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 the Renaissance


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

Even a superficial study of the modal polyphony of the Renaissance demonstrates that composers trained in solmization in music schools, had been singers first; but the same singers had also been composers when in early medieval times they developed polyphony from the homophonic Gregorian Chant in vocal parts notated in superimposed hexachordal octaves.

            Contrary to what some may think, the kind of music sung by the professional singers in Renaissance European chapels of kings and churches was not improvisation, but the artistic interpretation of certain structural elements the composers inserted in their compositions. For, it was the responsibility of the composer to cue the passage from a relatively sharp scale to a relatively flat scale or vice versa, and it may not be exaggerated to say that at no other time of the history of music as in Renaissance modal polyphony, have the composer and the performer been so closely associated for a musical production.

            Singers trained in selective hearing (1) could “hear” the changes in the superimposed hexachordal octaves triggered by the melodic movements and leaps, as well as the rests(2) inserting or removing fourths  or fifths in octaves leading to the identification of modulations(3).

            In accord with the convention mentioned by Jacob of Liege (4) to consider the opening notes of a piece of music as belonging to the octaves of the natural scale, a singer proceeded to note the melodic range of the vocal part with its species of fourths and fifths, the hexachordal sixths and other structural elements that could lead to the identification of the modes involved and the possible modulations.

            Once the individual surveys were completed, the singers must have discussed their findings, identifying the principal and secondary modal octaves and their possible modulations on the flat or the sharp sides of the system, together with the possible transpositions, constantly reading the vocal parts so as to mentally see the notes in the natural scale.

            For its basic expression, the art of counterpoint before 1600 made use of the natural scale and its transposition on the flat side of the system forming the superimposed hexachordal octaves G-C-g-c-gg-cc and F-C-f-c-ff-cc of the polyphonic web possible with the three-hexachord Guidonian hand, and covering the vocal range of children and male adults. These hexachordal octaves giving  the modulations in ascending by the sharp or the becuadro sign, and descending by the flat sign make up what I call the rule of John of Mantua(5) quoted in my treatise on pp. 92 and 93.

            This type of modulation involving the three basic hexachords in contrasting oscillations from B-natural to B-flat and back can be seen in the signed melismas on the word “eum” in the gradual Gloria et honore, or the “it” of posuit in the tract Beatus vir among other chants of the Early Christian Church. Its  transposition on the sharp and flat sides of the system, was also the ideal form of expression for the E-natural to E-flat, A-natural to A-flat, F-sharp to F-natural, C-sharp to C-natural, oscillations so very popular with the composers of pre-1600 modal polyphony.

            The big hurdle facing modern musicians wanting to transcribe the music of the Middle Ages and the Renaissance found in partially unsigned manuscripts and early prints, lies in the fact that we modern musicians have to recreate a practice obeying the theoretical principles governing  a different notational practice based on a structurally different polyphony than the one in which we were trained.

            Our system is based on the white keys of the piano in the harmonically divided octave C-c or A-a transposed on the sharp of the flat side of the system in a cycle of fifths, but their system was based on the white keys of the piano in the arithmetically divided octave G-g and the harmonically divided octave C-c in the expression of the twelve modal octaves of the Dodecachordon (6) in their regular or irregular position on the flat or sharp side of the system.

            Where in our music the major scale of C-c or the minor scale of A-a is transposed for modulations, in their system it was the hexachordal octaves G-C-g and C-g-c that were transposed on the flat or sharp side of the system, in modulations expressing the modal octaves superimposed in the polyphonic web of  two, three, four or five vocal parts also called voices.

            Finally where in our music the major or the minor octave is the motor for modulations, in their music it was not the modal octaves themselves that were the motor for modulations by the hexachordal octaves G-C-g-c-gg, C-f-c-ff-cc, etc…

            In the hexachord system the hexachordal octave formed by the G- Hexachord interlocked with the C-Hexachord in a lower voice can be pitted against the hexachordal octave c-gg-cc or c-ff-cc in a higher voice. But as can be seen in Mus. Ex. 1, the contrasting hexachordal octaves can be overlapping as in octave C-g-c under f-c-ff in m. 5 transposed down to the natural scale, octave C-g-c under g-cc-gg in m.7, octave C-g-c under f-c-ff in m. 7,  and octave f-cc-ff under g-cc-gg in measures 7 and 8,

            The first great problem between the two systems, ours and theirs, rests in the key signatures because if in our system the b-flat sign cues a fa of F-ut, in the hexachord system the b-flat sign in the signature cued a fa of C-ut unless the melodic range of the lowest vocal part of the polyphonic web be octave F-Bb-f.

