Honestly, Eric, I intended to discuss this in abstract irrespective of the circuit itself but maybe it is good to look at the circuit.
Just in case, please note that I needed to give some delay to trigger the attack and decay generators or otherwise they would not be properly "launched", well they would not start at all..
hi,
The problem is due to the Attack, it Starts at 0V,[ which is full volume] then jumps to +V [ which is minimum volume] then decays towards zero to increase the Volume.
Radio Shack had a wireless chime used as a motion detector. Its ding-dong was irritating squarewaves that I filtered into a mellow sinewaves then it sounded good. But it also produced a very loud THUMP like yours at its beginning.
To simulate a bell realistically, in addition to the attack and decay envelope I think you will also need to add amplitude modulation having a frequency of a few Hz.
My home was built with an American (Edwards?) ding-dong doorbell that had two different sized metal bars hit one after the other by a solenoid. It was not loud enough to be heard everywhere in the house. I replaced it with a cheap Chinese one that had plastic resonant chambers over each metal bar and it is MUCH louder.
I searched Google for my doorbell sound but most of them went clank-clank instead of ding-dong and some were out-of-tune.