Sharps, flats and circle of fifths. How to write alterations

My students often ask me when to use sharps and when to use flat when writing a note or chord. The answer to this question is not so simple, what is true for single notes is not always true for scales and chords. So let’s see how to use sharps and flats to write notes, scales and chords. We will also discover how the circle of fifths works.

What are sharps and flats for? First case, sounds without a name

When the notes were given names, both the ancient Latin A B C D E F G and the Italian Do Re Mi Fa Sol La Si, only seven notes were used. Therefore, both systems use seven names only. Later, the chromatic scale came into use, which uses twelve sounds instead.

When these five additional sounds came into use permanently, instead of giving them a new name it was preferred to call them by the name of the neighbouring notes. Here, then, is the first use of sharps and flats: naming five sounds that have no name of their own. The note between F and G can be called F sharp (note above F) or G flat (note below G).

When five ‘extra’ notes were added to the original seven notes Do Re Mi Fa Sol La Si Do, the first seven still maintained a special quality. In fact, the original seven notes form the major scale, which remained the basis of the tonal music system even when the twelve-tone chromatic scale came into definitive use. The two scales are compared below.

Seven-notes major scale: Do Re Mi Fa Sol La Si Do

Twelve-notes chromatic scale: Do Do#/Reb Re Re#/Mib Mi Fa Fa#/Solb Sol Sol#/Lab La La#/Sib Si Do

Notes can have two names: enharmony

The principle by which certain sounds can have two names (e.g. F sharp and G flat) has a very definite name: it is called enharmony. Enharmony does not only apply to ‘unnamed notes’, such as the note that lies between F and G and must be named after one of its neighbours, thus being called F sharp or G flat.

Enharmony also applies to scale sounds that already have a name, but can sometimes be called by a different name, using sharps or flats. Let’s take an example: on the chromatic scale after E there is F. Well, it can happen that E is written F flat (F ‘lowered’) or that F is called E sharp (E ‘raised’).

The sound we normally call E can also be called F-flat

The sound we normally call F, can also be called E-sharp

The reason why this may be the case will become clear later in the lesson, at least I hope so! For now, let us just reaffirm the concepts introduced so far.

• Sharp and flat are used to indicate those sounds of the chromatic scale that do not have a name of their own
• A sharp indicates a sound ‘raised’ by a semitone, a flat indicates a sound ‘lowered’ by a semitone
• Sometimes, even sounds that have their own name are named using sharps and flats
• The possibility of giving a sound an alternative name is called enharmony.

Now that we have seen how sharps and flats are used to write single notes, let’s find out how they are used to write major scales.

Sharp or flat to write major scales. The circle of fifths

To find out when sharps and when flat are used in writing major scales, we use a scheme called the ‘circle of fifths’.

In the circle of fifths, in the top centre is the C major scale, which uses neither sharps nor flats. Keys that use sharps are placed on the right-hand side, keys that use flats are placed on the left-hand side.

The right side of the circle of fifths: tonalities with sharps

Major scales are ordered in fifths according to this principle:

On the right side of the circle of fifths, go up a fifth and add a sharp on the seventh note of the scale

So, going from C to G, I will add a sharp on the seventh note of the G scale. The seven notes starting from G are G A B C D E F G, putting a sharp on the seventh degree we get G A B C D E F# G.

If I go up a fifth more, I start on the note D and have to add a sharps on the seventh note C. The previously used sharps remain, so I also keep the F# used in the G scale. The scale of D will therefore be D E F# G A B C#.

If I go up another fifth, I reach the note A. I add one more sharps on the seventh degree G. In this way we can reach the scale of F sharp, which uses six sharps.

If I wanted to go further, I would get the C-sharp scale, which uses seven sharps, C# D# E# F# G# A# B#. In reality this scale is not used, let’s go to the left side of the circle of fifths and find out why.

The left side of the circle of fifths: tonalities with flats

Still starting with C, if you go back a fifth, you will find the tonalities that use flats.

On the left side of the circle of fifths, we go down a fifth and add a flat on the fourth note of the scale

So, moving from C to F, we add a flat on the fourth note of the F scale. The seven notes starting from F are F G A B C D E, putting a flat on the fourth degree we get F G A Bb C D E.

