I don't understand the meaning of "if not" and grammar of the sentence in bold:
As early as the 14th century, the organ supplied polyphony, in which case the odd-numbered verses of text were omitted altogether. This role for the organ grew steadily in importance in the late Renaissance.
Until the middle of the 17th century, organ versets were based on the chants they replaced, thus invoking if not presenting the appropriate words. During the next hundred years this large organ literature made little reference to a cantus firmus, reaching its artistic zenith and liturgical nadir in France.
[Source: The Harvard Dictionary of Music' By Don Michael Randel]