EM 1990 Newes

Writing, Reading and Memorizing: The Transmission and Resolution of Retrograde Canonsfrom the 14th and Early 15th CenturiesAuthor(s): Virginia NewesSource: Early Music, Vol. 18, No. 2 (May, 1990), pp. 218-234Published by: Oxford University PressStable URL: http://www.jstor.org/stable/3127810Accessed: 12/03/2009 08:25

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Virginia Newes

Writing, reading and memorizing: the

transmission and resolution of retrograde canons

from the 14th and early 15th centuries

Musical symmetry seems to have held a special fascination for late Medieval composers. The reshap- ing of non-repeating, rhythmically neutral melodies into regularly recurring taleae, the balancing of propor- tionally related sectional divisions and even of symmetrically organized mensurations in motets and secular songs all demonstrate that what we might call the extra-auditory dimension of music was valued as highly as what was heard. Retrograde imitation, which complements a forward-moving line with an identical line stated in reverse, cannot be perceived by the ear alone; it too belongs among those architectural devices that seem to have originated in a desire for formal symmetry. The ability to match rhythmic and melodic patterns with their retrograde images was more than a mere conceit; it demonstrated a composer's knowledge of mensural notation and counterpoint as much as it tested his skill at fashioning canonic riddles.

Retrograde imitation was described in Renaissance and Baroque treatises by such writers as Vicentino,1 Morley2 and Marpurg,3 and found renewed importance in the strict counterpoint of the Second Viennese School; it does not seem to have been mentioned, however, by theorists before 1500. Yet cancrizan writing must have been well known to composers of the preceding century and a half, judging from the number and variety of retrograde pieces that have survived. In this study, I shall focus on a small number of compositions from the 14th and 15th centuries, all of which feature retrograde duplication in one or more voices. I shall attempt to demonstrate, on the one hand, the transmission of recurrent structural patterns in compositions that belong to separate but intercon- nected repertories, and, on the other, some ambiguities in notation and performance rubrics that touch directly on the manner in which music was read and performed in the late Middle Ages.

Retrograde duplication in a single voice

Retrograde duplication of a single line can be traced at least as far back at the late 12th century. Illus. 1 and 2 are taken from ff. 150-1 50v of the Florence manuscript of the Magnus liber, compiled for use at the cathedral of Notre-Dame in Paris. These folios represent the final pages of a section of the manuscript containing two- voice clausulae based on excerpts from the Christmas gradual Viderunt omnes. Just underneath the tenor at the beginning of the third system on f. 150v we find the curious word NUSMIDO. This is the clue to the tenor's derivation from the melody DOMINUS, the basis of the group of ten clausulae immediately preceding.4 The setting of NUSMIDO actually begins at the end of the second system, immediately after the final note of the last DOMINUS clausula. It then continues with a mirror image of the DOMINUS tenor melody, although in a rhythmic configuration different from that employed in the previous clausula, and without its internal repetition. Ex. 1 is a transcription from the end of the DOMINUS clausula and the beginning of the NUSMIDO clausula.

Retrograde tenors in later compositions generally had to be derived from a given voice according to a verbal canon, often couched in deliberately obscure terms. But the tenor of NUSMIDO was actually written out in its retrograde form, so that its realization presented no riddles for the performer. Once the tenor had been laid out, there was no particular technical difficulty involved in the composition of the NUSMI- DO clausula, since only the tenor was in retrograde and a new upper voice was composed to go with it. Furthermore, the thorny problems of alteration and imperfection that were to be encountered in retrograde compositions employing mensural notation in ternary metrical divisions do not obtain here.

NUSMIDO appears as an isolated occurence of

218 EARLY MUSIC MAY 1990

Ex. 1 Tenor of the final DOMINUS clausula and the NUSMIDO clausula from the Magnus liber manuscript Florence, Biblioteca Medicea Laurenziana Plut.29.1, ff.150r-150v

End of Dominus clausula A , , I

8 [Do]

j J. J IJ. ' 1. J - r [ I

8

8 mi - nus

8

Beginning of Nusmido clausula

8r r l: r 'll: r' r X ls Nus - mi

4 ?r r I; l; J. I- J. 1I 8 do

. . IJ, J. I- J. l- 1 8?

melodic retrograde in Parisian organum. In fact, there are no other known compositions employing melodic retrograde until a century and a half later. Rhythmic retrograde, on the other hand, appears about two generations earlier, in the tenor of a motet attributed to Philippe de Vitry. Since both of its texts refer to specific events involving political corruption at the court of Philip the Fair, the motet can be dated quite accurately in the year 1314.5 This work forms an important conceptual link to later compositions employing both rhythmic and melodic retrograde. Not only is it based on a principle of palindromic notational design that seems to have sprung from the same concern for symmetry (see below); it also exemplifies the difficulties composers and performers were to encounter when they tried to reverse the order of ternary rhythmic patterns notated according to the newly-codified mensural system.

