Modern music notation developed out of the so-called square notation and this out of the Latin neumes. The question of where these neumes came from has long been the subject of scholarly debate. As the author demonstrated in his three-volume "Universale Neumenkunde" published in German in 1970, there is a very close relationship between the Paleo-Byzantine notation and the Latin neumes. Although the study aroused a great deal of dispute, more recent studies have revealed that the relevance of the "Neumenkunde" remains essentially unchallenged after 40 years. Those path-breaking research results on the relationship of the Greek and Latin notational systems are now available for the first time in a completely revised and augmented English translation.