THEORY OF HEXACHORDAL MODULATION

We know that music was one of the most important adornment at the princely courts of Francis I and Henry 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 structure. Our music of Haydn and Mozart is built 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 maitrise 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.. 1450-1562), is a case in point of a boy from ordinary townspeople extraction who received his musical education at the maitrise of the royal collegiate church of Saint-Quentin in northern France to become the most important composer of the French 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. And a 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 contrary to the above philosophy this website is based on the following three-pronged assumption that: 1.- The unsigned but sung ficta notes Eflat, Aflat, Fsharp, and Csharp 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 the content of  their own 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, Musicological Studies and Documents 24, 165 pages American Institute of Musicology, 1972. Already in this primer I had ascertained that the familiar coniuncts Eflat, Aflat, Fsharp and Csharp had been used since the Middle Ages by the transposition of the hexachordal octaves 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,I was able to reconstruct the ancient forgotten and secret art of the Renaissance polyphonic singers. Possibly the most important notion I never encountered in any treatise or writing dating before 1600, is that of the rest removing a hexachordal fourth or fifth in order to allow another hexachord to become active in the superimposed octaves of the polyphony.This compositional procedure can be illustrated with a Bassus line singing in the C-Hexachord under a Tenor line singing notes of the g-Hexachord until a rest removes that hexachord, and is immediately replaced by the notes of the f-Hexachord. Thus in the four part superimposed hexachordal octaves of the polyphonic web, by means of the rests   the music can oscillate from hexachord octave C-g-c-gg-c to C-f-c-ff-cc and vice versa, C–g-c-gg to d-g-e-gg-dd and vice versa, etc...