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
Regular tuning and temperament itself and its sharpened version, the chromatic semitone, is 7"f" − 4 of an octave. The common size of the intervals C–D, D–E, F–G, G–A and A–B, the whole tone, is the sum of the diatonic and chromatic semitones, or 2"f" − 1 of an octave. The diatonic semitone is larger than, smaller than, or equal to, the chromatic semitone according as "f" is less than, greater than, or equal to, 7/12. In the last case, the diatonic and chromatic semitones are both 1/12 of an octave, exactly half the size of a tone, and the tuning is 12-tone equal