THE DE M‘JSiCA E‘QENSURABEU POSHKJ OF IDHANNES DE GARLANDIA: TRANSLATION AND CGMMENTARY Bissefization for the Degree of Ph. D. MECHEGRM STATE "JE‘H‘JERSEW CHARLES STEPHEN LARKGWSKI 1977 This is to certify that the thesis entitled THE DE MUSICA MENSURABILI POSITIO OF JOHANNES DE GARLANDIA: TRANSLATION AND COMMENTARY presented by Charles Stephen Larkowski has been accepted towards fulfillment ' of the requirements for __P_1L._D_._degree in Musicology QerLQ~Sf Major professor Date August 124 1977 0-7639 .. —— —-<.p—.—.~'u—. .—-..- ‘ . W: cm: LIBRARY Michigan State University In the : ::;5:IU£E Vials :fEi‘ it “*STA for s," W a.” J e‘k L ‘xl a, 55‘ . Laue lacks «‘Me ‘- ‘~~:~cus V‘I CIp~¢ y‘rn t: a ‘a 5““. 9‘ 3‘35! t‘wgs I" C I «:3 in t ‘ l'r ‘ 7. 1 N‘ 3 C "51‘ ‘L§ es»: 5‘ m‘ h "313:” ABSTRACT THE DE MUSICA MENSURABILI POSITIO OF JOHANNES DE GARLANDIA: TRANSLATION AND COMMENTARY BY Charles Stephen Larkowski In the mid-thirteenth century, modal notation of discant and organum was fairly uniformly established; a system of mensural nota- tion for syllabic music was emerging, but was as yet unstable. Within a framework of common concepts there were many differences of detail. Thus, a complete knowledge of this notation is possible only through a thorough study of all the individual treatises. The major theorists of the thirteenth century before Franco of Cologne include Walter Odington, Magister Lambertus, Anonymous IV, Anonymous VII, and Johannes de Garlandia. The treatises of these men all concern the same material, but they often differ in emphasis. Anonymous IV, for example, concentrates a great deal of his attention on rhythmic values of ligatures in non-modal contexts, a subject dis- cussed much less extensively by Garlandia. Odington gives complete examples of the hocket, rondellus, and copula, whereas Garlandia and Anonymous IV a tteorists spea are a few of tj of the time. Th Di “039 the more tin of both me; PCIEThOnic gene; Zi‘c‘w DVQ‘A», and a his”. A‘:~ "we of the 32:: ' . D} recent 57 - v ”s -:erls tra.s~ - :‘J s‘h‘Cr ‘ of part ‘9» Charles Stephen Larkowski Anonymous IV are content with verbal description. While most of these theorists speak of six rhythmic modes, Lambertus admits nine. These are a few of the many variations to be found in the theoretical works of the time. The De musica mensurabili positio of Johannes de Garlandia is among the more comprehensive of these treatises. It explains the nota— tion of both melismatic and syllabic music, and discusses all the major polyphonic genera then used. There are numerous examples of two—voice discant, and a section on consonance and dissonance. Thus, this work is both speculative and practical, and is an important part of our knowledge of the thirteenth century. However, it has not been dealt with by recent scholars in a comprehensive way. Except for Luther Dittmer's translation of Anonymous IV's treatise and Jay Huff's trans- lation of Part VI of the treatise by Walter Odington, the theoretical writings of the thirteenth century are unavailable in English, and only small portions of them have been commented upon in present-day scholarly research. This study includes an English translation of the Positio with transcriptions of examples where appropriate, placed alongside the Latin text; chapter-by-chapter commentary; and complete transcriptions of three representative examples of thirteenth-century pOlyphony. The cementary str‘ l l ‘ esgecially the: Just a: 1 all the various Pertise in med; 11 their entire end so it remair in ‘ ¢ ‘Ih. ' ' I re a’allahil-‘H. V A ‘m . inleuge be Com Charles Stephen Larkowski commentary stresses points of comparison with contemporary treatises, especially those of Anonymous IV and Walter Odington. Just as theologians develop a concept of theology by studying all the various books of Scripture, so musicologists must develop ex- pertise in medieval notation by examining all the pertinent treatises in their entirety. The student of the Middle Ages must not be content merely to sample the primary sources of our historical understanding, and so it remains for musicologists to complete this work by dealing in a comprehensive way with each of the treatises in turn. Only with the availability of this entire corpus of theoretical writings can our knowledge be complete. THE DE MUSICA MENSURABILI POSITIO OF JOHANNES DE GARLANDIA: TRANSLATION AND COMMENTARY by Charles Stephen Larkowski A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Music 1977 bl” “ll? ‘1 g 10'7079 C) Copyright by Charles Stephen Larkowski 1977 ii ACKNOWLEGEMENTS Appreciation must be expressed to Professor’ Richard E. Klausli, whose assistance in the preparation of this dissertation was indispensable; and sincere thanks also to the other members of the Guidance Com— mittee, Professor Theodore Johnson, Professor Russell Friedewald, and Professor David Liptak, for many valu- able suggestions. Finally, gratitude is due to Pro- fessor Richard E. Sullivan for serving as representa- tive of the College of Arts and Letters at the final examination. iii :rmoucrron. o VPEIQIX I INTRODUCTION. . . . . DE MUSICA MENSURABILI COMMENTARY. . . . . . APPENDIX I. C O O O 0 APPENDIX II 0 C O O O BIBLIOGRAPHY. . . . . TABLE POSITIO: OF CONTENTS TRANSLATION iv Page 128 189 211 221 The t. de Garlandia a Of these, Ema They are relat Dedes and the: smailic notat w! 15th the Tractatu S INTRODUCTION The treatise on mensural music generally attributed to Johannes de Garlandia appears in three versions in the medieval manuscripts. Two of these, Bruges 528 and.Rome, Vaticana 5325, are nearly identical. They are relatively short and.include explanations of the rhythmic modes and their notation as well as a particular form of prefranconian syllabic notation. A third.version, entitled De musica mensurabili positio, is the object of this study. It appears as an insertion in the Tractatus de musica-ofnJerome of Moravia, along with the anonymous Discantus positio vulgaris,.the Ars cantus mensurabilis.of Franco of Cologne, and the Musica mensurabilis of Petrus Picardus. This version is much longer than the others. The first chapter of the Positio con- tains several interpolations, mostly concerned with general terminology; the second chapter is much the same in all three versions; the third through the eighth chapters also correspond closely with the other versions, but there is considerable variation in the placement of chap- ter divisions. The shorter versions and with the discussion of rests, but the Positio has five more chapters: two on consonance and dissonance; a long chapter on discant, including illustrations of all possible modal combinations;.and-separate-chapters on organum triplum and organum. guadrgplum. .The.finalitwo.chapters andthe interpolated parts of the first are probably spurious. The.literary style changes significantly in the last chapters, which.are in many respects nearly unintelligible. A significant portion of these sections is, however, similar to corre- sponding parts of the.treatise of Anonymous IV, suggesting borrowing on the part of the.copyist.-.(For a detailed comparison of the contents of these treatises, see Rudolph A. Rasch, Johannes de Garlandia, 1969, pp. 7-24.) The identification of Johannes de Garlandia has been a diffi- cult problem. The author.of the musical treatise is generally identi- fied as a grammarian who was born in England around 1195, and who was later a member of the faculties of the Universities of Paris and Tou- louse. His surname probably came from the clos de Garlande, a Paris district which included part of the University. This person is known to be the author of several works in verse and prose, including a word- list, the Dictionarius; a didactic poem on the proper behavior of uni- versity students, the Morale scholarium; a long poem which is essen- tially an apology for the.crusades, the De triggphis ecclesiae; and several treatises on rhetoric and metrics. A more complete account of the works of Garlandia and the problem of identification can be found in.The Life and:Works of John of Garland by Louis J. Paetow (Memoirs of the University of California, Vol. IV, No. 2, 1927, esp. pp. 83-148). There is little indication in the authenticated works of Gar— landia that he had any special expertise in music other than that at- tained by any student of the liberal arts. Also, though there are nu- merous cross-references to other works,.there is no mention of any mu- sical treatises. The relatively plain literary style of the musical treatises generally attributed to Garlandia bears little resemblance to the rhetorical diction of the other writings, but the method of presenta- tion employed often bears the marks of a scholasticism that approaches the sophistic. Thus, any attribution is problematic, but of the many treatises on music which have been ascribed to him, some may definitely be dismissed. These include the Introductio musicae planae secundum J ohannem de Garlandia and the Optima introductio in contrapunctum, as well as ascribed quotations in treatises by Robert de Handlo and Johannes Hanboys. This leaves the De musica mensurabili and De musica plana, found side by side in the above-mentioned Vatican manuscript. The Others include notational features which could only date from the four- teenth century, and this has led Coussemaker and others to postulate the EXiStence of a Johannes de Garlandia the Younger. There is, however, no further evidence for the existence of such a person, and so it seems likely that the ascriptions were made simPly for reasons 0f authority, a Practice comon enough at the time (see Gustave Reese, Music in the W, 1940, p. 287). This study includes a Latin text and a translation of the Posi- tio. The