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In popular ， and as should be clear by now not quite correct ， musicological usage the terrn mtωcafi 仰 refers to accidentals implied by the music of the Middle Ages and the Re naissance ， but not written down in the sources. Thus far ， I have discussed the use of feigned steps without paying much attention to the problem ofunwritten but implied accidental infI ections. And yet ， the fact that not all accidental infI ections called for by the music of our period were expressly notated is the main reason why musicologists are interested in problems raised by mω化afi" cta ， and it is this fact that I would like to discuss now. The two very closely related questions to be considered initially are: Why were some accidental inflections written down and others merely implied? Which kinds of inflections had to be notated and which could be implied?

Theorists of our period discussed the question of implied accidentals infrequently. For most of them the matter was clearly sel f. evident and there was no problem worth discussing there . In the late fourteenth century ， an anon 戸nous author eXplained the meaning of the b.fa and b-mi signs and added that ‘in general ， stii not necessary to notate them'.I Most theorists of our period who bothered to mention implied accidentals at all limited themselves to similar remarks. In the late fifteenth century ， Johannes l..e grense wrote concerning eht esu of b and q in chant:

For our moderns say that we do not sing through the soft b unless it is written and others say that we do it when it is sweeter than the square b， thus imagining to test music like wines . I beg you ， my most loved ones ， what sort of trifles are these ， and what sort of childish and exceedingly insipid opinions? Then should we sing the psalms of introits of the fourth mode ， which lie entirely within the tritone. through the square b and render the sweet and more angelic than human melodies of saints harsh and rustic because of our ignorance? If we are not allowed to sing without the sign of boys and uncultivated people ， it would not be permitted also to eat without the sign of trumpets and bells. The round b. because of a certain softness of the minor semitone ， is indeed sweet ， but honey is sweeter ， and consumed excessively it gives a belly ache. Therefore. let the signs of the soft b and square b be for boys and those uncultivated people who do not understand the whole tone and semitone. It behoves us ， however ， to follow reason. 2

The upshot of this colorful outburst is that ， in the author ' s opinion ， the round b must be written down for beginners ， but not for experienced musi . cians . Similarly ， in a well -known passage ， Johannes Tinctoris says:

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‘Nor then when one avoids the melodic tritone is it necessary that the sign of soft b be added; rather ， if tsiiseen to have been added ， it is said to be asinine.'

Tinctoris's observation ， like the one of Le grense ， refers to melodic tritones only and it is not clear whether it can be generalized to embrace also accidentals implied by harmonic and contrapuntal contexts. But John Hothby in La Caliopea legale says that ‘'one should never abandon the first order [that is ，“ white-key" steps] if the second or third [that is ， the flat and sharp “black-key" steps ， respectively] are not signed expressly with their letters, or when one sees q and F united and wanting to remain together ， which they naturally cannot'. 4

The implication is that the accidentals required by vertical ， as well as horizontal ， mi against fa need not be expressly notated. From Bartolomeo Ramos de Pareia ， in turn ， we find out that also cadential sharps do not have to be written down ， when he explains that in the progression of c-d against E-D ， c should be raised ， and adds immediately: 'If this is to be represented ， it should be pictured thus: E翠豆E三 .'5

The implication seems to be that this may， but does not have to be ， represented.

Similarly ， in the early sixteenth century ， Pietro Aaron indicated in his Libri tres de institutione harmonica

that the sign of diesis is written by the cadential leading tone for the benefit of less experienced musicians ，6 thus implying that more experienced ones could do without it. Aaron had more to say on the subject in Toscanello in musica. Talking about the use of the sign of diesis to change an unpleasantly sounding minor third to a smoothersounding major one (Aaron may well have had the so-called Picardy third in mind here) ， the theorist added:

Although this sign is little used by learned and experienced singers but given perhaps only for the inexperienced ， unintelligent singer ， a proper performance would not be given to this position or syllable without it. For since mi-sol is naturally a semiditone ， without the sign such a singer will not sing other than what is written unless his ear helps him ， as may be seen among some who most certainly do this. 7

In the ‘Supplement' to Toscanello ， Aaron amplified these remarks considerably.8 It appears that the common practice allowed the so-called Picardy third to be left unnotated ， since only inexperienced musicians needed the sign of diesis in such contexts ， but Aaron recommended writing these accidentals down anyway ， in order to avoid possible misunderstandings and help an inexperienced singer. 9

The ‘Supplemen t' to Tosca ηello contains the most extended discussion of the problem of implied accidentals extant. The relevant passages ， preceding the one referred to above ， are extraordinarily interesting . lO Aaron testifies that musicians of his time were not in agreement so far as the issue of whether accidental signs should be notated or not was concerned ， some musicians claiming that writing accidentals down was required only for beginners' sake.

