Will a sound composed of the frequencies 450Hz, 650Hz 850Hz have a clearly defined musical pitch? Why? According to my lecturer, the perceived pitch of a sound composed of the following harmonics: 750Hz, 1000Hz, 1250Hz is equal to the fundamental frequency which is the highest common factor of the harmonic frequencies; so 250Hz.
He also said that the harmonic frequencies 450Hz, 650Hz 850Hz do not have a clearly defined musical pitch.
How can this be true when the harmonic frequencies have a highest common factor and therefore a fundamental frequency of 50Hz?
 A: The brain is quite good at filling in for a few missing harmonics. For example music still sounds reasonable on a smartphone speaker even though that speaker is incapable of creating low frequencies. This Wikipedia article explains the phenomenon (thanks to Glen for the link).
So it's possible that if you heard the 2nd, 3rd and 4th overtones of 250Hz your brain would fill in the blanks and it would still sound like a 250hz note. I use the qualifier possible because I'd want to try the experiment before committing myself - taking out both the fundamental and the first overtone seems quite a big change.
However for 450Hz, 650hz and 850Hz to sound like a 50Hz note you brain would have to fill in the fundamental and the first seven overtones. I suspect this would be a mental step too far, and this combination of frequencies would instead sound like a dischord.
There must be sound synthesis apps for PCs that could generate this combination of frequencies. It would be an interesting experiment to try.
