I have "dead silence" with my ear to the tweeter on my 104 dB sensitive Volti K-horns...
However, few years back, I had a annoying tweeter hum on my system. I traced it back to my McIntosh MR-78 tuner which had a capacitor fail on the antenna boost circuit (a cap that was NOT needed in my system). I removed the capacitor & the hum was gone. Funny thing was, during troubleshooting, the MR-78 was switched off and still got hum. It wasn't until I "unplugged" the tuner that the hum went away... Also crazy that it was my only solid state piece in my rig contributing the noise!
My point is that it can be many anomalies causing the tweeter hum. With methological troubleshooting, you'll find the source of your hum.
My $0.02,
Pete