Meyer, Christian : De Synemmenis and its Tradition: Contribution to the Study of Monochord Measuring Towards the End of the Thirteenth Century


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Meyer, Christian : De Synemmenis and its Tradition: Contribution to the Study of Monochord Measuring Towards the End of the Thirteenth Century
   Notes et documents 1** *  DE SYNEMMENIS  AND ITS TRADITION:CONTRIBUTION TO THE STUDY OF MONOCHORD MEASURINGTOWARDS THE END OF THE THIRTEENTH CENTURYThe division of the monochord was probably among the most fertile and richlyimaginative areas in medieval music theory. In 1953 Smits van Waesberghe hadidentified seventeen different procedures based on 71 measuring methods compiledbetween c 850 and c 1200, transmitted in a corpus of altogether 107 witnesses. 1 Theappearance of RISM B III, the still ongoing manuscript inventory of medieval musictheory, and the expansion of its chronological range to c 1500, bring the corpus of authorsto a total of about 180, and prompt a review of that typology.Unlike other areas in Medieval musical pitch theory, 2 monochord measurement hasremained significantly underexplored, despite important work done in recent years. 3 Thisneglect may be due in part to the tentative nature of studies devoted to the srcins anddevelopment of the medieval pitch system, but also to a prejudice, not wholly unjustified,against the hegemony of the Medieval Pythagorean system. Nevertheless, MichaelMarkovits’s study of the srcins of the pitch system, and of the scales in the Carolingianand Ottonian periods, has offered a wealth of perspectives that bring home the centralimportance of monochord measurement to that system. In particular, it has allowed us tosee more clearly the relations between procedures of string division, on the one hand,and, on the other, such decisively important theoretical models as scale construction(tetrachordal or heptatonic) or the theory of modal octaves. It has also affirmed themonochord’s fundamental role, not only in music pedagogy, but also more generally inthe physical, geometric, and sometimes mathematical approaches of the pitch system, andtheir practical implications in the determination of organ pipe measures or the weightproportions of bells. The following observations regarding the « monochord of   ficta steps » will provide one sample of the theoretical implications of monochord division.The chronological boundary of 1200 adopted by Smits van Waesberghe was based onthe view that procedures of monochord division had exhausted themselves after that date. 1 J. Smits van Waesberghe,  De musico-paedagogico et theoretico Guidone Aretino eiusque vita et moribus (Florence, 1953), pp. 151–185. 2 J. Smits van Waesberghe, Cymbala. Bells in the Middle Ages (Rome: American Institute of Musicology, 1951;  Musicological Studies and Documents , 1); Klaus-Jürgen Sachs,  Mensura fistularum. Die Mensurierung der Orgelpfeifen im Mittelalter  (Stuttgart, 1970). 3 Particularly the studies by Cecil Adkins, The Theory and Practice of the Monochord  (Ph.D. diss.,University of Iowa, 1963; also, by the same author, « The Technique of the Monochord »,  Actamusicologica , XXXIX [1967], 34–43) and Michael Markovits,  Das Tonsystem der abendländischen Musik im frühen Mittelalter  (Bern: P. Haupt, 1977; Publikationen der schweizerischen musikforschendenGesellschaft  , Series II, vol. 30). [83][84]  2  Revue de Musicologie, 76/1 (1990) This view calls for a reconsideration. The  Musica speculativa (1323) by Johannes deMuris, 4 and the Parvus tractatulus de modo monacordum dividendi (1413) byProsdocimo de Beldomandi, 5 demonstrate that the monochord remained in use both as apractical tool and as a research instrument, and that it continued to claim the attention of theorists engaged in reflection on the pitch system. Moreover, one can observe aresurgence of interest in the monochord in the last third of the thirteenth century, aswitnessed by the measuring method offered in Sequitur de synemmenis , 6 a treatise inwhose tradition Prosdocimo’s Tractatulus actually situates itself.The measuring method de synemmenis proposes two monochord divisions. The firstyields the intermediate steps between F and G, c and d, G and a, D and E, b mollis and b quadratus , as well as their octaves within the scale Γ – e e . These steps are generated bymeans of successive ascending fifths starting on B in the first octave; their octaveequivalents are obtained through division or multiplication. The second division producesthe same steps (between D and E, G and a, C and D, F and G, and their octaves), but bymeans of successive ascending fourths starting on b mollis . This particular method of establishing  ficta steps is not known to us from any other treatise.  De synemmenis is transmitted in two manuscripts that were once kept at theBenedictine Abbey of Bury St Edmunds. 