Latin is.essentially.the.rendition.of.Coussemaker (Scriptorum de musica medii aevi, I, pp. 97-117),.but it includes many changes in- corporated from the edition of the Tractatus de musica published by Simon Cserba (Hieronymus de Moravia, O.P.:, Tractatus de musica, 1935, pp. 194-229), as well as editorial revisions and corrections of passages which were obviously incorrect or unclear in the original. Thus, this is intended as a practical text rather than a critical edition. (A critical edition of the shorter version of the treatise was published by Erich Reimer in 1972 [see Bibliography1.) The second part attempts to clarify the more obscure points of the treatise and to supply comparisons with other treatises which are roughly contemporary, notably those of Anonymous IV and Walter Odington. This is a chapter—by-chapter commentary, although some points of dis- cussion necessarily draw on materials of several chapters. Following standard practice, the transcriptions given as part of the translation and in the Appendix are in 8. and the pliga_is indi- cated by a short stroke through the stem of the plica—tone. Editorial additions and emendations are indicated by brackets. In many cases, the transcription is admittedly only one of several possible solutions, and sometimes no fully satisfactory rendition is possible without al- teration of the original. DE MUSICA MENSURABILI POSITIO: TRANSLATION De musica mensurabili positio Habito, inquit Johannes, de cognitione planae musicae et om— nium specierum soni, dicendum est de longitudine et brevitate eor- undum, quae apud nos modus soni appellatur. Uhde modus est cog- nitio soni in acuitate et gravi— tate, secundum longitudinem tem- poris et brevitatem. Et potest dupliciter sumi, aut communiter aut proprie. Modus communis est qui versatur circa omnem longi- tudinem at brevitatem. omnium sonorum. Medusyproprius est qui versatur circa VI modes antiques. Treatise on Mensural Music I have spoken, says Johannes, about the knowledge of plain music and all the species of sound, and now the length and brevity of these sounds must be spoken of, which among us is called £2925, Modus is the study of sound in its sharp- ness and gravity, according to the length or shortness of time. And this can be understood in two ways, either commonly or properly. The common mode is that which is con- cerned with the length and brevity of all tones. The proper mode is that which involves the six ancient modes. Quorum modorum primus con- stat longa brevi, longa brevi, etc.; secundus brevi longa, brevi longa; tertius longa duabus brevi- bus, longa duabus brevibus, etc.; quartus duabus brevibus longa, etc.; quintus omnibus longis; sex— tus omnibus brevibus. Aliqui addunt modos alios, sed non est necessarium illos numerare, ut duae longae et brevis, quia per istos VI sufficientiam possumus habere. Omnium aliorum sonorum triplex est modus: unus in plen- itudine vocis, alter est sub voce cassa, tertius sub voce amissa. Recta brevis est quae unum tempus continet. tvnum tempus est quad minimum in plenitudine vocis est. ,Recta longa est duas recta breves continens tantum. Obligua Of these modes the first con- sists of long, breve, long, breve, etc.; the second, breve, long, breve, long; the third, long, two breves, long, two breves, etc.; the fourth, two breves and a long, etc.; the fifth, all longs; the sixth, all breves. Other writers add additional modes, such as two longs and a breve, but it is not necessary to list them, because these six are sufficient. Of all other sounds there are three types: in plenitudine vocis, sub voce cassa, and sub voce amissa. The correct breve is that which contains one tempu . A tempus is that unit which in singing is small- est. The longa recta contains only two breves rectae. The oblique long is that which exceeds the value of the longaprecta. The duplex longa longa est quae abundat super rec- tam longam. Duplex longa est guae plures longas in se continet. Ali- qua longa est guae circumflectit se versus acuitatem vel gravitatem. Et dicitur recta et obliqua. Mbdorum alius perfectus alius imperfectus. Perfectus modus dici- tur qui finit per talem guantitatem per qualem incipit, ut longa, brevis, longa. Imperfectus est qui terminatur per aliam guam per illam in qua incipit. Sic apparet, quod sunt XII modi cum perfectis et im- perfectis, sine aliis. Modus rectus est qui procedit per rectas longas et rectas breves. Obliquus est qui precedit per ali- guas longas et aliquas breves. Regula cognitionis temporum: longa ante longa valet tria tempera. Se- cunda.regula est: duae rectae is that which contains more than one long in itself. Another type of long is that which bends itself toward sharpness or gravity. It is called both resta_and oblique. Some modes are perfect, others imperfect. A mode is said to be perfect which ends with the same value with which it began, such as long-breve-long. It is imperfect when it ends with a value other than that with which it begins. Thus it is clear that there are twelve modes counting the perfect and the imperfect, and no others. The modus rectus is that which proceeds with rectae longs and breves, and the oblique is that which proceeds with other types of longs and breves. A rule for the a long determination of duration: before a long has a value of three breves valent una rectam langam. Tertia regula est: multitudo brevium simul quanta magis appra- pinquatur fini, tanto debet lan- giar proferri. Uhde sequitur quad primus, secundus, sextus dicuntur modi recti, tertius, quartus, quintus dicuntur obli- qui. Sed aliqui volunt quad quintus noster modus sit primus amnium; et bona ratio, quia per istum modum precedit omnes nas- tras modos. Sed qua ad tempara dognoscenda, prius est modus rectus quam obliquus, et sic nan valet quad dicitur, quad quintus est primus. 0rda modarum est numera punctarum ante pausatian- em. Iste arda dividitur in pri- mum, secundum et tertium, etc. 0rda autem procedit ab uno prin- cipia, principium a radice. tempora. A second rule is this: two rectae breves have the value of one longa recta. A third rule is this: the more the end of a great number of breves is approached, the longer they ought to be sus- tained. Whence it follows that the first, second, and sixth modes are called modi recti, and the third, fourth, and fifth are called oblique. But some hold that our fifth mode should be the first. And there is good reason, for this mode precedes all our other modes. But in order to detenmine the durations it first must be determined.whether the mode is rectus or oblique, and thus it does not matter whether it is said that the fifth mode is the first. The eggggof the modes is the number of puncti (pattern repetitions) be- fore a pause. The arda is divided Radix est quilibet cantus primo datus. Exemplum primum primae radicis: Et natandum quad principium cujuslibet modi caret amni pausatione. Primus arda primi modi per- fecti: Madus obliquus habet.Plures consideratianes, ut patet in ter- tio, quia tertius constant ex longa et duabus brevibus, et duae breves equipollent longae, et longa ante into first, second, third, etc. The arda, moreover, proceeds from one principle, and the principle from a root. This root is whatever cantus was first given. The first example of the first root: It should be noted that the founda- tion (principle) of any mode lacks any pauses. The first 2£g2_of the perfect first mode: An oblique mode has further considerations, as is clear in the case of the third mode, be- cause the third mode consists of a long and two breves, and two breves 10 longam valet longam et brevem, at sic valet tria tempora. Quare longa ante duas breves valet tria tempora, et sic valet longam et brevem vel brevem et longam. Item duae breves equipollent longae. Ergo si panantur ante longam valent tria tempora, ergo valent longam et brevem vel e converso. Uhde regula: si sint plures breves in madis obliquis, quae magis appropinquant fini, langiar debet proferri; ergo il- lae duae valent brevem et longam et non longam et brevem. Quare tertius modus et quartus potius reducuntur ad secundum quam ad pmimum. Sed quintus indifferen- ter ad primum et secundum patest reduci, unde quintus modus con- Et sic stat ex omnibus longis. quaelibet longa est ante aliam are equivalent to a long, and a long before a long is equivalent to a long plus a breve, and thus has the value of three tempera. For this reason a long before two breves has the value of three tempera, and thus equals a long plus a breve, or a breve plus a long. 