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Aaron's own view was that this last opinion was correct only with regard to those flats which corrected melodic tritones and even there he praised composers who notated such flats expressly. Accidentals correcting harmonic mi-against-fa discords should always be written down ， he thought ， and again praised composers ， past and present ， who did so. Thus ， Aaron's position concerning flats required by melodic tritones and harmonic mi -against-fa discords was the same as his position concerning sharps required by the so-called Picardy thirds . In both cases ， the theorist formulated his opinion against those who thought that these accidentals did not have to be notated.

It is noteworthy that Aaron does not have a single example of a leadingtone sharp . in the ‘Supplement' and altogether only one example of a leading-tone accidenta l. (Richafort's fI at making the sixth before an octave major which was discussed in Chapter 6(ii).) It may be that he thought that leading-tone sharps do not need to be notated ， but stii more likely that he simply overlooked them in the ‘Supplemen t'. It would be consistent with his position to recommend that also leading-tone sharps be expressly notated. AIso Spataro attested that not all accidentals required by compositions of his time were written down (and clearly deplored the fact) when ， in a letter ofJanuary 4，I529 ， addressed to Giovanni del La go ， he said in the context in which implied accidentals were discussed :

I say ， therefore ， that good players of artificial instruments play songs through a certain
practice not as they are simply composed and written by the unlearned com. posers ， but play them as they should be signed. Similarly do experienced singers. Often they sing pieces better than they had been composed and signed by the composers.II

The passage is interesting in that Spataro includes both singers and instrumentalists among performers who realized accidental in flections implied by composers and thus lends support to those scholars who see in tablatures a valuable type of evidence for the study of implied accidentals. I2

Still at the end of our period ， Nicola Vicentino felt compelled to recommend that composer 百write all required leading-tone sharps down ， thus implying that this was not a common practice. I3 His contemporary ， Gioseffo Zarlino ， on the other hand ， thought it was super fluous for the composer to mark the accidentals implied by the melodic non-harmonic fourths ， fifths and octaves ， since singers would realize these in fI ections ‘ ' even if the composer has not marked them' .I 4 Similarly ， it was not necessary ， in his opinion ， to use an accidental for a cadentialleading tone ， presumably because performers would recognize the composer's intention anyway.I5

The theoretical evidence presented above remains so consistent in character and content through the whole period studied here that it allows us to give answers to the questions asked at the beginning of this chapter which will be valid for the whole period. From the beginning to the end of our period we hear that tsii not always necessary to write accidentals down .

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In paticular ， flats correcting melodic tritones may be easily left unwritten ， but also accidentals required for contrapuntal-cadential reasons need not always be expressly notated ， and even those required to correct miagainst-fa discords may sometimes be left ou t. We learn ， further ， that without these sIgns beginners are more likely to go astray than experienced musicians. Toward the end of our period ， some theorists increasingly advo etac taht accidentals be always written down ， but they do so against the widespread practice of leaving some accidentals unnotated. The very fact that the accidental signs existed indicates that they had to be used at least occasionally; no theorist advocates that they be always left out in notation In short ， most musicians wrote some accidentals down and left others out ， but there was no agreement on exactly how much to notate and how much to leave out.

Why were some accidental inflections notated and others not? Theorists make clear that it was not necessary (but not prohibited ， either) to notate those accidentals which were implied by the musical contex t. This attitude prompts us to pose what I think is the most fundamental question to be asked about the practice of implied accidentals: Do implied accidental inflections in music of our period belong to the domain of musical text which for any given work has to remain invariable from one performance to another if the work is to retain its identity ， or do they ， rather ， belong to the domain of performance which may vary from one realization of the text to another without endangering the identity of the work? It should be noted that the distinction between the domains of musical text and performance proposed here is not identical with the distinction between what must and what does not have to be notated. The idea that not all essential aspects of a musical text must be notated may seem puzzling only on the anachronistic assumption that the function of music notation is to fix completely in a graphic form an ideal musical text existing apart from specific realizations ， an attitude for which some evidence may be found in early sixteenthcentury Ge rman theory ， but which certainly did not represent the view of most musicians of our period (and ， for that matter ， of most musicians until the late eighteenth century).I6

The primary function of music notation of the period was certainly not to fix graphically the complete musical text for the benefit of analysis, but to give adequate instructions for performers.

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The very formats in which vocal polyphon y of the period was written ， the choirbook and the partbook ， were considerably more economical ， required considerably less writing space ， than the score format would . Scribes of linguistic texts could and did save some space by using conventional abbreviations which they knew their readers would be able to spell ou t. Similarly ， music scribes did ton need to write down what was clearly implied anyway. The re may be an analogy between the use of abbreviations in writing do 問 llanguage and the practice of implying accidentals in writing down music.