7 Its transmission history is of some interest andmerits a brief review. In both of its sources,  De synemmenis is copied as a sort of appendix directly after the well-known treatise by Anonymous IV. Its dependence on thislatter treatise is made explicit by the incipit « Sequitur », which is attested in bothsources. Anonymous IV, as well known, was directly acquainted with music teachingtraditions at Paris. According to F. Reckow, he was probably a master from the Parisianenvironment who was familiar with the teachings of Johannes de Garlandia. 8 His treatise,Reckow suggests, was written for the use of English students, and must have been puttogether some time after the compilation of Franco’s Compendium , which according torecent research 9 is datable around 1280. In the light of all this, one cannot helpwondering: is there any possibility that the treatise  De synemmenis , despite itsexclusively English transmission, was the product of Parisian teaching traditions as well?The Bibliothèque nationale at Paris keeps, under the call number Lat. 18514(abbreviated hereafter as P), a manuscript that srcinally belonged to the library of the 4 For the transmission history of this treatise, see U. Michels,  Die Musiktraktate des Johannes de Muris (Wiesbaden, 1970;  Beihefte zum Archiv für Musikwissenschaft  , 8), pp. 17–24. Ms. ElzbietaWitowska-Zaremba (Warsaw) is preparing an edition of version A of this treatise. 5 Prosdocimo de’ Beldomandi,  Brevis summula proportionum (…) and Parvulus tractatulus de modomonacordum dividendi , a new critical text and translation (...) by Jan Herlinger (Lincoln, London:University of Nebraska Press, 1987; Greek and Latin Music Theory ; see the review of this edition in  Revuede musicologie , 73 [1987], 270–271). 6 Ed. Jan Herlinger, op. cit. , pp. 123–135. 7   GB LBl Royal 12 C. VI, fols. 80 v –81 v , Cotton Tiberius B. IX., fol. 224 r-v . 8 Fritz Reckow,  Der Musiktraktat des Anonymus 4 (Wiesbaden, 1967;  Beihefte zum Archiv für  Musikwissenschaft  , 4 and 5), II, pp. 1–22. See also Max Haas, « Die Musiklehre von Garlandia bisFranco », Die Mittelalterliche Lehre von der Mehrstimmigkeit  (Darmstadt, 1984; Geschichte der  Musiktheorie , ed. Frieder Zaminer, 5), p. 100. 9 Cf. Wulf Arlt and Max Haas, « Pariser modale Mehrstimmigkeit in einem Fragment der BaslerUniversitätsbibliothek », Forum musicologicum. Basler Studien zur Musikgeschichte , I (1975), p. 233. [85]   Notes et documents 3Collège de Navarre. 10 This volume contains two texts: Boethius’s  De institutione musica  (f. 1-85 r ), 11 and a treatise that brings together elements of both « speculative » music andplainchant (f. 85 r -94 r ). 12 This second treatise is copied directly after the  Musica of Boethius, and fills out the last gathering. 13 The manuscript as a whole appears to be thework of a single scribe. The volume has been dated variously in the thirteenth century(Royer, RISM A III 1 ) and the fourteenth (L. Delisle; C. M. Bower 14 ). Both the decoration(f. 19 v , 29 v , 30, 51 v , 81 v ) and the script suggest a date in the first third of the fourteenthcentury. According to C. Bower the manuscript was probably copied in SouthwestFrance, possibly after an examplar from Normandy. The ex libris is comparatively late(towards the end of the sixteenth century), and we cannot be certain that the volume waskept at the Collège de Navarre during the fourteenth century. 15  The second treatise is headed by an inscription in red ink, in which the contents areexplicitly linked to the preceding  De institutione : « Tractatus de musica collectus ex hiisquae dicta sunt a Boetio supra atque declaratio musice practice ». This Tractatus demusica , then, consists of a « musica speculativa » and a « musica practica ». The first« speculative » part includes a general classification of music, a definition of the diatonic,chromatic, and enharmonic genera, a short treatise on proportions, another on specificallymusical proportions, and finally a treatise setting forth three monochord divisions. It isthis latter treatise that will concern us here. The second « practical » part continues withthe study of the monochord and successively expounds the principles of alphabeticnotation, the « proprieties of the voces » (the three positions of the hexachords), the« diastematisation » of pitch heights, the theory of  mutatio , and finally the theory of intervals. 10 Its provenance is attested by an ex libris from the late fifteenth or early sixteenth century: « Prolibraria Regalis collegii Campaniae alias Nauarrae parisius fundati » (f. 94 r ). Cf. H. Omont, Cataloguegénéral des manuscrits français. Ancien petit fonds français , III (Paris, 1897), p. 411, no. 95. 