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
Short octave The actual note assignments can be seen in the following diagram: It can be seen that only two notes of the chromatic scale, C and D, are missing. An analogous arrangement existed for keyboards with G instead of C at the bottom. According to Trevor Pinnock, the short octave is characteristic of instruments of the 16th century. He adds, "in the second half of the 17th century, when more accidentals were required in the bass, 'broken octave' was often used." The short/broken octave principle not only survived, but was even developed further in one particular location, namely Vienna. The "Viennese