'Likewise, two breves are equiv— alent to a long. Therefore, if they are placed before a long, they have the value of three tempora, or a long plus a breve or vice versa. Hence the rule: if there are several breves in the oblique modes, the more they approach the end, the longer they ought to be held. Therefore these two (breves) have the value of a breve and a long, and not a long and a breve. For this reason the third and fourth.modes are re- duced to the second mode and not to 11 longam. Quare quaelibet valet tria tempora confuse et non dis- tincte, et sic valet langam et brevem vel e converso. Et sic potest reduci ad primum et secun- dum confuse, et mediante secunda potest reduci ad tertium et ad quartum, quamvis omnes modi ad primum et ad secundum possunt reduci. Sed in isto modo aliter respicimus pausationem quam in aliis modis; cum in aliis modis quanta est penultima, tanta est pausatio. Et hic ex toto ista regula non observatur, sed in parts, quia est pausatio longa et aliquotiens brevis, sive fue- rit modus perfectus, sive imper- fectus. Sed si fuerit longa, erit propria sua pausatio brevis acammoda, at in sequentibus patebit. the first. But the fifth mode can be reduced to the first or second mode interchangeably, since it con- sists of all longs. Thus each long is before another long. For this reason each one has the value of three tempora with no distinction between them, and each one has the value of a long and a breve or vice versa. Thus it can be reduced to the first or second mode equally well, and, with the underlying pulse of the second mode, can be reduced to the third or fourth mode, to the extent that any mode can be reduced to the first or second. But in this mode we con- sider the pause differently from that of.other modes, since in other modes the pause is as long as the penultimate note: here this rule is not observed totally, but only in I Sextus : ad primum ve. do reducitur in longam et Imius tampon ducitur ad se Per breVem et duorum tempor: Mum totalit. Culariter; So; tiones brev es bus Si V9 Pez-f. tis I Semndum M“ tertii 12 Sextus madus potest reduci ad primum vel secundum. Sed quan- db reducitur ad primum, terminatur in longam et habet pausationem unius temparis; quando autem re- ducitur ad secundum, tunc finitur per brevem et habet pausationem duorum temporum. Sed ad proprium modum totaliter non fit, sed cir- culariter; soni ultimi et paus- tiones breves semper et in ardini- bus sive perfectis sive imperfec- tis, secundum.magis et minus ad modum tertdi perfecti vel imper- Habito de modis fecti erunt. existunt et de eorum partibus. part, because the pause is some- times long and sometimes short, according to whether the mode is perfect or imperfect. If it should have been long, it might fittingly be short, so that it falls in proper sequence. The sixth mode can be reduced to either the first or the second. But when it reduces to the first mode, it ends with a long and has a pause of one tempus; when it is reduced to the second mode, then it ends with a breve and has a pause of two tempera. But this is not always done according to the proper mode, but only sometimes; the last notes and the rests are always breves in both perfect and imperfect ordines, usually in com— bination with the third mode, wheth- er perfect ar imperfect. I have spoken of the modes and of their parts. Sequitu: eanm sig Figura , est signum de: 501205 secunda: is atque brev: Tu‘aedam Simple ita vel ligdta Simplicium qua Waedam brew/is dictum;- Punct. Mus, SCilice 5:98:31)qu ans tug 17°“ trans om tractu deg 13 Sequitur de figuris et earum significatianibus Figure, ut hic accipitur, est signum denatans sanum vel sonos secundum tempus longitudin- is atque brevitatis. Figurarum quaedam simplex, quaedam compas- ita vel ligata, quad idem est. Simplicium quaedam dicitur longa, quaedam brevis. Longarum quae dicuntur puncta longa triplex est madus, scilicet recta longa et superabundans et plica. Recta longa est cujus lati- tudo non transit longitudinem, cum tractu descendente a parts dextra, ut hic: II. Concerning the notes and their meanings A figure, as this is under- stood, is a sign denoting a tone or tones according to its length or brevity. Certain figures are simple, and others are composite or ligated, which is the same. Some single notes are said to be longs, some breves. Of longs, which are called puncta longa, there are three types, that is, £2353, superabundans, and plig§_ .9222- The recta longa is that whose width does not exceed its length, with a stem on the right side, as here: 2. 2m: 14 Superabundans sive duplex longa, quad idem est, cujus lati- tudo transit langitudinem cum tractu praedicta, ut hic declara- tur: The superabundans or duplex $2232, which are the same, is that whose width exceeds its length, with a stem as above, as is shown here: 3' 31-3-— Plica duplex est, ascendens et descendens. Descendens cum duplici tractu fit, ascendens cum tractu vel duplici, sed semper longior est tractus a parts dex- tra, ut hic: The pligg_is of two types, either ascending or descending. Descending, it is made with two stems; ascending, with one or two stems, but the longer stem is always on the right, as here: 4- :nfi: Brevium triplex est modus, scilicet‘recta brevis recto pos- its, at est .cujus latituda non There are three types of breve, that is the recta brevis, placed squarely, its width not exceeding 15 transit langitudinem et sine its length, and without a stem, tractu, ut hic patet: as is shown here: Et est semibrevis abliqua And there is the semibrevis, posita, ut hic apparet: placed obliquely, as it appears here: 6. 4.93—— Est et alia plica brevis, And there is the plica brevis, et fit quando longior tractus fit made when a longer stem is placed a parte sinistra, ut hic: on the left, as here: .Figura composite vel ligata A figure is composite or est, quando‘plura puncta in unum ligated when several notes are conjunguntur a puncta ad punc- tum, ascendentes vel descendentes: joined into one, one note to another, ascending or descending: Figurarum quaedam dicuntur ascendenda, quaedam descendendo, et hoc a parte principii vel finis. Item quaedam dicuntur perfectae, item quaedam cum pro- prietate, quaedam sine. Descendens dicitur figura, quando secundus punctus inferior est prima, ascendens e converso. Cum praprietate descendants dicimus, quando primus punctus habet tractum descendentem a latere sinistro. Si tractus fue- rit ascendens, cum proprietate. apposita dicitur, ut hic: Some figures are called ascend- ing, some descending, and this is according to the beginning or end. Likewise some are called perfect, and some are said to be cum pro- prietate and some sine proprietate. A figure is said to be descend- ing when the second note is lower than the first, and vice versa for an ascending figure. A descending figure is said to be cum proprietate when the first note has a descending stem on the left; if the stem ascends, it is said to be cum.oppositaqproprietate as here: 17 In figure ascendente praprie- In the case of an ascending tas sua est, quando primus punctus figure its propriety is when the non habet tractum, ut hic patet: first note has no stem, as is shown here: lo. ' M Sed sine proprietate dicitur, si But it is termed sine proprietate habet tractum, ut hic: if it has a stem, as here: 11. W s Et sic intellegimus de figura de- And thus we mean the contrary in scendente ad suum cantrarium, ut the case of a descending figure, hic: as here : 18 Figure perfecte in fine dici- A figure is said to be perfect tur, quando tractus e paenultima with respect to its end when a de- ad ultimm fuerit descendens per— scending perpendicular line is pendiculariter, et hoc in figure drawn from the penultimate to the descendente in fine; et hac est, last note, and this is for a figure quando ultime fuerit inferior which descends at the end. This is paenultima, ut hic: when the last note is lower than the penultimate, as here: 13. WW I Sed in figure ascendente in But the perfection of a figure fine est perfectia cujus ultimus ascending at the end is when the punctus recte jacet super paenul- last note lies squarely above the timum: penultimate : 1..-— W Imperfe sive fuerit dens, si ult1 obliquus ad 5 patet: Sequh fi gun- 19 Imperfecta vero dicitur, It is said to be imperfect, sive fuerit ascendens vel descen- whether ascending or descending, dens, si ultimus punctus fuerit if the last note is oblique with obliquus ad paenultimam, ut hic respect to the penultimate, as patet: is shown here: 15.1. £2'Bfifi £2? Sequitur de regulis III. Concerning the rules figurerum ad invicem for ligated figures ligatarum in turn Omnis Figure ligata cum pro- In the case «of any ligated Prietate posita et perfecte, pee.- figure,with propriety and perfec- nultime dicitur esse brevis, et tion the penultimate note is said ultime longa; si sint precedentes, to be a breve and the final note tunc amnes panuntur pro longa, ut a long. If there are one or more hic: preceding notes, then all together have the value of a long, as here: 20 16.- l ; Omnis figure sine proprietate Any figure without propriety et perfecte posita valet opposite and with perfection has the value cum proprietate, ut hic patet: of a figure with apposite pro- priety, as is shown here: W 17. Regula est, quad nunquam po- The rule is that twa,three, .nuntur duee breves, V91 tres, V61 or four breves never take the value cguatuor pro breVir Ubi possunt of a breve where they can take the poni pro longa. value of a long. 21 Omnis ligature cum praprie- In the case of any ligature tate opposite et perfecta, ultima with opposite propriety and with est longa, et omnes precedentes perfection the final note is a ponuntur pro brevi, si sint ibi long, and all preceding notes to- plures: gether take the value of a breve, if there are more than one: Lee—33m 18. Sed si sint duae tantum, non But if there are only two notes, valent nisi brevem, ut hic they equal only one breve, as is patet: shown here : Omnis figure cum plica et cum In the case”of any figure with ‘proprietate et perfecte, ultime 4 plica and with propriety and 22 cum plica valet longam; quad non aliud est quam signum dividens sonum diversum, ut hic: perfection, the last note with the plica equals a long, because this is nothing other than a sign divid— ing a tone into two, as here: 20. Omnis figure cum plica, sine opposite proprietate sumitur ut cum proprietate vel non, et perfecta vel imperfecta. Omnis figure imperfecte sumi- tur tripliciter, aut cum proprie- tate et plica, vel sine plica: Any ligated figure with pliga_ and without opposite propriety is understood as with or without pro- priety and with or without perfec- tion. «a Any imperfect figure is under- stood in three ways, either with propriety and plica, or without plica: 23 aut sine proprietate et cum plica, vel sine plica, ut sumitur hic: 22. aut cum proprietate opposite et cum plica, vel sine plica, ut hic: 23. Regula est quad amnis figure