‘ARTES NOVAE’

Adhuc sum de numero Antiquorum quos horum aliqui rudes vocant. Sum senex, illi acuti et iuvenes. ...etsi in hoc opere dicturus aliqua sum contra dicta Modernorum ubi obviant dictis Antiquorum, diligo tamen personas illorum. I am now one of the ancients who are called backward-looking by some. I am old. They are clever and young. ...although in this work some things will be said against the opinions of the moderni, where they oppose the views of the antiqui, I still hold them dear personally.

that builds on many of Desmond's claims, 16 and for the present observations. Jacobus will be a recurrent presence in what follows.

JOHANNES DE MURIS AND THE DATING OF HIS MUSIC TREATISES
As Desmond demonstrated, Muris's astronomical writings, with their dependence on observation, are distributed throughout his career. By contrast, the received datings of Muris's early music treatises, which are the only ones now securely attributed to him alone, are concentrated in the years 1319-25, as corroborated in the recent research of Elż bieta Witkowska-Zaremba. 17 Then there is a long gap before the aforementioned Libellus, traditionally credited to Muris, but in which his role may have been little more than an assembler, given Desmond's identification of its close textual dependence on the Vitriacan Omni desideranti. 18 There is thus no datable evidence of original musical activity by Muris after 1325. Noting the regularity of his astronomy output, Desmond seeks to space his music treatises more evenly throughout his career. But music theory, like mathematics, was not subject to the same kinds of external pressure as astronomical observation. The fact that Muris revisited his astronomical writings does not, I think, preclude him having had a concentrated period (perhaps his main burst) of musictheoretical activity in the few years around 1320, just as he seems to have had a similarly intense mathematical engagement to produce four treatises dated c.1324.
The Notitia and its Conclusiones Muris's first music treatise is known as the Notitia from a subsequent reference he made to it. Its first book is devoted to music theory in terms to which Jacobus could hardly have objected. It was the contents of book 2 and their practical implications, which clearly went beyond what his 'ancients' had recognized, that aroused his objections. Desmond carefully analyses the contents of book 2, differentiates it from previous works of Franco of Cologne and Johannes de Garlandia, and records its innovations. In all five complete manuscripts of the Notitia, the second book is followed directly by a set of Conclusiones, which have been treated as self-evidently conclusions to the Notitia, forming a single treatise written in two stages. 19 In the earliest extant source, BnF lat. 7378A, at the end of book 2, '1319 explicit', at the end of a line, precedes what has been edited as the final paragraph of the Notitia (the third and final paragraph of chapter 7 in Michels and Meyer), starting 'In arte nostra hac', on a new line with a large capital 'I'. 20 Desmond convincingly proposes that this paragraph belongs with the immediately following Conclusiones: 21 In arte nostra hac inclusa sunt aliqua quasi abscondita intus latentia, quae si essent exterius enodata, cessarent statim quamplurimi super aliquibus conclusionibus iugiter altercantes. Inde est, quod nos amore ipsorum magis quam veritatis aliquas conclusiones, super quibus nunc magis est orta disputatio, concinne volumus approbare. Nec insurgat invidus reprehensor, si qua dicere cogamur inaudita modos vocis apparentiaque salvantes insequendo semper limites antiquorum. Some things included in our Ars [i.e. the preceding treatise] are implicit, which, if they were made explicit, ought immediately to silence many of those who dispute various conclusions. For this reason, more from love of [those colleagues] than for [a further need for] accuracy, we want to justify concisely certain conclusions regarding which there has now arisen considerable controversy. Let no invidious critic rise up if we are compelled to say unheard-of things while defending the systems and manifestations of sound, still following the paths of the ancients. 22 The Conclusiones, then, were formulated in response to detractors following the release of book 2: their purpose is to resolve disputes about things that were implicit but might not have been entirely clear in the existing version of the Notitia, supplementing it without establishing radically new teachings. The question to be resolved is how soon after the Notitia they were written.
In the explicit to his mathematical treatise Canones tabulae tabularum, Muris stated that his 'notitia artis musice' ('knowledge of the art of music'), both mensural and plainsong, became clear to him in 1321: 'Eodemque anno notitia artis musice proferende figurande tam mensurabilis quam plane ad omnem modum possibilem discantandi non solum per integra sed usque ad minutissimas fractiones, … nobis claruit.' (And in the very same year there became clear to us the knowledge of the art of producing and notating music, both mensurable and plain, in every possible manner of descanting, not only through whole [notes] but right down to the smallest fractions …) 23 This eureka moment extended to realizations in mathematics and astronomy. Heinrich Besseler and then Michels took this personal statement to mean that Muris completed the Notitia in 1321, including its conclusions, overruling the 1319 explicit date in BnF lat. 20 BnF lat. 7378A, fo. 60 v : 'quae posteris bene dubitantibus apparebunt. Completum est hoc opus anno domini .1319. explicit' (Desmond,Moderni,29 with facsimile of the manuscript page); colour images available on Gallica. Desmond, 'Jean des Murs and the Three Libelli', 49-51, refines the dating of the layers of BnF lat. 7378A, placing the section relevant here possibly around 1350. 21 Desmond, Moderni, 28-31. It could be argued to the contrary that all other sources lack this intermediate explicit. At least in Oxford, Bodleian Library, Bodley 300 (facsimile in Michels, CSM 17, 86) there is not even a punctuation break before 'In hac arte nostra' (as that manuscript reads), thus eradicating the disjunction implied in BnF lat. 7378A. The Conclusiones follow that paragraph with a prominent heading; there is nothing to suggest that they are not conclusions to what has gone before. Explicits at the end of the united treatise seem to confirm their unity, as reported by Michels, ibid. 107 and Desmond, Moderni, 30-1, 80, and 81. It may no longer have been necessary to signal the two-stage completion of the treatise. Desmond, Moderni, 31 reports that Jacobus's readings for the Conclusiones appear to follow the manuscript tradition of the 16th-c. MS Ghent, Universiteitsbibliotheek 70 (71), which presents them alone. (On this see also Michels,CSM 17,115.) But there they are clearly excerpted and not preceded by the paragraph beginning 'In arte nostra'. They thus do not support the idea that that paragraph belongs to the Conclusiones as a separate treatise in a form Jacobus might have known. 22 I am not entirely happy with the translation I offer here, which differs from those of Desmond, Strunk, and Meyer. The last sentence is particularly difficult to construe. Leofranc Holford-Strevens writes: "'Saving the phenomena" bears its usual sense, originating with Greek cosmologists, of an explanation that respects observed facts; contexts, in the broad sense of mathematics that includes astronomy and music, and is therefore a phrase one might very well expect in Muris' (email of 1 Feb. 2022). The language of this paragraph is echoed by Jacobus in SM 7.1: 'hi novi amore veritatis se scribere dicunt' (they claim to be writing for love of truth). 23 Desmond's translation (Moderni, 86). 7378A, which Michels had judged to be a 'doubtful interpolation'. 24 Christian Meyer proposed that it was precisely the debates following the 1319 publication of the first version of the Notitia that stimulated Muris to be so exercised about music theory in 1321, and that (as indicated above) this is the most likely time for him to have felt the need to add the Conclusiones. 