Major scale

A major scale in musical theory is a scale in which each note rises in pitch in the order: Tone, Tone, Semitone, Tone, Tone, Tone, Semitone....

Probably the simplest major scale is C-major. It is unique in that it is the only scale not to feature accidentals. The two main accidentals are sharps and flats; these respectively raise or lower the pitch of a note by a semitone.

Fig 1. The C-major scale

When writing out major (and minor scales), every rung has to be filled. This has the effect of forcing the key signature to feature just sharps or just flats - major scales can never include both.

Constructing major scales

Analysing scales with sharps

Scales and key signatures are closely linked in music. It is necessary to construct a key signature - consisting of a number of sharps or flats - in order to know which accidentals a particular major scale will have. An easy, but time consuming, way to do this would be to use the pattern of tone/tone/semitone/etc... given above. If we choose to write the scale of D-major, we know immediately that the scale begins on a D. The next note will be a tone above - an E. The note after that will also be a tone above, however it is not simply an F as would seem obvious. Because the difference between an E and an F is actually a semitone (look on a piano keyboard, there is no 'black note' in-between them) it is necessary to raise the F to become an F-sharp to achieve a difference of a whole tone.

This could be followed to create a whole scale, with all the sharps (or with a different scale, flats) put correctly in. However a cleverer way of constructing scales arises from analysing patterns in the whole series of major scales. Starting on the scale of C-major, there exists no sharps or flats. If you start a new scale on the 5th of C-major - G-major - you will find one sharp, augmenting the F. Starting the scale on the 5th of G major (a D) it will be necessary to put 2 sharps in - an F-sharp and a C-sharp. Writing this pattern out for all the scales looks like this:

 C  - 0 sharps 
 G  - 1 sharp  - F# (meaning F-sharp)
 D  - 2 sharps - F#, C#
 A  - 3 sharps - F#, C#, G#
 E  - 4 sharps - F#, C#, G#, D#
 B  - 5 sharps - F#, C#, G#, D#, A#
 F# - 6 sharps - F#, C#, G#, D#, A#, E#
      7 sharps - F#, C#, G#, D#, A#, E#, B#

In this table it can be seen that for each new scale (starting on the fifth of the previous scale) it is necessary to add a new sharp. The order of sharps which need to be added follows: F#, C#, G#, D#, A#, E#, B#. This pattern of the sharps can be easily remembered through the use of the mnemonic?:

   F       C      G    D   A   E     B
 Father Charles Goes Down And Ends Battle

Looking closer, the tonic (1st note) of each new scale - C, G, D, A, E - seems to match the new sharp that must be added to the key signature - (after F#) C#, G#, D#, E# ... The last accidental added matches the tonic of the scale two-fithd before it.

Analysing major scales with flats

A similar table can be constructed for major scales with flats in them. In this case each new scale starts on the 5th below the previous one:

 C  - 0 flats 
 F  - 1 flat  - Bb (meaning B-flat)
 Bb - 2 flats - Bb Eb
 Eb - 3 flats - Bb Eb Ab
 Ab - 4 flats - Bb Eb Ab Db
 Db - 5 flats - Bb Eb Ab Db Gb
 Gb - 6 flats - Bb Eb Ab Db Gb Cb
      7 flats - Bb Eb Ab Db Gb Cb Fb

Here, a similar pattern can be recognised, each new scale keeps all the flats of the previous scale but adds a new one following the sequence: Bb, Eb, Ab, Db, Gb, Cb, Fb. Interestingly this is the direct inverse of the pattern of sharps given above. Luckily (!) the mnemonic can now be reversed to form the sentence:

    B    E    A   D    G      C       F
 Battle Ends And Down Goes Charles' Father.

Again there is a similar, but reversed, relationship between tonics and accidentals. The tonic matches the second-to-last accidental added on.

The circle of fifths

The information gathered from analysing scales can be used in constructing the circle of fifths:

This is a useful way of finding key signatures of major scales. Starting clockwise from the top C each new letter represents a new scale, a fifth above the one before it. This means that each new scale (clockwise) requires an extra sharp to be added to its key signature. The exact sharp to be added are found by reading off the letters starting one anticlockwise to the top C - the F. For example, if you needed to know how many, and what, sharps a scale of E major requires, you note that E is at position 4 - it requires 4 sharps. These sharps are (starting at the F on the circle): F#, C#, G#, D#. If you were faced with a key signature of 5 sharps, you would count off 5 from the top to arrive at B - it is the scale of B major.

Fig 2. The b-major scale

Similarly, key signatures with flats can be created. Each new letter starting from F represents a new scale, and the position of the letter indicates how many flats it has. The actual flats are read anticlockwise from the Bb on position 2. Ab is on position 2 - so it has 2 flats. These are Bb and Eb.