Octave species 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" . Those octave species that cannot be mapped onto the system are therefore rejected . 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
Octave mandolin also varies widely, from as few as 17 to as many as 24 frets: 18 or 19 frets is typical. From the mid-20th century on, a number of makers have produced octave mandolins with guitar-shaped (e.g., the "hourglass" or "figure-8") bodies. These instruments are typically constructed essentially like acoustic guitars, with similar woods and internal bracing. the neck, however, is much narrower, and supports the mandolin string layout, rather than the traditional 6-strings of the guitar. As with the mandolin and mandola, the octave mandolin has four courses of two strings each. The two strings in each course are tuned