25 I agree. Neither the 1319 date (for the two books of the Notitia), nor the 1321 date (for its completion with the Conclusiones), then has to be explained away. This timing seems entirely plausible, immediate critical reactions to the Notitia occasioning Muris's frenzy of activity and his move to clarification. But elsewhere in Moderni Desmond maintains that the Conclusiones are a separate and later work of the 'mid-to-late 1320s'. 26 By p. 238 her position has moved forward, suggesting that 'ars nova notation was first systematised only in the 1330s with the Conclusiones of Des Murs, followed by the Ars vetus et nova of the doctor modernus and the composition of the first motets that exploited the possibilities of the new notation'. Desmond's important recognition that the 'In arte nostra' paragraph introduces the added Conclusiones does not require their separation from the Notitia. Although they had some limited separate transmission as excerpts, I see no basis for dating them up to a full decade later. Rather, Muris's account in that paragraph of the lively controversy implies that the Conclusiones complete the Notitia, and his assertion about 1321 in the Canones binds them together even more immediately. Conclusions are usually attached to a preceding text, as in the set of Conclusiones following the propositions of the first part of Muris's Musica speculativa. If the Conclusiones were a separate work, especially if considerably later, one would expect more independent transmission. The Notitia and Conclusiones are copied continuously in most sources, obliterating any break before 'In arte nostra'; in addition to the above testimony, this would favour them being fairly close in date, and having been received and treated as a unit. It does seem that the few separate transmissions of the Conclusiones lack that linking paragraph, which could again argue against its circulation as a separate self-contained treatise: those writers may have extracted just the conclusions from a full copy of the Notitia, without needing the introductory paragraph. All five sources that include the Conclusiones with the Notitia conclude with differently worded explicits: they refer to Muris's 'musica organica', 'musica practica', and in BnF lat. 7378A his 'ars nova musice' (fo. 61 v ), described in the Canones as his notitia artis musice and in the paragraph introducing the Conclusiones as 'hac arte', this Ars, which I take to refer to the preceding two books, not to 'our art of music' in general. 27 The Notitia with its Conclusiones might as legitimately be called his Ars musicae, Ars musica, or even Ars nova musicae. 28 The Compendium Muris's Compendium is largely a compact version of book 2 of the Notitia in dialogue form, with a more practical emphasis. It is usually dated c.1322, and its teachings offer 24 Ed. Michels no reason for it to be much later. 29 Desmond previously accepted this date, but she now favours the later 1320s, partly on the grounds that the Compendium bears a relationship to the second of three unedited libelli in BnF lat. 7378A (Partes prolationis). 30 The first libellus begins Omnes homines, and the third libellus has been dated to 1326-7. Assuming that the three form a unit, Desmond places the Compendium after that. Even faced with a manuscript that is hard to read (BnF lat. 7378A), and in the absence of a modern edition, it is clear that there are significant differences between the second libellus and the Compendium, notably the former's insistence on four partes prolationis, which Desmond takes as earlier than five, as in the latter. If one was adapted from the other, it is not clear in which direction, and I do not think sufficient textual evidence has yet been presented that the Compendium must post-date the libelli. 31 Desmond Musica speculativa Two versions of this explicitly Boethian treatise exist, one dated 1323, and a revision in 1325. 34 That 'B' version, or an intermediate 'A/B' version, had been suggested as Jacobus's source for his extensive quotations (from the 18th Conclusio and the third Propositio) but, meanwhile, Witkowska-Zaremba has, in my view, convincingly demonstrated that the version cited by Jacobus was the earlier 'A' version securely dated to June 1323. 35 In addition, she gives a solid and subtle textual demonstration that Jacobus knew the Compendium before he read the 1323 Musica speculativa. She now gives termini ante quos for those treatises, showing that the Compendium precedes 1323 and follows the Notitia-with-Conclusiones, confirming the 1319/21 date for the latter and c.1322 for the Compendium.
Most importantly, Witkowska-Zaremba shows that in discussing the interval of the fourth, Muris changed the 'sub diapason' of the 1323 'A' version to 'supra diapason' in the 1325 'B' version, a correction he got from Jacobus's reasoned critique in SM 7, ch. 6, or even from an interim oral version of it. This is not a trivial adjustment; it bears on the status of the fourth as a perfect consonance. Jacobus did not adjust his chapter 6 to reflect Muris's 1325 correction; we cannot know whether this was because he had moved away from Paris by then, or had called closure on new material in order to complete his writing. Jacobus evidently had prompt access to Muris's treatises as they were completed. This in turn increases the likelihood that Desmond's suggestion of possible personal contact between the two men might be projected back to post-Notitia debates c.1320; that could cast Jacobus as the principal critic who provoked the Conclusiones. 36 Such contact may also be implied by Jacobus's assertion, quoted at the head of this article, that professional disagreements did not affect his personal esteem for those he disagreed with; Muris expressed a similar sentiment in the 'In arte nostra' paragraph cited above. Just as Jacobus was provoked by Muris, Muris's intensive activity on music theory around 1320 may in turn have been provoked, in part, by Jacobus. These indications of direct interaction suggest that Jacobus was already thinking about SM 7 in the early 1320s, and perhaps drafting it. All the Muris treatises he quoted are now datable to 1319-23, countering Desmond's open-ended later datings. Jacobus evidently knew them by 1323-4; no further input is later, thus yielding a terminus ante quem for datable Muris materials quoted in SM 7. It is the Musica speculativa and not SM 7 that provides a 1323 terminus ante quem for the early Muris treatises; and it is the Musica speculativa and not the papal bull Docta sanctorum that provides a terminus ante quem of c. 1323  are notated, and upstems for minims are inconsistently applied. 38 Jacobus objects to a number of notational features that are undocumented or uncertainly attested at what was evidently a time of flux: the moderns cannot agree among themselves, he says. 39 Besides various practices of stemming, he cites half-full notes, semiminims, dragmas, and syncopation. Various guesses have been made as to what Jacobus may have meant by these terms, without requiring a much later date. 40 Zayaruznaya wonders whether the puzzling note shapes Jacobus names or describes could already be those of the late fourteenth-century ars subtilior, some documented only in manuscripts after 1400. But since that is clearly too late for Jacobus, she speculates: 'In the 1350s, the first glimmers of the notational complexity we call "ars subtilior" might have become visible. It is around this time, I propose, that the author of the Speculum musice wrote the latest passages in his treatise and decided to stop revising.' 41 Such note shapes would not be the only puzzles described in music theory treatises that may refer to things for which the evidence has disappeared. 42 Lost practical sources from the 1320s may have deprived us of the many experimental or inconsistent notations that Jacobus had seen, although much of what he 'saw' seems to have been in treatises. Neither hypothesis is proven, but the datings in the 1320s proposed here favour those years for the phenomena referred to by Jacobus. Despite the shortage of extant evidence, Jacobus bears witness to a period of notational variety and even confusion, rather than to the more settled notational practice of the 1330s, the stage in the development of 'ars nova notation' that Desmond identifies as Jacobus's vantage point when she dates SM 7 in that decade.
