This study deals with the methods of derivation of the Greek Systema Teleion in Boethius' influential treatise De Institutione Musica. Boethius applied two basic methods of division: geometrical and arithmetical. The geometrical one is related to diatonic division of a string of the monochord, the arithmetical one is related to detailed description of tetrachord species.
tetrachord; systema teleion; De institutione musica; Greek genera; quadrivium
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