Major scale

A major scale in musical theory is a scale whereby each note rises in pitch following the sequence: Tone, Tone, Semitone, Tone, Tone, Tone, Semitone....

Probably the simplest major scale is C-major. The C-major scale begins on a C, and each note increases according to the pattern given above. It is unique in that it is the only scale to not feature accidentals. The two main accidentals are sharps and flats; these alter the sound of a note by respectively raising or lowering it a semitone.

When writing out major (and minor scales), every rung has to be filled. This also has the effect of forcing major scales to have just sharps or just flats - they can never have 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 variable number of sharps or flats - in order to describe which accidentals a particular major scale must 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. A clever way of constructing scales arises from analysing patterns seen when you look at a series of 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