[Smt-talk] rationalizing the octenary system

Richard Porterfield porterfr at hotmail.com
Fri Apr 17 21:57:01 PDT 2009

Dear Nicolas, 

Besides the Credo, also note for example the Alleluia for Advent III (Excita, Domine: LU 336) and the Offertory for Midnight Mass of the Nativity Laetentur caeli (LU 394-95). Since these have only b-flat and not b-natural over the final E, they could easily be notated to end on b, if desired. Other melodies can only be notated on E because they have above it at one point b-flat and in another place b-natural, such as the Offertory Benedixisti (LU 337) and the Invitatory Christus natus est nobis with its verses (LU 368-71). All of the above are of Mode 4 (deuterus plagal); for a Mode-3 example see the Alleluia Veni, Domine for Advent IV (LU 354-55). 

What does not happen in deuterus modes, as far as I can tell, is for the plagal ambitus to descend to B-natural under E, which it should do according to octave-species theory. Instead it goes down as far as C, sometimes to B-flat (!), and in the Advent IV Alleluia, down to A.   

Nicolas Meeus wrote: 

It would theoretically have been possible to write melodies on E with B flat (corresponding to modes on B), but these merely do not exist. 


Richard Porterfield

Instructor, Mannes College

Ph.D. Candidate in Music Theory, CUNY GC

porterfr at hotmail.com    

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