That brings us to Vitry, for whose partly reconstructed treatise Desmond inclines to a date in the 1330s, a decade or more later than hitherto thought, implicitly encouraged by her later datings for Muris that are now challenged. If Muris's treatises do not stretch to c.1330, it becomes harder to place Vitry's that late, especially if he was, as widely accepted, the composer of some of the most innovative Fauvel motets more than a decade earlier. Although there are no dated colophons, the explicitly ars nova teachings recoverable from the 'nova' section of Vitry's putative Ars vetus et nova seem to reflect practices of the years around 1320. They name Fauvel motets firmly datable to the late 1310s, and others like them, thereby inviting a dating in the early 1320s. If the surviving witnesses are excerpted from a preceding Ars vetus et nova, that too must pre-date them, earlier and more precisely than Desmond's 'before 1340'. She places Vitry's ancestor text a decade later, in the late 1320s or early 1330s, 43 the extant digests presumably later still, and Jacobus SM 7 (which quotes from them) after that. This is in line with her late 38 Dated by Andrew Wathey, 'The Marriage of Edward III and the Transmission of French Motets to England', Journal of the American Musicological Society, 45 (1992), 1-29 at 14-18. Wathey established that the volume uses English illuminators, and that it was illustrated and finished in Hainault by English artists in the service of Isabella, Queen of Edward II of England. It was not a Parisian source. 39 'For among the moderns there has been great dissent regarding the formation and figuration of the semibreve' (see SM 7, ch. 23). In ch. 24 Jacobus attests great variety and disagreement in the caudation of semibreves ('now they practice many novelties'), while admitting that upward minim stems have gained more general acceptance. See also SM 7, ch. 34. 40 Desmond, Moderni, 123-4 gives examples from Vitriacan treatises of some possible candidates: dragmas from CS3anon3; syncopation from Vitriacan and pseudo-Muris treatises (Desmond, Moderni, 59 and 60 n. 64), including red notes, and exemplified on p. 124. 41 Zayaruznaya,'Old, New', 136. 42 Some (but not yet all) of the notational practices described in Handlo's treatise of 1326 have been found in practical sources. While he knew Franco and Petrus, many of his theories are confined to England and had no perceptible Continental influence. Practical sources are often unavailable to validate theoretical mentions. 43 Desmond, Moderni, 34.
datings for some of the Muris treatises discussed above that now invite revision. But elsewhere in Moderni she places the Ars vetus et nova before Handlo's treatise of 1326, which accords with a more plausible dating in the early 1320s. 44 A dating of the Vitriacan treatises closer to that of the Fauvel motets, and others like them, gains support from the Muris datings; Jacobus criticizes both side by side for similar transgressions, as if their authors were contemporaneous. In estimating dates for some of these treatises, as also for SM 7, Desmond tends to favour later dates within her estimated ranges, and then to build further arguments on those later dates. In some cases this reflects justifiable caution about the status of the later copies on which we necessarily depend. She asserts that neither the Compendium nor Conclusiones has to date from before 1324; 45 but nor did they have to date after it. Witkowska-Zaremba finds that both date from before 1323. Some of Desmond's late datings assume that theory must precede practice, loading too much weight onto Jacobus's lament that theory has descended to practice (SM 7, ch. 23). The opposite is normal, and often demonstrable; theoretical precedence probably applies neither to the motets by Petrus de Cruce in the seventh fascicle of Montpellier reported later by Jacobus, nor to the more advanced Fauvel motets, which also antedate applicable surviving theoretical formulations; nor need it apply to the notational phenomena seen and castigated by Jacobus. Such arguments of priority are impaired by a lack of early copies of relevant treatises, but countered by the citation in those treatises of specific pre-existing compositions and notated phenomena. Moreover, his 'would that this speculation had not descended to practice' ends a disapproving discussion of precisely the combinations of perfect and imperfect tempus and modus that are already found in motets named in the early ars nova treatises. Desmond finds this descent to practice better exemplified in the much later motet Apta/Flos, to be discussed below. 46 In support of her datings of ars nova notational innovations to c.1330, Desmond invokes the Carthusian monk Heinrich Eger von Kalkar, whose Cantuagium of 1380 refers with apparently striking precision to events fifty years earlier, around 1330 (when he was two years old) for 'magni artiste' in Paris to have 'devised a set of notational rules applied to note shapes and rests that could signify the exact measurement of their duration' (Moderni, p. 5). It is not clear exactly what he assigns to that year, as he refers only in general terms to time values and shows no theoretical or notational awareness beyond Franco, to whom alone the reader is referred. I have elsewhere questioned in more detail the reliability of a report that must depend on hearsay, given his shaky account and a demonstrable lack of polyphonic and mensural knowledge, which he admits. I conclude that he is not a knowledgeable reporter of specific notational innovations, let alone of their date. 47 44  Desmond's chapter 4 'investigates whether the innovations of the ars nova merely tweaked at the edges of the previous ars antiqua system and offered nothing substantially new, or whether they represent a moment of real discontinuity in the theory and practice of music'. 48 The received view, before Desmond, is that some of the most advanced motets in Fauvel mark the beginnings of a new art, their multiple innovations including longer and more complex compositions mapped out on a larger canvas, with a wider palette of long to short note values (a range already set out in Muris's gradus system of 1319, which foreshadows what would later be called prolation). Most innovatively, they show a prevalence of imperfect tempus. These and other motets of similar date are named with their mensural features in treatises purporting to propound the new art, and have long been accepted as its first manifestations. Those same treatises attest combinations of perfect and imperfect tempus in named motets, some lost, and give standard default values for unstemmed or downstemmed strings of semibreves separated by dots, in patterns that would soon be notated with upstemmed minims and subsumed under major prolation.
The strongest departure by Desmond from this consensus is to classify the semibreves of the Fauvel motets as ars antiqua notation; Zayaruznaya agrees. 49 They align them with the motets associated with Petrus de Cruce in the seventh and eighth fascicles of Montpellier, two of which are cited approvingly with musical examples in SM 7, ch. 17 (together with one by 'someone else'). They downplay the important difference that Petrus's motets are in perfect tempus, while most Fauvel motets are in the new imperfect tempus, abhorred by Jacobus. Both in the Petrus motets and in Fauvel, brevial groups of semibreves are separated by dots. It is through the surface appearance of this notational feature that Desmond and Zayaruznaya challenge the ars nova status of the Fauvel motets, because they lack the systematic application of minim stems established in later notated sources and theoretical formulations. 50 While Desmond may be literally justified in claiming with respect to these groups of semibreves that 'while a handful of Fauv motets were cited as examples within the Vitriacan Ars nova witnesses (see Appendix 1), for the most part, as will be explored within, the notation of Fauv has much more in common with ars antiqua notation than with ars nova notation', 51 this only applies to those features during a transitional period of notation, but not to its more fundamental conceptual shifts-shifts including those elegantly documented in Desmond's chapter 'Trees to Degrees', and above all to imperfect time and combinations of perfect and imperfect mensurations.
But the Fauvel semibreves are not unstemmed. Desmond says 'the notation of these sources [including the eleven motets with downstemmed semibreves in Fauvel] follows the manner of the Vitriacan witnesses' antiqui and veteri', 52 but she does not say where in these treatises she finds a licence for stemmed semibreves in the ars antiqua. There are no Gilles Rico, 'Music in the Arts Faculty of Paris in the Thirteenth and Early Fourteenth Centuries' (D.Phil. thesis, University of Oxford, 2005), 232f., in attaching more importance to Kalkar than he may deserve. 48 Desmond, Moderni, 19. On p. 120 she sets out a version of the existing narrative against which she is arguing. 49 Desmond, Moderni, 15, 120, 130. Zayaruznaya,'Old, New', 134 n. 139: 'Although Fauvel is often described as the first great monument of the ars nova, its notational system is broadly continuous with the notation favored by Petrus de Cruce, which requires singers to apply predetermined patterns to chains of semibreves set off by dots, though with the difference that some of the motets in Fauvel seem to call for a duple division of the breve.' 50  semibreve stems of any kind in Montpellier or in other major sources securely datable before Fauvel, no 'tagged' semibreves in 'Petronian' motets with strings of semibreves. 53 If some of those eleven Fauvel motets notated with downstems could be named and described (and perhaps composed) by theorists of the early ars nova, and the practice of stemming criticized by Jacobus as an aberration of the moderns, this surely weakens the claim that they are in 'ars antiqua notation'. Zayaruznaya alleges that Jacobus condones downstems in SM 7, ch. 35, suggesting that because of his approval they can be classified as ars antiqua. 54 Not exactly: 'Dicerent forsan aliqui quod si semibrevis sola caudetur, sicut de facto sit a Modernis, hoc <minus> irrationabiliter fieri videtur de maiore vel minore semibrevi quam de minima.' I think there is another way of reading this passage: 'if a single semibreve [i.e. just one of a pair, not a 'lone' semibreve] is to be stemmed, as the moderns do in practice, then it seems less irrational to do this with the major or minor semibreve than the semibrevis minima'. Jacobus seems to recognize that the moderns need to caudate, but if they (regrettably) must do so, it would be more logical to mark longer notes [with downstems] than shorter ones [with upstems]. I see nothing that defines this as other than a practice of the moderns. Jacobus addresses the logic (or illogic) of their notational forms, while making it clear that he dislikes any kind of semibreve stemming (SM 7, ch. 36).