imperfecte, si sit cum proprietate, extenditur quoad perfectionem pmimi modi usque ad primam longam sequentem; si sit sine proprie- tate, extenditur quoad perfec- tionem secundi modi, usque ad primam brevem sequentem. Et totum hoc intellegitur in canductis et in motellis, quando sumuntur sine or without propriety and with or without plica, as is shown here: or with opposite propriety and with or without plica, as here: The rule is that any imperfect fig- ure, if it is with propriety, is extended to the perfection of the first mode, up to the first follow- ing long; if it is without propri- ety, it extends to the perfection of the second mode, up to the first following breve. And all of this is meant with respect to the con- ductus and the motet, whether littera vel cum littera. Si pro- prio modo figurantur, omnes fig- ures fere accipiuntur imperfecte, et hoc intellegitur in discentu, et ubicunque rectus modus eccip- itur. Sequitur de prabetiane modorum per figures Prime regula primi modi dici- tur esse tres ligatae ad invicem in principio et consequenter cum duae et duae et duae, etc., at hoc totum cum proprietate et perfec- tione: written sine littera or cum lit- tera. If they are written in a proper manner, all figures are as a rule considered imperfect, and this is meant in discant and wherever modus rectus is used. IV. Concerning the demonstra- tion of the modes as written in figures The first rule of the first mode is said to be a three note ligature and then two and two and two, etc., and all of these with propriety and perfection: , a 24. r . .4pflefizf 25 Alia regula re eodem: tres Another rule of the same mode: cum brevi pausatiane, et tres cum a ternaria with a breve-rest, and brevi, etc., et dicitur esse pri- a ternaria with breve—rest, etc., mus arda primi modi perfecti, ut and this is said to be the first hic: 9£§9_of the perfect first mode, as here: Secundi modi prime regula The first rule of the second sumitur ’ita: duae, duae, duae, mode isvunderstood thus: two, two, ‘ cum proprietate et perfectione and two with propriety and 26 et tres in fine sine proprietate perfection and a ternaria at the et perfectae, ut hic: end without propriety and with perfection, as here: 26. $ ISLE: H ’2' “E Fifi}? 1 Cfiflhan: Aliter de eodem: tres sine Another rule of the same mode: proprietate et cum perfectione, A ternaria without propriety and cum longa pausatione, et sic in with perfection with a long-rest, infinitum, ut hic, et est primus and so on as here, and this is the arda ejusdem secundi: first ggdg of the second mode: ga/aam 27 Tertius modus prabatur ita per figures, quoniam prime est longa et postee tres ligatae et tres liga- tae cum proprietate et perfectione, ut hic: The third mode is shown thus in figures: the first is long and afterward ternaria and ternaria with propriety and perfection, as here: (flunquc Quartus modus sumitur hic: tres et tres cum proprietate et perfectione, et duae imperfectae The fourth mode is understood in this way: three and three with propriety and perfection and an 28 in fine at cum longa pausatione, imperfect. binaria at.the end with ut hic: a long-rest, as here: Quintus modus sumitur hac The fifth mode is understood modo: omnes langae cum longa in this way: all longs with a pause vel brevi, ut hic patet: long or breve-rest, as is shown here: 29 Item elia regula de eodem: Likewise, another rule of the tres cum proprietate et perfec- same made: three with propriety tione, et cum longa pausatione, and perfection and with a long-rest, et hoc in infinitum. Et hoc fit and so on. This is done for the cause brevitatis. Et non praprie sake of brevity. It is not proper sumitur ita, sed usus est, ut ita to do it thus, but it is the custom in tenoribus accipiatur: that it is done in this way in tenors: E? ghusnif Sextus accipitur hoc modo: The sixth mode is shown in \\ quetuor cum proprietate et perfec- this way: Four with propriety and tione cum duae et duae et duae cum perfection with two and two and 3O proprietate et plica, ut sumitur two with propriety and plica, as hic: is done here: Alia regula de eodem. Sed Another rule of the same mode. non prabatur per istam artem, sed It is not approved by this system, bene prabatur per exemplum quad but it is well approved according invenitur in Alleluga Posui adju- to the example found in the trip- torium in triplo, scilicet quatuor lum of the Alleluia Posui adjutor— cum proprietate et perfectione et ium, namely, four with propriety tres et tres et tres cum proprie- and perfection and three and three tate, etc., at sumitur in hoc and three with propriety, etc., as exemplo:; is shown in this example: 31 33. 30" Sequitur de modis im- V. Concerning the imperfect perfectis, quomado et modes and how they are qualiter figurentur written Uhde primus modus figuratur The first mode is written in hac modo: tres cum proprietate this way: three with propriety and et perfectione, cum duae et duae perfection with two and two and et tres in fine sine proprietate, three at the end without propriety, ut hic patet: as is shown here: 34. {L A fludi #1,: 32 Alia regula de eodem: duae sine proprietate et debita paus- atione, et duae cum proprietate et pausetione debita similiter, ut hic sumitur: 35. Secundus modus imperfectus sumitur hoc modo: duae, duae, duae cum proprietate et Another rule of the same made: two without propriety and the proper rest and, like- wise, two with propriety and the proper rest, as is done here: The imperfect second mode is written in this way, two, two, and two with propriety and 33 et perfectione ut in exemplo se- cundi modi perfecti. Alia regula de eodem: duae cum proprietate et perfectione et debita pausatione, et etiam sine proprietate et cum perfec- tione et debita pausatione, ut hic: perfection, just as in the ex- ample of the perfect second mode. Another rule of the same made: two with propriety and perfection and the proper rest, and then (two) without propriety and with perfection and the proper rest, as here: . $4 Kaleam 1 Aliter de eadem, tres sine proprietate et cum perfectione, et duae sine proprietate et cum perfectione et debitis pause- tianibus, ut hic: Another rule of the same made: three without propriety and with perfection and two without propriety and with per- fection and the proper rests, as here: 37. ‘1‘ Tertius modus imperfectus sumitur hoc modo: sumetur una longa cum tribus, tribus, tri- bus, etc. cum proprietate et perfectiane et in fine duae cum proprietate et imperfec- tiane, ut hic: The imperfect third mode is done in this way: a long is written with three, three, and three, etc., with propriety and with perfection and at the end two with propriety and without perfection, as here: 38. EM ('amqua 35 Aliter de eodem: sumatur una Another rule of the same longa cum duabus cum proprietate mode: a long is written with et perfectione et longa pausa- two with propriety and perfec- tione, et sic quantum placuerit, tion and a long-rest, and so on ut hic: as far as one wishes, as here: 39. Aliter de eodem: Sumatur Another rule of the same une longa cum tribus et una brevi mode: a long is written with irzfine et debita pausatiane, three and at the end a breve etc: with the proper rest, etc. 40. QCjnaw‘ Quartus modus sumitur mul- tis modis scilicet imperfectis. Et hic primo modo sic sumatur: tres, tres, tres, etc. cum pro- prietate et perfectione et longa pausatione, at his patet: 41. (Eynaf 36 The fourth mode is done in many ways when imperfect. It is done thus in the first way: three, three, and three, etc., with propriety and perfection and a long-rest, as is shown here: 37 Aliter de eodem: tres cum Another rule of the same una brevi in fine et debita pau- made: three with a breve at the satione, et sic quantum placue- end and the proper rest, and so rit servando in perfectione sic: on as far as one pleases in order to preserve the perfec- tion, thus: , —1 55— _ 42. TI . , , . Quintus modus imperfectus The imperfect fifth mode is hoc modo sumitur: amnes longae done in this way: all longs in in pari numero, ut hic apparet: an even number, as appears here: 43. Sextus modus imperfectus sumitur hoc modo: quatuor cum plica et duae et duae cum plica et proprietate, si reducetur ad primum modum, ut hic patet: 44. The imperfect sixth mode is done is done this way: four with pligg_and two and two with plig§_and propriety, if it is reduced to the first mode, as is shown here: 39 Si-madus iste ecoiptur per reductionem and secundum, talis est regula: duae, duae, duae, etc., cum proprietate et perfec- tione et cum plica et ultime simplici nata. amnes breves dicuntur, ut hic apparet: 4S. If this mode is used in reduction to the second mode, this is the rule: two, two, and two, etc., with propriety and perfection and with plig§_ and the last note a simplex. All notes are said to be breves, as appears here: Et hoc est ad propositum omnium madarum perfectorum et imperfectorum. And this is the explanation of all the perfect and imperfect modes. 