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 usually, but not always, tells us the key of the piece.

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 eighteenth century. Music from the 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 eighteenth 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

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 (also called Heinichen's circle of fifths or cycle 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 semibreve (whole note) 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 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.

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.

Lesson 27 considers these matters in much greater detail.

We set out the enharmonic notes under equal temperament in the table below using the
	(sharp),		(double sharp),		(flat),		(double flat) and		(natural) signs.

Because we are working in equal temperament, all the notes in any one column are at the same pitch. Similarly, 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 those for a double-sharp and double-flat.

The rules for applying accidentals are simple to state today, but, hundreds of years ago, the rules varied from composer to composer and from country to country. They could be said to be 'confused' and for us today 'confusing'. 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 are the most general rules applied to the use of 'accidentals' today?

	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 [refer here for Accidentals and Ornamentation]
	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. [It is worth adding a comment on this 'so-called' rule. Many modern composers expect the accidental to apply to all notes in the same bar of the same pitch-class. Thus, their accidentals behave like the sharps and flats in a key-signature. While this may be the rule by which these composers work, modern players, who have to work with both conventions, need some reassurance and we strongly recommend the use of courtesy accidentals on all notes of the same pitch class, within the same bar, but at octaves that differ from the note to which the accidental was first applied. Similarly, if a passage is repeated under an 8va sign, the accidentals should be repeated.]
	When used, the accidental applies only until 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 Bs 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; any note following, even the same note not tied to it, will, after the end of the tie, have to be marked with an accidental again. If however the tie persists through several bars, the original note bearing an accidental will remain unchanged. Both the Cs in the second bar are C natural.
	Where there might be any doubt, precautionary marks (sometimes called 'courtesy accidentals') may be used - accidentals, sometimes, but not necessarily, 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 to confirm the C sharp in the second bar. We agree with Thomas Mccanna that precautionary accidentals should be used where there might be any possibility of doubt.

Accidentals and Ornamentation

Accidentals may also be found in combination with ornamental signs (trills, mordents, turns, etc.). If any of the auxiliary notes in an ornament include accidentals, for instance a C sharp in the key of G major, this is shown by writing an accidental, in this case a sharp sign, above or below the ornament sign. In the case of an F natural in the key of G major, the sign would be a natural. However, if F# is required in the key of G major, no sharp sign is necessary as F# is diatonic in this key. The convention is that if the inflection applies to a note lying above the principal note then the accidental is written above the sign for the ornament, but if the inflected auxiliary note lies below the principal note, the accidental sign is placed below the sign for the ornament. Obviously, if the principal note itself is inflected then the accidental is placed to the immediate left of the principal note head and not with the sign for the ornament.

Note: this convention is not always observed. Thus, where there is only one auxiliary note (for example, in a mordent) then some editors place an accidental applying to the auxiliary above the ornament sign even if the auxiliary lies below the principal note

Reference:

Other Conventions for the Use of Accidentals

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 compound signs used to indicate the cancellation of only one of a pair of double sharps or double flats:

the two signs are

(natural sharp)  and

(natural flat) respectively.

There is a third compound sign used to indicate the cancellation of both of a pair of double sharps or double flats:

the sign is

(double natural).

The table below sets out the names of the inflections in various languages.

Notes and Keys in Various Languages

Our thanks to Erik Magnus Johansson for advising us of the correct spelling of the Swedish entries and for the comment that follows:

Note Naming in Sweden

Erik Magnus Johansson informs us that regarding the tone names b and its inflections there are in Sweden today two ways of naming them:

The first is still the most used but the second is becoming more and more common especially among younger musicians.

Writing the Keys of Musical Pieces in Various Languages

In English, the key of a piece of music might be written in the form Suite in G major (sometimes shortened to Suite in G where major is understood), Suite in D minor or Suite in E flat major, with no change of case between major and minor keys.

In German, the keys of similar pieces of music would be written in the form Suite G-Dur (in English, G major), Suite d-Moll (in English, D minor) or Suite Es-Dur (in English, E flat major). h-Moll Messe is the German name of Bach's Mass in B minor. Note the use of the hyphen, the use of upper case for major keys, and the use of lower case for minor keys.

In French, the keys of similar pieces of music would be written Suite en Sol Majeur (in English, G major), Suite en ré mineur (in English, D minor) or Suite en Mi bémol Majeur (in English, E flat major). Note the the use of upper case for major keys, and the use of lower case for minor keys.

In Italian, the keys of pieces of music follow the French pattern: for example, Suite in Mi maggiore (in English, E major), Suite in re minore (in English, D minor) or Suite in si minore (in English, B minor).