Wouldn't it be nice if a chain would wear evenly? But they don't. For a number of reasons, different parts of the chain wear unevenly. This causes "loose" and "tight" spots on the chain, and depending on where they are in relation to the sprokets, you will have tight and loose spots on the rotation of the rear wheel.
If you adjust the chain where it is the loosest, it will be too tight on other parts of the rotation, this is normally the cause of the "thrumming" you described. The Chain is in fact too tight. Even though you readjusted the chain, you still may have it too tight.
The other description people here are describing is one or more links of the chain being sticky or bound up. This can happen due to damage to a link (eg: hit by a rock, etc) or similar. Either way, the link no longer moves freely, causing a similar effect.
1. Fully clean the chain and look for sticky or damaged links as others have described.
2. Adjust the chain so it has the correct clearance on its "tightest" part of the wheel rotation.
If these don't correct your problem, or if the chain has severe "tight" and "loose" spots, it's time to consider replacing the chain.
There is an outside chance (somewhat unlikely) that during the time the chain was too tight, that you have damaged a wheel bearing, which is what you are feeling now.