I can't see how increasing memory would improve sound quality, not from 8GB to 16GB, probably not from 4GB to 16GB. I would not really increase sound quality in any case, but could possibly keep something (another app or OS process) from affecting sound quality
What increasing memory can do for you is:
- allow more programs to run at the same time, and to run more smoothly (you probably are not running multiple programs if you are listening to music with this computer)
- allow you to run one or more virtual machines with, for example, VMware Fusion (like a windows or linux virtual PC) and run them more smoothly
- allow the operating system to run more smoothly in general, if you don't currently have enough RAM
In your case, even doing these things may not require more memory if you already have, say 8GB
16GB is a lot of memory - I have it on one of my Windows 7 machines, and I am not sure it is really getting used much over 8GB. I would get 4GB + 4GB matched (matched ensures the best performance of the memory). If you are using the mini as a true network server I would go with 16GB.
It is tempting to get more memory with these prices, just in case you may want it on that machine for the future, so why not, it can't hurt. I just don't think you will se a difference for sound quality.