Theory of Hexachordal Modulations
We know that music was one of the most important adornment at the princely courts of Francis I and Henri VIII; both kings had studied music, and were quite adept at it if we judge by the polyphonic chansons which, rightly or wrongly, were ascribed to them in the sixteenth century.
But their music, although not foreign to our musical ears was different from ours in its structuration. Our music of Haydn and Mozart is structured around the major and minor octaves of our system in which the flat and sharp signs cue the black notes of the keyboard in the notation. But theirs was structured around series of six notes, called hexachords, in a partially unsigned notation requiring from singers a special training in the performance of the five black notes of their system called ficta notes: Bflat, Eflat, Aflat, Fsharp and Csharp. There was the time when the son of poor peasants gifted with a beautiful voice and talent for music, trained in a maîtrise from the age of six, could anticipate a later life of privilege and luxury as singer-composer, music director and professor at princely courts.
Josquin des Prez (c. 1450-1521), is a case in point of a boy from ordinary townspeople extraction who received his musical education at the maîtrise of the royal collegiate church of Saint-Quentin in Northern France to become the most important composer of the Renaissance. He inaugurated his professional career as singer at the cathedral of Milan in Italy, where also he was attached to the duchy of the Sforza family. Later we find him at the papal chapel in Rome, at the court of the duchy of Ferrara, and finally Paris in the early sixteenth century at the court of Louis XII. Choirmaster at the cathedrals of Cambrai and Saint-Quentin for some time, Josquin spent the last ten years of his life as canon of the church.
Traditional musicology recognized two types of modulation:
A first type which consisted in passing from one pattern of whole and half steps to a different one expressed with the notes of the diatonic natural scale formed by interlocking the G-Hexachord with the C-Hexachord or vice versa, for the expression of the twelve authentic and plagal modes,in regular position, of Glarean's Dodecachordon of 1547---The equivalence in modern music to passing from the C-major scale to the A-minor natural scale on the white keys of the piano.
Second type by interlocking the C-Hexachord with the F-Hexachord or vice versa in a natural scale transposed by a lower fourth, but failing to recognize the other diatonic transpositions possible because of the scant manuscript and early printed sources that show the so-called ficta notes in notation.
The philosophy of traditional musicology regarding modal polyphony of the Renaissance was anchored on the principle that no diatonic modulation of the second type existed in early music, unless the flat, the sharp or the becuadro signs were present in the notation to cue the modulations.
But contrarily to the above philosophy, this web site is based on the three-pronged assumption that:
1.- The unsigned but sung ficta notes E-flat, A-flat, F-sharp, and C-sharp of early polyphony, belonged to the hexachords of the natural scale transposed on the flat and sharp sides of the system;
2.- The composers inserted in their polyphonic web such structural elements as rests allowing the removal of a melodic hexachordal fourth from a vocal part, and ascending and/or descending melodic movements or leaps of fourths or fifths, all of which triggered changes in the formation of the superimposed hexachordal octaves of the unsigned notation;
3.-The especially trained professional singers of the Renaissance sang the ficta notes of the partially unsigned notation, after a mental analysis of the structural elements of the contrapuntal context heard sung by the other singers, with respect to their individual vocal part.
The theoretical notions of the pre-1600 modal polyphony can be found in my treatise The Theory of Hexachords, Solmization and the Modal System, MSD 24, AIM, 1972.
Already in this primer I had ascertained that the familiar coniuncts E-flat, A-flat, F-sharp, and C-sharp, had been used since the Middle Ages by the transposition of the hexachordal octave G-C-g and C-g-c on the flat and sharp sides of the system. However, my ignorance of certain essential notions not mentioned in the numerous early treatises I consulted, prevented me from being able to effectuate totally correct transcriptions of musical examples in that book. But little by little, especially starting with the first paper with Revue belge de Musicologie in 1992, in the following bibliography, I was able to reconstruct the ancient forgotten and secret art of the Renaissance polyphonic singers.