The treatise purporting to be the Ars nova of Philippe de Vitry cites Garritgallus-In nova fert as an example of red notation with mensural significance, and the motet has long been accepted as a work of Vitry's on the basis of this citation.6 The notion that a single written treatise by Philippe de Vitry ever existed has

recently been challenged, however, by Sarah Fuller, who has demonstrated that the surviving versions of the text attributed to him are more likely to represent student reports of Vitry's teaching than a treatise of his own authorship.7 Even so, the motets cited to exemplify the most novel facets of the new teaching are probably his.8

New in Garrit gallus, and therefore worthy of mention in the three principal manuscript sources of

Vitry's teaching, is the use of red notes to indicate a change of mensural organization, in this case from ternary to binary metre in the tenor. In none of the three accounts, however, do we find any mention of the fact that the red notes in the tenor also mark the centre of the doubly palindromic structure shown in ex. 2: in each talea, two ternary red ligatures framing a

Ex.2 Outline of the tenor pattern of the motet Garrit gallus-In nova fert, by Philippe de Vitry

r -I = Red notes

r - r -

L BB BB L L L BB BB L

J. IJJ 1j IJ _l J I,j I JJ IJ. IG central rest are themselves symmetrically framed by two ternary black ligatures.9

Only a desire for palindromic symmetry, in fact, can explain a notational anomaly in Vitry's tenor that has been silently corrected in all editions to date.10 Co- ordination with the upper voices requires 'alteration', or doubling, of the second of the first two breves. This is in violation, of course, of the rule that was stated by the late 13th-century theorist Franco of Cologne and that remained in force throughout the 14th and 15th centuries: a breve can only be altered if it is followed by a long, and not when it is followed, as here, by another breve.

How can we explain this aberration (it occurs in both manuscript sources of Garritgallus) on the part of a composer renowned as a master of the Ars nova mensural system? It seems likely that Vitry was aware of the normal practice, but wanted the tenor's initial ligature to read long-breve-breve in order to mirror the succession of note designations in the final ligature, correctly notated there as breve-altered breve-long. (This hypothesis implies that Vitry began by laying out the second half of his rhythmic talea, and then constructed the first half to match its pattern in

EARLY MUSIC MAY 1990 219

I

Ct-I

/' ' /

' -a n- ,i An .... itPL~ I ' Trfi./~r-{ '

-'v . , ' - - ~el ~-~ ~,- ~ , ,&_j.l

.- w . ~~~~~~~~-

. . .i . . ....

;.:....::. ., ..-

...... , .....^

reverse.) Were it not for the requirements of the palindrome, the temporal values of the first ligature could have been better expressed as perfect long- breve-imperfect long. As the transcription shows, the realized values of the two halves of the talea do not exactly mirror one another, however, since the reversal of a ligature in ternary mensuration also changes its mensural context. Palindromic symmetry in Vitry's tenor is expressed therefore in the succession of note designations (long-breve-breve; breve- breve-long) and in the notational picture itself, but not in the realized note durations.

We can compare Vitry's palindrome with the more elaborate tenor design of a motet composed over a

hundred years later, Dufay's Balsamus et munda cera- Isti sunt agni novelli, outlined in ex.3." Here, too, ligatures and single notes must have been arranged with an eye to their visual symmetry. (The centre of the palindrome is again a rest.) A verbal canon directs that the entire tenor be repeated in retrograde, completing one melodic color, then repeated forwards and backwards again but diminished by half for the second color. When the melodic sequence is reversed, the result, of course, is a changed series of pitches. The palindromically arranged rhythmic symbols, on the other hand, produce exactly the same note values in their retrograde as in their forward version, constituting in effect a talea repetition. Thus, while the melodic


gLqL' N rnAMAL

. .~ - .... - r-'- . -, - --. ---

7 . 1

1.2 Florence. Biblioteca Medicea Laurenziana. Plut.29.1. ff. 150-150v, showing the end of the section devoted to two-voice clausulae

Ex.3 Outline of the tenor pattern of the motet Balsamus et munda cera-lsti sunt agni novelli by Guillaume Dufay

* . I.1I ..,. .." 1.1 . BBL LBI LBL BBBBBBBBBB LBL BBL

Tenor dicitur de modo perfecto et tempore imperfecto, simili modo retrogradendo. Tenor dicitur per semi et eodemn modo retrograditur accipiendo pro fine nigras.

9F -r, I r- I r f r r' lr~ t - I - rf I

-9 - t I Ir - - rI is olr utionr r - Il - I f If retrograde resolution


:

,~~~~~'7 . -v.'.- ' I

-a I j s ROM

retrograde mirrors the pitches of the given tenor, the rhythmic retrograde, because of the changed mensural context of the ligatures, results in a repetition rather than a reversal of the sequence of realized values. Dufay must have taken a special delight in the intricacies of this tenor design.

Reversing the order of a tenor melodic sequence was a straightforward enough procedure, involving no special difficulties of interpretation. The primary technical difficulty in reading retrograde tenors was rhythmic and resulted from the contextual nature of mensural notation in ternary divisions. The value of a particular note in ternary metre, instead of being absolute, depends on its position within a ternary grouping and on the value of the notes that precede and follow it. Reversing a rhythmic sequence in one of the ternary mensurations therefore necessitated some sort of compromise with literal retrograde. Either the notational symbols were read in retrograde, in which case the resulting note values did not exactly mirror those of the 'forward' version, as in the motets by Vitry and Dufay I have just cited, or the realized note values themselves were exactly reversed in the retrograde version, without regard to the changed mensural context of the notational signs. Nothing in the canonic rubrics tells us which type of reading is desired; only

the musical context can provide the correct solution in each individual case.

