Yet why do minor or major chords invoke different emotions, is my question.
I suggest you (and everyone else) check out "How Music Works" by Howard Goodall on YouTube.
In it he explains the theory behind melody - it seems like each and every human instinctively recognises 5 notes that form the basis for folk music world over. As Goodall explains they are as characteristic of humans as the five fingers of the hand (semantic quibbling about thumbs and mutations to be saved for another day if you please).
This taken it is likely that the five notes might be some sort of evolutionary legacy - perhaps related to mating or alarm calls of hominid ancestors.
The five notes form the basis of the pentatonic scale (pentas - Greek for five). Now extra notes have been added to the five by different cultures, in the west we use 8 notes (plus various sharps and flats), in India there are more than 20. But the same five do seem universally used.
Now in the harmony episode he explains the clever bit, if you pluck a note on an instrument like a harp what you actually hear is a chord, each note is really made of two or more quite audibly different notes. You can reveal these notes on a stringed instrument (guitar will do but harp is best) by muting the string at certain lengths and listening for the harmonics. These notes are quite audible - but quieter than the main note and harmonic with it - so you parse them as a single note when you hear a string being plucked.
YouTube - How Music Works 3 - Harmony - Part 2
Once it was found what these "hidden notes" were western composers first thought of harmonising them. For example the hidden notes in the note C (called the first) include E (called the third) and G (called the fifth). Because instruments used by western composers such as lute and spinnet easily facilitated playing multiple notes at once (other cultures at the time did not have many instruments like this) it led to them experimenting with harmony. If you play C, E and G at once what you are doing is playing a chord - C major.
Minor chords are played by lowering by third by a single step - so the E in C major becomes the E flat in C minor.
That's the theory - now for the hypothesis:
Why do major and minor chords (and by extension scales and keys) help evoke strong emotions?
Well, I reckon the major effects a strong positive response due to being one of these "naturally" recognised notes beefed up to the max. It is something we naturally respond to in the singing voice but amped up due to the hidden notes being made explicit and harmonic. Hence why major chords are often thought of to be uplifting "happy" sounds.
A minor chord is slightly dischordant, it is literally emptier because of the reduction of the third. In effect you are hearing something that, subconciously at least, you recognise as missing something. Hence why minor chords are often thought of as unsettling "sad" sounds.