"Note to my paper 'Two Hidden Canons in the Theoretical Notions in the Polyphony of the Renaissance'" forthcoming in International Journal of Musicology, Vol. 9.
"The Forgotten Art of Modulation in Renaissance Polyphony" in Revue Belge de Musicologie [RBM], LVII (2003), p. 5-58.
"Two Hidden Canons in the Theoretical Notions of Notation in the Polyphony of the Renaissance" in IJM, Vol. 8, (1999), p. 93-115.
"Die Notation vokaler und instrumentaler Mehrstimmigkeit vor 1600 Voraussetzungen und Konsequenzen einer strukturellen Analyse"in Die Musikforschung 54/4 (2000), p. 361-377; translation of a paper in English, by the editor Prof. Dr. Christian Berger.
"A Sample of Hexachordal-Modal Analysis for Vocal and Instrumental Polyphony of the Renaissance" in Musica Disciplina, XLVIII (1994) , p. 259-283.
"Performance Practice Idiosyncracies of the Modes of the Fa-fa and Ut-sol Fifth Species in pre-1600 polyphony" in RBM, LI (1997), p. 63-81.
"Debunking the Myth of Musica Ficta" in Tijdschrift Verenigen voor Nederlandse Muziekgeschiedenis, XLV/2 (1995), p.110-127.
"Rediscovering Modulations in the Secular and Sacred Works of Palestrina" in Recercare Rivista [per lo studio et la practica della musica antica], (1995), p. 1-34.
"Some Overlooked Modulations in the Works of Josquin des Prés?" in RBM, XLVI (1992), p. 33-53.
"A Theoretical Analysis of the Modulations in the Kyrie Sections of the Masses Mi-mi by Johannes Ockeghem and Mattheus Pipelare", in Journal of the Science and Practice of Music, No. 4, The Music Research Center, Hanying University, Korea, (1987-1988), p. 19-56
"Preface" to the edition of the modern transcription of the works of Claudin de Sermisy (1490?-1562), Missa II, by the American Institute of Musicology, (1986), p. IX-XX.
"Projet de recherche sur la théorie de la musique du Moyen Age et de la Renaissance", Revue de l'Université de Moncton, 15/1 (1982), p. 119-130.
"Les énigmes de l'Antefana et du double hoquet de Machault: une tentative de solution", in Revue de Musicologie, (Paris, 1981, 66/1), p. 22-57.
"Des dièses et des bémols dans les modes transposés de la musique de la Renaissance", in CAUSM Journal de l'ACEUM, IX/2 (1981), P. 1-14.[Canadian Association of University Schools of Music/Association Canadienne Ecoles Universitaires de Musique]
"Les sensibles haussées dans la musique polyphonique avant 1600", in CAUSM Journal de l"ACEUM, IX/1 (1979), p. 48-73.
"L'apport de la typographie et de la musique à la poésie française du début du seizième siècle", dans Renaissance and/et Réforme, (1978), XIV/2. p. 127-141.
"Peculiar Signatures in 14th, 15th, and 16th-Century Sources", in CAUSM Journal de l'ACEUM, VII, (1977), p.52-91.
The Theory of Hexachords, Solmization and the Modal System: A Practical Application, MSD 24, American Insitute of Musicology (Rome, 1972), 165 pages.
"L'essor de l'imprimerie musicale en France sous François Ier", dans La Revue de l'Université de Moncton, II, (1969), No. 3.
"La rythmique de notre langue parlée" La Revue de l'Université de Moncton, (1968), ?; reprint in Educational Review (New Brunswick Teachers Association), Vol. 83, No. 2 (1969)
"Les Messes de Claudin de Sermisy", in Revue de Musicologie, (Paris, 1967),53/1 p. 28-40.
"Francis I and the Polyphonic Chanson of the French Renaissance", The Boston University Graduate Journal, (April-1958), ? .
"Poet-Musicians and Musician-Poets of the French Renaissance", The Boston University Graduate Journal, V/8 (April-1957), p. 121-124.