Welcome to AllaireFictaMusic.com
The Website Dedicated to The Research of Gaston Allaire, Ph.D.

Dedicated to the pursuit of knowledge in the development of
modal polyphony through the Middle Ages and Renaissance


Please Note
f in italics cues the flat sign and
notes B, b, bb, & bbb are B-naturals


The modulations yielding E-flats and A-flats in Josquin's motets O admirabile commercium and Quando natus est, and those suggested for his motet Ave Maria---Virgo Serena in my paper "Performance Practice etc..." in RBM Vol. LI (1997), are only the end result in the art of music from early medieval monophonic plainsong to late Renaissance modal polyphony.

If in the first centuries of Christian plainchant the artistic search was for the contrast between the authentic and the plagal octaves of a mode as passing from the tetrachord fa-sol-la-fa of the Dorian to the tetrachord re-mi-fa-sol of the Hypodorian or vice versa, later the acceptation of the note B-flat in contrast with the note B-natural introduced a new element of artistic variety in the monophony.
This search for contrast was carried over in the new development in the art of music with the birth of polyphony at the turn of the first millennium. And already in the repertoire of the Ars Nova (14th c.), in the French polyphonic chanson and the Italian ballata, we find contrasting cadences for the repeated sections of the form.

The musical alphabet itself contains the contrasting notes B-flat and B-natural belonging to the three basic hexachords of the Guidonian hand G-A-B-C-D-E, C-D-E-f-g-a, and F-G-A-Bf-C-D


The notes of the two first hexachords make up the hexachordal octaves G-C-g, C-g-c, g-c-gg and c-gg-cc of what is called the natural scale, while the two last, the hexachordal octaves C-f-c, c-f-cc, f-c-ff, and c-ff-cc make up the natural scale transposed by an ascending fourth.
In the technique of reading pre-1600 music called solmization, singers had too learn to transpose their vocal part to the degrees of the natural scale, if necessary, to which they applied the syllables UT, RE, or MI for ascending, and the syllables LA, SOL, or FA for descending.
RULE OF SIGNS: The flat sign and the becuadro or sharp signs cue respectively the la-fa and mi-fa semitones of octaves.

Click Here for Josquin's Ave Maria... Virgo Serena Musical Example



Measures 1 to 24:
At the time of Josquin the modal counterpoint was relatively simple with its foundation on the interlocking G- and C-hexachords forming the hexachordal octaves G-C-g-c and C-g-c-gg of the natural scale (the white keys of the piano), and its transpositions on the flat and sharp side of the system in order to obtain the most familiar ficta notes B-flat, E-flat, A-flat, F-sharp, and C-sharp.

Likewise trained singers could sing the unsignalled ficta notes just mentioned, through mental analysis of what they heard sung by the other singers compared with the music in their own vocal part.
Hence the example from Josquin's motet Ave Maria ... virgo serena illustrated above, is notated entirely in the natural scale of the G-g-gg and C-c-cc hexachords of the contrapuntal polyphonic web supplemented by the flat and sharp signs inserted above the notes to cue the unsigned modulations revealed by a careful analysis.

If we examine this motet at m. 7 in hexachordal octaves G-C-g-c-gg-cc, we see in the Bassus the note C on the third beat of that measure, a fa of the G-Hexachord becoming an ut of the C-Hexachord on the first beat of m. 8, and the cc-sol up in the Superius, a twelfth above and descending. How could that cc be something else but sol from ff-ut since the c in the Tenor and the C in the Bassus had been freed from the G Hexachord by the ascending movement of a fourth in the two lower voices in mm. 5 and 7?
But the justification for the ff-Hexachord above the C-Hexachord in m. 10 is found in m. 11, where the rests removing the C-Hexachord in the Bassus, causes a hexachordal octave c-g-cc allowing the contrasting B-naturals in the Superius, in a cadence of the Ionian mode in regular position.
Later, at the same time as an ascent to the c-Hexachord is done by the Altus in m. 12, the Tenor in the octave C-F-c descends to the f-Hexachord for a repeated musical chair like contrapuntal device of alternating flat and sharp hexachordal octaves ending in m. 17.

In m. 16, with the hexachordal octave f-cc-ff in the Superius, that voice ascends by ut-re-mi and turns to descend by sol-fa-mi-sol-fa as if that melodic line was transposed down by a fourth to the natural scale justifying the B-flats in mm. 19 and 21.