            Therefore a B-flat sign in the signature of a polyphonic web having a melodic range between C-c-cc implied the possible hexachordal  octaves C-g-c-gg or C-f-c-ff all depending on the fourths and fifths of the melodic lines; see Chanson Adieu m’amour by Binchois above. This remark applies also to the E-flats in the signature, when the melodic range of the voices is between F- Bb-f- bb-ff-bbb and F-C-f-cc-ff-ccc.

             The duo Pleni sunt caeli from the Missa Ab initio by Claudin de Sermisy with B-flat signs in the signature in the natural scale transposed a fourth up, features the hexachordal octave F-C-f and F-Bb-F.

CLICK HERE FOR Pleni sunt caeli by Claudin de Sermisy

Featuring the modes Mixolydian (octave  F-G-A-Bb-C-D-E-f ) twice flat and the Ionian (octave F-G-A-Bb-C-D-E-f) once flat, with their common fifth F-C in contrast to  one another this duet was probably read in the hexachordal octave G-C-g modulating to the octave F-C-f and vice versa following the old theorist’s prescription “When notated in Faut it must be read Csolfaut.” (9).

            The following discussion of the modulations of the Pleni sunt caeli stresses some structural points of interest, the first of which is the mobility of the superimposed re-la fifths bisecting the hexachordal octaves of the first nine bars. From the key signature and the vocal parts we know that the Tenor starts in the hexachordal octave C-f-c moving to f-c-ff, while the Superius is in the hexachordal octave F-f-cc.

            When the Tenor reaches measure 4 and sings a descending fifth la-re (d-c-bb-a-g), this is “heard” by the Superius who is automatically cued to sing a descending fifth la-re (g-f-eb-d-c) in measure 5; the note g as pivot solmization syllable sol/la  is used to modulate to the flat hexachordal octave bb-f-bbb.

            The voices having gone down by a fourth to hexachordal octave C-f-c-ff in measure 6, the Tenor ascending the f-Hexachord  on the last beat of that bar, cues the Superius to sing the ascending re-la fifth of the hexachordal octave bb-f-bbb on the second half of measure 7. This is followed by the pivotal note g as la/sol for a modulation to an ascending re-la fifth d-e-f-g-a of the hexachordal octave c-f-cc for the Phrygian cadence once flat in measures  8 and 9.

            An important characteristic of that music is the syllables of solmization which are also precious in detecting modulations and which, at times, have been the victim of arrogant contempt (10) on account of their simplicity for teaching music to children.

            A case in point can be seen in measure 9 where the note a in the Superius is lengthened in order to be modulated from la to mi above the quarter note rest in the Tenor, for a descending major third mi-sol between the two voices on the last beat of that measure. The modulation from hexachordal octave f-c-ff to f-bb-ff establishes the Hypomixolydian octave in the Tenor for a cadence of the Mixolydian mode twice flat at measures 14-15.

            The next point of imitation belongs to the hexachordal octave f-c-ff leading to a cadence of the dominant on the note gg as re-sol in measure 19 of the Superius, note lengthened to cover the first note entering a new point of imitation in the Tenor in measure 20, and compelling the voice to stay in the flat scale for the expression of the Ionian mode once flat in the final cadence of that piece.

            As far as modes are concerned, we find two cadences of the ut-sol modal families, the Mixolydian-Hypomixolydian twice transposed on the flat side of the system in measures 14-15, and the Ionian-Hypoionian once flat in the last cadence of the work. The modes of the re-la fifth are also represented by the cadence of the Hypoaeolian in measure 9, and by the superimposed descending fifths la-re of bars 4, 5, 6, and 7.

            A thorough analysis of the twelve modal octaves of Glarean’s Dodecachordon reveals that most modes fall into two large groups depending on the solmization syllables of the modal fourths and fifths; those of the fifth species ut-sol, the octave of which features the fourth species ut-fa or re-sol in their octave, and those of the fifth species re-la, the octave of which features the fourth re-sol or mi-la in their octave.

            The modes of the re-la fifth species can occur with the re-sol fourth species in the Dorian and Hypodorian octaves, but with the mi-la fourth species in the Aeolian-Hypoaeolian octaves, while the fifth species mi-mi of the Phrygian-Hypophrygian octaves occurs with the fourth species mi-la only.

