sostingut) c double sharp do doppio diesis ut double-dièse Cisis cisis cisis cisis cisis do doble sostenido (do doble diesi) d double flat re doppio bemolle ré double-bémol Deses deses deses deses deses re doble bemol (re doble bemoll) d flat re bemolle ré bémol Des des des des des re bemol (re bemoll) d re ré D d d d d re (re) d sharp re diesis ré dièse Dis dis dis dis dis re sostenido (re sostingut) d double sharp re doppio diesis ré double-dièse Disis disis disis disis disis re doble sostenido (re doble diesi) e double flat mi doppio bemolle mi double-bémol Eses eses eses eses eses mi doble bemol (mi doble bemoll) e flat mi bemolle mi bémol Es es es es es mi bemol (mi bemoll) e mi mi E e e e e mi (mi) e sharp mi diesis mi dièse Eis eis eis> eis eis mi sostenido (mi sostingut) e double sharp mi doppio diesis mi double-dièse Eisis eisis eisis eisis eisis mi doble sostenido (mi doble diesi) f double flat fa doppio bemolle fa double-bémol Feses feses feses feses feses fa doble bemol (fa doble bemoll) f flat fa bemolle fa bémol Fes fes fes fes fes fa bemol (fa bemoll) f fa fa F f f f f fa (fa) f sharp fa diesis fa dièse Fis fis fis fis fis fa sostenido (fa sostingut ) f double sharp fa doppio diesis fa double-dièse Fisis fisis fisis fisis fisis fa doble sostenido (fa doble diesi) g double flat sol doppio bemolle sol double-bémol Geses geses geses geses geses sol doble bemol (sol doble bemoll) g flat sol bemolle sol bémol Ges ges ges ges ges sol bemol (sol bemoll) g sol sol G g g g g sol (sol) g sharp sol diesis sol dièse Gis gis gis gis gis sol sostenido (sol sostingut) g double sharp sol doppio diesis sol double-dièse Gisis gisis gisis gisis gisis sol doble sostenido (sol doble diesi) a double flat la doppio bemolle la double-bémol Ases ases ases ases ases la doble bemol (la doble bemolle) a flat la bemolle la bémol As as as as as la bemol (la bemolle) a la la A a a a a la (la) a sharp la diesis la dièse Ais ais ais ais ais la sostenido (la sostingut) a double sharp la doppio diesis la double-dièse Aisis aisis aisis aisis aisis la doble sostenido (la doble diesi) b double flat si doppio bemolle si double-bémol Bes beses bes bes bes si doble bemol (si doble bemoll) b flat si bemolle si bémol B bes b b b si bemol (si bemoll) b si si H b h h h si (si) b sharp si diesis si dièse His bis his his his si sostenido (si sostingut) b double sharp si doppio diesis si double-dièse Hisis bisis hisis hisis hisis si doble sostenido (si doble diesi) sharp diesis dièse Kreuz kruis kryds korsförtecken korotusmerkki sostenido or elevación de un semitono (diesi or sostingut) double sharp doppio diesis double dièse Doppelkreuz dubbelkruis dobbeltkryds dubbelkors kaksoisylennysmerkki doble sostenido or elevación de dos semitonos (doble diesi or elevació de dos semitons) flat bemolle bémol B(e) mol b beförtecken alennusmerkki bemol or bajada de un semitono (bemolle or disminució d’un semitò) double flat doppio bemolle double bémol Doppel-B(e) dubbelmol dobbelt-b dubbelbe kaksoisalennusmerkki doble bemol or bajada de dos semitonos (doble bemolle) natural bequadro bécarre or naturel Auflösungszeichen or Quadrat herstellingsteken opløsningstegn återställningstecken palautusmerkki becuadro (becaire) major (for keys and intervals) maggiore (for keys and intervals) majeur (for keys and intervals) Dur (for keys); gross (for intervals) majeur dur dur duuri mayor (major) minor (for keys and intervals) minore (for keys and intervals) mineur (for keys and intervals) Moll (for keys); klein (for intervals) mineur mol moll molli menor (menor)