In summary, here is a list of all common intervals in an octave, measured in semitones. Each new interval is one semitone further 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).
Here are the previous intervals ascending within one octave, starting and ending on the note C.