Octave species

In early Greek music theory, an octave species (εἶδος τοῦ διὰ πασῶν, or σχῆμα τοῦ διὰ πασῶν) is a sequence of incomposite intervals (ditones, minor thirds, whole tones, semitones of various sizes, or quarter tones) making up a complete octave (Barbera 1984, 231–32). The concept was also important in Medieval and Renaissance music theory.

Greek theorists used two terms interchangeably to describe what we call species: eidos (εἶδος) and skhēma (σχῆμα), defined as "a change in the arrangement of incomposite [intervals] making up a compound magnitude while the number and size of the intervals remains the same" (Aristoxenus 1954, 92.7–8 & 92.9–11 (da Rios), translated in Barbera 1984, 230). Cleonides (the Aristoxenian tradition) described (in the diatonic genus) three species of diatessaron, four of diapente and seven of diapason. Ptolemy in his "Harmonics" called them all generally "species of primary consonances" (εἴδη τῶν πρώτων συμφωνιῶν). Boethius, who inherited Ptolemy's generalization under the term "species primarum consonantiarum" (Inst. mus. IV,14), expanded species theory of Greeks; along with the traditional orderings of three primary species he introduced three further their orderings (Boethius 1989, 149). 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" (Boethius 1989, 153).

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" (Gombosi 1951, 22). The species defined by the different positioning of the intervals within the tetrachord in turn depend upon genus first being established (Barbera 1984, 229). Incomposite in this context refers to intervals not composed of smaller intervals.

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