Desmond rightly emphasizes: 'The moderni were keen to stress the continuity of their theoretical model with the ars of the antiqui.' 55 Early ars nova theorists were accordingly eager to avoid or resolve controversy when claiming, as Muris did, that they were 'still following the paths of the ancients', a possibly disingenuous attempt to disguise innovation (and Muris admitted that some things in his Notitia were left implicit), but one that did not deceive Jacobus. But might we perhaps also see, in the Fauvel motets, a similar motive of leaving some novel things partly concealed, in minimizing the downstems placed on semibreves, both in number (and therefore in consistency) and in the sometimes near imperceptibility of the stems, so tentative that Apel, wrongly, took them to be later additions? Contemporary musicians looking superficially would see mostly stemless semibreves and perhaps be lulled into agreeing that the notational appearance of the old art was maintained. There is a general reluctance in music, even until the twentieth century, to overnotate things that would be self-evident to intended users, albeit underprescriptive by later standards for users with whom a common understanding no longer existed. In Montpellier's old corpus, and still in fascicle 7, the 'default' is that a chain of syllabic semibreves is to be parsed in groups of two per breve, but always in triple time, short-long. No dots are needed to clarify these semibreve chains because the default is established. Dots are only used in the main body of fascicle 7 for motets that mix threesemibreve and two-semibreve syllabic groups, and for 'Petronian' motets. 56 Stems were not necessary in music manuscripts so long as understood defaults applied to stemless evaluation (and even after stems were added, the defaults were for a while still largely adhered to); this would have been true of the 'Petronian' motets as well as those in Fauvel. It could be that notators of the new motets resisted the unnecessary overnotation in 53 'Tagged' is Desmond's term for stemmed semibreves, mostly downstems, as in Fauvel. See Desmond, Moderni, 136-41. 54 Zayaruznaya, 'Old, New', 108 n. 45: 'a downward stem on the longer semibreve would do the trick-he condones this practice in the following chapter'. 55  practical manuscripts of minim stems whose values they were nevertheless prepared to spell out in treatises, as understood defaults or for pedagogical reasons. 57 Like dots and the signs of musica ficta, stemming was at that stage an 'accidental' practice (explicitly so for Marchettus), not essential except to resolve ambiguity. Consistency is not to be expected.
Where present, the downstems in Fauvel, nearly all on first beats, are confirmatory of the defaults set out in the ars nova treatises, and consistent with later copies of those motets with upstemmed minims instead of downstemmed semibreves, showing that the defaults were widely understood. The inconsistent presence of these 'accidental' downstems leads Desmond to look for difference where none may have been intended, and to treat as erroneous that the same rhythm should be shown both with and without a downstem. She assumes that a downstemmed note is not merely long, but that it must be longer than any unstemmed note, rather than just confirming that it is not short; and that a downward stem would indicate departure from, not confirmation of, expected patterns; 58 it can do either. She wonders why CS3anon3 placed apparently redundant ascending stems on the semibreves of what was intended to show the default 'untagged' pattern; I read this as precisely an instruction for construing such unmarked semibreve strings. If this is the terminology of Muris and the Vitriacan ars nova treatises, if these defaults apply to unstemmed groups of semibreves in Fauvel, and if any 'tagging' of semibreves ('semibreves signata'), up or down, is a practice of the ars nova (as Desmond seems to admit on p. 136), with values corroborated by those treatises, what grounds remain for designating the notation of semibreves (let alone other features) in the Fauvel motets as ars antiqua?

UPDATED NOTATION
One reason for the downstemmed 'tagging' of first beats as long may have been to remind users that the expected Franconian preference for placing shorter notes first was no longer in effect. 59 The same misplaced expectation of consistency leads Desmond to find the notation of some of the Fauvel motets, including Garrit/In nova, ambiguous as to perfect or imperfect time, and thus to treat the later notational translations of these motets with explicit minims as possibly representing a change from the originally intended rhythm rather than a confirmation of it. 60 She carefully writes of ars antiqua 57 This mindset could also result from the principle that one should not do with more what can be done with less, documented in many forms from Aristotle onwards and common among 13th-c. scholastics. Jacobus's wording corresponds closely to Ockham's 'Frustra fit per plura quod potest fieri per pauciora', commonly known as 'Ockham's razor' (cf. Ockham, Summa Totius Logicae, i. 12, cited by Jacobus in SM 7, ch. 35, and by many other music theorists). Antonia Fitzpatrick, email to me of 30 July 2014, 'putting this idea together with one of Aristotle's best-known axioms … could potentially yield [variants of] the "frusta fit…" formulation for more than one theologian working independently'. Wegman cites Aristotle, Physics, 188a17-18. See the discussion in Zayaruznaya, 'Old, New', 132. 58 Desmond, Moderni, 138: 'Is it possible that [cited theorists] … mistakenly gave the same rhythm for both the tagged and untagged versions?' and 136: 'ad hoc tagging'. 59 There were no stems to guide the evaluation of the groups of 'up to 7' semibreves in perfect time in the Petronian motets in Montpellier. As Desmond says (Moderni, 138) older practice following Franco was to put shorter 'recta' breves and semibreves first. Yet the most advanced Fauvel motets are all in imperfect time, with some 'tagging' to confirm that longer notes are first. To quote Vitry from BAV 307: 'Item sciendum est quod, quando pro isto minimo tempore duae ponuntur semibreves, prima maior debet esse et nunquam secunda, nisi signetur, licet secundum artem veterem superius probaverimus quod secunda debet esse maior' (CSM 8, 29) ('Note that when two semibreves are placed in that minimum tempus, the first should be major and never the second, unless it is signed, although according to the old art we have proved above that the second should be major'). 60 'depending on whether one interprets the tempus of Garrit/In nova as imperfect or perfect', and 'possibly some ambiguity as to the division of the breve into two equal or three equal parts' (Desmond, Moderni, 153, 156). 'notation', and does not here go quite so far as to suggest that a motet qualifying as an ars antiqua 'composition' can become an ars nova work undergoing not only a change of notation but a change of rhythmic intent; she later comes close to doing so (and see below on Tribum). For Zayaruznaya 'the question "Is Firmissime/Adesto an ars nova motet?"' is best countered with the follow-up 'In which source?' 61 This would make the classification of the motet as a composition dependent on its notation. There are enough other revolutionary features about those motets, besides the notation of short values, to qualify them as ars nova compositions, not to mention their citation in treatises to exemplify ars nova practices. For Desmond and Zayaruznaya, the artes antiquae and novae are defined notationally, but it is a short and dangerous step from there to extend an ars antiqua classification to the motets themselves, setting a boundary between the old art and the new that is at odds with theory and practice c.1320.
