Noise from tweeter

There is going to be some noise (HISS sound); it won't be dead quiet. If you have to put your ear right up to the tweeter to hear the noise, then it might be normal....

Now if what you hear is a low HUM and not a HISS, then it could be a "ground loop hum" problem. It can be fixed by removing the electrical AC ground on the component causing the problem (I assume the amplifier in your case). The way to test it (and fix it quickly) is to put a "cheater plug" on the AC power cord of your amp (or the component causing the hum). A "cheater plug" is one of those adapters that allow you to plug a 3 prong AC cord into a AC socket without the third ground input.

Assuming it is a ground loop hum and you do not want to use a cheater plug with a high end power cord as a permanent solution; you could take the power cord plug apart and disconnect the ground wire. If you are not comfortable with this, some audio power cord makers will make you a custom cord with the ground disconnected.

Do you hear distortion when playing the music?
To check it more clear turn on quiet the music preferably with emphisized cymbals and alphas and listen closer to the tweeter. Vary the volume safely to hear distortions go up or don't appear at all.
Also you can check the same with piano passages. Play some Revolutionary Ethude of Chopin. I have Vladimir Ashkenazi Ethudes on London records that is my reference piano recording.

The noise is more of a static noise, as opposed to a hum. Thank you, Henry