Jaice, I understand where you are coming from in pointing out that the geometry is what matters to the sound production. But I'd like to hear your thoughts on whether you think the metal material resonance adds to the sound complexity? In this video (@ 14:30) this guy demonstrates how taping the different metal bodies cause them to sound very different. When we play, the sound we create must excite the metal resonances in a similar way as the taping of them in this video, therefore changing the color of the sound, don't you think?Ok I'll bite. So from an acoustics and scientific perspective finishes on the outside of the horn make zero difference. The same is true for engraving. What does make a difference is the material the neck is made of and how easily it retains or dissipates heat. Anyone who has played a super 20 with a sterling neck knows it takes time to "warn up" the neck, and when you do it's hot to the touch. It's incredibly efficient at maintaining a warmer air column which in turn reduces resistance emphasizing more higher partials and creating a "brighter" sound. Copper and other non-alloy metals behave similarly but dissipate ambient heat at different rates. Brass, being an alloy, is molecularly less able to retain heat.
Now this phenomenon is only part of the equation. As a player warms up any neck, it's going to lower resistance. It just happens at different rates and dissipates faster or slower. Taper of the neck, especially at the mouthpiece end has much more influence on sound because of air speed. I think the majority of neck producers know this and have narrowed the entry point to give that noticeable "brightness" at the cost of whole horn intonation. That's another thread though.
Materials matter only in how they act as a variable in the physics necessary to create a vibrating air column.