During the time of the byzantine empire the theory of music, together with arithmetic, geometry and astronomy, maintained the part of one of the four sciences (quadrivium), the foundation of which were the numbers. Moreover, the current theory of the impact of music and its elements on the human soul (ʻEthoslehre') obtained in the same period a place within the sciences of grammar, rhetoric and dialectic (trivium), the foundation of which is the word. Therefore, music held an important position

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... in education in byzantine times, perpetuating this way the tradition of the writings of Aristoxenus and his school, of Aristides Quintilianus, of Ptolemaeus and Pseudo-Plutarch and so forth. In this curriculum of higher education the learned musicians and composers of church music (μελοποιοί) participated too, while the simple church singers, who used the treasury of hymns of the byzantine church, were satisfied with the knowledge of the different systems of byzantine notation and the eight byzantine keys (ἦχοι). 1 The first byzantine book on music, the so called ʻAnonymi Bellermann', 2 is a compilation of five different treatises, of which the first explains the ancient rhythmical notation and the use of melodic formulas, the second and the third aristoxenean harmonics, and the fourth the ancient melodic notation. The fifth treatise repeats the first in a different version. There follow examples of instrumental music. 3 The compilation can be dated to the 6 th century AD, while the treatises themselves may be older. The second byzantine book on music, the introduction to music of a certain Baccheius, 4 is again a compilation of different treatises: Baccheius produced a survey of aristoxenean harmonics, attaching a survey of pythagorean harmonics and the elements of metric and rhythmic. After that follows a treatise on music of a certain Dionysius, who supports the pythagorean doctrine. 5 Dionysius dedicated the treatise of Baccheius with his own supplements to the em-1