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A specific scale is defined by its intervallic formula. In other words, it is not necessarily the specific notes, but the pattern of intervals that defines a specific scale. And it’s also this same pattern of intervals that gives the scale its characteristic feel or tonality. By altering the intervallic scale formula, we change the type of scale being played. We can change the key of the scale by starting the intervallic formula on a different note.

For instance, the major scale is defined by the following pattern of intervals:

W-W-H-W-W-W-H

(Where W=whole step and H=half step)

So, if you take the C major scale as an example (C, D, E, F, G, A, B, C), you will see that it follows the pattern above. If you take a look at your guitar fretboard, you will be able to determine whole steps because they are two frets apart. Half steps, on the other hand, are adjacent to each with no fret between them.

So let’s compare the C major scale with the major scale intervallic pattern: C and D are a whole step apart. D and E are a whole step apart. E and F are adjacent to each other and so, are a half step apart. F and G, G and A and A and B are each a whole step apart. Only a half step separates B and C. So we have demonstrated to ourselves that the C major scale conforms to the major scale intervallic formula.

To form major scales in other keys, we simply start with a new root note and apply the intervallic formula. The key of the scale is determined by the root note. So, for instance, to form the D major scale; we start at D and apply the W-W-H-W-W-W-H major scale formula.

A whole step up from D is E.
A whole step up from E is F#
A half step up from F# is G
A whole step up from G is A
A whole step up from A is B
A whole step up from B is C#
A half step up from C# is D

So the D major scale is D, E, F#, G, A, B, C#, D

The natural minor scale is defined by the following pattern of intervals:

W-H-W-W-H-W-W

As you can see, this pattern is different from the major scale intervallic formula. It is these differences in interval placement that give these two scales different characteristic feels or sounds from each other.

The major scale tends to create a lighter, happier mood. It is often used in country and folk music.

The natural minor scale has a darker, edgier sound and is frequently used in heavy metal and rock music.

The type of scale e.g. major, minor, diminished, augmented, etc. is determined by the intervallic pattern of whole and half steps. Altering the intervallic formula changes the scale type. The key of the scale is determined by the root note of the scale. By starting the same intervallic formula on different root notes, we retain the scale type buy change the key.