11 The copy of   De institutione musica by Boethius ends with the words: « uero ut in diatonicisgeneribus nusquam vna. LONGOBARDORVM invidia non. Explicit MVSICA ». The same tag« Longobardorum invidia non » is found also in the Bruges manuscript directly after the « regular » explicit(Bruges, Bibliothèque publique, Ms. 531; 11th c.) where it was added at a later point (?13th c.). Cf. RogerBragard, « Boethiana. Études sur le  De Institutione Musica de Boèce »,  Hommages à Charles Van Den Borren (Antwerp, 1945), 84–139, cf. p. 123. 12 Cf. RISM B III 1 , pp. 124–125. Léopold Delisle,  Inventaire des manuscrits latins (...) numéros16719–18613 (Paris, 1871), p. 100. Louis Royer, « Catalogue des écrits des théoriciens de la musiqueconservés dans le fonds latin des manuscrits de la Bibliothèque nationale »,  L’Année musicale , III (1913),239–240. 13 The manuscript is made up of eight senios: f. 1-12, 13–24, 25–36, 37–48, 49–60, 61–72, 73–84, 85–94 (VI-2). The gatherings are marked: a b c d e f g j [!]. 14 Calvin M. Bower, « Boethius  De institutione musica : A Handlist of Manuscripts », Scriptorium ,XLII/2 (1988), 205–251, esp. p. 236. 15 The Collège de Navarre, second in importance after the Sorbonne, and seat of the French nation,was founded in 1316. The oldest catalog of the library of the Collège de Navarre dates from the seventeenthcentury (and is devoted only to French manuscripts). Cf.  Bibliothèques de manuscrits médiévaux enFrance , A.-M. Genevois, J.-F. Genest, A. Chalandon (Paris: C.N.R.S., 1987), pp. 165–166. On the Collègede Navarre in the fourteenth and fifteenth centuries, see Gilbert Ouy, « Le Collège de Navarre, berceau del’humanisme français »,  Actes du 95 e Congrès national des Sociétés Savantes (Reims, 1970) (Paris, 1975),vol. 1, p. 276–299, and Isabelle Chiavassa-Gouron,  Les lectures des maîtres et des étudiants du Collège de Navarre: un aspect de la vie intellectuelle à l’Université de Paris (1380–1520) , Thèse de l’École Nationaledes Chartes, Paris, 1985. Cf. École Nationale des Chartes. Positions des thèses (...) de 1985 (Paris, 1985),pp. 31–37. [86]  4  Revue de Musicologie, 76/1 (1990) The Tractatus is known to us from two other manuscript versions; I speak of « versions » since there are numerous variants which indicate that we are not dealing withcopies stricto sensu . Yet the connection between the three sources is indisputable. Thetwo other sources are the following: 1.  Rome, Biblioteca Vaticana , Vat. lat. 5325 (abbreviated below as V 1 ). Parchment; 30 folios;137–139 × 91 mm; early fourteenth century (according to B. Bischoff); French srcin. 16 In thissource, which is roughly contemporary with the manuscript in the Bibliothèque Nationale (lat.18514), the treatise is followed by a copy of Johannes de Garlandia’s De mensurabili musica (f.12–30 v ). The text that concerns us here appears on f. 1–11 v :1 r : « Mvsica est ueraciter canendi scientia... » 9 v : « ... et sic omnes consonantiae in infinitumpossunt ascendere ».10 r : « Super sonum datum ascendere semitonium et ab eodem alium at similiter descendere… »11 v : Expl. « ... Ascendere dyapason descendere ditonum cum diapente etc. et similiterdescendere ».2.  Rome, Biblioteca Vaticana ,  Barb. lat. 307  (abbreviated below as V 2 ). Parchment; 33 folios; c 270 × c 308 mm; late fourteenth century; Italian srcin. 17 The concordant text has beenassociated with the  Ars nova by Philippe de Vitry.17 r : « Musice tria sunt genera: mundanum, humanum et instrumentale... «20 v : Expl. « ... sicut maius tempus perfectum. Explicit ars nova magistri philippi de vetri. deogratias amen amen amen ». The scope of this enquiry does not permit us to deal in depth with this text and itstransmission. Yet we may take it as accepted that Philippe de Vitry was not the author.There are two reasons for this: first, the earliest sources P and V 1 were probably copiedbefore Vitry was active as a theorist; second, the other two sources for the  Ars nova ( F Pn  7378A, f. 16 v –62 [fourteenth century] and GB Lbl Add. f. 1–6 [ c 1400]) do not containthis treatise at all. On the other hand, the section « Scientia est cognitio rei sicut est... »,which is found exclusively in the P version, was cited by Hieronymus de Moravia, whoattributed it to Johannes de Garlandia. On the basis of this citation, E. Reimer has broughttogether a range of indications which justify extending the attribution to the treatise as awhole. 18  A study of the measuring methods in P adds a further element to Reimer’s hypothesis.The version P does in fact contain three methods, 19 of which the last allows the derivationof   ficta steps by means of a procedure comparable to those in  De synemmenis . Given that  De synemmenis appears to be part of the treatise by Anonymous IV, an author whoprobably had received direct instruction in the theory of Garlandia, this « concordance »[in measuring methods] strengthens the possibility of Garlandia’s authorship of the Pversion. This new indication seems all the more compelling since the Parisian DominicanHieronymus of Moravia gives a reading very close to the completely srcinal definition 16 Description of the manuscript in Erich Reimer,  Johannes de Garlandia: De mensurabili musica  (Wiesbaden, 1972;  Beihefte zum Archiv für Musikwissenschaft  , 10 and 11), vol. I, pp. 18–19. See alsoRISM B III 2 , pp. 100–101. 