Eric, thank you for the reply. Thank you for sharing the previous posts. I don't feel that they address the problem, but it was helpful to read through them for some background information.
My problem is not so much the start up chime, but the fact that the volume through the headphone jack always goes bac to Full Volume no matter what it was at sign off.
I did try resetting PRAM and that has had no effect. I am also confused by references to MIDI settings as I never do anything involving creating music on my Mac; not talented that way.
I have gone to the System Preferences Window to try to set things. I will see if that affects things the next time I do a restart. I am a little confused as I have 3 options: internal speakers, Soundflower (2 ch) and Soundflower (16ch)
Also the archived articles you shared don't seem to address any changes in Mountain Lion which is when I noticed the change.
You are welcome - I just wish it had fixed your problem. At the top right hand side of the page there is a "More Like This" box. It allows you to search other threads. Each thread you open usually presents some other threads to look at. Maybe you can find another fix there. I also found another thread which had solved someone's problem:
Indeed, this isn't normal. On reboot, the level should be set the same as it was when you shut down.
Your signature says you're using 10.8.1. If correct, you should call up the App Store and hopefully find updates to 10.8.2, plus a Supplemental Update for 10.8.2. Try that?
If it doesn't help, you should carefully think and check if you're using any 3rd-party apps, tools or drivers that are dealing with music/sound/video, and if they are 100% ML-compatible.
Usually you could verify by booting into Safe Mode (takes longer than usual), but frankly, I'm not sure what Safe Mode does to level settings - it could be that it ignores this, anyway. Worth a try if you want to invest the time.