Hi Metalbandit,
I do not see how you can reduce harshness by using a graphic equalizer. I have used a very good quality graphic equalizer for 19 years, and I would not understand how it could reduce harshness. Graphic equalizers and any tone controls are not really advisable for a well-recorded source material. I have some recordings from early last century, and sometimes (not always) the equalizer helps.
We need to know what exactly you mean by harshness? Do you mean the music to be too shrill, with too much high frequency components? In that case an equalizer would help.
But by harshness I would mean lack of consonance in music, that is simultaneous presence of frequencies which are not harmonically related, for example the frequencies which are in the so-called Wolf interval. If such things happen, I would presume they are happening from your electronics and perhaps also cables (because they actually have non-linear response to electric signals in general, although it is not really clear to me) and I would not know how to get rid of them through a graphic equalizer.
In some cases, sound also seems harsh if there are no extensions of the musical notes. Presence of non-consonant frequencies would actually mean a complete absence of resonance and therefore non extension and this has been discussed in the above paragraph. But it can perhaps also happen due to placement of speakers, at wrong positions (as Cranky suggested), or on wrong or bad stands. This has actually happened to me once, and for a long time I could not understand how come there were no extensions of the sound, it was all very dry. There was no forum like this in those days, I finally found out accidentally when I had to move the speakers for some other reason.
Best wishes!