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 the perfect intervals (including unison, perfect fourth, and perfect fifth), the octave is designated P8. Other interval qualities are also possible, though rare. The octave above or below an indicated note is sometimes abbreviated "8" or "8" (), "8 bassa" (, sometimes also "8"), or simply "8" for the octave in the direction indicated by placing this mark above or below the staff. For example, if one note has a frequency of 440 Hz, the note one octave above is at 880 Hz, and the note one octave below is at 220 Hz. The ratio of frequencies of two notes