But at m. 23 the hexachordal octave has moved a fourth down to octave C-g-c allowing the Tenor to modulate to hexachordal octave D-g-d in m. 24, for a cadential unison fa/fa of the Ionian mode once sharp between Altus and Tenor, before a return to octaves C-g-c-gg-cc in m. 25.

Measures 30-53:
After a dominant of dominant-tonic cadence of the Ionian mode in regular position at mm. 29 and 30, the Altus and Superius in paired voices sing a duet in Hypoaeolian from mm. 31 to 35, repeated an octave lower by the Bassus and Tenor from m. 35 to 39 also in paired voices, and belonging to the same natural scale for the principal mode of the motet. A four part counterpoint modulating to a sequential passage on the sharp side of the hexachords, is cued by the flat sign preceding the note B in m. 43 of the Bass voice, for the la-fa semitone B-C of the octave G-A-B-C-D-E-f#-g.

A flat sign affecting the note bb in the Altus, on the first beat of m. 47, and a flat sign affecting the note b on the first beat of m. 48 in the Bassus, in other early sources, confirm the la-fa semitone hexachordal octaves D-g-d-gg-dd-ggg from m. 44 to 49 included. We can speculate that in the three hexachord Guidonian hand the flat sign indicating the la-fa semitone replaced the becuadro sign of the two hexachord hand of early polyphony, see "The Secret Life of the Becuadro" further on this site.
In m. 49 the quarter-note rest in the Altus removes the d-Hexachord, and allows octaves g-c-gg-cc in m. 50.

Measures 92-110:
In mm. 92 and 93 the hexachordal octave C-g-c allows a cadence of the Ionian mode in regular position ending the first section of the motet. Unlike today, music in early prints did not carry indications of tempo, dynamics, accentuation, nor signs for interpretation such as accelerando, ritardando, etc... but speculatively it is unlikely that sensitive music directors refrained from subjective renditions that underlined the emotive content of a text.

Such is the case with the words Ave Regina ....virginitas in this ternary meter section modulating from major sounding Ionian to minor sounding Dorian twice flat, where on the first beat of m. 94 an e-flat for the Dorian modulation is delicately uttered by the Altus to bridge the gap between the two sections of the motet.

In m. 94 a structural modulation takes place from the hexachordal octaves C-g-c in m. 93, to the hexachordal octaves f-bf-ff-bbf justifying the E-flat on the first beat of the Contratenor. We must understand here that hexachordal superimposed octaves can be at a fourth or a fifth from one another; for instance the octave C-c can be either C-g-c or C-f-c, but nothing else hexachordal-wise.
Therefore at m. 94, the hexachordal octave is f-ff because the rest on the first beat removes the g-Hexachord and the hexachordal octaves could be either f-c-ff or f-bf-ff. But since the lone c in the bassus is a sol of f-ut the ef in the Altus is the fa of the fa-supra-la tetrachord of the arithmetic division of hexachordal octave f-bf-ff. No doubt a competent Altus prefered a descending perfect fifth from m. 94 to 95, to the bad voice-leading fifth f-bn with the doubled B-naturals on the first beat of m. 96. This passage is repeated from m. 98 to m. 101 where only the fifth cc-g, in unison between the lowest and highest voices, brings back the c-Hexachord in m.101.

Follows in m. 104 octaves Bf-f-bf-ff-bbf-fff alternating with octaves Bf-Ef-bf-ef till the start of the last section in binary meter in octaves C-g-c-gg-cc, where in m. 109 the Altus utters the e-natural of the Ionian mode.

We must note here that modulations from the Ionian in regular position to the Dorian transposed twice on the flat side of the system was logical as the notes C and G are common respectively to the fifths ut-sol and re-la of those modes.

Finally we must recognize that the rapid modulations in the first section of this motet are justified by changes in the hexachordal octaves, and should not be construed as an example of chromatic cadential-like inflections some contemporary people could be tempted to accept as a generalized practice of pre-Renaissance singers.

That such chromatic inflections may have been practiced by some singers is attested by a celebrated outburst attributed to Josquin berating a singer who had added ornementation to the composer's music as is quoted by Castiglione in The Book of the Courtier (London,1967), p. 143.