The tenor patterns of the two motets I wish to discuss now are so similar as to suggest the possibility, if not of direct emulation, then at least of the transmission of retrograde models. From the point of view of actual realization, however, they represent the two opposing approaches outlined above: on the one hand, literal reversal of a series of note values; on the other, rereading of the note symbols in reversed order, with a resultant change in mensural context. We can describe these two methods of realization as 'literal' versus 'contextual', requiring either memorization or rereading of the given part.

The motetAlpha vibrans-Cetus venit-Amicum querit from the Chantilly manuscript was composed some- time after 1380.12 It has a complex tenor design that is based on the alternation of forward and reverse pitch successions as well as of integral and diminished rhythmic patterns. The single color, consisting of 36 notated pitches in all, has two statements of a very elaborate two-part talea, outlined in ex.4. This pattern introduces changes from perfect to imperfect mensuration in 'reverse colouration' (red notes for perfect, black notes for imperfect modus) and must be completed canonically according to the rubric from

Ex.4 Outline of the tenor pattern of the anonymous motet Alpha vibrans-Coetus venit-Amicum querit, from the manuscript Chantilly, Musee Conde 564, ff.64v-65

r -1 = Red notes _ I- - -1

o

r ? X rf C O' -] r X

I I 1 1 o. 1 I l L L L L LB B B L Retrograde, diminutio dupla

3:^ r r r \ r r

diminutio dupla

9{-'s^ r 0 ? f rf ir 1 r r1 I 7r 1

* s .. 1 .1 1 B L L B B B L L L Retrograde, diminutio dupla

9 : ~r . Ir I - f it r f it diminutio dupla

Rubric: Rubee dicuntur modo perfecto, nigre imperfecto. Et in qualibet talia antequam pausetur retroeatur per semi ab ultima ad primam ipsius tallie notam. Et iterum eodem modo diminuendo a prima ad notam ultimam eiusdem tallie redicatur


two separate nine-note sequences. In each talea, a nine-note segment is stated once in forward succession and in integral values, followed by a repetition with halved values and in reverse order; the nine notes are then restated in the normal order but still in diminution. The second part of the talea is based on the next nine-note segment in a new rhythmic pattern, subjected to exactly the same retrograde and diminution manipulations as the first.

In reading the notation of the first segment of the tenor talea backwards, we immediately run into difficulties. The dot of division separating the two red ligatures results in a forward reading of long-breve/ breve-altered breve/long, adding up to a total of three ternary modus measures. When these two ligatures are reversed, however, we cannot, according to the rules, lengthen either of the first two breves (or semibreves in diminution) to fill out a ternary measure. Similar problems arise in the retrograde rereading of the second segment of the talea. In this case, it is not the notational symbols themselves but the actual temporal values they represent that are to be reproduced literally in retrograde and diminution, an interpretation that also produces satisfactory consonances with the upper voices. The tenor, once he had read through each nine-note melodic segment of his part, had to reproduce its realized durations from memory in reversed order and reduced by half; rereading the notational symbols backwards would not have pro- duced the desired rhythmic sequence.'

Exactly the opposite situation prevails in the tenor

Ex.5 Outline of the tenor pattern of the anonymous motet Gratiosus fervidus-Magnanimus opere from the manuscripts Padua, Biblioteca universitaria 1475, f.3 (olim 47) and Modena, Biblioteca Estense, 5.24, f.64v-65

1 11 1 1 1 111 1 1 1

^' , , I I "- I --1- = --7- 79 o i i m 1 - m 1 m 1 1 t

2

"9:i t=' T-i 1 " 1- I" V ii 'M 3 >

Modus maior perfectus: rests are all longae imperfectae.

Rubric: Tenor iste dicitur ter: primo eundo, secundo redeundo, tercio a primo principio ipsum resumendo

of the motet Gratiosus fervidus-Magnanimus opere, outlined in ex.5.13 Dedicated to St George, the patron saint of the city, and preserved in the late 14th-century manuscript known as 'Padua A', this work was probably composed for or in Padua.14 The Paduan motet is not as complex as Alpha vibrans and, like most motets of the Italian type, it has no subdivision into taleae.s5 Nevertheless, there are striking similarities between the tenor structures of the two motets. Both tenors are based on the number nine: nine notes in each section of the Chantilly motet's talea, nine notes in each color of the Padua motet. Furthermore, like the Chantilly motet, the Padua tenor states its nine-note pattern first forwards, then backwards, then forwards from the beginning again, although without applying diminution in any of its repetitions.

Let us return now to the resolution of the Padua tenor, shown in ex.5. Its mensuration is modus major perfectus throughout. The rules of alteration and imperfection must therefore be applied to the tenor at the maximodus level of rhythmic organization, although the division is binary at all other levels. It is apparent from the context of the other voices that in this case, as with Vitry's and Dufay's palindromic tenors, the retrograde portion of the tenor is based on a rereading of the notational symbols themselves rather than on a reversal of their realized values. For this reason, the actual durations in the retrograde realization do not exactly mirror those of the normal version, and because the retrograde statement ends on the first note of a modus maior perfection, there is a further rhythmic displacement at the beginning of the final 'forward' statement of the tenor pattern.

