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. Together with the species of fourth and fifth, the octave species remained in use as a basis of the theory of modes, in combination with other elements, particularly the system of octoechos borrowed from the Eastern Orthodox Church .