You may be wondering why these intervals seem not to be directly related to the number of semitones between things. In the C major chord described above by friedo, the E has a frequency 5/4 times C, and G has 6/4 times C. (The 6th is the same note as the 3rd, as well, one octave higher.) The 4th, 5th, and 6th multiples are the major chord. The 2nd and 4th multiples are just A, one and two octaves higher. So, since we’re used to them, or maybe there’s even an underlying physical reason, they sound good together. So, we might hear an A, but also to varying degrees the 2nd, 3rd, 4th, 5th, 6th multiple of the frequency of that A.
There may be a fundamental note, but various overtones may also sound. Whenever something with a natural resonance is sounded, we hear harmonics. The notes also come directly from the C-major scale, C, D, E, F, G, A, B, C. C-major is called “major” because it sounds full, happy and complete.
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