Distortion in sound after multiplying frequency spectrum by constant
Chance are your output is clipping. Most commercial wave files are highly compressed (in terms of dynamics) and any type of processing is likely to cause clipping, unless you remove a lot of gain or apply a suitable limiter.
Processing directly in the frequency domain is difficult and likely to result in time domain aliasing. That seems like a poor choice for an audio equalizer
Your band selection is unusual. Most audio equalizer use log-spaced frequency bands to better match human auditory perception. You'll find, that there is almost no energy at all in the 15k-20k band.