Harmony

Superposition provides us with an explanation regarding the phenomenon of harmony.  For some reason, certain notes when played together create a pleasant sound, whilst other combinations just don't sound right.  (Note:  This is different to the Pythagorean 'Octave' harmonies described earlier.)  The note pair C and G is an example of a good harmony, whereas E and F# don't provide the same effect.

To produce the sound wave of the harmony, all that is required is to add the waves of the individual notes.  When scientists analyse the two harmony waves, that of the C-G pair has a more regular repeated pattern than that of the E-F# pair, and this appears to be the reason that the first pair produces a more desirable harmony than the second.   The simpler the ratio between the wavelengths (and thus the frequencies) of the individual notes, the more regular and repeated the combined wave is, and thus again, the important factor appears to be the ratio between the frequencies.