Later copies of some of the Fauvel motets with explicit minim stems confirm that the treatise default readings of the unmarked semibreves in imperfect tempus were well understood by later musicians. Such updating seems to have started already in the 1320s, and corroborates the values of downstemmed notes as confirmatory of the defaults. The recently discovered BnF n.a.fr. 934 attests to such revision in the addition of minim stems to originally stemless semibreves. 62 Sometimes the retention of redundant dots betrays an origin in unstemmed semibreve groups. Explicit notation of minims in both older and newer motets only became essential (to avoid ambiguity) when composers began to extend their rhythmic vocabulary beyond the unstemmed defaults, though the defaults were still largely followed in practice. Desmond identifies the requirement for more advanced notational feaures as the time when 'composers actually began to compose motets in ars nova notation'. 63 It clearly makes sense to classify as ars nova notation the settled practice of the 1330s onwards, including minim stems, remote imperfection, minim rests, and more. Some compositions with other features described in the ars nova treatises, and which we know only in this notation, may or must have been composed and notated at an earlier stage. The period of notational transition represented by Fauvel in the late 1310s may well have been more gradual than the sharp black-and-white contrast between old and new promulgated by Jacobus in SM 7, which in turn has influenced modern scholars to adopt that polarization, drawn at various points depending on when they date SM 7. But in evaluating where Jacobus stands, we need to consider where he draws that line, even if for other historical purposes we might tell a slightly different story from his. His heroes, Franco of Cologne and Petrus de Cruce, worked only in perfect modus and tempus. Petrus's division of the breve into up to seven semibreves and that of an unnamed other in up to nine paved the way for what would later be known as perfect time and major prolation. If Jacobus was right to say that his approved 61 63 Desmond, Moderni, 147. She associates the treatise explanations of the evaluation for unstemmed semibreves with the antiqui, citing Johannes Wolf, 'Ein anonymer Musiktraktat aus der ersten Zeit der "Ars nova",' Kirchenmusikalisches Jahrbuch, 21 (1908), 33-8, but that only gives them for perfect tempus. It is the early ars nova treatises that give the evaluations for imperfect time. My view that these evaluations stood as a guide to singers in the early 1320s is not incompatible with Desmond's suggestion (p. 145) that they may have been 'a guide for copyists who wanted to "upgrade" motets copied in the older style' and that they stood as a guide to singers in the early 1320s.
antiqui were able to notate unambiguously without stems, they must have been following defaults that are clearer to us from Franco (the principle that three are equal but the last of two is longer) than for the 'Petronian' motets. The defaults that permitted unambiguous notation without stems in the Fauvel motets are different again, spelt out in treatises, using imperfect time, and placing longer notes first.

DUPLE TIME, LONE SEMIBREVES
It is in the cultivation of duple time that the Fauvel motets are most revolutionary. Jacobus devotes at least as much effort to castigating imperfection as he does to the notation of semibreves. Duple time in the more advanced Fauvel motets is generally regarded as a primary marker of ars nova, and a central plank of Jacobus's objections, but both Desmond and Zayaruznaya downplay this in favour of notational appearance, especially of semibreves. Desmond's theorists' examples are only for default values for what she calls the 'modal', i.e. unstemmed, semibreve groups according to the antiqui, and in table 4.3 (p. 132) the moderni, but only in perfect tempus. She does not give a similar tabulation of the theorists' prescribed defaults for the imperfect tempus prevalent in the early ars nova motets in Fauvel and beyond. There is more to ars nova than the notation of minim stems, but they are for Desmond a criterion for defining at least a first stage of ars nova. But the minim is already fully present in 1319 in the gradus system of the Notitia, contemporary with the completion of Fauvel, illustrated in chapter 5, described in words in chapter 4 ('caudata sursum'), and spelt out in the Conclusiones. 64 Jacobus objects to the use of a lone semibreve occurring in tempus perfectum when a breve is imperfected by a semibreve. 65 Because few extant new motets in perfect tempus date from the 1320s, there are fewer early opportunities for the breve thus to be imperfected. Vitry's Douce/Garison is one such; it is mentioned in early treatises and must date from the early 1320s, though preserved only much later in the Ivrea manuscript (Biblioteca capitolare, MS 115). The original notation of BnF n.a.fr. 934 includes many core features of ars nova notation; breves imperfected by semibreves in tempus perfectum; red notation; combinations of perfect and imperfect tempus. The semibreve rhythms (with groups separated by dots) remain within the defaults, as confirmed by the added minim stems and traces of some erased downstems. 66 It appears to date no later than the early 1320s. Imperfection of the breve by a semibreve is specifically permitted in the Conclusiones (but not referenced in Desmond, "'One is the loneliest number"') and already implicit in Notitia (book 2, ch. 6: 'distinctio perfecti secundum situm in quolibet gradu'). These instances, and the Muris redatings, should allay doubts as to whether Jacobus could have seen this usage before the 1330s. 67 64 It is present both conceptually and as a stemmed symbol. In case there is doubt about the status of the diagrams in later copies, it is also described as 'obtusiangula caudata sursum' (Michels,CSM 17,. 65  This last sentence takes us directly into the heart of the debate. Zayaruznaya cites this passage at the head of her article, taking it as a defence of a modernus; that Jacobus 'censured an unnamed teacher for incorrectly ascribing some notational doctrine [the use of duplex longs in ligature and/or imperfected by breves] to the ars antiqua but then partially acquitted him'. 69 In the continuation (perhaps tinged with sarcasm directed towards Vitry's stance) Jacobus refers to what he judges to be a modern misdesignation of ars antiqua. He here acknowledges at least two stages of moderns, of which the older 'new' may appear old by comparison with the newer 'new', but is still 'new'. Jacobus may have judged the Fauvel motets as older among ars nova works, but in no way would they have qualified as works of his approved antiqui either on compositional or notational grounds. If his older moderns were represented by the Fauvel motets of the late 1310s, of which Super/Presidentes, Firmissime /Adesto, Garrit/In nova, Tribum/Quoniam are named in treatises, the more recent moderns were the current perpetrators at the time he was writing, a few years later. He could have been reacting to 'confused' stems (perhaps like those in BnF fr. 571, erratic both in incidence and calligraphy), and possibly to enough advances for him even to have known a motet such as Vos/Gratissima, which may date from the later 1320s. 70 Both stages on this continuum of development are nova: both were new in their own time. Desmond (like Zayaruznaya, above, in 'And 68 SM 7, ch. 27. Translation adapted from Wegman, The Mirror of Music. The first part of this passage is discussed in Desmond, Moderni, 150. 69 Zayaruznaya,'Old, New', 95-6. In support of her much later dating of SM 7 she writes 'some doctrines that Jacobus would class as ars nova innovations could accurately be described as "old" at the time when he was writing', implying that although old, this was still for him modern, [early] ars nova; but then that 'if the ars nova emerged ca. 1320, can it really be that around 1330 the earliest doctrines of the moderni could be categorized, however mistakenly, as ars antiqua?' (pp. . Frank Hentschel, 'Der Streit um die Ars nova -nur ein Scherz?', Archiv f ür Musikwissenschaft, 58 (2001), 110-30, develops Jacobus's own characterization of SM 7 as a 'satirical and polemical work'. 70 In Moderni, ch. 6, Desmond gives an insightful discussion of this motet (which she dates in the 1330s; p. 202), with particular attention to the power of the dot to achieve 'transgression across a mensural unit'. See Desmond, Moderni, yet, perhaps the said teacher means by "old art" one that deals with the new manner of singing and notating') assumes that Jacobus's older stage here refers to the antiqui: 'When Jacobus critiques the Ars Nova, then, I suggest that his criticisms were aimed at post-Fauv theory and practice, the period for which I contend the current use of the term "Ars Nova" ought to be reserved.' 