FOOTNOTES
 

(1) I have explained and illustrated “selective hearing” in the first chapter of my paper “The Forgotten Art of Modulation in Renaissance Modal Polyphony”.

(2) The theory of Renaissance modal polyphony accepted only one step modulations that could be achieved by two hexachordal octaves with common octave or common tonic or hexachordal keynotes: C-f-c- to C-g-c, F-C-f to G-C-g; consequently one can modulate from a scale featuring the note B-flat to a scale featuring the note F-sharp only by passing from hexachordal octaves C-f-c to C-g-c to G-D-g.

(3) Nowhere in all the early music treatises I have consulted and/or studied did I find a simple allusion to rests having the property of altering the composition of superimposed hexachordal octaves in modal polyphony of the Renaissance. It is only in 1992, twenty years after the publication of my treatise in 1972,  in my first paper in Revue belge de Musicologie, that I was able to connect the interchangeability of the fundamental and mutation tetrachords with the rests removing a hexachordal fourth so that another hexachordal fourth could create a   new scale.

(4) Speculum musicae, “Alias si non signetur, semper usus fiat .h. quadrati.”

(5) The natural scale formed by the octaves G-g and C-c is a relatively sharp scale with the note B-natural in the two hexachordal octaves G-C-g and C-g-c which Glarean used to illustrate the twelve authentic and plagal modal octaves in his treatise the Dodecachordon.

(6) A long familiarity with the early sources of modal polyphony teaches that in octave formation the flat sign was identified with the fa or the la of the fa-supra-la semitone of the mutation tetrachord (fa-sol-la-fa), while the becuadro (h) was identified with the mi or the fa of the mi-fa semitone of the fundamental tetrachord (ut-re-mi-fa). Hence the numerous unsigned F-Bf (ut-re-mi-fa) fourths of fundamental tetrachord found so often in the manuscript and printed sources of pre-1600 polyphony thought to have been copists’ negligence or oversight, for the flat sign was not usually associated with the mi-fa semitone in the notational practice of the time.

(7) This rule was capable by itself almost, to dispense singers from training in selective hearing, as this melodic  progression was extensively used and transposed to all contrasting scales of modulations, this attested by its use by Josquin and Claudin in Musical Examples on this website.

But this rule is confirmed by the rondeau Ay las quant je pans (Lucca Codex, MS.1844, Perugia) transcribed on the flat and sharp sides of the system, respectively

signed by the becuadro cueing the f-fa of C-ut  and the Bf-fa of F-ut  in the first  version of the song, while g-fa of D-ut and C-fa of G-ut in the second; see ‘”Notes to my paper” Two Hidden Canons” forthcoming in IJM.

(8) Missa Ab initio,   p.20.    

(9) Anonymous Wolf 4: Quod notentur in ffaut debent cantare in Csolfaut 

(10) The same kind of contempt for an old music not conform to the tenets of our “classical” music theory that led someone to declare that “the modes were irrelevant in Renaissance polyphony“; and choirmasters conducting incompletely signed works to instruct the singers “to sing sharp in ascending and flat in descending” as if all melodic lines could fall under the rule of John of Mantua and Glareans’s Dodecachordon had been published for the birds.

8) Viginti mottetorum, Attaingnant 1542, No. 28.