4O Sequitur de quibusdam regulis communibus unde prima regula est, quad nunquem debet poni aliqua figure sine proprietate, ubi patest poni cum proprietate. Alia regula est, quad nun- quam debet poni simplex vel non ligata, ubi patest pani ligata vel composite. Omnis ligaturerum ordinatio debet fieri per eundem ardinem campasitarum, id est per eandem liaguram. amnes voces eodem sano acceptae non passunt ligari vel fecere campasitam, quie omnis figure composite vel ligata dici- tur ascendenda vel descendenda. Et quaecunque sunt in eodem sono, non dicuntur ascendendo vel de- scenda. Ergo ex his non fit VI. Concerning certain general rules The first rule is that no figure without propriety should be used whenever a figure with propriety can be used. Another rule is that a sim- plex or non-ligated note should not be used whenever a ligated or composite figure can be used. The arrangement of all lig- atures should be done according to the same system of combina- tion, that is, according to the same kind of ligation. Notes sung to the same pitch cannot be ligated or made composite, because any composite figure or ligature is said to be ascending or descending. What— ever notes are on the same pitch may not be said to be ascending 41 figuratura, id est figure ligata. Omnis figure non ligata debet reduci ad ligatam per equipollentiam. Omnis figure ultra tres sua proprio modo reducitir ad tres. Item tres, quarum altera est simplex et duae ligatae, reduc- untur ad tres ligatas per equi- pollentiam, et hac secundum propriam praprietetem, quie reducuntur ad aliquem modum proprium. Item notandum est quad ubicunque invenitur brevium multitudo, id est semibrevium, semper participat cum praece- dente, quie praecedens cum eis non reputatur in valore, nisi‘ pro una teli sicut et praece- dens: or descending, and therefore ligatures, that is, ligated figures, may not be made of them. Any non-ligated figure should be reduced to a ligated figure through the principle of equipollentia (equivalence). Any figure of more than three notes is reduced to the value of three in its proper mode. Likewise, three notes, of which one is single and the other two are ligated, are re- duced by equipallentia to the value of three ligated notes, and this is according to a par- ticular propriety, because they are reduced to a particular mode. Likewise, it must be noted that wherever a great number of 46. sequitur de pause- tianibus undo vivondum est quid sit pausatio. Pausatio est divisio soni facts in debita quantitate. Pausatianum quaedam simplex, quaedam composite. Pausatia simplex dicitur esse, quando pausatur secundum quantitatam alicujus madi vel maneriei, ut hic: 42 breves is found, or rather semi- breves, they always share in the value of the preceding one, for only one preceding note is reckoned with them in value: VII- Concerning rests It must be understood what a rest is. A rest is a division of a sound made according to a proper quantity. Certain rests are simple, others are composite. A rest is said to be simple when- ever it is done according to a particular mode, as here: Simplicium quaedam est per- fects, quaedam imperfecta. Per- fecta dicitur esse illa quae non transmutat modum propter sui ad- ventum. Imperfects autem dicitur quae transmutat modum praeceden- tam. Et utraque istarum pause- tionum patet in exemplo supra data. undo regula: amnis paus- atio simplex dicitur equalis paenultimae madi praecedentis. Si autem modus ante pausationem sit perfectus, et pausatio dici- tur perfecta. Si vero sit Some simple rests are per- fect, others are imperfect. A rest is said to be perfect which does not alter the mode by its appearance. It is said to be imperfect, however, when it al- ters the preceding mode. Both of these types of rests appear in the example(s) given above. Whence the rule: any simple rest is said to be equal to the penultimate note of the preced- ing mode. If the made before the rest is perfect, the rest 44 imperfectus, et pausatio erit imperfecta. Omnis pausatio sumitur per oppositum quoad tempus secundum modum perfectum sui modi prae- cedentis, vel etiam secundum numerum, quie puncti perfecti modi sunt impares et pausetio est par. It has est a parte principii vel finis, sed secun- dum.madum imperfectum a parte finis tantum et non principii. Si pausatia sit perfecte, et modus praecedens erit perfectus. Si imperfecta, et modus erit imperfectus. Pausatio composite vel du- plex dicitur esse quando simplex duplatur vel tripletur vel quad- Compositarum ruplatur, etc. quaedam perfecte, quaedam vero is said to be perfect, and if the mode is perfect, the rest will be imperfect. Any rest is understood as contrary to the time-value of the last note of the preceding perfect mode, or even according to the number of notes, because the number of notes in a perfect mode is uneven, and the rest makes it even. And this can be determined from the beginning or the end [of the preceding page], but in the case of an imperfect mode, only from the end and not the beginning. If a rest is perfect, the preceding mode will be perfect: if it is imperfect, the mode will be imperfect. A rest is said to be com- posite or duplex when a simple 45 imperfecta, ut superius sim- plici, etc. Omnis pausetio sumitur con- traria modo sui madi preeceden- tis, in prima, secunda, tertia, quarto, qunito secundum numerum, et in sexto, quando reducitur ad primum vel secundum. Sed secun- dum suum proprium modum equelis est principio et fini, nec recep- it cantrerietetem, nisi secun- dum nemerum aliquem parem vel imperem. Et notandum quad in omni perfecta pausetione debet naturaliter tractus et inter- valli camputari pro pausetione. In omni imperfecta sine inter- vallo debet camputari. rest is doubled, or tripled, or quadrupled, etc. Certain com- posite rests are perfect, others are imperfect, just as the simple rests above, etc. Any rest is reckoned con- trary to the preceding mode in the first, second, third or fourth, and according to number in the fifth, and in the sixth when it reduces to the first or second. But when, according to the proper mode, the beginning and end are equal it is not reckoned in a contrary manner, except according to the number of notes, whether even or un- even. And it must be noted that a perfect rest ought to be reckoned according to the length of the line, and imperfect rests 46 Sequitur de figuris pausetionum Figure pausetionis est sig- -num vel tractus significans di- visionem soni fectam in debita quentitate. Pausetionum quaedam dicitur recte brevis, quaedam longa,.quaedam finis punctorum, quaedam divisio modorum, quaedam divisio syllabarum, quaedam su- spiratio. Recte brevis est tractus respciens latitudinem unius spa- tii. Recta longa est tractus cantinens duo spatia vel plura. Finis:punctorum dicitur esse, ubi tractus respicit lati- tudinem omnium linearum et should be reckoned without con- sideration for that length. VIII. Concerning the nota- tion of rests The figure for a rest is a sign or line indicating a divi- sion of sound made in a proper A certain rest is quantity. called recta brevis, another longa, another finis punctorum, another divisio modorum, another divisio syllabarum, another suspiratio. The recta brevis is a line covering the distance of one space. The recta longa is a line containing two spaces or more. It is called finis punc- torum when the line spans the 47 spatiorum. Divisio modorum est tractus aliquo modo positus et hoc su- periori perte et minor apperet recte brevi. Divisio syllabarum dicitur idem, sed accipitur in inferiori parte. Suspiratio dicitur esse apperens pausetio et non existens. Et hoc est supponendum, quie sus- piratio patest fieri cum tractu et sine tractu, et est minor recte brevi. Et accipe hic exemplum omnium pausetionum. 48. width of all the lines and spaces. The divisio modorum is a line placed in such a way that it appears in the upper part (of the stave) and is shorter than the recte brevis. The divisio syllabarum is the same, but it appears in the lower part. The suspiratio appears to be a rest but is not. This must be understood, because the gpgf piratio can be done with or without the line, and is smaller than the recte brevis. And here is the example of all the rests: Sequitur de conson- antiis in eodem tempore sive in .diversis tem~ poribus in eodem voce Consonantiarum quaedam di- cuntur concordantiae, quaedam discordantiae. Concordantie dicitur esse quando duae voces junguntur in eodem tempore, ita quad une patest compati cum elia secundum auditum. Discordantie dicitur contrario modo. Con- dordentiarum triplex est modus, quie quaedam sunt perfectae, quaedam imperfectae, quaedam mediae. Perfecte dicitur, quando duae voces junguntur in eodem tempore, ita quad una secundum auditum non percipitur ab elia Et dici- propter concordantiem. tur equisonantiam, ut in unisono 48 IX, Concerning consonances, whether sounding at the same time or at different times in the same voice Certain intervals are said to be consonances, others dis- sonances. It is said to be a consonance when two voices are joined at the same time, so that one can be in agreement with the other according to the ear. Dis- sonance is said to be the oppo- site Of thiS- There are three types of consonances, for some are perfect, some imperfect, and some media. It is called perfect when two voices are joined at the same time such that, according to the ear, one is not distin— guished from the other, because of the consonance. It is et diapason: 49. Imperfectae autem dicuntur, quando duae voces junguntur ita, quad una ex tot perciptur ad alia secundum auditum et con- cordantiam. Et sunt duae spe- cies, scilicet ditonus et semi- ditonus: considered equivalent in sound, as in the case of the unison and octave: They are called imperfect, how- ever, when two voices are joined such that one can be distin— guished from the other according to ear and the consonance. And there are two types, namely the major third and minor third: so. .. Mediae autem dicuntur, quando duae voces junguntur in eodem tempore, quae neque dicun- tur perfectae neque imperfectae, They are called media when two voices are joined at the same time which are neither per- fect nor imperfect, but belong SO sed partim conveniunt cum perfec- partly with the perfect and tis, et partim cum imperfectis. partly with the imperfect. And Et sunt duae species, scilicet there are two types, namely the diepente et dietessaron. Et fifth and the fourth. These istae duae species patent in two types appear in this example: hoc exemplo: 51. Sic