This paper begins by pointing out the previously unobserved fact that the accentuation of the Greek New Testament text of the Complutensian Polyglot (1514) follows a monotonic system almost exactly the same as that now in use in Modern Greek. Next is considered the information on the matter in the preface to the volume. The Greek text of the preface is presented with English translation and notes. A number of misconceptions are dealt with. The question of the identity of the inventor of the accentuation is then explored in full. The evidence in favour of Dimitrios Doukas as editor of the text and author of the preface is summarised and augmented. The paper then argues that it was he who conceived and applied the system of accentuation. Possible other sources of the idea are considered and eliminated. Finally the question of who might have been behind the initial intention to print an unaccented text is discussed.