[sdiy] a stupid question

[hexor]

i know it's a stupid question, but i have this little doubt and since i
still haven't studied signal theory and other stuff like that i can't
solve it. a friend of mine is into electronic music so he knows
alot about software synths and music making programs, altough he has
little or no knowledge about maths or electronics. a few days ago he was
explaining me that his favourite program, called reason, stores every
single note for every single instruments. so i said "what a waste of
space, wouldn't it be easier if it stored only a frequency and then
get all the other ones when needed?", but he told me he is sure that it's
impossible, he says that the only way to do this would be to shrink or
enlarge the time of the wave, thus modifyng the sound too, expecially for
big frequency differences. i think it could be done with fourier series,
i mean it could find a reasonable number of harmonics, and then shift
by the same frequency every single harmonic and remix them. would that
work, or i'm missing something? we can't agree
so i ask the question to you, thanks in advance.