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).
The following example demonstrates all of the common intervals ascending within one octave starting and ending on the note C.
As mentioned at the start of this lesson, intervals can be melodic or harmonic. Shown below are examples of 3rd intervals written melodically in repetition on various pitches (a sequence) and harmonically (a melody harmonised in 3rds)