I understand that you very likely have a scientific rationale on top of your own experience that support this view but I perceive a difference in response between different finishes and ribbed vs non-ribbed models. Over a long time, lots of horns. Lots of people have argued both sides of that one, so I don't think it's a straight-up "Just for the record" sort of thing.
If I coat something in a light density clear coat, versus say, baking a thick ceramic coating on top of it, or another type of thick coating like we see with the new era of matte finishes (think Reference saxes antique PAO or some Mauriat horns)... it could affect the response and sound. Taking it another direction - if I plate something with silver versus plating it with gold, or nickel... it's going to change the way that the whole thing vibrates, resonates.
What about different copper content in the brass let's say or different brass from different locations and time periods? It makes a difference. Materials are each their own "living" thing. One thing I can say I have a lot of experience with is playing student saxes compared to professional saxes from the same manufacturer. My Yamaha student horns had like no "resistance" and were incredibly free-blowing, whereas my 62II was resistant and "darker" sounding, and I believe the difference was the annealing of the brass. One of the most freely responding saxes I owned was a Keilwerth with post on body key work but regular tone holes. It also had an oxidized brass finish with a very light clear lacquer over top. Very close to an un-lacquered, bare brass idea.
I have owned and played several different Reference 54 altos and tenors and I could always hear the difference between the rose gold lacquered and antique matte finish lacquers. Same mouthpiece and reed. I actually don't mind whatever people want to think but I believe that densities, thickness, properties of the material and added mass can all affect resonance and tone quality. It's why a plastic saxophone, no matter how well designed, just never sounds like brass.
There is a lot here to answer, but the fact is that you are incorrect. There are only two things that can affect the sound output based on wall materials and their vibrations, if the material is of the same smoothness. The first is how the vibrations affect the geometry of the bore, and the second is whether the vibrating walls produce a sound of their own, which is added to the sound produced by the vibrating air column. If you think about it a minute, you will see that there are no other physical mechanisms of sound production. \
First, let's consider sound output of the vibrating walls. It has been measured that the pressure of the standing wave causes the walls to expand about one millionth of a meter (a micron). This is equivalent to a sound output 10,000x times weaker than that of the air column, or about -40 dB. This is simply not enough to make a perceptible difference in the final sound. Guitars and other instruments that depend on wall vibrations all have walls that couple and resonate at playing frequencies. In order for a wall to vibrate at an appreciable amplitude, it must have resonant frequencies that allow it to produce sympathetic vibrations. A flat metal plate the thickness of a saxophone wall will have many such frequencies, but once you curve it into a circular shape, it raises the resonant frequencies of the metal well above any playing frequency or significant partial thereof. It has been shown that there is no part of the saxophone, at least one made and played normally, that can couple and vibrate in a way that would affect the output sound enough to make any difference.
The other way that vibrating walls could conceivably change the sound is by changing the geometry of the bore. Geometry is the--by far--major determinant of sound and response in a woodwind or saxophone. If the walls were to vibrate, that would equate to a local enlargement of the bore at the point of vibration. But again, there is not enough vibration for this to happen, even if the walls were to be made twice or three times as thin as they are now. There is no single scientific study that points to the possibility of wall materials being significant. Even plastic is plenty rigid enough to fit the bill.
So, we have to ask ourselves, why do so many people report, as you do, that they are confident that they can tell the difference between saxes in various metals and/or finishes. This can be explained in errors of perception, based on expectation. There have been numerous studies where very experienced musicians, who claimed to be able to discern differences based on wall materials and finishes, have been completely unable to do so under controlled, double-blind conditions. I am happy to post links to those studies if you are interested.
This is not to say that there are no differences between instruments, but those are always based on differences in dimensions. There are secondary effects of materials that can come into play, such as the fact that different metals do react differently to manufacturing processes, and so subtle differences caused by how the metal springs off the mandrel, for instance, could conceivably cause enough geometrical differences to affect the sound or response. But this is certainly not true of any kind of exterior coating.
Arthur H. Benade, a quite accomplished player himself and one of the most noted acoustic scientists of the 20th century, and who was a consultant of Conn and many other instrument manufacturers, had this to say about it:
"A fable, all the more remarkable since it is always discussed, is that the material of which a wind instrument is made has an influence upon the sound of the same. That this is not so rests upon incontrovertible acoustic laws, about which there should be absolutely no more discussion."
