If the notes on the white keys (except for the I and the VIII that are obviously fixed as starting points) could "move" only to the nearest black key, you would see that some of them could move in both directions (II, V, VI) and some only in one (III, IV, VII).

So the Fifth interval can be 'Perfect' (C-G or 3 and a half Tones), 'Augmented' (C-G# or 4 Tones) or 'Diminished' (C-Gb or 3 Tones). If it moved further to A or F it would not be a fifth anymore but a VI or a VI. The same is true for the Second and Sixth intervals.

Augmented intervals are also called 'Sharp' while diminished are also referred to as 'Flat'.

The Third can be 'Major' (C-E or 2 Tones) or 'Minor' (C-Eb or 1 and a half tones) and so can the Seventh.

The Fourth can be 'Perfect' (C-F or 2 and a half tones) or 'Augmented' (C-F# or 3 Tones).

We can now find the interval between any two notes by counting the tones that separate them: D-F is a minor Third (1 and a half tones), F-C is a perfect Fifth (3 and a half Tones), G-F is a minor Seventh (5 tones) and C-C is an Octave (six tones).

As an exercise you could play different intervals and try to hear and memorize the difference between them, the feeling of the different sounds, especially those in the same 'group' like a major and minor Third or Seventh.

You may have noticed that intervals with the same name can have different values and intervals with different names can have the same value: an augmented Fourth and a diminished Fifth are actually the same (3 tones) but in one case we'll use F# and in the other Gb to represent them.

In the figure below we can see all possible intervals and their values for a major scale.

Root		fixed		C
2nd degree		Diminished	1/2 Tone	D b
		Major	1 Tone	D
		Augmented	1 Tone +1/2	D#
3th degree		Minor	1 Tone +1/2	E b
		Major	2 Tones	E
4th degree		Perfect	2 Tones +1/2	F
		Augmented	3 Tones	F #
5th degree		Diminished	3 Tones	G b
		Perfect	3 Tones +1/2	G
		Augmented	4 Tones	G #
6th degree		Minor	4 Tones	A b
		Major	4 Tones +1/2	A
		Augmented	5 Tones	A #
7th degree		Minor	5 Tones	B b
		Major	5 Tones +1/2	B
Octave		fixed	6 Tones	C

There is a case where the Seventh may be 'Diminished' (C-Bbb or 4 and a half tones) and apparently 'move' over the VI, but that's because it's an interval generated by a different kind of scale (where the sixth is flat).

It may seem confusing, using two names for the same note or interval but it will all be clear if you go to the scales section, where we will learn that a note or an interval can appear only one time in a given chord or scale.