The supposed reference to unheightened neumes

Since at least 1905, when the second volume of Wagner's Einführung in die Gregorianischen Melodien was published, it has been widely assumed that a passage of the Summa musice refers to the continuing use of unheighted neumes. Following the indication in Gerbert's edition, Wagner accepted the Summa musice as a work of Johannes de Muris and he therefore interpreted the apparent reference to unheighted neumes as a sign that the treatise was written in Germany since the use of staff notation was fully established in Italy and France in the lifetime of Johannes de Muris. In 1926 Besseler alluded to this argument and tacitly approved it. Smits van Waesberghe rejected this interpretation in his edition of the De musica by John ‘of Affligem’, but in recent years it has surfaced again. In his survey of the music treatises by Johannes de Muris, Ulrich Michels states that in the milieu of the Summa musice there were two systems of musical notation in use, one (with staves) that could be relied upon and another imperfect system (without staves) which could not. Michels also repeats Wagner's contention that on these grounds the Summa musice would appear to have been written in an area of German speech.

This is not quite correct. Having discussed the various forms of neumes, the authors of the Summa musice have this to say: ‘But to this point (sed adhuc), a chant can only be imperfectly (minus perfecte) recognised by these signs, nor can anyone learn a chant from it in solitude’ (536–8).