The intervals
An interval gives us the "distance" between two notes. It is not important here if the notes sound one after the other or at the same time. Nor does it matter if the second note is higher or lower than the first. The interval is an absolute distance dimension for notes, so to speak.
Let's look once again at our now (hopefully) familiar C major scale.

If we now want to express the "distance" between notes C and D, we do so with the help of an interval. The interval names are derived from the Latin.
| Latin | English | Interval |
|---|---|---|
| primus | The first | Prime |
| secundus | The second | Second |
| tertius | The third | Third |
| quartus | The fourth | Fourth |
| quintus | The fifth | Fifth |
| sextus | The sixth | Sixth |
| septus | The seventh | Seventh |
| oktavus | The eighth | Octave |
To determine an interval we will count off the tone steps and then name the interval accordingly. The major scale of the fundamental serves as our basis here.
Now let's determine the C - D interval: D is the second note of the C major scale. The C - D interval is a second.
We can continue this for all notes of the scale:
The C - E interval is a third (E is the third note in C major),
C - F is a fourth (F is the fourth note in C major),
C - G is a fifth (G is the fifth note in C major; see also, The circle of fifths),
C - A is a sixth (A is the sixth note in C major),
C - B is a seventh (H is the seventh note in C major),
C - C is an octave, when the C is the eighth note or
C - C is a prime, when it is the same note both times.
Here is an overview:

We have now determined all intervals for the C major scale. We now want to determine the intervals of the notes that do not originate from the C major scale (in C major the black keys).
Let’s look at the C - E flat interval, for example. If we count off, C - D - E flat, we get a third. It is the third note seen from C. Now, it is not sufficient to say that the C - E flat interval is a third. We have also specified this for the C - E interval.
We must make a finer differentiation. Both intervals are thirds, but C - E flat is a smaller interval than C - E, which is why we say C - E flat is a minor third, and C - E is a major third.
If we now continue this for the remaining notes we get:
C - D flat is a minor second, C - D is a major second,
C - A flat is a minor sixth, C - A is a major sixth,
C - B flat is a minor seventh, C - H is a major seventh.
With the C - F fourth, the C - G fifth and the C - C octave it is not possible to specify a minor or major interval, which is why we say pure intervals.
Here once again is an overview of the pure, minor and major intervals:

If you have now reached the, "my head is smoking" stage, then take a break first, because in the next few pieces on the intervals we're really going to get down to business!
