The Kedushat Levi answers this question through answering another question.  The People of Israel were happy over the salvation at the Red Sea.  Happiness is essentially an inner emotional experience, in the heart. Why was there a need for Israel to sing at all? Was it not enough to feel the inner joy?   

The answer is based on an emotional reality.  Inner happiness can be fleeting and end after a short period of time.  The people of Israel wanted to hold on to their joy and celebrate with G-d for an extended period of time, on and on.  Speech, verbalization, and singing holds on to joy, expands it, cultivates it and enlarges it.  They sang so they could stay joyous even longer and prolong their joyous love of G-d after the miracle he did for them. 

This is what “leimor” means in the verse.  Moshe and the People of Israel spoke in order to keep on speaking – even though they were not speaking to anyone else.  They continued to sing so that the joy would continue and they could keep on experiencing love of G-d through joy.

[prepared by Eliezer Kwass]