17 See the description by Pieter Fischer in RISM B III 2 , pp. 102–103 and Gilbert Reaney, André Gillesand Jean Maillard, Philippi de Vitriaco Ars Nova (American Institute of Musicology, 1964; Corpusscriptorum de musica , 8), pp. 10–11, siglum V. 18 Reimer, op. cit. , vol. I, pp. 4–10. 19 The version V 1 lacks a folio which probably contained the measuring method or methods. Theversion V 2 transmits only the second of the three methods of P.   Notes et documents 5of the « synemmenon » in the Tractatus de musica , 20 which strengthens the hypothesis of Continental (specifically Parisian) provenance of   De synemmenis .The chapter devoted to the monochord is preceded by a long introduction whichdeals, on the one hand, with the complementarity of the intervals that constitute theoctave, fourth, major third and whole tone, and, on the other, with the diatonicconstruction of the monochord. This second part is based on an approach that is bothtetrachordal and octochordal (or heptatonic). The author distinguishes three « orders »that correspond, respectively, to the octaves Γ –G and G–g and the steps g–d d .Nevertheless, the internal articulation — which will require the procedure of monochorddivision — follows a tetrachordal composition built on an ascending TTS tetrachord. Thefirst « order » consists of two conjunct tetrachords TTS ( Γ –C, C–F) plus a whole tone(F–G), thereby realising the octave construction « bis diatessaron cum tono » (which isprecisely one of the theoretical premises of the introduction in question).Yet it seems that the author of this text was also familiar with a more sophisticatedapproach to the pitch system. The three manuscript versions of the introduction all agreeon a curious phrase that appears again and again in the text (« usque ad .xii.d. »), andwhich the editors of the  Ars nova (CSM 8) chose to emend to « .viii.G. » and « .xv.g. »The text is as follows: Item si uis super lineam datam constituereomnes proporciones musice secundumdiatonicum genus, primo ponendus est tonusdeinde alius tonus postea semitonium etc. usquead .xii.d.If you wish to mark on a given line all the musicalproportions according to the diatonic genus , thenyou must first write a whole tone, then anotherwhole tone, then a semitone, and so forth until.xii.d. If we are to assume that « .xii.d. » signifies the twelfth step of the scale, that is, « d »[counting from Γ ], then the expression makes little sense here, all the more so as the verysame expression is used in connection with the second « order » (G-g). The unanimousagreement between the sources should surely persuade us rather to keep the text and torevise our interpretation instead.As it happens, the expression takes on a very precise meaning if we interpret the letter« d » as an abbreviation of « diesis » Thus the author could have indicated that oneproceeds by juxtaposition: tone – tone – semitone, until the number of  diesis has reachedtwelve. The issue of the subdivision of the tone was in fact addressed quite frequentlyfrom the last third of the thirteenth century onwards, and the concepts of  diesis  ( semitonium minus ) and apotome ( semitonium maius ) are entirely relevant and testify tothe attentive reading of Boethius’s  De institutione musica . 21 An important humanist 20 Cf. Tractatus de musica compilatus a fratre Jeronimo Moravo... , ch. 23, ed. Cserba, pp. 172.29–173.3. Esther Lenaerts-Lachapelle, Guy Lobrichon and Marcel Pérès are currently preparing a new editionand translation of this text. 21 Especially III, 5 (division of the whole tone according to Philolaus). This chapter was known toHieronymus de Moravia ( Tractatus , ch. xv, cf. CS I, p. 32 a–b), yet does not seem to have been read againuntil after the second half of the thirteenth century. It is not yet encountered among the excerpts fromBoethius compiled by Vincent of Beauvais in his Speculum doctrinale . On the other hand, Uguccio of Pisadid know the theory, for he wrote the following under the entry « Tono » in his  Derivationes : « … Itemponitur semitonus et semitonium non plenus tonus sed est maius et minus semitonium minus appellaturlima uel diesis, maius aphotonie [!] et dicitur [aphotome] quasi decisio quia cum f’e (?) accedat ad tonum.accedit tum ab integritate toni. lima uel diesis dicitur quasi corruptio quia fit cum quodam planctu uelplausu sed haec melius in philosophia distinguntur » (after Strasbourg, Bib. Nat. et Univ., Ms. 11, fol. [87]
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