I just completed a cool experiment that didn't result in any definite findings, but did give me some perspective on what I'm doing in the ProShop when working with saxophones and necks. I know this experiment is pretty flawed, but I'm sharing it with you for your enjoyment on this fine day anyway!
Here's what happened.
I was playing this Tenor that I'm considering as a basis for a sax that I will produce (before you ask, it's going to be a while, if ever, until that instrument will be for sale). There were some stuffy notes on the horn that I wanted to free up. Running out of ideas for the day, I started to focus on the neck. This particular horn came to me with 8 necks, because I was planning to do experiments with them. So, as you can imagine I started thinking of experiments.
I considered the hardness of the neck and how it may or may not vibrate. Wondering how I could change this, I grabbed the other 7 necks that came with the horn, played them, and found two that seemed to play exactly the same. When I went into the shop to get the guys' opinions, they all agreed that the two necks sounded exactly the same. With this in mind, I wanted to quickly see if I could alter the resistance (in the first octave) between the necks in any way using something other than bore taper in the neck or body.
I grabbed one of the necks and quickly unsoldered the parts such as the octave key, guide, and receiver. I removed all the solder and annealed the tube to make the brass very soft. (annealing brass means to heat it red hot, which softens the brass greatly). I put the new annealed neck back together and played for the guys again. No one, including me, noticed a difference between the original work hardened neck and the now annealed neck.
Since the neck was basically ruined, I grabbed it and quickly bent the curve on the smaller end straight. Now the neck looked very odd and certainly would sound different! We "AB'ed" the two necks and everyone agreed that the necks still sounded and felt the same.
I took the test neck apart again and bent it back to the normal tenor-neck shape. I annealed it again (just in case my bending hardened it) and considered what else I could quickly do to change the resistance or tone. I grabbed another Tenor neck and stripped it down to the tube and annealed it. Then I cut it in half lengthwise and wired it around the first test neck, leaving a lot of space between the two necks to gob a bunch of solder. I filled the gaps as much as possible with solder and re-assembled the neck. Now the test neck was annealed, bent, and encased within another neck with a bunch of solder weighing the whole thing down. I played the necks for the guys again and still no difference.
With that I quit this experiment. It's important to note that it was not done well and, like I said, is only anecdotal in its usefulness. I always try to run quick experiments like this before I do a 'real' one. It's also important to keep the findings in perspective. Just because my flawed experiment did not find a difference between the necks does not mean that weight or hardness of a neck do not affect a horn. It only means that they did not affect it in this experiment, as far as we could hear.
Hope this got you thinking!