Retrograde chansons Recurrent structural patterns based on retrograde duplication can be found in polyphonic chansons from the 14th and early 15th centuries as well as in motets. Two important differences in retrograde procedure, however, distinguish these two genres from one another. First of all, retrograde duplication in motets occurs only within a single voice, the tenor, whereas all the known retrograde chansons use this procedure in the realization of at least one voice in addition to the notated parts. Secondly, in the motet tenors we have just examined, retrograde repetition of patterns in ternary mensurations was complicated by such notational factors as coloration, diminution, alteration and imperfection. The surviving retrograde chansons, on the other hand, usually employed minor


prolation and imperfect time, generally avoiding the difficult mensurations involving alteration and imperfection. Table I lists in order the retrograde chansons I shall consider here.

Table 1: Retrograde chansons discussed in this article

1 Machaut. Rondeau 14 Ma fin est mon commencement

rubric: in rondeau text

2 Dominicus de Ferraria 0 dolce compagno

_ L -: *--. '- L -!....

F-Pn 1584, f.479v F-Pn 1585, f.309 F-Pn 22546, f.153 F-Pn 9221, f.136 GB-Ob 229 (PadA), f.38

GB-Ob 213, f.135 facs. in Apel, Notation.

p. 143 ruDric: in Dadata text Contratenor: Et dicitur eundo et redeundo

3 Anon. 11 vient bien

rubric: in rondeau text

4 Anon.

J'ay mis ce rondelet

(Der Krepsgang) rondeau

F-Pn 6771, f.63v Gunther, 'Fourteenth-

Century Music with Texts Revealing Performance Prac- tice', pp.258-9 (facs. an(d transcr.)

F-Sm 222. f.79

Apel CMM 53/3, no.252

rubric: Tenor iste facit contratenorem retrograde reincipiendo ad morem cantus

5 Anon. Tres doulz amis -

Dame de pris rondeau

F-Sm 222, f.78

Apel, CMM 53/3, no.282

rubric: Tenor istorum duorum rondellorum facit contratenorem retrogrando. at end of cantus II: Sciendum quod isti duo rondelli

suprascripti possunt dicilrel cum duobus. tribus, quatuor.

quinque vel sex retrogradando ipsos ad modum tenoris

MO-US-;zi 4 ' U^t' $ t

^ i_ . _

_- _ _ f- i --. ^

uo1u- j I

ii - , - . I .

. 01

::,Teti- matn mnmtmn-t.

i;?a efn ?tMo mon wmnzatgr (a .F tnnurctMetiunr a tttd ii '

6 Anon. textless rondeau

I-TRmn 90, f.357v

Loyan, CMM 38, no. 12

3 Guillaume de Machaut, rondeau 14, Ma fin est mon commencement (Paris, Bibliotheque Nationale, fonds francais 22546 (Mach G)}, f. 153r


I

I

i

t*^S^^^r

_ - -i1 I_ i . I '' i. Ili-,Si LT r

The earliest known piece based entirely on retrograde procedures, Machauts rondeau Ma fin est mon commencement, was included in the Machaut manuscripts, A, B, Vogiue, G and E, and was also copied into the Italian repertory manuscript Padua A; its absence from the Machaut manuscript C may or may not mean that it was composed after 1356.16 A facsimile of the rondeau from manuscript G is shown in illus.3. The complete text and translation follow:

Ma fin est mon commencement et mon commencement ma fin. Et teneure vraiement Ma fin est mon commencement. Mes tiers chans iii fois seulement se retrograde et einsi fin. Ma fin est mon commencement et mon commencement ma fin.

My end is my beginning and my beginning my end and the tenor [is sung] in the normal way. My end is my beginning. My third voice three times only turns back on itself and thus ends. My end is my beginning and my beginning my end.

The refrain text, 'Ma fin est mon commencement, et mon commencement ma fin', is the clue to the

retrograde realization of the cantus. The third line of the text, 'et teneure vraiement', tells us that the tenor has to read the principal melody in the normal way; 'mes tier chans' in line 5 must therefore refer to the contratenor. Only the tenor is written out in full; the cantus has to be realized by reading the tenor backwards, while the B section of the contratenor also has to be supplied by repeating the A section in

retrograde. The correct realization of Machaut's

retrograde rondeau thus requires both the complete text, which serves as its canonic rubric, and correct

labelling of the voices. With minor exceptions, the notation in all sources

of Ma fin est mon commencement is the same, but

discrepancies in texting suggest that the scribes of the later manuscripts may not have completely under- stood the solution of the musical puzzle. In manu-

scripts E and Padua A, both of which were compiled after Machaut's death,'7 the words 'tenor de ma fin'

appear upside down underneath the contratenor part, where they make no sense. 18 Furthermore, in Padua A

only the text of the rondeau refrain, but not that of the

strophe, is given, leaving the canonic rubric incom-

plete. The compiler of manuscript E (or of his

exemplar) may have had some awareness of the retrograde structure of rondeau 14, however, since he placed it next to motet 5, a four-voice composition whose tenor and contratenor (shown in ex.6) are paired in a simple palindromic voice-exchange based on rhythmic retrograde.

