What is the physical theory behind harmony?

Answer 1

The reason a major chord sounds pleasing to the ear is the lack of dissonance (as someone already mentioned here). When you play a note on any instrument, lots of harmonics are being played:

Say you play an A on a piano (440 Hz I think), the A is the zeroth harmonic and sounds most loudly, however the first harmonic (an octave above A) also sounds at 880 Hz because the wavelenth of the 440 Hz frequency is an integer multiple of the wavelength of the 880 Hz frequency (standing waves).

If you play an A on any instrument, due to the lower harmonics, an A is played as well as another A (an octive higher), an E and a C#... all getting progressively higher. If you play that A and play an E and a C# the frequencies all resonate together constructively. Our brains find this to be a pleasant sound and, hence, it sounds 'happy'. The simplest kind of dissonance is the minor chord, where the median note is flattened by a semitone.

A C major chord is related to an A minor chord with a different root note, which is why the progression from C to A minor is so pleasing for the ear. Progressing from an A minor to an F major sounds pleasing because the F major chord resonates with the C major chord (which itself is related to the A minor chord as it shares many of the same resonances). The final chord in this progression is obviously the G major chord, because this resonates with the C major chord in the same way the C major chord resonates with the F major chord.

So, constructive resonance is what gives harmony its 'colour'. A very popular harmonic tool for jazz musicians is the minor seventh chord. This sounds pleasing to the ear whilst at the same time sounding jerky because it resonates with the tonic note (the root note) whilst at the same time being dissonant with the dominant (the fifth note). Interesting resonances like this make music fun and exciting to listen to.

NOTE: The harmonics that make a violin sounds different to a piano, for example, are much higher order.

Answer 2

Check here
http://en.wikipedia.org/wiki/Harmony

Answer 3

Harmony is when two singers sing the same part at musically consonant intervals - different pitches. Certain musical frequency ratios sound good to the ear, and these ratios are called consonant. Ratios that don't sound good are called dissonant.