            This is the modal contrasts, no doubt, Josquin des Prés wanted to exploit if we analyze the motets O admirabile commercium and Quando natus est, two of the five antiphons commemorating the Circumcision of the Child Jesus.

CLICK HERE FOR O admirabile commercium by Josquin Des Prez

In the O admirabile commercium  Josquin seems to have wanted to suffuse his counterpoint with the brighter---today we would say “major”---sounding fourths ut-fa-::fa-ut and fifths ut-sol::sol-ut suggesting the ethereal light of a divine conception… indeed this is almost perfect word painting!

            Right at the beginning of the motet Josquin applied the rule of  John of Mantua to ascend in sharp and descend in flat in measures 6-7-8 of the Superius.

            In term of modes this is ascending by the Ionian in regular position C-D-E-f-g-a-b-c and descending by the Mixolydian once flat C-D-E-f-g-a-c. which modes have the fifth C-g in common but the contrasting fourths ut-fa and re-sol.

            The rest on the first beat of measure 6 in the Superius, allowed the removal of the f-Hexachord and the note g of the third beat to be considered that of the c-Hexachord ascending the g-Hexachord with B-natural. The above entrance is imitated in the Altus, a fifth lower, ascending in one flat and descending in two flats in measures 8-9 and 10.

            Later, between measures 24 and 31 the octave of the Ionian mode is presented in the Bassus accompanied by the Tenor, and this pairing of the voices is imitated by the Superius above the Altus singing a descending Hypomixolydian octave twice flat.

            From measures 68 to 70 is seen the Mixolydian octave thrice flat featuring the seldom used A-flat conjunct leading to a passage of a faulty tentative analysis which I illustrated on this website in earlier times. Here I am referring to the note d on the third half of measure 74 in the Tenor, which I flattened, to conform to a tonal propensity I imagine, in order to avoid a tritone with the Bassus, and tritone also in theTenor voice with the a-flat of the first half of measure 76.

            However I am obliged to consider that here we are dealing with modal polyphony structured by superimposed hexachords, and here already on the first beat of measure 72 the rests in the Altus and Tenor voices remove the hexachordal octave Bb-f-bb of the preceding measure, hence the a-natural in the Altus.

            With the rests on the first beat of the Bassus and the Superius, in measure 74, we are left with a third which must belong to the f-Hexachord taken the B-flat sign in the key signature, hence the a-natural and the d-natural in that measure. But, the Bassus is compelled to reestablish the a-flat in measure 75 on account of the E-flat on the first beat of measure 77.

            On the other hand we must consider that many singers dotted with a beautiful voice but lacking in solmization training may have been active in some churches too poor to afford renowned professional singers. Recalling the altercation between Josquin and a “bad” singer reported by Castiglione in his Book of the Courtier already mentioned, we speculate that some more or less well-trained singers may have sung more or less by ear, by chromatic inflexions, and trying to avoid melodic tritones.

            The John of Mantua progression seems to have been especially appreciated by Josquin des Prez as we find it also in the beginning of his motet Ave Maria Virgo Serena which is discussed earlier on this site, in the opening measures of his Italian song El grillo, and in a kind of inverted manner in the opening of his motet Quando natus est discussed later. The so-so-called rule of Mantua was an indispensable compositional element of Renaissance modal polyphony and we must expect to find its use  part of the composers’ “palette” of that period.

CLICK HERE FOR Quando natus est by Josquin Des Prez

            The motet Quando natus est is a hodgepodge of modes, Dorian-Phrygian- Mixolydian-Ionian-Aeolian related by their fourths or their fifths and variously transposed on the flat side of the system which Josquin exploits adroitly.

            It presents also in measures 5 and 6 of the Superius, and measures 7 and 8 of the Altus, a rule of John of Mantua somewhat inverted in which the notes ascending by the sharp scale are replaced by those of the flat scale, and those descending by the flat scale replaced by those of the sharp scale.

            Thus in the opening octave is presented the ascending Hypodorian mode thrice flat in the Superius followed by the Altus ascending in Hypodorian twice flat at a fifth lower. This is accomplished here, from measure 1 to 6 in the Superius, by a la-sol second in the hexachordal octave f-bb-f leaping up by a fourth to hexachordal octave eb-be-eeb, and imitated from measure 3 to 8, in the Altus in hexachordal octave C-f-c leaping by an ascending fourth to hexachordal octave f-bb-ff      

            The descending opening notes cannot be re-ut, but la-sol to descend as per the rules for solmization, followed by the ascending fourth re-sol. The rest in the first half of measure 6 in the Altus removes the b-flat hexachord and triggers a modulation in the upper voice from hexachordal octave eb-bb-eeb to f-bb-ff justifying the a-natural in the upper voice in that measure. 

