This is the final verse of the sidra Vayelech, though the actual words of Moses’ song come at the beginning of the next sidra, Ha’azinu.
A wonderful interpretation of the verse is offered by the Yehudi HaKadosh, the “Holy Jew” (Rabbi Ya’akov Yitzchak of Pzhysha, d. 1814). He links the word tummam with tam or tamim, “wholehearted”.
According to this view, what Moses did was to continue to “sing” to the emotions of the people of Israel until all deviousness, backsliding and transgression receded and they became truly at one with the Almighty.
There is something we can add to this remarkable insight. We know from the Midrash that Moses had a miraculous pen which never dried up and never ran out of ink. If the pen of Moses continued to write throughout the ages to produce a constant stream of Torah wisdom, surely the song of Moses also never ceased and will sing to our hearts until we become tamim.
This thought is indeed hinted at in the Song of the Red Sea, which begins Az yashir Moshe – literally, “Then will Moses sing” (Ex. 15:1). The sages say that because this means, “Then – in the future – will Moses and the Children of Israel sing”, it intimates that there will be a resurrection of the dead (Sanh. 91b).