apparet quad VI sunt Thus it is clear that there species concordantiee, sclicet are six types 0f consonance, unisonus, diapason, diepente, namely the unison, OCtaVe: fifth: diatessaron, semiditonus, di- fourth, minor third, and major tonus. Et dicuntur genera third. These are considered to generalissime omnium concor- be the most common types 0f dentiarum. consonances. Sciendum quad supredictae It must be understood that concordantiae possunt sumi in the above-mentioned consonances infinitum. Probatio: primus can be used in infinitum. sonus sic detus supra primum G: Demonstration: the first voice secundus sonus supra secundum g, 15 given on the note 9, and the 51 quod dicitur unisonus vel equi- sonantia, quad idem est. Dico quod quidquid concordat secunda 9 et primo. Probatio: quae equalie sunt eidem, sibi invicem sunt equalie. Sed diepente bene concordat secundum suam speciem secunda g, ergo et primo. Et non e converso, quie si illud quad videtur minus inesse inest, et illud quad magis et e conver- so. Et omne totum ponit sues partes et non e converso, quie omne totum majus est sue parte et non e converso. Tunc dico sic: semiditonus bene concordet secunda g, ergo et primo et non' e converso per praecedentie. Et vocetur semiditonus cum diapason. Et sic de ditono, et vocetur di- tonus cum diapason, et sic de aliis in infinitum ascendi second on a second g! which is called a unison, and is the same. I maintain that whatever is consonant with the second 2 is consonant with the first. Demonstration: whatever things are equal are the same; they are equivalent one to the other. The fifth is consonant with the second g, and therefore also with the first. But not the converse, because that which seems to be in the lesser is in it, and also in the greater, and vice versa. Any whole contains its parts and not vice versa, for any whole is greater than its parts, and not vice versa. Thus I say this: the minor third is consonant with the second g and therefore also with the first, but not vice 52 patest. Et haec sufficient de propriis concordantiis. Discordantia dicitur esse, quando duae voces junguntur in eodem tempore ita, quad secundum auditum una vox non possit compati cum alia. Discordantiarum quaedam dicuntur perfectae, quaedam imper- fectae, quaedam vera mediae. Perfectae dicuntur, quando duae voces non junguntur aliquo modo secundum compassionem vocum, ita quad secundum auditum una non possit campati cum elia. Et is- tae sunt tres species, scilicet semitonium, tritonus, ditonus cum diepente: versa, as was demonstrated above. This is called semiditonus cum diapason. And thus also with the major third, called ditonus cum diapason, and so on with the others in infinite ascent. These remarks are sufficient concerning the particular con- sonances. There is said to be a dis- sonance when two voices are joined at the same time such that, according to the ear, one voice cannot be in agreement with the other. Some disson- ances are called perfect, some imperfect, and some media. They are called perfect when two voices are not joined in any way according to the allowances of singing, such that one voice cannot be in agreement 52. Imperfectae dicuntur, quando duae voces junguntur ita, quad secundum auditum possunt aliquo modo compati, tamen non concord- ant. Et sunt duae species, sci- licet tonus cum diepente et semi- ditonus cum diapente. Et istae duae species non concordant, campatiuntur tamen, ut hic apparet: 53. 53 with the other. And there are three types of these, namely the semitone, tritone, and major seventh: They are called imperfect when two voices are joined such that, according to the ear, they can be in agreement in some way, but are nevertheless not conson- ant. There are two types, namely the major sixth and minor seventh. These two types are not consonant, and yet they are in agreement, as it appears here: 54 Mediae dicuntur, quando duae voices junguntur ita, quad partim conveniunt cum perfectis, partim cum imperfectis. Et is- tae sunt duae species, scilicet tonus et semitonium cum diepente, ut hic patet: 54; Istae species dissanantiae sunt VII, scilicet semitonium, tritonus, ditonus cum diepente, tonus cum diepente, semiditonus cum diepente, tonus et semiton— ium cum diapente. Et possint sumi usque in infinitum sicut et concordantiae, scilicet semi- tonium cum diapason, ditonus cum diapason, tritonus cum diepason, They are called mgdig_when two voices are joined such that they belong partly with the perfect and partly with the im— perfect. Of these there are two types, namely the whole-tone and the minor sixth, as is shown here: These types of dissonances 0 are seven in number, namely the semitone, tritone, major seventh, major sixth, minor seventh, whole- tone, and minor sixth. These can be infinitely extended, just like the consonances, namely the minor ninth, major ninth, tritone plus octave, etc., up to the double OC- tave and as far beyond as one might wish. etc. usque ad bis diapason, et ulterius quantum placuerit: 55. Sequitur de consanan- tiis et dissonentiis, scilicet quae magis concordant et quae minus Concordantiarum prime dici— tur unisonus, qui procedit ab equelitate immediate. Idea meliorem cunctis cancordiam habet. Secunde diapason, qui sumitur in dupla proportione. Tertia est diepente, qui sumitur in sesquialtera proportione. Quarta est diatessaron, qui sum- itur in sesquitertia. Quinta est ditonus, qui accipitur in minori superpartiente quam 55 X. Concerning the conso- nances and dissonances, namely, which are more consonant and which less, and which are more dis— sonant and which less The first of the consonan- ces is called the unison, which proceeds from immediate equality. Therefore, it has better concord than all the others. Second is the octave, which is a 2:1 pro- portion (dupla ; third is the fifth, which is the 3:2 prOpor- tion (sesquialtera); fourth is the fourth, which is‘4:3 (ses- qpitertia); fifth is the major third, which is closer to 56 semi-ditonus, ut est super sep- tem partiens LX quartus. Sexta est semiditonius, qui sumitur in minori superpartiente allis se- quentibus, ut est superquinque- partiens vigesimas septemas. Unde regula: quae magis et appropinquiori procedunt ab equelitate, magis concordant in sono, et quae minus appro- pinguant equalitati, minus con— cordant secundum auditum° Sed istae VI species prius nominates multum appropinquant ipsi equali- tati. Aliae vero septum species sequentes multum distant ab equelitate, ergo primae VI bene concordant et dicuntur concor- dantiae, aliae autem non con- cordant, sed potius discordant, quare nominantur discordant- iae. equality than the minor third, so that it is 81.64. Sixth is the minor third, which is closer to equality than the following intervals, so that it is 32:27. Whence the rule: the nearer they approach equality, the more they are consonant in sound, and the less consonant, and therefore they are more dissonant according to the ear. The six types named above are quite close to equality. The other seven types are quite distant from equality, and there- fore the first six are consonant and are called concordances; the others, however, are not conson- ant, but rather are dissonant, and for this reason they are called discards. The tritone is said to be the first of the discards, for 57 Discordantiarum prime dici- tur tritonus, quie magis dicitur perfects discordantia; ea quad magis discedit ab equelitate, quia accipitur super ducenta decem et septem partiens quingen- tas duodecimas ut LXXXXIX ad quingenta XII. Secunda est semitonium, et dicitur insuper tredecim CCXLIIIas, ut CCLVI ad CCXLIII. Tertia est ditonus cum diepente, et accipitur super du- centas tricesimas partiens CCLVI, ut CCCCLXXXVI ad CCLVI. Quarta est tonus cum diepente, et ac- cipitur super XXIIas partiens XXXII. Quinta est semitonium cum diepente, et accipitur super CCLXII partiens CCCCLXXXVI, ut septingenta VIII ad CCCCLXXXVI. Sexta est semiditonus cum die- pente, et accipitur super VII it is said to be the more per- fect discord, because it is far- thest from equality, having the proportion 729:512. Second is the semitone, with the prOpor- tion 256:243. Third is the ma- jor seventh, with the proportion 486:256 [243:128]. Fourth is the major sixth, 54:32 [27:16]. Fifth is the minor sixth, which is 364:243 [384:243 is correct]. Sixth is the minor seventh, Seventh is the whole- 16:9. tone, 9:8 (sesquioctava). Thus the seven discards are shown, and which of them are more discordant and which less; and it should be noted that any discord before a perfect or m§§i§_consonance should be equivalent to a mgdi§_discord. This is especially true before 58 partiens nonas, ut XVI ad IX. Septima est tonus et sumitur in sesquioctava proportione, ut IX ed octo. Sic apparent VII discordan- tiae, et quae eerum magis dis- cordant et quae minus, et nontan- dem quad omnis discordantia ante perfectam concordantiam sive me- diam equipollet mediae. Et haec proprie sumitur ante unisonum vel diapasan. Sciendum est quad nunquam ponitur discordantia ante perfectam cancordantiam, nisi cause coloris musicae. Haec de cans-nantiis suffi- ciant. a unison or octave. It must be understood that a discord is never placed before a perfect consonance, except for reason of the color of the music. These remarks about con- sonances are sufficient. y.|.. il‘llu afl‘! . . 