I'm a Dummy, Tell Me About Turntable Mats

If your definition of record noise is “a high frequency copy of the music” then we’re probably both talking about the same phenomenon. I find it varies in audibility in relation to cartridge output voltage magnitude. I have always felt it comes with the territory, and I pay no attention to it, because my listening seat is far enough away from the turntable that I never hear it while I am trying to concentrate on what is coming out of the speakers. What’s the big deal?

No felt. No tape. No weight. No problem.

@lewm, It is not really record noise. You are hearing the mechanical system of the record/stylus/cantilever/tonearm vibrating. Ideally, all the energy spent in moving the stylus should be translated into an electrical signal. Some is turned into heat and some is turned into noise. The noise is a problem because it reflects back on the structures creating it which you theoretically can hear amplified along with the music. 
Let us call this "tracking noise." Tracking noise has been mentioned by others as a measure of the quality of the playback system. Certainly, those old ceramic needles were very loud and I remember my fathers old Rec O Cut with its old Empire cartridge was easily audible 3-4 feet away.
My current combination is very quiet but my main point is that clamping the record properly makes an obvious improvement. 
I had a Transcriptors turntable at one point decades ago, the one that set the record on 6 brass weights. I hated it. It was pitiful in comparison to an LP12. I blamed the platter for that.
I'm sure Chakster and Rauliruegas can comment on this.

Mijo, You wrote, "It is not really record noise. You are hearing the mechanical system of the record/stylus/cantilever/tonearm vibrating."  How does that contradict anything I wrote?  Moreover, your statement itself is a bit contradictory internally (to say it is not "record noise", which was your term, not mine, and then define it as in part due to mechanical energy due to the record, along with the other factors you name).  Anyway, I view it as a "problem" endemic to vinyl reproduction, and it probably varies all over the place based on the tonearm design and construction and the cartridge design and construction, and I have better things to worry about. Is there any test or are there any measurements that correlate SQ with reduction of this "noise"?  In other words, if you believe it to be undesireable, what does one do to reduce it, and does that result in better SQ?

It’s called stylus jitter. https://youtu.be/F65mODzn4Gk?t=778Yes the problem is endemic. Yes it varies all over the place just like you said. I just bought a SG200 so hopefully will hear all the wonderful benefits PL talks about here.