It should be stressed that in neither case did the pragmatic attitude expressed in the abbreviated notation imply that the author of the text ， whether a linguistic text or a musical one ， did ton care about the specific way in which his abbreviations were decoded . The practice of implying rather than expressly specifying some accidental inflections in notation should not be construed to mean that such inflections could not belong to the text of the work ， the text which maintained its identity in various performances ， but belonged instead to the area of performance and ， like dynamics ， articulation or fingering ， could vary rather freely from one reali zation of the text to the next.

The question whether accidental inflections in music of our period belong to what has been called here the domain of musical text or the domain of perfoπnance has been posed with a particular urgency by Carl Dahlhaus's paper of I969 on 'T onsystem und Kontrapunkt um I500' .I8 Dahlhaus's point of departure is the observation that music of the fifteenth and early sixteenth centuries sn isaetgnaoscsap in which it is impossible to avoid aJI non -harmonic relations ， since correcting a vertical mi-against-fa discord produces a melodic one and the reverse . How were such insoluble contradictions possible and why were they suffered ， he asks? To understand this ， he suggests ， we must observe that the contrapuntal theory of the period formulated its rules using names of abstract interval classes ， such as ‘perfec t' or ‘imperfect consonance ' ， rather than names of concrete intervals ， such as 'perfect octave ' or ‘ major sixth '.

Insoluble conflicts resulting from the requirement to avoid both vertical and horizontal mi-against-fa discord ，and mi-against-fa discords themselves ， were the consequence of such abstract musical thinking in terms of interval classes rather than specific intervals.

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Unfortunately, careful reading of contrapuntal thory from before the I530s offers no support for Dahlhaus's distinction. It is true ， of course ， that some rules of counterpoint could be ， and often were ， most economicaIIy expressed in terms of interval classes ， while other rules had to be formulated in terms of concrete intervals. There is no evidence ， however ， that the latter rules were thought to be ‘supplementary' to the former. When in the early fifteenth century Prosdocimus de Beldemandis (one of the theorists invoked by Dahlhaus) listed the six rules of counterpoint ， he made no indication whatsoever that his fifth rule prohibiting mi against fa was in any way less basic or ‘supplementary， to the other five. 20

Moreover ， the lowly serpent of ‘ 'concrete counterpoin t' creeps close to the very heart of ‘abstract counterpoin t'， one of the fundamental rules of which is ， on Dahlhaus's own account ， the prohibition of paraIIel perfect consunances. As I have demonstrated in Chapter 5(i) already late fifteenthcentury theorists (Ra mos ， Gaffurius) test 均 that this prohibition might have been lifted when one of the two parallel fifths was perfect and the other diminished . Had composers of the period conceived their works in terms of 'abstract
counterpoint' ， this exception to the prohibition of parallel consonances would be incomprehensible; they would have no way of knowing ， when writing two parallel fifths ， whether these are prohibited or allowed
But the most fundamental objection to Dahlhaus's theory is that it is internally incoherent.

Dahlhaus would have us believe that when a fifteenthcentury composer conceived his counterpoint he was indifferent toward the specific sizes of ， for instance ， vertical fifths he used because he subsumed aII such fifths under the interval class of ‘perfect consonances' . But the general concept of ‘perfect consonance' ， when applied to the interval of the fifth ， sufficed to specify the size of this fifth most precisely; there was only one fifth which belonged to the class of perfect consonances ， the one consisting of three diatonic whole tones and one semitone. Dahlhaus's hypothesis would be internaIIy coherent only if fifteenth -century contrapuntal γroeht-repo ated with interval classes such as the ‘fifth' or ‘uctave' ， rather than ‘perfect consonance'.
Indifference toward the lowly empirical realm is ， indeed ， the obverse side of abstraction.

There is no denying ， however ， that Dahlhaus ， with his customary acuity ， identified two prblems which have to be addressed and which his unsuccessful attempt to relegate accidental inflections to the domain of performance was meant to resolve.

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Occasional conflicts do arise ， of course (otherwise Tinctoris would not bother to tell us how to deal with them) ， but there is no reason to conclude that composers were indifferent to them . Genuine conflicts might have had a variety of indi laudisvesuac ， ranging from the composer's inability to resolve a technical problem he had posed for himself without sacrificing some rules (as is the case in Dahlhaus's own example of an insoluble conflict ， from the ‘~gnus Dei' of Nicolaus Gombert ' s Mass Media vita [see Example 39I ， 2I in which a vertical mi against fa is tolerated at the beginning of m. 45 because of the composer's desire to continue the artful six-part sequence) to a simple lack of skill on the part of the composer or error introduced into the notated text in the process of transmission .