71 I think Jacobus means, rather, and satirically, that things are moving so fast now, in the 1320s, that what would have seemed new a short time ago is now considered old. In removing Fauvel motets from the early ars nova, Desmond and Zayaruznaya remove from that designation the earlier stage of moderni to which I suggest Jacobus was referring. Both look to a (later) period of explicit notation of minims with upstems before the term ars nova can apply. SUBTLETY The discussion of subtlety in Desmond's chapter 2 is eloquent and wide-ranging, with some fascinating testimony, often involving intergenerational criticism, and a thorough survey of positive and negative aspects of subtilitas. But in ranging so widely chronologically, it perhaps makes insufficient allowance for changes over time in what was considered laudably subtle at a particular date. It was not only 'in the middle decades of the fourteenth century' that 'subtilitas was a desired compositional aesthetic of the ars nova'. 72 References by Jacobus to subtlety are entirely positive. Citing Isidore, he favours the subtlety of soft instruments over the noise of 'tubarum, tympanorum et nakariorum' (SM 1, ch. 26). In SM 7, too, subtlety is overwhelmingly a positive feature; the moderns' claims of subtlety offended Jacobus because they did not conform to his conservative criteria. His criticisms of them seem to be directed not at actual subtlety as a negative trait, but rather at their misplaced claims of subtlety for innovations he disapproves of, as well as their habit of mistakenly crediting some of their innovations to the antiqui. Some of the longer explicits to the combined Notitia and Conclusiones hail Muris as very subtle: 'per magistrum Johannem de Muris musicum sapientissimum ac totius orbis subtilissimum expertum'. 73 Desmond takes a brave leap into medieval aesthetics by interpreting the judgement of the anonymous author of the late fourteenth-century Tractatus figurarum that a work she dates c.1350, Apta/Flos, was more subtle than a 'crude' one of several decades earlier, Tribum/Quoniam. 74 Here is the relevant part of the Prologue: Et licet magistri nostri antiqui primum intellectum musicalem habuerunt, et hoc satis grosso modo sicut adhuc patet in motetis ipsorum magistrorum videlicet Tribum que non abhorruit, et in aliis et cetera. Tamen ipsi post modum subtiliorem modum considerantes, primum relinquerunt, et artem magis subtiliter ordinaverunt ut patet in Apta caro. Sic nunc successive venientes, habentes 199 n. 5 for various datings. Its tenor was copied into Muris's notebook not long after 1330 (ibid. 198-9). For an earlier discussion of the dots in this motet, see Elina Hamilton, 'Philippe de Vitry in England: Musical Quotations in the Quatuor Principalia and the Gratissima Tenors', Studi musicali, ns 9 (2018), 9-45. For a complementary discussion of Vos/Gratissima, see Bent, Motet, ch. 8, which suggests a different reading of the dot and the parsing of the tenor and contratenor. It refers to other discussions of this motet, including questions of priority raised by the fact that its tenor is shared with Machaut's motet 17 and a motet in BnF n.a.fr. 934, fo. 79 r . 71 Desmond, "'One is the loneliest number"', 403. 72  et intelligentes que primi magistri relinquerunt maiores subtilitates per studium sunt confecti ut quod per antecessores imperfectum relictum fuit per successores reformetur. 75 Desmond applies 'grosso modo' directly to Tribum, first translating this as its 'plain manner', but soon shifting the translation to 'crude and unrefined', which makes the comparison unduly negative. 76 The tone of the passage seems more respectful to older composers than she suggests. But, in fact, 'grosso modo' does not apply as a descriptor of Tribum, but means something like 'by and large', 'in general', 'speaking loosely'. 77 Jacobus juxtaposes subtlety and 'grosso modo' with no connotations of crudeness: 'Et quia multum exquisita de hac loqui materia, quae subtilis est et pulchra, non habemus, breviter et grosso modo pertranseundo de unitate distinguimus et forma.' 78 (And since we have little to say about this subtle and beautiful material, we will run through a brief and approximate distinction between unity and form.) I therefore offer the following translation, with advice from Leofranc Holford-Strevens: Although our old masters had a basic musical understanding, as is by and large amply manifest in the motets of these same masters, for example Tribum que non abhorruit and other [similar motets], etc., yet after conceiving a subtler manner they abandoned the former [style] and organized the art more subtly, as shown in Apta caro. Thus, now, those coming after, having and understanding what the earlier masters left behind, [have achieved] greater subtleties through study, so that what was left imperfect by our predecessors may be reformed by their successors.
For this writer in the late fourteenth century, 'our old masters' now refer to composers of the Fauvel motets (for which I retain their early ars nova status), not the antiqui of Jacobus (Franco and Petrus). Oldness and newness move with time. Tribum was new and radical in its own time, a complex, original, sophisticated-indeed subtle-type of motet, and not only for its novel use of imperfect time. 79 A later writer was likely to find a motet of his own time subtler than an older one, although Tribum continued to be copied into the fifteenth century in almost as many sources as Apta. 80 Desmond makes no reference to an excellent discussion of subtlety in the later fourteenth century by Anne Stone, which takes the same citation from the Tractatus figurarum as its starting point and, as here, interprets 'grosso modo' as a harmless generalization. 81 Stone covers with greater precision many of the same issues Desmond addresses, including an engagement with Gü nther's ars subtilior. Desmond states (p. 36) that 'The focus of this chapter is not Gü nther's ars subtilior'; but she leaves the reader wondering how the mid-to-late fourteenth-century perception of musical subtlety she sets out so engagingly relates to Gü nther's proposal, given that all three authors take the Tractatus figurarum as a point of departure. Apta caro of perhaps c.1350 was 'composed in the modus subtilior' (p. 47). Does she propose to abandon or realign the term, having situated the fully developed ars nova closer in date to the phenomena associated with ars subtilior? Gü nther drew on precisely this passage and its description of Apta caro (which she dates c.1355) to define the beginning of what she dubbed the ars subtilior and the transition from ars nova, 82 whereas Desmond now treats Apta caro as the final arrival of fully fledged ars nova (as opposed to its early stages in the 1330s). She acknowledges that both Tribum and Apta have at various times been attributed to Vitry, but she does not evaluate his possible authorship in relation to the qualitative contrast alleged between the two motets. Tribum is judged unsubtle in comparison with Apta, which receives sensitive and interesting treatment.
In a particularly explosive outburst, Jacobus declares: 'Some moderns consider those singers crude, stupid, foolish, and ignorant who do not know the new art, or who sing not according to it but to the ancient; and they consequently consider the ancient art crude and almost irrational, the new, however, subtle and rational.' 83 Desmond compares the resonances of Jacobus's language here with that of the twelfth-century philosopher John of Salisbury, who reported how his moderni ridiculed the older teachers. She reports Jacobus's tirade thus: 'the moderni explicitly positioned the subtlety of their compositions against the crudity of the ars antiqua', directly followed by: 'Their compositions persuaded listeners through their delicate and finely crafted surfaces, as opposed to the direct and oppositional musical rhetoric of the older style exemplified in Tribum/Quoniam.' 84 But whose compositions? Which moderni? This leaps to a later generation of moderni and their compositions, presumably including Apta/Flos, as evaluated by the author of the Tractatus figurarum. Desmond now conflates Jacobus's statement about his moderns in relation to his antiqui with the stance of an anonymous author decades later, who is referring to a much later set of moderni for whom more subtlety is claimed than for Fauvel motets (Tribum and others), which by that time were 'old'. It is not Jacobus who cites (or would have regarded) Tribum as old-fashioned, but the later anonymous author who, as we have seen, did not dismiss Tribum as severely as Desmond claimed. Given a moving window of newness, the Tractatus figurarum's old masters include the Fauvel composers (a generation beyond Jacobus's antiqui), who are respected but can now be improved on in subtlety by a new generation of modern composers. That author praises his moderni, implying progress and improvement. Jacobus, on the other hand, writing much earlier, is hostile to his moderni. Their notational and compositional outrages (including features demonstrable in the Fauvel motets and described in the associated treatises) are contrasted unfavourably with his revered deceased antiqui (Franco and Petrus).
