In summary, here is a list of the distances of all common intervals up to an octave measured in semitones. Each new interval is one semitone wider apart than the previous one. Notice that the interval of an octave is exactly twelve semitones.
This is because there are twelve different notes in the chromatic scale. Notice also that the interval which has a distance of six semitones can be called either an augmented 4th or a diminished 5th. This interval is also often called a tritone (6 semitones = 3 tones).
Shown below is the notation all of the common intervals ascending within one octave starting and ending on the note C. Practice them for a short time each day and try to memorize the sound of each interval.
The next example demonstrates all of the common intervals descending within one octave starting and ending on the note Bb. These examples are only a starting point. If you want to become a good musician, it is important to learn all possible intervals up and down from all twelve notes of the chromatic scale.