Ex.6 Outline of the tenor and contratenor pattern of the motet Aucune gent-Qui plus aimme-Fiat voluntas tua (motet no.5) by Guillaume de Machaut

Ct

FJ" 0- -0 0 0

r 1- 1 1 1 oI oI - io o. I ? I

T r

Te I?' I?eo Ihs te 1 o r i pr -- I

The contratenor has the tenor rhythmic pattern in retrograde. * The additional breve rests, found in all manuscripts, are

mensurally inconsistent.

By the same token, the scribe of Padua A might have noticed a structural analogy between Machaufs rondeau and the anonymous motet Gratiosus fervidus from the same manuscript discussed earlier.19 I have

already pointed out the similarities between the tenor of this motet and that of Alpha vibrans, a French motet from the Chantilly manuscript. Although no copy of

Alpha vibrans has been found in an Italian repertory manuscript, other motets of French provenance do

appear in north Italian manuscripts, and it is therefore not inconceivable that a Paduan composer could have had access to a copy of the Chantilly motet and set out to emulate its retrograde structure.

Ma fin est mon commencement (transcribed in ex.7) seems to have served either directly or indirectly as a model for other retrograde chansons that circulated in France, northern Italy, and southern Germany in the late 14th and early 15th centuries. // vient bien sans

appeller (no.3 in table 1) is an anonymous rondeau preserved only in the Reina manuscript (F-Pn 6771), a collection of Italian and French secular songs copied in the Veneto in the first decades of the 15th century. Only half of each part is notated. In the cantus and contratenor parts, the B section is realized by repeating the A section backwards; this is the

retrograde pattern of Machaut's contratenor. The tenor, on the other hand, has to start off by reading his


part backwards, reading it forwards to complete the B section. The solution to the puzzle is hinted at both by the text line 'Comment qu'il soit retrograde' underlaid to the tenor part, and by the three longs with fermatas that frame each of the realized parts.20

II vient bien may have been composed in imitation of Ma fin est mon commencement, but it does not entirely follow Machaut's pattern of notation and realization. A retrograde schema exactly identical with that of Il vient bien can be found in 0 dolce conpagno, a ballata by the otherwise unknown composer Dominicus de Ferraria (see the transcription in ex.8).21 The unique source of this piece, Oxford, Canonici misc.213, was copied in the same region as the slightly earlier Reina manuscript, suggesting that the Italian composer could have patterned his ballata on the French rondeau.

Aside from the contratenor rubric 'Et dicitur eundo et redeundo' (and it is sung going and returning), the key to the puzzle is once again to be found in the poetic text:

0 dolce conpagno se tu voy cantare

Dyapason piglia senca demorare. Et sel te piace fa che la doncella Alquanto dica con mii melodia Perho che tu or dirai novella Consonante con dolce armonia. Tal che per la fede mia Ben potremo biscantare. 0 dolce conpagno se tu voy cantare Dyapason piglia senqa demorare.

O sweet companion, if you would sing, Take the diapason without delay. And if you please, let the girl Sing as much with my melody. But now you'll sing it anew Consonantly with sweet harmony, Such that, by my faith, Well shall we duet. O sweet companion, if you would sing, Take the diapason without delay.

Only the first two lines of the ballata, constituting the ripresa, are underlaid to what appears to be a continuous melodic line for the cantus. The remaining lines of the ballata strophe are copied below the music, and were probably not intended to be sung. Although the text is somewhat ambiguous, the following interpretation seems closest to the correct musical realization.22

The cantus invites his companion (the tenor) to join in the singing by starting an octave below him; since

the notated melody begins on g" and ends of g', the tenor has to begin at the end and sing backwards towards the middle. While the two friends sing, the 'girl' sings 'as much' (in other words, the same number of bars in the contratenor part). The midpoint of the melody where the two friends meet is marked by the consonance of the fifth between cantus and tenor. The companion now repeats his part going forward from the middle to the end, duetting in'sweet harmony' with the cantus, who sings backwards from the midpoint to the beginning while the contratenor completes her part by repeating it backwards.

If ligatures are broken up to accommodate extra syllables, it is just possible to sing the piedi and the volta to the realized cantus and tenor lines. In this arrangement, however, a satisfactory cadence cannot be found for the end of the ripresa which completes the ballata strophe. The rondeau form on which this piece was modelled has a bipartite musical structure, with its final cadence at the end of the B section. It cannot easily be made to fit the form of the ballata, which requires a final cadence at the end of the A music to which both volta and ripresa are sung.23

Machauts rondeau was unique in combining two different types of retrograde resolution within a single


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Ex.7 Rondeau Ma fin est mon commencement by Guillaume de Machaut, from Leo Schrade, ed. The Works of Guillaume de Machaut (Polyphonic Music of the Fourteenth Century, vol 3). (Monaco, 1956)

9:

Tenor

i ,?

