In the discussion of 15 octave species (chapter VI), Aurelian ascends from the lowest octave of Hypodorian (A—g—a) up to the highest octave a ninth higher which he called "Hyperlydian" (b—aa—bb). Including this conclusion at the end, the whole passage was compiled literally from Aurelius Cassiodorus. This only reference to a triphonic tone system within Carolingian chant theory, also known as the "lesser perfect system" within the Aristoxenian school, was probably the reason for Aurelian's own name as author and compiler of music theory. It proves that the early use of b flat was more influenced by triphonia. The tone system behind the 15 octaves is built in three conjunct ("synemmena") tetrachords (ypodorius—dorius—hyperdorius: A—D—G—c), with another tetrachord below (hypo) and a third one above (hyper). Within triphonia, three species like Dorian (D—c—d defined by the tetrachord "tone—half tone—tone"), Phrygian (E—d—e defined by the tetrachord "half tone—tone—tone"), and Lydian were already enough to represent the tone system, as it was needed during the use of b flat. But Cassiodorus' simplification corrupted the Lydian tonus, so that the tetrachords were based on C#—F#—b—e as a kind of transposed Phrygian species, and the Eolian tonus (C—F—♭—e♭) replaced it.