59 Sequitur de discantu et de ejus speciebus Discantus est aliquorum di- versorum cantuum consonantia se- cundum modum et secundum equipol- lentis equipollentiam. Et sunt tot species sicut et in modo a parte equipollentis qui dicitur secundus cantus, quot a parte tenoris qui dicitur primus can- tus. Sunt autem sex species ejus, ut dicitur. Et sciendum quod a parte primi tria sunt consideranda, scilicet sonus ordinatio et modus. Sonus hic accipitur pro musica. Ordinatio hic sumitur numerus punctorum ante pausa- tionem. Mbdus pro quantitate longarum vel brevium notarum. Similiter eadem a parte secundi consideranda sunt. Praeterea XI. Concerning discant' and its types Discant is the sounding- together of various different voices according to mode and equipollentia of equivalent voices. There are as many types of equivalent voices, called second cantus, as there are of the tenor, called first cantus. There are six types, so it is said. Let it be known that for the first cantus there are three things to be considered, namely sonus, ordinatio, and modus. Sonus here means the music, ordinatio the number of notes before a pause, and modus the quantity of long or short notes. Likewise, the same things must be considered on the part of 60 primus et secundus in tribus sunt cansideranda, scilicet in numera, in modo, et in cancor- dantia. In numera, ut tat sunt puncti secundum equipollentiam a parte secundi, quot a parte primi vel e converso. In modo, ut sit longa contra langam, vel breves equipollentes langae. In cancordantia, ut primus bene cancordet secunda et e converso. unde regula: omne quad fit impari debet cancordari cum omni illa quad fit in impari, si sit in primo vel secunda vel tertio modo. Sed dua puncti sumentur hic pro una, et aliquanda unus earum ponitur in discardantiam, . propter calarem musicae, et hic primus vel secundus. Et hac bene permittitur ab auctaribus primis et Iicentiatur. HOG autem the second cantus. Therefore the first and second cantus must be considered in three ways, namely in number, in mode, and in concordance. In number, so that there are as many notes, according to equipollentia, in the second part as in the first, or vice versa. In mode, so that there might be long set against long, or breves equivalent to the long. In concordance, so that the first might be conson- ant with the second and vice versa. Whence the rule: anything which is odd ought to be brought into concordance with that which is add, if it be in the first, But two second, or third mode. notes may be substituted for 61 invenitur in argana in pluribus lacis et praecipue in matellis. Et notandum quad sunt tres species discantus, aut rectus positus contra rectum, quad est prima species, aut modus per ultra mensuram ad madum per ul— tra mensuram, quad est secunda species, aut rectus contra per ultra mensuram, quad est tertia species. Rectus ad rectum sumitur dupliciter, aut eodem ardine aut ordine converso. Rectus ad rec- tum dupliciter, aut rectus ad se ipsum aut ad reliquum. Rectus ad se ipsum patest cambinari tripliciter secundum quad triplex est modus rectus, aut primus contra primam, ut hic patet: one, and sometimes one of them is placed in discord for the sake of the color of the music, and it may be either the first or the second. This is fully permitted and approved by the foremost authorities. It is found in many passages in organum, and especially in motets. It should be noted that there are three types of dis- cant: rectus placed against rectus, which is the first type, or ultra mensuram.with ultra mensuram which is the second type, or rectus with ultra men- suram, which is the third type. Rectus with rectus is done in two ways, either with the same g£§9_or with opposite 957 dines. This is also done in 56. 62 two other ways, either a.gg§g§' rectus with itself, or with another. A.modus rectus can be com- bined with itself in three ways, because there are three 229;. 5323;} either the first mode with itSelf, as is shown here: .r 63 Aut secundus contra secundum, or the second with the second, ut hic: as here: FIFE % 57. _— M1 Aut sextus contra sextum, ut hic: or the sixth with the sixth, as here: 64 -:n_"'——-L 58, _uL".-_hjl Rectus contra reliquum pa- test dupliciter cambinari vel accipi, aut primus contra sextum aur secundus contra sextum. Primus contra sextum dupli- citer, aut primus an laca primi accipitur et sextus in loco secundi, ut hic apparet: A modus rectus with another can be combined in two ways, either the first with the sixth, or the second with the sixth. The first with the sixth is done in two ways, either the first mode in the first voice and the sixth in the second voice, as it appears here: 65 59. Ant 0 converso, scilicet sextus or vice versa, namely the sixth in loco primi et primus in loco mode in the first voice and the secundi, ut hic: first in the second voice, as here: 60. .‘ulr. 66 Secundus contra sextum po- test dupliciter combinari, aut secundus in loco primi et sextus in loco secundi: The second.mode can be com- bined with the sixth in two ways, either the second mode in the first voice and the sixth in the second: 67 61. Aut flat 9 converso, scilicet or vice versa. namely the sixth saxtug in loco primi et secun- mode in the first voice and the dus in loco secundi, ut hic second in the second, as it declaratur: appears here: 68 62.- Rectus ad rectum ordine converso sumitur tripliciter, aut primus ad secundum out Rectus can be combined with rectus, with opposite 257 dines, in three ways, either 69 primus ad sextum secundum or- dinem secundi aut secundus ad sextum. Primus secunda dupliciter, aut primus in laca primi et se- cundus in loco secundi, ut hic the first mode with the second, or the first with the sixth, when the latter is written according to the grdg of the second mode, or the second with the sixth. patet: The first mode with the second is done in two ways, either the first mode in the first voice and the second in the second, as is shown here: ‘ -Ilrt1l: . IIIIIIIEIHIIIIIIBIHIIIIIIrllfll I g! 63. W 70 Aut e converso, scilicet secun- or vice versa, namely the second dus in loco primi et primus in mode in the first voice and the loco secundi, ut hic: first in the second voice, as here: 64. ! 71 Item primus contra sextum Likewise, the first mode secundum ardinem secundi sumi- is combined with the sixth, in tur dupliciter, aut primus in the ordo of the second mode, in loco primi et sextus in loco two ways, either the first mode secundi, ut hic: in the first voice and the sixth in the second voice, as here: 65. — aut e converso, scilicet sextus in loco primi et primus in loco secundi, ut hic apparet: 72 or vice versa, namely the sixth mode in the first voice and the first in the second voice, as it appears here: 73 66. Secundus sexto dupliciter, The second mode with the ant secundus loco primi at sex- sixth in two ways, either the tus loco secundi: second mode in the first voice and the sixth in the second voice: 74 67. aut e converso, scilicet sextus in loco primi et secundus in loco secundi, ut hic: or vice versa, namely the sixth mode in the first voice and the second in the second voice, as here: iii} I1!:I.|1 i 1‘“ 75 68. Modus pot ultra Mbnauxlh The ultra.mensuram.modes sumitur dupliciter, ant-lodhm , may be combined in two ways, ardinc aut converso. laden either with the same ordo or 76 ardine tripliciter, aud ad se ipsum aut ad reliquum aut ad rectum. Ad se ipsum triplici- ter, aut tertius ad se ipsum, ut hic patet: with apposite ordines. With the same ordo in three ways, either a mode with itself, or with another, or with a modus rectus. With itself in three ways, either the third mode with itself, as is shown here: 69. 77 aut quartus ad se ipsum, ut hic: or the fourth mode with it- self, as here: ka 70. 78 aut quintus contra se ipsum, or the fifth mode with itself, ut in exempla subsequenti: as in the following example: % 71. (“I Madus per ultra mensuram vel ad reliquum vel ad rectum in eodem ordune sumitur duplici- ter, auc’tertius contra quintum, aut quartus ad quintum. Tertius ad quintum dupliciter, aut ter- tius in loco primi et quintus in loco secundi: 79 An ultra'mensuram mode com- bined with another or with a modus rectus with the same ordo is done in two ways, either the third mode with the fifth, or the fourth with the fifth. The third mode with the fifth in two ways, either the third mode in the first voice and the fifth in the second voice: 72. 80 aut e converso, scilicet quin- or vice versa, namely the fifth tus in loco primi et tertius mode in the first voice and the in loco secundi, ut hic: third in the second voice, as here: 73. 81 Quartus contra quintum du— The fourth mode with the pliciter, aut quartus in loco fifth in two ways, either the primi et quintus in loco se- fourth mode in the first voice cundi: and the fifth in the second voice: " " TH: E I 74. 82 aut fiet e converso, scilicet quintus in loco primi et quar- tus in loco secundi, ut hic apparet: or it may be done conversely, namely the fifth mode in the first voice and the fourth in the second voice, as it appears here: 75. 83 Madus per ultra mensuram ad madum per ultra mensuram or- dine converso sumitur dupliciter vel etiam tripliciter, aut ter- tius quarto aut tertius quinta aut quartus quinta. Tertius quarto patest dupliciter cam— binari, aut tertius in loco primi et quartus in loco se- cundi, at in hoc exemplo A mode ultra mensuram with another ultra mensuram with opposite ordines is done in two ways or even three, either the third mode with the fourth, or the third with the fifth, or the fourth with the fifth. The third mode can be combined with the fourth in two ways, either the third mode is placed in the apparet: first voice and the fourth in the second voice, as it appears in this example: ' ‘fi fi‘“ 1 T a A I ' I 76. T— - fi «HF 84 Aut e converso, scilicet quar- or vice versa, namely the tus in loco primi et tertius fourth mode in the first voice in loco secundi, ut hic: and the third in the second voice, as here: 77. 