You're description is characteristic for a single speed or fixed wheel with the chain too tight. In that situation an eccentric chainring (they all are to a degree) will cause the chain to be too short and bind twice per revolution.

This would not normally be an issue with a derailleur bike since the RD cage would take up any difference. However if your chain is wa-a-a-a-y too short, so it just barely loops two sprockets then you could have the same issue.

The correct minimum length is that which loops the two largest sprockets (crossed big/big combination) with an inch to spare. That ensures that there's always slack in the lower loop for the RD to take up.

If you do have slack in the lower loop, then it isn't a chain length issue, and you have to look elsewhere for the problem. I'd start by slipping the chain over the crank arm and off the crankest, pulling it back at the FD, and seeing if the cranks spin free and true without the chain attached.