0 Fr f r I1 ; ji Cantus

i 0 s 1.4.7. Ma

3. Et 5. Mes

Contratenor

9): o

Ir F r I I I I

fin te

tiers

I ; 'I- F r j' r ;i o F --

rr

r 0finrf'0-T'I m,4 f r -7

- IF ~ If~~r;

;Fr fr t Or r i? ILFr, Fr t;'r r . o corn

re fois

F' \ IO^

if. F If

:r tFr [Lr- i 1 -

I I

- f Io

Ir F if r ir moll corn - men - ce - ment

re - tro grade et ein 2.8. Et

6. Se

9: F F Ir F io fr W F J


I d

est ne

chans

mon

; I N ~ F F ;, trois

F IJ

14

[*u i 1 F

1o

t-r I- - -1I

men vrai seu

o , l

p - i f r

21

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piece: one additional voice was supplied by reading the given voice backwards, while the third voice was completed by repeating its first half in retrograde. II vient bien and 0 dolce conpagno. as we have seen, are based entirely on the latter type of duplication, while only the first type of retrograde realization appears in the remaining chansons on our list.

The two retrograde rondeaux in the early 15th- century Strasbourg manuscript were copied by Cousse- maker before the manuscript's destruction in 1870. They are listed as nos.4 and 5 in table 1.

The rondeau entitled DerKrepsgang is textless except for the cantus incipit 'J'ay mis ce rondelet. The tenor rubric reads: 'Tenor iste facit contratenorem retrograde reincipiendo ad morem cantus.' (This tenor produces a contratenor in retrograde beginning again in the manner of the cantus.) The tenor combines easily with its own retrograde, particularly since the mensuration is tempus imperfectum, prolatio minor. A problem of interpretation arises, however, with the words 'ad morem cantus'. According to Willi Apel's reading of the rubric, the cantus, like the tenor, should be doubled by its own retrograde.24 Apel's solution, however, is problematic. As may be seen in ex.9, which shows the beginning and end of the rondeau, the retrograde cantus makes a good final cadence with the notated tenor, yet it increases the overall level of

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dissonance, even if primarily at the minim level. Moreover, while the tenor has no dots of addition, there are dots of addition in the cantus, and these cannot be read correctly in retrograde. Writing about retrograde canon in 1597, Thomas Morley warned: 'You must not set any dot in all the song, for though in singing the part forward it will go well yet when the other cometh backward it will make a disturbance in the music, because the singer will be in a doubt to which note the dot belongeth'.25 In fact, dots do not appear in the three chansons I have discussed so far that are based entirely on retrograde resolutions.

Perhaps we need to re-examine the rubric of the rondelet. Since no instructions are given for the cantus part itself, there is no reason to expect the tenor to read his own rubric with reference to a non-existent rubric for the cantus. 'Reincipiendo ad morem cantus' could, however, refer in a more general way to the repetition scheme of the rondeau form itself, which returns to its beginning several times. In this respect only, the tenor and contratenor could then be said to be performed 'in the same manner as the cantus'.

The Strasbourg manuscript also contained a double rondeau (no.5 in table 1), whose two refrain texts, beginning 'Dame de pris' and 'Tres douls amis', like the triple text of Machaut's canonic ballade Sans cuer m'envois-Amis dolens-Dame par vous. depict sim-


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Ex.9 Bars 1-8 and 53-60 of the anonymous rondeau J'ay mis ce rondelet. From Willi Apel, ed. French Secular Compositions of the Fourteenth Century (Corpus Mensurabilis Musicae 53, vol.3), (Neuhausen-Stuttgart. 1970)

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ultaneously a lover's supplication and his lady's answer. The tenor rubric, 'Tenor istorum duorum rondellorum facit contratenorem retrogrando' (the tenor of these two rondeaux produces a contratenor in retrograde), is similar to that of Jay mis ce rondelet. The only difficulty in its realization stems from the ternary mensuration of tempus perfectum, prolatio minor. As in the motet Alpha vibrans, the polyphonic context tells us that the retrograde realization of the contratenor must be based on the actual durations of the tenor notes, including the alterations and imperfections that have been applied to them, rather than on a rereading of the notational symbols themselves. Here again, the retrograde realization is derived not by reading the note symbols backwards, but by memorizing the realized values of the tenor and reproducing them in reverse order.

The rubric that appears at the end of the second cantus part is more problematic: 'Sciendum quod isti duo rondelli suprascripti possunt dicire cum duobus, tribus, quatuor, quinque vel sex retrogradando ipsos ad modum tenoris.' (Know that the two rondeaux above can be sung with two, three, four, five or six reversing themselves in the manner of the tenor.) Taken at face value, this tells us that the double rondeau can be performed by as many as six voices by

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duplicating each of the cantus parts in retrograde in the same manner as the tenor. A glance at this realization, the beginning and ending of which are given in ex.10, shows that the addition to the four- voice texture of two more cantus parts in retrograde adds a large number of dissonances to an already imperfect contrapuntal texture, not to mention the awkward problem of reversing the dotted notes in the two cantus parts. Perhaps the addition of retrograde upper voices represents the attempt of an unskilled composer (or of an editor-scribe) to match the ingenuity demonstrated in Machaut's retrograde rondeau or in pieces like it. There is also the possibility that the rubric was added or altered in the copying process. (Might it even have been supplied by Coussemaker himself?) Hampered as we are by the secondhand transmission of the Strasbourg source in Coussemaker's copy, there is no way we can unravel this particular mystery with complete certainty.