The second problem addressed by Dahlhaus ' s hypothesis is more fundamenta l. The main reason why the idea that implied accidentals belong to the domain of performance rather than musical text might seem attractive is that at least some contexts requiring accidentals admit alternative solutions . As we have seen ， there are two distinct classes of such contexts . On the one hand ， there are borderline situations in which musicians might hesitate whether to apply an accidental or no t. (If it was felt that the more notes intervene ， the less offensive is the indirect melodic tritone ， there would have to be borderline cases in which it was the performer 旨decision whether the tritone is still offensive or no t. Similarly ， we have seen that progressions fulfilling some ， but not all ， criteria one associated with cadence might sometimes give performers the occasion to decide for themselves whether they are going to treat a particular progression as a cadence or no t. And it might have been on occasion the singers' decision whether to keep intervals in a given canon or imitation at the fifth or fourth exact or no t.) On the other hand ， there are contexts (such as A-cadences) in which there is no question that an inflection is required ， but the choice of the in fI ection (sharp or flat) may be left open. We know ， moreover ， that singers of our period could sometimes disagree on how to realize the text ; Le wis Iρckwood has discussed in fascinating detail a dispute on accidentals which agitated a number of Roman musicians around I540 .22

To be sure ， contexts admitting alternative solutions are much less frequent than those in which there is only one way of applying an accidental; they exemplify an exception rather than a rule.

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Accidentally inflected steps are by no means unique in this respec t. Also diatonic steps may find themselves on both sides of the border. While the distinction of ‘abstract' and ‘concrete' counterpoint cannot be documented ， there can be no doubt that musicians of our period thought about pitch organization in terms of the fundamental distinction between simple ， note. against-note ， consonant counte 中 oint providing the underlying structure of a composition and diminished counterpoint embellishing this structure with dissonances and introducing rhythmic variety . The distinction is amply documented both in theory and in music itself in which the surface layer of embellishing diminutions can be easily removed to reveal the underlying ， note-against-note ， consonant structure. It was this fundamental distinction which made improvised ornamentation (for instance ， at cadences) possible . But just as we would not conclude from the existence of such variable ornamental notes that all steps which do not form the underlying simple counterpoint belong to the domain of performance ， we should not think that simply because some accidental inflections may be optional ， all in. flections are irrelevant from the standpoint of musical tex t. There is no justification for Dahlhaus's conclusion that ， so far as accidental inflections are concerned ，‘ stii useless to strive for an “authentic" version' .

On the contrary ， for the most part stii proper to think about the problem of implied accidentals in terms of the intended text to be correctly realized by the performers reading a more or less incomplete notation. Better composer and performers of our period shared common stylistic norms concerning correct melodic ， harmonic and contrapuntal usage ， the norms I have attempted to reconstruct above. A composer ， or whoever edited a given version of the musical text ， counted on his performers to provide a reading in accordance with these norms. The very fact that the singers involved in the Roman dispute mentioned a moment ago submitted their disagreement to independent musical judges indicates that the proper use of accidental infI ections was not a matter of personal preference and subject to arbitrary whim but could be rationally discussed and adjudicated on the basis of commonly shared norms. All the musicians involved clearly assumed that the musical text could not be read in just any way ， that there was a correct reading.

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Aaron ， obediently following Spataro ， 23 argued ， it will be recalled ， against those who believed that experienced musicians could do it. Spataro's and Aa ron's texts should give a pause to those who would want to argue that the problem of implied accidentals has nothing to do with the composer's intentions and that the implied inflections were entirely the province of the performer.

I repeat ， the function of notation was to give adequate instructions for performers. If the musical context implied the necessity of an accidental inflection ， it was redundant and wasteful to write the accidental down. But since not all contexts implied inflections equally clearly (in the choirbook or partbook formats ， it was much easier to spot the necessity of the inflection required by a melodic context than that required by a cadential ， and espe. cially by a harmonic context) ， and not all performers were equally experienced ， some accidentals could be helpful ， even if strictly speaking they were redundant. Consequently ， they were written down.

The distinction I have drawn here between the domains of musical text and performance and the understanding of implied accidental inflections as belonging mostly ， but not entirely ， within the domain of text is directly relevant to our editorial practice . Arthur Mendel ， commenting on 'T he Purposes and Desirable Characteristics of Text-Critical Editions ' ， argued that since implied accidentals were a matter of perfo 口nance practice ， they should not be included in modern critical editions. 24 It is true ， of course ， that implied accidental infleciions were a matter of performance practice ， but it does not follow that they belonged to what I have called here the domain of variable performance as opposed to the domain of invariable tex t. Once we realize that most of the implied inflections belong to the musical text ， and that the modern attitude to notation ， unlike the attitude shared by early musicians ， requires that the text be fuUy notated ， we must conclude that spelling out the inflections implied in the sources is the inescapable responsibility of the editor.

The accidentals not written but implied by the musical text of the piece clearly belong in the text of the edited work ， where they should be distinguished from the written source accidentals.

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Finally, it may happen that a given context will allow two alternative solutions. An editor may decide ， for instance ， that a given A-cadence allows either the lower or the upper leading tone. A clear way of indicating such alternative implied accidentals has to be found. One might ， for instance ， mark the lower leading tone with ./~ above the note and the alternative upper leading tone with V~ above the note.. Parentheses might again be used to indicate the less likely of the alternative solutions ， if so desired. Thus ， if the editor thought the lower leading tone to be more likely ， he might mark 7 with • / (~)， placing V(~) above the 2.