            The ascent of a fourth, in the Altus in the second half of measure 6, brings back the hexachordal octave bb-eb-bbb to measure 7 where the ascent by a fourth on the second half of that measure causes the hexachordal octaves to revert to hexachordal octaves C-f-c-ff in measures 8 and 9.

            In measures 4 to 5 we notice the ascending Hypodorian fifth re-la as ff-cc, in the Superius, the same Hypodorian fifth re-la as c-gg, in the Altus in measures 6 to 7, and a third Hypodorian fifth re-la again in the Superius but this time as gg-dd from measure 7 to 9.

But the rest on the third beat of measure 9 in the Altus plus the descent by a fifth in the Superius causes the hexachordal octave Bb-f-bb to justify the e-flat on the last beat of measure 9. This leads to the rest in the Superius of measure 11 for the hexachordal octave of C-f-c modulating to hexachordal of-bb-ff, followed by a descending Mixolydian octave twice flat in the Altus in bars 11, 12, and 13.

Is is interesting to see how Josquin pitts against one another the contrasting descending fourth sol-fa-mi-re in superimposed hexachordal octaves eb-bb-eeb with the ascending ut-re-mi-fa fourth of octave f-bb-ff from measure 19 to 20 in the Bassus, against the same contrasting fourths in superimposed hexachordal octaves f-bb-ff moving to octave f-c-ff from measure 19 to 21 in the Tenor, this leading to a Phrygian cadence twice flat.

To resume we can say that Josquin dealt with the five modal families here in that the Hypomixolydian and the Dorian could have the fourth re-sol in common in their position the Hypophrygian and the Aeolian the fourth mi-la, the Dorian and the Aeolian the fifth re-la, while the Ionian and the Mixolydian the fifth ut-sol.

In conclusion I dare say that the analysis of the opening strain of the two motets by Josquin des Prez, in which a rest removing a hexachordal fourth triggers a change of hexachord in an “inverted” rule of  Mantua, constitute an irrefutable proof of the correctness of the theory of hexachords presented and discussed on this website.

CLICK HERE FOR Benedictum by Claudin de Sermisy

            In this motet by Claudin one mode, the Hypoaeolian once sharp E-Fs-g-a-bh-c-d-e ---not yet illustrated on this website---and the Phrygian in regular position E-f-g-a-bh-c-d-e, are compatible because they have the fourth mi-la, bh-e, in common.

            As required by the convention, this motet opens with its first note in the natural scale but soon, in measure 4, the relatively sharp scale is revealed by the ascending fourth e-fs-g-aa in the Contratenor under the fourth bbh-cc-dd-ee in the Superius.

            But in measure 6 the rest on the first beat of the contratenor removes the d-Hexachord and the scale is back in the hexachordal octaves C-g-c-gg as far as measure 10 where the quarter note rest on the third beat of the Bassus, triggers a modulation to the octave D-g-d for an Ionian cadence once sharp in measure 12.

Immediately in measure 12 the rest on the third beat of the Contratenor, establishes the octaves C-f-c-gg lasting till the Phrygian-E pedal in the Bassus of measures 16 to 18, under the two upper voices modulating to the octave d-g-d triggered by their respective melodic movements.      

In measure 21 an additional modulation to the hexachordal octave a-d-aa triggered by the octave leap in the Contratenor and the ascending Bassus is followed in measure 23 by octaves g-c-gg and C-g-c in measure 24, the latter modulated to octave G-d-gg by the rest on the first beat of measure 25 removing the c-Hexachord in the Superius.

At the same time a point of imitation in ascending ut-fa of octave C-g-c in measure 26, is followed by a descending point of imitation in the same octave until measure 29 is reached. There the leap of an octave in the Bassus triggers a modulation to octave D-g-d-gg modulating back to octave C-g-c-gg and vice versa, leading to a cadence of the tonic of the Aeolian mode once sharp on a raised third of Picardy chord in measure 48.

A very appropriate remark concerning the melodic progressions must be made here regarding the F-natural and the F-sharp of measures 38 and 39 in the Bassus. Most probably this motet may have been mentally transposed so as to be seen in the three- hexachord  Guidonian hand for its notes under the rule of John of Mantua, for the ascent toward the note g by the B-durum in measure 40, and the descent toward the note F by B-flat in measure 4.

Click Here For Footnotes