The tradition of the retrograde rondeau continued into the mid-15th century. Illus.4 shows a facsimile from the manuscript Trent 90 of a textless piece with only two notated voices in an unusually high range. The clue to the realization of a third voice lies in the single word 'Tenor' written upside down at the end of the cantus part and circled in the third stave of the


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facsimile.26 As in 0 dolce conpagno, this part has to be derived from the cantus by reading it backwards. The contratenor, on the other hand, is freely composed. The mensuration in all voices is tempus imperfectum, prolatio minor; as we have seen, this is the metre that lends itself most easily to retrograde solutions. That the anonymous composer was well aware of the rhythmic problems of retrograde canon is demonstra-

ted by the distinction he made between the canonic and non-canonic voices. While the cantus voice carefully avoids using dots of addition, they do appear in the non-retrogradable contratenor part; they are circled on the facsimile.

Like many French songs that were copied in areas outside the French linguistic boundaries, the Trent

retrograde canon has survived without text. Neverthe-


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Ex.10 Bars 1-4 and 31-34 of the anonymous rondeau Dame de pris-Tres douls amis. From Willi Apel, ed. French Secular Compositions of the Fourteenth Century (Corpus Mensurabilis Musicae 53, vol.3), (Neuhausen- Stuttgart, 1970)

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less, rondeau form is clearly indicated in the manuscript, a fact that the modern editor seems to have overlooked. An ouvert cadence at midpoint is indicated both by a fermata in the cantus (circled in the second stave of the facsimile) and by a signum congruentiae in the contratenor (near the beginning of the fifth

stave). The tenor's signum appears upside down in the second stave just after the fermata; the congruence of the three signs in the realized canon can be seen in ex. 11.

It is probably not by coincidence that among the three principal poetic formes fixes, the rondeau was the one selected for retrograde treatment. (The only

exception on our list, Dominicus de Ferraria's ballata, appears to have been modelled on a French ron-

deau.) By the latter part of the 14th century, the rondeau had increasingly come to be seen as a vehicle for erudite formal games in both the verbal and the musical spheres. One has only to recall the punning rhymes onguerredon nee, guerredonnee and guerre donnee in Machaut's rondeau no.7, or the pan-isorhythmic structure of the rondeau Se doit il plus by Johannes de Alte Curie from the Chantilly manuscript (F-CH564, f. 1 5v).

One of the unique features of the rondeau from a formal standpoint is the bi-directional function, so to

speak, of the A part of the refrain. The best faiseurs of rondeaux constructed their stanzas so that the return of the first part of the refrain in the middle of the rondeau was felt not as a syntactical break, but as a

cleverly contrived link between sections.27 Late Medieval composers, themselves often poets as well as musicians, must have been well aware of this Janus-like quality of the rondeau refrain, and have

perceived its analogy to retrograde composition. Finally, we can speculate on the possible symbolic

intent behind compositions that return backwards to their beginnings. It seems likely that the clausula NUSMIDO, coming at the end of a series of polyphonic elaborations on the central word of the Christmas Gradual, was intended as a concrete demonstration of DOMINUS as Alpha and Omega, God made man and


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returned to the Father. Friedrich Ludwig suggested that the text of Machaut's rondeau refrain might also have a religious significance, noting that, some two centuries after Machaut, Mary Queen of Scots commissioned an embroidery of the motto 'En ma fin est mon commencement'.28 Daniel Poirion has read in these lines a reflection either of a metaphysical view of death as rebirth, or of the ideal circle of the courtly ethic.29 Whatever extramusical significance we may attach to Machaut's text, however, a delight in symmetrical design for its own sake and a love of notational games were important elements in the Medieval musical universe. The transmission and emulation of retrograde canonic patterns and the ambiguities involved in their resolution are part of that world.

Virginia Newes is an assistant professor of Music History and Musicology at the Eastman School of Music, University of Rochester. New York.

'N. Vicentino, L'antica musica ridotta alia moderna prattica (Rome, 1555, R/1959), b4, ch.40, f.93v

2T. Morley, A Plain and Easy Introduction to Practical Music (2nd edn, 1608), ed. R. Alec Harman (New York, 1963/1973), p.288

3F. W. Marpurg, Abhandlung von der Fuge (Berlin, 1753-4) in A. Mann, The Study of Fugue (New York, 1965), pp.148, 158

4F. Ludwig, Repertorium organorum recentioris et motetorum vetustis- simi stili, i: Catalogue raisonne der Quellen, I: Handschriften in Quadratnotation (Halle, 1910, R/1964), p.80

'L. Schrade, The Roman de Fauvel; The Works of Philippe de Vitry; French Cycles of the Ordinarium missae, Polyphonic Music of the Fourteenth Century, i (Monaco, 1956), Commentary, pp.31-2

6E. H. Sanders, 'Vitry, Philippe de', New Grove 7S. Fuller, 'A Phantom Treatise of the Fourteenth Century? The Ars

Nova' Journal of Musicology, iv (1985-6), pp.23-50 8Fuller, 'A Phantom Treatise', p.47 9R. Hoppin, Medieval Music (New York, 1978), p.262 "?See, for example, the edition by Schrade cited in n.5, and R.