If we go down a fifth further, we find the note Bb. We add a flat on the fourth note (E). The flats used previously remain, so we also keep the B flat used in the F scale. The B-flat scale will therefore consist of Bb C D Eb F G A Bb.

If I go down another fifth I reach the note Eb, and add one more flat on the fourth degree (A flat). In this way we continue until the scale of G flat, which uses six flats. If I wanted to go further on, I would get the C flat scale, which uses seven flats but which we do not use, because it coincides with the B scale.

To the C flat major scale that would use seven flats, we prefer the B major scale that uses only five sharps. Similarly, to the scale of C sharp major that would use seven sharps, we prefer the scale of D flat major that uses only five flats.

As far as F#/Gb is concerned, there is no advantage in using one scale or the other, because both use six alterations. Instead, in the other two cases, we have a scale that uses fewer alterations: hence, we prefer Db to C#, and we prefer B to Cb.

Circolo delle quinte ascendenti e discendenti

The circle of fifths is also used to perform many harmony exercises, e.g. to learn chords in all keys. It is therefore worth memorising the order of the notes in the ascending fifths circle, i.e. going clockwise in the circle. The notes you will find are these.

C G D A E B Gb Db Ab EB Bb F

Sometimes we prefer to use the circle of descending fifths, i.e. starting from C and going anticlockwise to the left. For simplicity’s sake, instead of thinking of descending fifths, we can think of ascending fourths.

In fact going backwards by a fifth is equivalent to going forwards by a fourth. For example, starting from C, the descending fifth interval takes us to F. I find the same note F even if starting from C I go up a fourth.

The opposite is also true, the descending fourth interval is equivalent to the ascending fifth interval. For example, C G.

The interval of the descending fifth is equivalent to an ascending fourth

The descending fourth interval is equivalent to an ascending fifth interval

I recommend that you also memorise the order of the notes in the circle of descending fifths, i.e. going counterclockwise in the circle. The notes you find are these.

C F Bb Eb Ab Db Gb B E A D G

Now that we have discovered how the circle of fifths works and how sharps and flats are used in scale writing, we will see how to choose sharps or flats in other specific cases.

When to use sharps and when to use flats: the chromatic scale

In chromatic scale writing, the rule is very simple: in the ascending chromatic scale, sharps are used; in the descending chromatic scale, flats are used. This rule is also used when playing a chromatic scale fragment only and not necessarily the whole chromatic scale.

In the ascending chromatic scale, sharps are used.

In the descending chromatic scale, flats are used

We have so far considered the use of sharps and flats in the writing of single notes and scales, let us now see how they are used in chords symbols.

Sharps and flats in chord symbols

When the altered note is part of a chord, the use of sharps and flats depends on a careful analysis of the harmony. Starting from the chord derived from the key scale, we use sharp if the note is altered in an ascending manner, we use flat if the note is altered in a descending manner. For example, in a chord of C7(#5) we would use a sharp, while we would use a flat on C7(b5).

Normally, chord abbreviations follow the name of the individual notes in the scale. When chords start instead from a note outside the scale of the tonality, the same principle is used as for alterations in the scale.

• If the scale uses sharps, chord abbreviations also use sharps
• If the scale uses flats, the chord abbreviations also use flats

There are particular cases in which this rule can be contradicted. In particular, chord symbols in modern music are almost always written as simply as possible. Due to the effect of enharmony, we call chords by their most immediate and easily deciphered name.

So we will not write Fb7 but E7, we will not write B#7 but we will prefer C7. Chord symbols are in fact a ‘shortcut’ to tell the performer which chord to play, and it is common practice to use the abbreviations that are easiest to understand.

Conclusion: when to use sharp or flat

The use of sharps or flats is closely related to how music works, particularly the modern musical system called the ‘tonal system’. If you want to put your knowledge in order and deepen your study of harmony, I recommend the harmony course on this site, one of the most popular among my students.

In general, you can remember that sharps and flats depend on the major scale of origin, and you should try to memorise the circle of fifths and the position of the alterations in the various scales.

Also, remember how the chromatic scale works: use the sharps going up and the flats going down. If you have any questions or would like to write your opinion about this lesson, please do so in the comments space below. Thank you!