Octave species

[2] Cleonides, working in the Aristoxenian tradition, describes three species of diatessaron, four of diapente, and seven of diapason in the diatonic genus.

Ptolemy in his Harmonics calls them all generally "species of primary consonances" (εἴδη τῶν πρώτων συμφωνιῶν).

The older, central "characteristic octave", is made up of two first-species tetrachords separated by a tone of disjunction, and is called the Lesser Perfect System.

(A diagram is shown at systema ametabolon) The Lesser and Greater Perfect Systems exercise constraints on the possible octave species.

Some early theorists, such as Gaudentius in his Harmonic Introduction, recognized that, if the various available intervals could be combined in any order, even restricting species to just the diatonic genus would result in twelve ways of dividing the octave (and his 17th-century editor, Marcus Meibom, pointed out that the actual number is 21), but "only seven species or forms are melodic and symphonic".

[17] In chant theory beginning in the 9th century, the New Exposition of the composite treatise called Alia musica developed an eightfold modal system from the seven diatonic octave species of ancient Greek theory, transmitted to the West through the Latin writings of Martianus Capella, Cassiodorus, Isidore of Seville, and, most importantly, Boethius.