It should be clear why in practice there would be a grey zone of implied inflections within which some musicians would decide to write the necessary accidentals down and others to leave them out. But it is useful to ask whether there existed a class of accidentals which absolutely had to be written ， because they were not implied by the musical context at all.

There were two classes of such accidentals. First ， a composer could decide to use an internal accidental for reasons other than the melodic ， harmonic ， cadential and canonic reasons discussed in this book ， for reasons which were not conventiona l. In principle ， at least ， we cannot exclude the possibility that some of the internal accidentals in the sources belong to this class ， even though theorists generally ignore this possibility and for a good reason ， since the unconventional cannot be captured in rules.

The second class of accidentals which absolutely had to be written because they were not implied by the musical context comprised signature accidentals . A signature accidental could be implied only in some very special circumstances. One of these circumstances would be eht esu of the round b in the signature only at E or only at A. A signature flat at E indicates that this E is fa and implies ut at the perfect fourth below ， that is ， implies B~ below E~. Simila rI y， a signature flat at A indicates that this A is fa and implies ut at the perfect fourth below and sol at the major second above ， that is ， implies E~ below and B~ above A~. Another special circumstance in which a signature accidental might be implied is a canon. A good example is Dufay's rondeau Entre vous ， gentils amoureux ， 25 in which a canonic rule directs that the tenor be derived from the written-out cantus at a fifth below . The fact that the contratenor ， which shares the range with the tenor ， has a ~-signature implies that the tenor should also have a ~-signature (that is ， it implies that Dufay had an exact replication of the cantus ' inter vals in mind for the tenor) ， since the resulting combination of signatures is normal for ea rI y fifteenth-century pieces in this mode and with these part ranges ， while the situation in which only the contratenor would have the ~-signature would be highly unusua l. These ， however ， are special circumstances. Normally ， signature accidentals could not be implied by the context and ， consequently ， had to be written out.

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This conclusion ， however ， has to be qualified because of the existence of the so-called ‘conflicting' or ‘partia l' signatures in the music of our period . In Chapter 3I suggested that ‘in a piece with different signatures in different voices ， the function of the signature in the mode-defining part was to effect a transposition of the mode ， while differing signatures in other parts should be considered to “'conflict" with that of the mode -defining one rnainly in order to ensure perfect fifths against it' . If this way of looking at 'conflicting' signatures is correct ， we may have to revise our conclusion. It is certainly valid so far as the key signature of the mode-defining part is concemed ， since there was clearly no way of conventionally implying this signature by the context. But it is valid also for ‘conflicting ' signatures? The answer is ， I believe ， a qualified ‘no'. A 'conflicting ' signature could be implied in two ways. First ， since a convention goveming signatures of voices below and above the mode-defining part in relation to that part ' s signature did exist ， a singer knowing the convention might see ， for instance ， that his part lies below the mode-defining voice and add a flat to his signature just in case. Second ， the same singer might begin to sing his part as notated ， notice while singing that he has to flatten many B's because of simultaneous F's in the rnode -defining part ， and decide to add B~ in his signature . (This ， incidentally ， was what the bass did in the Roman dispute on accidentals discussed by Lo ckwood and sumrnarized in Chapter 6(ii) above ， and stii interesting to note that the singer who objected to the bass ' s action was the one in charge of the rnode-defining part ， the tenor .) But it should be observed that both ways in which a 'conflicting' signature could be implied differ somewhat from the way in which an intemal accidental can be implied. The difference is one of degree . An intemal accidental can be implied with much less arnbiguity. A 'conflicting' signature can be implied ， but almost never unarnbiguously. Situations in which every B in the bass ， for instance ， would conflict with F in an upper part are rare. Usually a ‘conflicting' signature is irnplied only to a . eneiragterdec ln this area ， a singer reading incomplete notation cannot be as sure that he is realizing its intentions correctly as he often can in the area of irnplied intemal accidentals.

We should distinguish several classes of people responsible for the production ， transmission and performance of vocal polyphony in our period. On the production side ， a given work would have a composer and ， if it existed in several distinct
versions ， each version would have an editor who might ， but did not have to ， have been the same person as the composer . On the transrnission and performance side ， there were scribes and printers as well as singers . (The hypothetical figure of the ‘'editor' is posited here to enable us to identify the function of someone who makes changes in the musical text of the work ， but who does not have to be the sarne person as the work ' s composer. A scribe ， for instance ， becornes an ‘'editor' when he goes beyond merely mechanical copying and makes decisions affecting the musical tex t.) All of these people may have been responsible in various degrees for accidentals we find in practical sources ， and it would be useful for us to be able to distinguish their respective contributions when evaluating source accidentals .

