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
Comma (music) several different commas. For instance, a commonly used version of five-limit tuning produces a 12-tone scale with four kinds of semitones and four commas. The size of commas is commonly expressed and compared in terms of cents – 1/1200 fractions of an octave on a logarithmic scale. In the column labeled "Difference between semitones", m2 is the minor second (diatonic semitone), A1 is the augmented unison (chromatic semitone), and S, S, S, S are semitones as defined here. In the columns labeled "Interval 1" and "Interval 2", all intervals are presumed to be tuned in just intonation. Notice that the