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
Semitone pitch. 12-tone equal temperament is a form of meantone tuning in which the diatonic and chromatic semitones are exactly the same, because its circle of fifths has no break. Each semitone is equal to one twelfth of an octave. This is a ratio of 2 (approximately 1.05946), or 100 cents, and is 11.7 cents narrower than the 16:15 ratio (its most common form in just intonation, discussed below). All diatonic intervals can be expressed as an equivalent number of semitones. For instance a whole tone equals two semitones. There are many approximations, rational or otherwise, to the equal-tempered semitone. To