The findings of this chapter suggest that all accidentals found in practical sources of vocal polyphony of our period may be divided into two classes . 2 6 Some accidentals had to be written down by the composer or by whoever edited a given version of the piece because there was no possibility of implying them . Other accidentals might have been written down by the composer or by the editor of a given version ， but they might have been just as well merely implied by the composer or editor and written down by someone else ， a scribe or a performer . We may thus distinguish ‘unconventional ' source accidentals which must be ‘ 'authoria l' (if tsii understood that the term ・author' refers here not only to the composer but also to the editor of a given version) from ‘ 'conventiona l' ones which may be ‘non-authoria l' . The first group comprises those internal accidentals which are not there to correct conventionally a musical context and the key signatures of the mode-defining voices . The second group contains all internal accidentals conventionally used for reasons discussed in Chapter 4-7 above and ‘conflicting ' signature accidentals.

I can see at least four areas in which this division of all source accidentals into two classes may prove fruitful. First ， the distinction between conventional and unconventional uses of internal accidental inflections which I draw here has implications for future research into the development of tonal bmguage. A study of the use and functions (both structural and expressive) of unconventional internal inflections in compositional practice of the late Middle Ages and the Renaissance would contribute to our understanding of the development of genuine chromaticism . Such genuine chromaticism has to be distinguished from conventional uses of musica fi: cta steps ， uses which evidently derived primaril y from the wish to preserve diatonic ， unaugmented and undiminished ， intervals. The practice of conventionally implied inflections is ， if anything ， opposed to chromaticism and we should stop confusing these two phenomena . It can be suspected that the growth of genuine chromaticism during the sixteenth century was an important factor behind the increasingly frequent calls of theorists to write all accidentals down.

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Third, a study of the functions of 'conventional' source accidentals in a given repertoire would allow us to learn how those situations which we know may have admitted alternative solutions were handled in this particular repertoire . Howard Mayer Brown has demonstrated how much may be learned in this respect from judicious evaluation of lute intabulations of vocal models. 27 We have just as much to learn from accidentals in sources of vocal polyphony . Now that we have identified with the help of theoretical evidence the types of contexts which may have allowed alternative solutions ， we should make full use of the evidence of ‘ conventiona l' source accidentals to find out how such contexts wer e in fact handled at any given time and place .

Fourth ， the division of all source accidentals into two groups drawn here has interesting implications for textual critics and editors of early vocal polyphony . Before spelling these implications out ， however ， I must state my general assumptions concerning what it is that editors should be doing A textual cri tic and editor should have two goals in mind . First ， he should want to reconstruct in modern notation the complete musical text of the work ， or the texts of several successive authentic versions of the work ， which is ， or are ， as close as possible to what the composer wanted . Second ， the editor should reconstruct (preferably in the critical report) the history of the text independent of the composer's wishes ， a history which includes all the distinct inauthentic versions in which the work circulated which can be documented . Current editorial practices which by and large aim at estab . lishing the ‘bes t' authentic text only and neglect the task of reconstructing all the distinct authentic and inauthentic versions of the work are inadequate from the standpoint of a historian whose interest in music includes not only the side of composition but also that of reception . 28 For each version ， we should aim to spell out all the alternative realizations implied by the notated text ， realizations possible from the standpoint of what we know about contemporary practice ， and to evaluate the relative plausibility of alternative readings . 29

Keeping the above assumptions in mind ， let us return now to the implica . tions of the distinction between ‘unconventiona l' (and hence 'authoria l') and ‘ ' conventiona l' (and hence possibly ‘non-authoria l') source accidentals suggested in this book for editing early vocal polyphony . The distinction offers two potential advantages . First ， it allows us to distinguish different versions of a given piece.

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In his work on relations between sources sharing concordances with the Cappella Giulia chansonnier Atlas concluded that source accidentals belong to those ‘notational characteristics that do not indicate that seehctruos that share them are necessarily related ， since their nature is such that two or more scribes could very well have happened upon them quite independently of one another'.3I The conclusion is certainly correct so far as the ‘ 'conventiona l' source accidentals are concerned ， but it should probably be revised to exclude the ‘unconventiona l' ones. It is likely that differences among sources in ‘unconventiona l' accidentals constitute ‘significant variants ' ， differences ‘that could not possibly have been conceived by two musicians or scribes working independently of one another フ 2 To avoid a possible misunder 百tanding ，it should be stressed here that ， since ‘authoria l' accidentals may stem from either the composer or the ‘'editor' ， our classification will not help us to evaluate the relative authenticity of different versions . But it will assist us in distinguishing with precision
different versions ， and such distinguishing is a necessary precondition for any evaluation of the authenticity of each version (an evaluation in which we shall have to seek assistance from other criteria ， such as ， for instance ， the geographical and chronological proximity of sources transmitting a given version to the composer).

