In early Greek music theory, an octave species is a sequence of incomposite intervals making up a complete octave. The concept was also important in Medieval and Renaissance musictheory.
Greek theorists used two terms interchangeably to describe what we call species: eidos and skhēma, defined as "a change in the arrangement of incomposite making up a compound magnitude while the number and size of the intervals remains the same". Cleonides described three species of diatessaron, four of diapente and seven of diapason. Ptolemy in his "Harmonics" called them all generally "species of primary consonances". Boethius, who inherited Ptolemy's generalization under the term "species primarum consonantiarum", expanded species theory of Greeks; along with the traditional orderings of three primary species he introduced three further their orderings. For epistemology of the Antiquity music theory, the most important of all was the octave species, because "from the species of the consonance of the diapason arise what are called modes".
Octave species
The basis of octave species was the smaller category of species of the perfect fourth, or diatessaron; when filled in with two intermediary notes, the resulting four notes and three consecutive intervals constitute a "tetrachord". The species defined by the different positioning of the intervals within the tetrachord in turn depend upon genus first being established. Incomposite in this context refers to intervals not composed of smaller intervals. Most Greek theorists distinguish three genera of the tetrachord: enharmonic, chromatic, and diatonic. The enharmonic and chromatic genera are defined by the size of their largest incomposite interval, which leaves a composite interval of two smaller parts, together referred to as a pyknon; in the diatonic genus, no single interval is larger than the other two combined. The earliest theorists to attempt a systematic treatment of octave species, the harmonicists of the late fifth century BC, confined their attention to the enharmonic genus, with the intervals in the resulting seven octave species being : Species of the perfect fifth are then created by the addition of a whole tone to the intervals of the tetrachord. The first, or original species in both cases has the pyknon or, in the diatonic genus, the semitone, at the bottom and, similarly, the lower interval of the pyknon must be smaller or equal to the higher one. The whole tone added to create the species of fifth is at the top in the first species; the remaining two species of fourth and three species of fifth are regular rotations of the constituent intervals, in which the lowest interval of each species becomes the highest of the next. Because of these constraints, tetrachords containing three different incomposite intervals still have only three species, rather than the six possible permutations of the three elements. Similar considerations apply to the species of fifth. The species of fourth and fifth are then combined into larger constructions called "systems". 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. It therefore includes a lower, first-species fifth and an upper, fourth-species fifth. To this central octave are added two flanking conjuct tetrachords. This constitutes the Greater Perfect System, with six fixed bounding tones of the four tetrachords, within each of which are two movable pitches. labels the resulting fourteen pitches with the letters from Α to Ο. 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, but "only seven species or forms are melodic and symphonic". Those octave species that cannot be mapped onto the system are therefore rejected.
Medieval theory
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. Species theory in general remained an important theoretical concept throughout Middle Ages. The following appreciation of species as a structural basis of a mode, found in the Lucidarium of Marchetto, can be seen as typical:
We declare that those who judge the mode of a melody exclusively with regard to ascent and descent cannot be called musicians, but rather blind men, singers of mistake... for, as Bernard said, "species are dishes at a musical banquet; they create modes".
