In Hebrew the word for song, Shir - שיר, can also refer to poetry. Na Nach Nachma Nachman MiUman is the "New Song" or the "New Poem", in most cases we find that the New Song should be song, like in the Psalms, King David says "sing to God the New Song", however in the special prayer "Al Hakol" (which the Noam Elimelech says that one should memorize) that is recited on Shabbos upon taking out the Tora, it says: 'and we will say before Him the New Song/Poem, as it says "sing to God..."'
The truth of the matter is that the Tora is called "shir", like it says "write for yourself this Shir" referring to the Holy Tora. When one recites the words of the Holy Tora even in the most toneless fashion, it aroused the most harmonious melody in all the worlds. Thus the same holds true to the root of the Holy Tora; Na Nach Nachma Nachman MiUman, however one says it is arouses great melody and music in all the worlds.
Great blessings of Na Nach Nachmu Nachman Meuman!