Desmond now seems (on the authority of the Tractatus) to claim Tribum and others like it (the Tractatus says 'Tribum … et in aliis et cetera') as compositions of the ars antiqua, thus taking a step beyond defining just their notation as ars antiqua. 85 85 Desmond, Moderni, 20: 'the ars nova critiqued by Jacobus probably dates somewhat later than current musicological narratives have tended to place it', and 'many of the motets that current musicological scholarship classifies as ars nova motets, at the time might not have been considered as being written in the new style' (singular again). status might apply compositionally to Garrit/In nova, 86 seeing its rhythm as potentially ambiguous, therefore not subject to the ars nova defaults, and possibly different in intent from its later transcriptions into 'fully fledged' ars nova notation; and this notwithstanding that it is named and its innovations described in early ars nova treatises. Zayaruznaya's similar verdict on Firmissime was noted above.
While 'fully fledged French ars nova notation' might reasonably be dated c.1330 or in the 1330s, to set it so late has implications for Desmond's dating of SM 7. 87 In line with the theorists' preoccupations, she has up to this point defined ars nova mainly notationally, in reserving Jacobus's ars nova for a settled post-Fauvel stage of notation with upstems for minims, which (along with late datings for treatises) she places in the 1330s. But then, in the subtlety chapter, having excluded the Fauvel motets from ars nova classification, together with the slippage from Jacobus to the later author of the Tractatus noted above, she adds an aesthetic dimension that I think proves to be the main fault line of the book. Desmond now says 'Jacobus must be referring to motets like Apta/Flos, and not motets like Tribum/Quoniam, when he reprimands the subtilitates of the moderni and their creation of many new and useless things'. 88 I have suggested above that it is not Jacobus's own identification of subtlety in the ars nova composers that he rejects, but their claims of subtlety, which he considers undeserved or inappropriate. But if Jacobus is writing in knowledge of motets datable to c.1350, this would bring her implied date for SM 7 forward by twenty years, to after 1350, in line with the new dating of SM 7 suggested by Zayaruznaya, based on her late datings of notational symbols, to the 1340s or 1350s. 89 Desmond's chronology here seems to imply incompatible things. First, as just noted, she still elsewhere mostly dates SM 7 to the 1330s, which she recognizes as the first stage qualifying as ars nova notation. Yet, she then wants to reserve the term ars nova for the fully mature 'subtler' ars nova of c.1350, simultaneously allowing the ars nova of Jacobus's moderni to be earlier and less developed (though still post-Fauvel) than the mid-century stage she now suggests as Jacobus's vantage point. But the incompatibility is removed if one recognizes Jacobus's ars nova as a period of notational experiment and uncertainty from the mid-1310s to the mid-1320s, not the more stable 1330s, let alone later.

THE 1320S
In order to give context to the new earlier datings set out above, I will now review briefly some of what we can know or surmise about this decade. Marchetto's Pomerium of c.1318-24 attests that French disposition of semibreves in imperfect time and the early use of stems were known outside Paris. Desmond mentions this, but not his distinction between Italian and Gallic practices. From Muris's statement in the Canones, and from the dates adduced by Witkowska-Zaremba, we can infer that Muris's Notitia (or Ars musica) of 1319 was followed by lively debates, completed with the Conclusiones in 1321, and followed by the Compendium in 1322 and the Musica speculativa in 1323, revised in 1325. 90 Although 86 Desmond, Moderni, 153; but defined as ars nova on p. 213. 87 'A date for Speculum musicae in the 1330s probably makes the most sense'; 'closer to c. 1330 or later' (Desmond,Moderni,28,33). Zayaruznaya, 'Old, New', 106, states: 'the idea of a Speculum musice completed in the 1320s or 1330s has outlived its usefulness'. 88 Desmond, Moderni, 68. 89 Zayaruznaya,'Old, New', 126. 90 Desmond, Moderni, 7 admits Muris was writing c.1320, but her later datings of some of his treatises and the Vitriacan witnesses are often open-ended and not strongly supported. Moderni, 28: 'Heinrich Besseler's dating of Notitia to 1321 [in MGG 1: Die Musik in Geschichte und Gegenwart (Kassel, 1949-86)] was based on Des Murs's statement in another work (on arithmetic) that "knowledge of the art of producing and notating music" became clear to him in the year 1321. But this a temporal connection between Jacobus and Docta sanctorum has been discounted, whoever formulated its musical strictures in 1324-5 already knew about recent innovations by the novellae scholae discipuli (disciples of the new school) who invent new notes that they prefer over those of the antiqui, who sing ecclesiastical chants in semibreves and minims and cut up melodies with small notes and hockets. 91 By the mid-1320s it must be the newer kinds of hocket that provoked objection, not the ars antiqua type, and certainly not the miserable hocket given as an example by Jacobus, who shows no knowledge of the ars nova hocketing first explored in the 1320s and consistent with the language of Docta sanctorum. 92 Few musical sources survive from what must have been a turbulent decade, with the notable exceptions of BnF fr. 571 and BnF n.a.fr. 934, noted above. As suggested already, lost sources may well have attested the proliferation of experimentation with stems and new note shapes that Jacobus abhorred, practices that had settled by the 1330s. Above all, Machaut is in some ways the elephant in the room; his formative years occupy a relatively minor role in Desmond's account. He must surely have been composing by the early 1320s, his twenties, possibly in notation that was editorially standardized before the earliest surviving copies in MS C (BnF fr. 1586) around 1350. Several motets have been dated in this decade on account of notational practices or mention in treatises, even if, like Douce/Garison, they survive only later. In one case, a motet has been dated on the basis of its topical text: Machaut's motet 18, Bone pastor, invites a dating of 1325; it honours a bishop of Reims who fell out with the canons following his enthronement in that year. Because the style and notation seem precocious for this early date, later proposals have been made. 93 Desmond has analysed the motet's advanced or controversial notational features (Moderni, 150), explaining them from Muris treatises that she dates to the late 1320s or 1330s, but which must pre-date even an early dating of the motet, for reasons now validated by Witkowska-Zaremba.
One of these features is notational imperfection by remote parts (non-adjacent values), and another is the ligation of a duplex long with a breve. Right at the beginning of the tenor of motet 18, a duplex long is imperfected from both sides by a breve rest and a breve (not in ligature), followed later by a breve in ligature with a duplex long, not imperfected. Both are outlawed by Jacobus. 94 David Maw points out that in an earlier rondeau by Adam de la Halle (Or est baiars), in a manuscript dated to the early 1290s, a duplex long is in ligature with a breve that imperfects it. 95 Remote imperfection is already explicit in the Conclusiones, but Desmond questions whether it was adopted by composers much before the mid-century, listing five French motets that she places around the middle of the century. 96 One of these is Apollinis/Zodiacum, which I date closer to 1330, in line with biographical data for the musicians named. 97 Desmond accepts the early date for the first section of motet 18, hypothesizing a revision of the reduced section from a more conservative earlier version, and that Jacobus could have known just its first, unreduced, section. 98 Single minim rests are not found in extant compositions until later, but there is a first time for everything, and I still think motet 18 could date from 1325. Internal evidence points to such a unified composition that I cannot accept Desmond's proposal that it was revised. 99 Dates in the later 1320s have been suggested for a number of other motets with complex but less controversial features; Vos/Gratissima has been mentioned.