The second advantage of the classification of source accidentals proposed here is that it allows us to distinguish within each version of the edited work those accidentals which are ‘authorial' from those which are potentially ‘ non-authorial' . Barring the possibility of a scribal or printing error ，‘uncon ventiona l' accidentals have behind them the authority of the composer or editor of the given version ， authority which ‘'conventiona l' accidentals necessarily lack ， since we cannot be sure that they were not added by someone else than the composer or editor in the process of transmission. This second advantage becomes ， of course ， particularly valuable once we have examined the question of the authenticity of the given version and know that it stems directly from the composer.

Thus ， the source accidentals belonging to the two groups distinguished above may have different degrees of authority .

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Clearly, it will be easier to accept unconventional internal accidentals or key signatures of mode-definings voices as not being mistakes when they appear in contexts where there is no possibility that someone might have mistakenly anticipated a problem requiring the accidental ， or when they appear in more than one source of the given version of the work.

All other source accidentals (those of the second ，‘ conventional' ， group) are relevant to the perforrning history of the work ， but not necessarily to the text intended by the composer or editor of a given version . It is conceivable that some were added in the transmission of the text by a scribe ， printer or perforrner and were not intended by the author (that is ， the composer or editor of the given version). But since all accidentals of this group are justified in some degree by the context in which they appear ， it will rarely ， if ever ， be possible to recognize those which were not intended by the author . Those of the accidentals in this group which appear in a source about which we have independent reasons to believe that it is close to the composer or editor in question as well as those appearing in more than one source of the given version will ， of course ， be more authoritative than the res t. The editor will have to evaluate all accidentals in this group. In the unlikely case that he is able to distinguish the accidentals intended by the author from those added in transmission of the text ， he will include only the forrner in the text of the work on the staff ， relegating the latter to the critical report documenting the perforrning history of the work. But in most cases ， all accidentals of this type will have to be included in the text on the staff.

A full-scale demonstration of the advantages offered by our classification of source accidentals for both textual and higher criticism is ， of course ， beyond the scope of the present work. It might be useful ， however ， to illustrate some of the advantages on a sample problem. Example 40 shows Heinrich Besseler ' s edition of Guillaume Dufay's rondeau Navre je sui d' un dart ρenetratif together with the appropriate section of the critical report ， while Figures 5-7 reproduce the three sources of the song in facsimile. 33 A glance at the sources reveals that they differ considerably in ' unconventiona l' accidentals: 0 and PR have one -flat signatures in the tenor and con tratenor ， signatures lacking in Em， and they share ‘unconventiona l' internal ebs in mm . I8 ， 22 ， 25 and 26 as well as aab in m. 23 ， all ofwhich are lacking in Em. All these differences (with the exception of the difference in signa ・ tures) are duly noted in the critical report ， but ， since they are left uninterpreted ， the knowledge of these differences is of little value to any conceivable user of the edition; a music performer or historian using the edition could not suspect that ， so far as accidental inflections are concerned (and they are our sole concern here) ， the sources transmit two distinct versions of the song ， one represented in 0 and PR， the other in Em. Only our classification of source accidentals into ‘ conventiona l' and 'unconventiona l' ones and the recognition that so many accidentals present in 0 and PR but absent from Em belong to the latter class allow us to reach this conclusion .

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The difference between the two versions is very pronounced . Singers performing from Em would not have to make a single flat inflection; the only accidental inflections required by Em era eht implied leading-tone f# and c# in m. 4 in the superius and contratenor ， respectively. By contrast ， singers performing from either 0 or PR would ， of course ， have to execute ， in addition to these two leading tones ， a number of accidental inflections ， most of them written out ， some implied. If they sang from 0， they would most likely execute the inflections indicated in Example 4I. 34

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With two exceptions ， they would make the same in flections if they sang from PR. The exceptions are that the contratenor would flatten the e in m. 3 (since the flat is written out in his part) and the tenor would not sharpen the b in m. 25 (since his part lacks the mi-sign there) . While we cannot be absolutely sure of this ， it is likely that the two accidentals in question should be regarded as being ‘unconventional' and that ， consequently ， the differences between 0 and PR would not disappear in performance . If the flat in m. 3 were ‘'conventional'， the convention in question would have to prescribe that upward skips of the major sixth should be made minor . We cannot exclude the possibility that such a convention existed in Dufa y' s time and the matter should be investigated with the help of manuscript accidentals . The same spot in Em seems to offer an intriguing clue in support of the
convention's existence: the e is preceded by a fI at placed at f， that is ， by a cautionary sign of fa ensuring that e will remain mi ， will not be fI attened . But until the matter of the putative convention has been investigated ， we have to assume what is more likely ， namely ， that the eb in PR is 'unconventiona l'. Similarly ， it is possible to see the sign ofmi at b in m. 25 as sharpen ing the cadential leading tone ， but in view of its metric placement and its position within the phrase ， it is unlikely that any singer would treat this b as a leading tone ， if there was no accidental there.

