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 (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 .