JACOBUS, TERMINI POST AND ANTE QUEM
The works of Muris cited by Jacobus are datable to 1319-23, and it is likely that his Vitry citations are no later. It remains true, as Desmond and Zayaruznaya point out, that since a relationship to Docta sanctorum was removed, there is no external anchorage for a terminus ante quem for SM 7. 100 This does not mean there is no guidance; the absence of such a terminus does not license indefinite forward projection into the fourteenth century. Dating estimates often have to be made with limited anchorage points, depending on circumstantial evidence, internal clues, and common-sense judgements. Although a terminus post quem does not entail a terminus ante quem, the longer the gap between the last datable reference and the putative dating of the treatise, the more is credulity strained. All Jacobus's notated music examples are from antiqua practice before or around 1300, still fresh in his mind although their authors were dead. Nothing cited or criticized by Jacobus now has to be dated after the mid-1320s. His sources were apparently almost entirely in written treatises. He had probably seen notated music with stems he disliked, but he references no contemporary repertory. As he was so hotly exercised by current transgressions, it seems unlikely that his targets would have been frozen at a stage of development much earlier than when he was writing. Desmond recognizes that his moderni were then still active. 101 What counts as new depends on the location in time of the author at the time of writing, and that may turn out to be the strongest indicator for dating SM 7.
I am suggesting, then, that the first wave of ars nova composition in the Fauvel motets of the late 1310s corresponds to Jacobus's 'older' moderni. Although more outraged by imperfection, he still objects to any stemming of semibreves, even if Fauvel's lengthening downstems are less bad than the later upstemmed minims. The combination of Witkowska-Zaremba's tightening of the treatise dates and the explicit to the Compendium in BAV 1146 brings Jacobus's personal contact with Muris (and probably also Vitry) to an earlier date. It was suggested above that Jacobus was one of the principal critics of Notitia who prompted the clarifications of the Conclusiones in 1321. It was Witkowska-Zaremba's crucial revelation of his direct exchanges with Muris, written or oral, that prompted revisions to the Musica speculativa in 1325. This period of heated debate with his moderni, still relatively young men, is surely when Jacobus was motivated to embark on SM 7, rather than in the 1330s, or even the 1350s, the last decade of Vitry's life and possibly after Muris's death, by which time Jacobus himself may too have been dead and no longer in a position to call his friends 'young and clever'. We can now propose that SM 7 was conceived in the early 1320s, simultaneously with the treatises it criticizes, and its writing at least begun then.
It seems clear from his own comments that Jacobus had written the whole vast Speculum calmly over a long period of time until provoked by current debates to the polemics of SM 7. The proemium to the whole Speculum, presumably written last, states that the first six books deal with musica plana, of which the first five deal with consonances, the sixth with the modes or tones, and the seventh book with mensurable music, probably always his intention (he needed seven books for his acrostic, JACOBVS); but then also (perhaps by hindsight) that it addresses how some modern singers differ from the art of Franco. In SM 7, ch. 6 he writes, referring to Muris's Musica speculativa: 'These are the words of the teacher to which I think I would have responded earlier, in its proper place, and also to certain other things in that work, if I had seen it', i.e. if he had seen it at the time, in this case, when he was writing books 2 and 4 about the status of the fourth. 102 If indeed SM 1, ch. 22 refers to the Notitia, it must have been added during such partial revisions. 103 Given his close engagement with early debates, and without evidence of his continuing contact with later writings, SM 7 would seem to have occupied Jacobus in the middle years of the 1320s, with completion perhaps well before 1330. If some was written in the heat of those debates in the early 1320s, parts of the older, cooler Franconian reporting in SM 7 could have been drafted even earlier. In my view, for purposes of dating SM 7, the testimony to early direct engagement between Jacobus, Vitry, and Muris weighs more heavily than arguments that some of his references might apply to much later phenomena.

PLURAL ARTES NOVAE
At the heart of the matter is how the term ars nova can be applied. Whose ars nova? How many stages of newness? Desmond acknowledges multiple stages of ars nova: 'their ars nova may not be the same as Jacobus's ars nova, nor the ars nova claimed and celebrated by Jacobus's moderni, nor the ars nova outlined in the Vitriacan Ars nova witnesses'. 104 Zayaruznaya writes: 'It appears that what Jacobus calls "ars nova" stretched across several generations of theorists and encompassed several waves of theory' and 'The possibility of radically different interpretations of ars nova chronology is a function of the paucity of sources, theoretical as well as practical, that can be confidently placed between the Roman de Fauvel and the early Machaut manuscripts at mid-century.' 105 And yet, both Desmond and Zayaruznaya seem to be in quest of a single ars nova. They constantly refer to 'it' in the singular (e.g. Moderni, 16: 'an aesthetic of the ars nova') and want to accord the dignity of the term and the stage that Jacobus knew to a single (late) stage in what was a constant evolution of musical styles, techniques, and notation through multiple waves or layers of newness, to a moment when everything was in place, both theoretically and in notational usage. 106 For Desmond, that stage is the Libellus of the 1340s, and compositions of the mid-century when 'fully fledged' ars nova notation was in place. Zayaruznaya takes this stage as a terminus post quem for SM 7, while Desmond mostly dates it earlier, in the 1330s, despite claiming that Jacobus 'knew' motets like Apta caro of c.1350. Her opening abstract begins: 'Music theorists labelled the musical art of the 1330s and 1340s as "new" and "modern"'; these terms reflect her late datings of the Muris and Vitry treatises and SM 7; but it is around 1320 that the innovations of the late 1310s were regarded as 'new'. The debates of c.1320 had cooled two or three decades later, to the point where the concept of 'ars nova' is no longer used in treatises such as Omni desideranti and Libellus. But each stage of newness was nova in its time, which should relieve the pressure to seek one defining moment of ars nova as the fullest realization of its notational and compositional potential. Ars nova will obviously continue as a general term to refer to evolving styles and notations in the fourteenth century, but always understood as a moving window.
Having headed this article with quotations from Jacobus, I end by paraphrasing and extending Muris's introduction to the Conclusiones: I hope that my arguments might persuade those who dispute earlier opinions. For this reason, more from love of the disputants than to criticize them, I hope to have reached some conclusions regarding which there has now arisen considerable controversy. I propose, for the sake of peace, that most of these arguments could disappear if we abandon the search for a single moment that fully deserves to be crowned as 'the' ars nova, and recognize instead multiple waves, artes novae, a moving window of newness and subtlety, as both Desmond and Zayaruznaya also allow. If, as Desmond shows, Jacobus was thinking of musical structures hierarchically in terms of trees, Muris with the new art was thinking of points along a continuum, instantiated in her insightful discussion of the dot as an agent of rhythmic subtlety. Perhaps we should adjust our view to such a continuum rather than trying to define which single point along it deserves a label that shifted with time to apply to many stages of development. There is much of importance and interest in the work of Desmond and Zayaruznaya that I have not discussed here. Rather, I have addressed the challenges to existing chronologies posed by their close scrutiny of difficult texts, and offer a revised chronology as a basis for the fresh evaluation they invite. 106 Desmond, Moderni, 133: 'fully fledged French ars nova notation such as perfect and imperfect semibreves and altered minims and semibreves'. Desmond downplays several features that were already implicit or explicit in the Notitia/Conclusiones of 1319/21-the breve imperfected by the semibreve, semibreve by minim, the altered semibreve, and prolation as later defined are arguably already implicit in the gradus system in the Notitia. 1336 is generally reckoned to be the first statement of the fully theorized prolation system, but not from a known centre such as Paris; Petrus dictus palma ociosa was a French provincial Cistercian who defines modus, tempus, and prolation as if they had been in use for some time. (Zayaruznaya,'Old, New', 135: 'The fully theorized system of major and minor prolation that stands behind the copious examples in Petrus's 1336 Compendium de discantu mensurabili confirms the impression that by the early 1330s the possibilities afforded by the theorizing of the previous decade were beginning to be worked out in practice'.)