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The Major Scale Formula

In the introductory major scale lesson, we learned its basic intervals - the whole step and half step building blocks of the scale. This lesson will delve a bit deeper into how these intervals are formed. We can call this the major scale formula.

The most effective way of breaking down this formula is to see it in relation to the chromatic scale - the entire twelve notes of the guitar. The major scale uses just seven notes from the twelve tone chromatic scale, which is what gives us its unique intervals - the spaces between each note in the scale.

The table below shows us the twelve chromatic scale degrees. Each one can be seen as a half step/semitone interval from the previous/next. I've highlighted in yellow which of these intervals are used by the major scale...

Chromatic Scale 1 b2 2 #2
3 4 #4
5 #5
6 #6
7 1

So as you can see, there are no sharp or flat degrees in the major scale - 1  2  3  4  5  6  7

We can also see that some degrees in the major scale are a half step apart and others a whole step apart.

1 - 2  =  Whole step
2 - 3  =  Whole step
3 - 4  =  Half step
4 - 5  =  Whole step
5 - 6  =  Whole step
6 - 7  =  Whole step
7 - 1  =  Half step

Just remember, there is a half step between the 3rd and 4th, 7th and root.

This gives us the interval formula of W W H W W W H. Two whole steps followed by three whole steps.

Each degree of the scale can also be given an interval name in relation to the root (1) note.

1 - 2  =  major second
1 - 3  =  major third
1 - 4  =  perfect fourth
1 - 5  =  perfect fifth
1 - 6  =  major sixth
1 - 7  =  major seventh
1 - 1  =  unison

Another way of looking at it is to see a sequence of major 3rd and minor 3rd intervals...

1 w
2 w
3 4 w
5 w
6 w
7 1 w 2

Major 3rd interval  =  two whole steps
Minor 3rd interval  =  one and a half steps

1 - 3  =  major 3rd
2 - 4  =  minor 3rd
3 - 5  =  minor 3rd
4 - 6  =  major 3rd
5 - 7  =  major 3rd
6 - 1  =  minor 3rd
7 - 2  =  minor 3rd

Later, we'll learn about the significance of these major and minor 3rd intervals, using them to build chords for harmonising the major scale.

If we use the same table as before, but this time use note names, we can see which notes make up the C major scale (it's C major because C is the root)...

Chromatic Scale C C#
D D#
E F F#
G G#
A A#

I have to admit, I never fully memorised the major scale's note names for every root. I prefer to memorise the interval relationships we looked at earlier. As long as you know the interval formula of the scale, you should be able to play the scale in any key simply by moving the root to the appropriate note (e.g. D major = D, E major = E, C# major = C#) and visualising the interval sequence from that position.

Of course, you'll need to be able to visualise the scale on the fretboard. See the links below for more lessons that will help you with this.

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Related Lessons

Major Scale Positions

Major Scale Exercises

More on Guitar Scales

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