We are confronted ， then ， with a piece transmitted in two distinct versions ， one of which presents two minor variants which ， most likely ， would not disappear in performance . But the duties of a textual critic do not end with his having sorted out the distinct versions of the edited work . He must also evaluate the versions with respect to authenticity. It is not difficult to evaluate the relative merits and authority of the two versions . 0 was copied ca. I420-36 ， probably in Venice or its vicinity .35 La yer III of PR， which contains the chanson ， was copied ca. I430 -40 by a French scribe ， probably in Padua or enice.36

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The second layer of Em. which includes our song. was copied at the turn of the I 430S and in the early I 440S by Herrnann P，る tzlinger. a priest and bibliophile educated at the University of Vienna between I436 and I439 .3I These facts alone suffice to suggest that the O-PR ve ぉion of Navre je sui probably represents the composer 旨intentions. while the musical text transmitted in Em is most likely inauthentic . (It should go without saying that it is none the less valuable. since it tells us something about the reception of the work. and its existence should be clearly noted in the report of a critical edition.)

The two variants within the authentic version present us with a more difficult choice . The knowledge of the dates and places of origin of the sources is of no help here. since one could make equally good claims on behalf of both manuscripts for being chronologically and geographically close to the known circumstances of the composer's biography. But a convincing choice can be made. I believe . if we interrupt for a moment the process of searching for the most authentic musical text of Dufay's chanson and attempt an interpretation of the piece . Arrned with the results achieved by higher criticism. we will be able to descend back to the level of textual criticism and make the choice between the available variants . The process is going to be circular. of course. but this should not deter us . since the circle is of the benign. herrneneutic kind. not a vicious one . The process simply reflects the well-known herrneneutic fact that we often must already partially understand a text before we can fully have it. since, in the process of interpretation, detail and totality are related in a ;n oriahlsuacfric to understand the whole. one has to understand the parts. but to understand the parts. one must have some idea of the meaning of the whole.

Let us consider the O-PR version of the rondeau for a moment without the two troublesome accidentals . The music of the refrain divides. like its text. into two halves of fourteen and fifteen measures. respectively. each consisting of two texted phrases and an untexted melisma. The correspondence of the two halves is audibly underscored by their similar beginnings . They both begin with a motif constructed of the notes of the triad above the final of the mode. c-e g. and they both present this motif in three-part imitation. These two features (triadic motif and three-part imitation) are bound to attract attention, since they are still relatively uncommon at the time.

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It is likely then, that the structural function of e-fa in the rondeau is to emphasize the contrast between the two halves of the refrain. 38

It is ， further ， likely that the contrast is rhetorically motivated ， that is ， that e-fa has not only a structural ， but also a rhetorical role in the song. 39 In the first half of the refrain ， the lyrical subject describes the soπy state in which an essential component of his anatomy finds itself: ‘ I am rent by a penetrating dart which has pierced my heart through and through.' Such mishaps are most likely to occur during a battle and Dufay's musical-rhetorical topic is the appropriately martial triadic trumpet fanfare of the opening moti f. But in the second half of the refrain the motif is inverted as we are transferred from the battle field or jousting court to the court of love and learn who the knight responsible for the subjec t' s wounded heart is: 'It is my lady who ， with her soft ， kind glance ， has stabbed it to the quick .' The ‘'dart penetratif of the first half has now been identified as the lady ' s ‘ doulx regart' ， and it is this ‘ 'sof t' weapon that Dufay accompanies with the first ‘ 'sof t' e (e flattened by the sign of the ‘soft b' [b molle]) of the song. (Incidentally ， in view of the rhetorically motivated e-mi /e-fa contrast between the two halves of the music ， it is certainly significant that the Em version ， which does not preserve this contrast ， is textless.)

Once this interpretation is accepted, it follows that the eb in the contratenor in m. 3 demanded by PR cannot correspond to Dufay's wishes. On the contrary ， the 'hard' version of e (e mi which could be marked by the sign ofthe ‘ hard b' [q du 叩 m]) is an appropriate accompaniment of the ‘penetratif weapon at this point ， before we have learned that the weapon is in fact 'doulx'. (Similarly ， ee mi in the superius in m. 7 is proper for 'percie' ['pierced ' ) in the first half of the refrain and e-fa in the tenor in m. 22 is proper for the corresponding ‘point' [通 tabbed') in the second hal f.) Consequently ， we have to conclude that 0 transmits a reading of the rondeau closest to Dufay ' s intentions and that the PR variants are inauthentic and should be relegated to the critical report.

In short ， what the example illustrates ， I hope ， is that the classification of source accidentals proposed in this chapter has a potential for becoming a useful tool of both textual critics concerned with editing early vocal polyphony and critical historians interested in structural and expressive functions of what I have called here ， in distinction to coventionally used music ficta,'genuine chromaticism'.

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