Notwithstanding differing scientific positions - whether the system of neumes in the 9th and 10th century was related to prosodic signs of the grammarians in Alexandria or newly developed by Carolingian writers - it is worth noticing, that from the 9th century similar techniques of notation were used in western Europe and in the Byzantine empire, which differed from older methods of notation. This change takes place during the late middle ages in the notation of new liturgical forms - such as the Sequence - and is described in theoretical treatises.
The change from notating pitches to notating intervals cannot be due to technical deficits in the ancient Greek notation. Moreover, ancient Greek notation can be shown to have been used for sacred music up to the 6th century.
A reason for the change in notation may be found in the association of ancient Greek notation with the Technites. Johannes Chrysostomos confirms that pagan music notation was thought unsuitable for Christian music. He calls for the singing of Psalms, Hymns and sacred songs, that is, for a music that places the text into its centre. This is the special quality of notation in neumes: it can show the musical direction of a sung text. [http://www.vml.de/e/inhalt.php?ISBN=978-3-89646-645-7]