Tightening your abdominal muscles to strengthen your core does not relieve chronic back pain. It is possible that this approach will even make things worse!
When you take the approach of strengthening or tightening the abdominal muscles in order to counterbalance tight back muscles, you are working against your body. It results in a co-contraction of both the front and back body muscles. This then creates a braced-liked situation that creates more layers of problems than solutions.