A major third is a note that is located two full tones away from the tonic (or 4 semitones), as it occurs on major scales. In other words, it is the third degree of the major scale. In C major scale, the third (an E) is just 2 tones away from the C.
A minor third is a note that is located one tone and a half away from the tonic (or 3 semitones), as in a minor scale. So, it is the third degree of the minor scale. If we take the A minor scale as an example, the third (a C note) is exactly 1 tone and a half away from the A note.
The interval of third is very important for chord formation, as we will see further on.
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