What an interesting picture for our own lives. When saying the words "tune my heart to sing Thy grace" I'm asking God to pull me how He needs to so that I will see and sing all that He has done for me. Sometimes it is hard to see what God is doing in our lives. We need God to tune our hearts so that we can see how He is working.
This is such a good reminder to me, not only to ask God to work on my heart to see how gracious He is to me. But also to take the time to read words of the songs I am singing in praise to Him and think more about what they mean.