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
Pitch interval Thus the ordered pitch class interval, i<"x", "y">, may be defined as: Ascending intervals are indicated by a positive value, and descending intervals by a negative one. Pitch interval In musical set theory, a pitch interval (PI or ip) is the number of semitones that separates one pitch from another, upward or downward. They are notated as follows: For example C4 to D4 is 3 semitones: While C4 to D5 is 15 semitones: However, under octave equivalence these are the same pitches (D4 & D5, ), thus the #Pitch-interval class may be used. In musical set theory, a pitch-interval class