Also, the remedy depends on whether you're dealing with a stereo mix (my example above) or can remix individual tracks. But since it was a general question, here's some general advice about one technique that's worked for me. Hopefully others will find it useful.
The ear is most sensitive between 1 and 6 kHz, with peak sensitivity between 3 and 4 kHz. So, more energy in that range raises the potential for harshness or stridency. To begin de-harshing a mix, loop the range that sounds the harshest. (If the harshness is throughout the song, then loop the part with the most instruments playing together.)
The first goal is to find the tracks that don't contribute to harshness. Mute, then unmute, individual tracks one at a time to see if the sound becomes less harsh when a track is muted. Leave the non-harsh-contributing tracks unmuted, but you can ignore them in the following.
Still with a looped section, the next goal is to find what's building up in the upper midrange. Here's the important part. Individual tracks will often sound okay by themselves, so to chase down harshness, play combinations of tracks (particularly layered synths and tracks with saturation). Deal with the tracks that contribute the most to the harshness, using EQ. Make any EQ edits in context with the music.
Finally, back to mastering for a second. The EQ curve shown above is like what I've used on some stereo files given to me for mastering. The client thought they sounded "strident." These were acoustic sessions. The problem was that all instruments had been tracked in the same room, and it had a room resonance that you couldn't really hear with a soloed instrument. But when mixing, multiple instruments playing in the same range at the same time generated a pretty strong level bump around the resonant frequency. Reducing that one resonance solved the problem.
Indeed. However, 400 Hz and 800 Hz peaks can also, all too often exgude boxy. So most any verbal offerings (I say most) can be vaguely helpful, and frequency discussion does help describe at least proximity. Lets not forget the below 120 Hz area where someone might only shelve and not properly contour invading or wallowing sub frequencies. The OP's use of harsh or silky doesn't warrant much detail to respond to.
Should they reduce some bass, to clear up what often could help clarify, or better detail the high end? That's a common path to help resolve a 1 Kz to 6 Kz harshness issue. Then to better hear what's going on, there.
So I simply offer suggesting an attachment. Otherwise, pot shot points are painful. Doctor: "On a scale of one to ten, how painful?"
(as a joke). ; )
As you say, define by removing non harsh tracks. A good start. Only, we also need to know the sum of all the parts as well. And then some. These hoo-doo fix all apps, typically miss the mark. But, promises to dangle, fix-er-up kiddie crack for the masses. Makes money, too. No thanks.
Harshness can rear its head, at most any buildup of resonance and also can be a desired, or not so desired trade-off. So we are really imagining something offered and is likely quite different than what the OP is suggesting. Yes, he implied the harsh (bad), should be silky (good). Likely a mid frequency area, only not knowing the possible disturbance(s) along the way, make this a rather vague discussion.
Hoping we get some genuine fodder like even a small audio clip, before we move on.
Coffee time
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