Why is it that every once in a while a musical noise comes from my computer speakers?  Sounds like when your cell phone gets a text message. ??)

Probably a notification of some sort by a program installed on your computer.
Go to the control panel and check under sounds and multimedia. Opening this should give you a list of sounds used by programs to notify you of some event.

Or your ocmputer might be like one I saw the other day, if the speaker wire plug was touched on the metal case the computer would act as an AM Radio Receiver for a local station here.

Strange!

  Thank you for your help.  Checked sounds in Control Panel.  There aren't any set, so, that didn't work.  The second answer to my question is interesting but, my speaker wires aren't touching anythin metal.

  Again, thank you both.  I had heard that if the speakers make a little musical soung for no reason, that means that the computer needs cleaning...like using canned air. I will try that. :) :)

I read somewhere that, that might be an indication of a low bios battery.

Will check out the bios battery.  Thanks for the suggestion.  Appreciated very much. :)

Jonathan Rolf sent me an email with the following information.  It may or may not apply to your situation.

   Be aware that there is a trojan loader going around that names itself winampa.exe . One variety beeps the computer speaker 200 times.  The one I got plays a repeating series of musical notes via winamp.
   It did NOT spread through email attachments, it was embedded in either a WMV file or compressed into a RAR Archive in a multimeida newsgroup download.  Some people blame the RIAA, some people blame botnet operators.
   The real winampa.exe exists to preverve winamp file associations and is not needed for Winamp's operation.

Process Name : Winampa

File Name : winampa.exe

Description: Added by the AGOBOT-GS WORM! Note - this is NOT the popular Winamp media player which has the same filename

Rating:       Typically viruses, spyware, adware and resource hogs.