Hoppin, ed., Anthology of Medieval Music {(New York, 1978), p. 120 '"Transcribed in Guillaume Dufay: Opera omnia, ed. H. Besseler,

Corpus Mensurabilis Musicae, i/2, (Rome, 1951), no.2 12Transcribed in F. Ll. Harrison, ed., Motets of French Provenance,

Polyphonic Music of the Fourteenth Century, v (Monaco, 1968), no.25; and U. Guinther, ed., The Motets of the Manuscripts Chantilly, Musee Conde, 564 and Modena, Biblioteca Estense, M.5.24, Corpus Mensurabilis Musicae, ;xxix (1965), no.6

"Transcribed in Guinther, op. cit., no. 11, and K. von Fischer and F. A. Gallo, eds., Italian Sacred Music, Polyphonic Music of the Fourteenth Century, xii (Monaco, 1976), no.43

14GUinther, op. cit., p.xxxiv. The motet is also found in the manuscript I-MOe 5.24 (Modena A), an early 15th-century anthology of French and Italian music.

"5See M. Bent, 'Ciconia and the Italian Motet, unpublished paper delivered at the international conference 'L'Europa e la musica del Trecento', Certaldo, July 1984

16E. A. Keitel, 'A Chronology of the Compositions of Guillaume de Machaut Based on a Study of Facsimile-manuscript Structure in the Larger Manuscripts' (diss., Cornell U., 1976), p.43ff

7On the dating of MS E see M. Bent, 'The Machaut Manuscripts

Vg, B and E', Musica disciplina, xxxvii (1983), pp. 61-2. The substantial portions of MS E that Bent found to have been copied from MS B do not, however, include any of Machaut's canonic pieces.

"'The scribe of manuscript E (or of his exemplar) either intentionally or unknowingly obscured the polyphonic realization of Machaut's other canonic works. He omitted all annotations such as 'chace' and 'statim et sine pause' from the two canonic lais nos. 16 and 17, and notated the melody of ballade 17 only once rather than three times, as in the other Machaut sources. Similarly, he obscured the polyphony in lais 23 and 24, notated monophonically but actually for two and three voices respectively. See R. Hoppin, 'An Unrecognized Polyphonic Lai of Machaut', Musica disciplina, xii (1958), pp.93-104, and M. Hasselman and T. Walker, 'More Hidden Polyphony in a Machaut Manuscript, Musica disciplina, xxiv (1970), pp.7-16

"9This possibility was suggested by Anne Hallmark in 'Some Evidence for French Influence in Northern Italy, c 1400', Studies in the Performance of Late Mediaeval Music, ed. S. Boorman (Cambridge, 1984), p.215

2'For a transcription and analysis of this rondeau, see U. Gunther, 'Fourteenth-century Music with Texts Revealing Performance Practice', Studies in the Performance of Late Mediaeval Music, ed. S. Boorman (Cambridge, 1983), pp.253-61, and 'Sinnbezuge zwischen Text und Musik in ars nova und ars subtilior', Music und Text in der Mehrstimmigheit des 14. and 15. Jahrhunderts (Kassel, 1984), pp.257- 63.

2'See L. Feininger, Die Fruhgeschichte des Kanons (Emsdetten, 1937), p.21. For a facsimile of the ballata, see W. Apel, The Notation of Polyphonic Music, 900-1600 (Cambridge, Mass., 1953), p. 143

22This interpretation, which differs somewhat from that of Feininger and Apel, was worked out in the course of preparing a performance at the Eastman School of Music. I should like to thank my colleagues Professor Patrick Macey for assistance in solving the musical puzzle, and Professor Massimo Ossi for his translation of the ballata text.

23A retrograde puzzle in the lower voices of another French-texted piece by a north Italian composer has recently been solved by John Nadas and James Haar. The four-voice rondeau Vous soyez tres bien venus by Antonio da Cividale (I-Las 184, f.41) has an ostinato tenor consisting of six repetitions of a short motive read first forwards, then backwards; the complementary contratenor pattern has to read backwards, then forwards. (John Nadas, 'The Lucca Codex: Provenance and Dating of a Song Collection from Early 15th- century Italy.' Unpublished paper read at New York University in March 1989.

24French Secular Compositions of the Fourteenth Century, Corpus Mensurabilis Musicae, liii/3 (1970-71), no.252

"Morley, A Plain and Easy Introduction, p.288 26R. Loyan, The Canons in the Trent Codices, Corpus Mensurabilis

Musicae, xxxviii (1967), no. 12 27H. Garey, 'The Fifteenth-century Rondeau as Aleatory Polytext',

Le moyen francais, v (1959), pp. 193-236 28F. Ludwig, ed., Guillaume de Machaut: Musihalische Werke

(Leipzig, 1926, R/1954), i, p.64 29Le Poete et le prince: levolution du lyrisme courtois de Guillaume de

Machaut a Charles d'Orleans (Grenoble, 1965), p.322

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