85 Tertius quinta dupliciter, The third mode with the aut tertius in loco primi et fifth in two ways, either the quintus in laca secundi: third mode in the first voice and the fifth in the second voice: 86 78. Aut e converso, scilicet quin- tus in laca primi et tertius in loco secundi, ut hic: or vice versa, namely the fifth mode in the first voice and the third in the second voice, as here: 87 79. Quartus contra quintum The fourth mode can be patest dupliciter cambinari, combined with the fifth in two aut quartus in laca primi ways, either the fourth mode 88 et quintus in loco secundi, in the first voice and the ut hic: fifth in the second voice, as here: 80. 89 Aut e converso, scilicet quintus or vice versa, namely the fifth in loco primi et quartus in mode in the first voice and the loco secundi, ut hic: fourth in the second voice, as here: 81. ' ' I ”r 9O Rectus modus ad madum per ultra mensuram sumitur duplici- ter, aut eodem ardine aut con- verso. Eodem ardine dupliciter, aut par contra parem aut par contra imparem. Par contra parem patest dupliciter accipi, aut secundus quarto aut sextus quarto. Secundus quarto dupli- citer, aut secundus in laca primi et quartus in laca secundi, ut hic patet: A modus rectus is combined with a modusgper ultra mensuram in two ways, either with the same ordo or with opposite_g£- dines. With the same ordo in two ways, either even against even, or even against odd. Even against even can be done in two ways, either the second mode against the fourth, or the sixth against the fourth. The second mode with the fourth in two ways, either the second mode in the first voice and the fourth in the second voice, as is shown here: W - 1 1 82. 91 Aut fiet e converso, scilicet or it may be done conversely, quartus in loco primi et secun- namely the fourth mode in the dus in loco secundi, ut hic: first voice and the second in the second voice, as here: 83. 92 Sextus quarto dupliciter, The sixth mode with the ant sextus loco primi et quar- fourth in two ways, either the tus loco secundi: sixth mode in the first voice and the fourth in the second voice: 84. 93 Aut fiet e converso, scilicet or it may be done conversely, quartus in loco primi et sextus namely the fourth mode in the in loco secundi: first voice and the sixth in the second voice: p 94 Impar contra imparem sumitur dupliciter, aut primus tertia, in tantum quad primus equipollet debita ardine sexto, aut sextus tertio mediante secunda. Et ita sumitur primus tertio, sed non proprie, sed per reductionem, aut primus quinto. Primus ter- tia dupliciter, aut primus in loco primi et tertius in loco secundi, ut patet in exemplo subsequenti: Odd against odd is done in two ways, either the first mode with the third, because the first mode is equivalent to the proper 2382.0f the sixth mode, or the sixth mode with the third, in reduction to the second mode. And thus the first mode is placed with the third, but not properly, but by reduction, or the first mode with the fifth. The first mode with the third in two ways, either the first mode in the first voice and the third in as is shown the second voice, in the following example: 86. Aut fiet e converso, scilicet tertius in loco primi et primus in loco secundi, ut hic patet: 95 or it may be done conversely, namely the third mode in the first voice and the first in the second voice, as is shown here: 96 87. Primus quinta dupliciter, The first mode with the ant primus loco primi et quin- fifth in two ways, either the tus loco secundi: first mode in the first voice and the fifth in the second voice: 97 88. Aut fiet e converso, scilicet or it may be done conversely, quintus in loco primi et primus namely the fifth mode in the in loco secundi, ut hic: first voice and the first in the second voice, as here: 89. 98 Tertius quinto dupliciter, The third mode with the ant tertius in loco primi et fifth in two ways, either the quintus in loco secundi, ut hic: third.mode in the first voice and the fifth in the second voice, as here: 90. 99 Aut fiet e converso, scilicet quintus in loco primi et ter- tius in loco secundi, ut hic apparet: or it may be done conversely, namely the fifth mode in the first voice and the third in the second voice, as it appears here: 91. I I ' Par contra imparem sumitur triplex, aut secundus contra aliquem aut quartus contra ali- quem aut sextus contra aliquem. Secundus contra aliquem est du- plex, aut secundus ad tertium aut idem secundus ad quintum. Secundus ad tertium patest du- pliciter cambinari, aut secun- dus in.loco primi et tertius Even is placed against add in three ways, either the second mode with another, the fourth with another, or the sixth with another. The second mode with another is in two ways, either the second mode with the third, or the second with the fifth. The second mode can be combined with the 101 in loco.secundi,vut hic third in two ways, either the patet: second mode in the first voice and the third in the second voice, as is shown here: (mnnllT-[I-IN Illllllllflrlhll Aut fiet e converso, silicet tertius in loco primi et se- cundus in loci secundi, ut hie: 102 or it may be done conversely, namely the third mode in the first voice and the second in the second voice, as here: 103 Secundus ad quintum patest The second mode can be taken accipi dupliciter, aut secundus with the fifth in two ways: loco primi et quintus loco se- either the second mode in the cundi, ut hic patet: first voice and the fifth in the second voice, as is shown here: 94 104 Ant 9 converso, scilicet quin- tus in loco primi et secundus in loco secundi, ut hic patet: or vice versa, namely the fifth mode in the first voice and the second in the second voice, as is shown here: 95. 105 Quartus contra aliquem po- test combinari tripliciter, aut quartus contra primum aut contra tertium aut contra quintum. Sed de istis nullum exemplum tradi- tur, ea quad eorum combinatia rara alicubi reperitur. Sextus contra aliquem po- test combinari tripliciter, aut sextus contra primum aut contra tertium aut contra quintum. Sextus contra primum dupliciter, aut sextus loco primi et primus loco secundi, aut e converso. Sed quia horum exempla superius dantur, idcirco qua ad praesens relinquantur. Sextus ad tertium duplici- ter, aut sextus in loco primi ’et tertius loco secundi, ut hic: The fourth mode can be com- bined with another in three ways, either with the first, or with the third, or with the sixth. But of these no example is given, because the combination of them is only rarely found. The sixth mode can be com- bined with another in three ways, either the sixth mode with the first, or with the third, or with the fifth. The sixth mode with the first in two ways, either the sixth mode in the first voice and the first in the second voice, or vice versa. But since examples of these are given above, they are omitted here. The sixth mode with the third in two ways, either the sixth mode in the first voice and the third in the second voice, as here: 106 96. Ant flat e converso, scilicet or it may be done conversely, tertius in loco primi et sextus namely the third mode in the in loco secundi, ut patet in first voice and the sixth in exempla subsequenti: 97. 107 the second-voice, as is shown in the following example: 108 Sextus contra quintum du- pliciter, aut sextus in loco primi at quintus in loco se- cundi, ut hic: The sixth mode with the fifth in two ways, either the sixth mode in the first voice and the fifth in the second voice, as here: 98. Aut flat 9 converso, scilicet quintus in loco primi et sextus in loco secundi, ut hic: or it may be done conversely, namely the fifth mode in the first voice and the sixth in the 0. second voice, as here: 109 99. Et sic de singulis ad invi- cem, secundum equipollentiam aliquorum modorum. Expliciunt amnes combina- tiones modorum, quantum sufficit ad discantum. Dicto de est de copula ad discantum, quam perfecte discantu dicendum quae multum valet quia discantus nun- scitur nisi And thus with each in turn according to the equipollentia of the various modes. All combinations of the modes are shown, as many as are “\ sufficient for discant. Discant having been discussed, the copula, which is very important in discant, must be discussed, be- cause discant is never understood 110 mediante copula. Unde copula esse id quad est inter discantum et or- ganum. Alia modo dicitur copula: copula est id quad praferter recto modo equipollente unisana. Alia modo dicitur: copula est id ubi- cumque fit multituda punctorum. Punctus, ut hic sumitur, est ubi- cumque fit multituda tractuum, et ista pars dividitur in duo equalia. Uhde pars prime dicitur antecedens, secunda vero cansequens, et utraque pars cantinet multitudinem trac- tuum. Uhde tractus fit ubicumque multituda specierum univoce, ut unisoni aut soni secundum numerum ordinatum ardine debita. Et haec sufficient ad discantum. Organum dicitur multiplici- ter, generaliter et specialiter. De argana generaliter dictum est superius, nunc autem dicendum perfectly except through knowl- edge of the copula. Qgpula is said to be that which is between discant and organum. The copula is described in another way: copula is that which proceeds to a unison by means of equipol- lentia with rectus modus. It is described in another way: there is a copula wherever a great number of puncti are written. A punctus, as the term is used here, is wherever there is a great number of tractus. The first part is called the ante- cedent, the second part the con- sequent, and each part contains a great number of species, such as unisons or whole-tones, in one voice, according to an arranged number in proper order. And these remarks suffice for discant. 111 est de ipsa in speciali. Organum in speciali dicitur dupliciter, aut per se aut cum alia. Organum per se dicitur id esse quidquid prafertur secundum aliquem madum rectum aut non rectum. Rectus modus sumitur hic ille per quem discantus prafertur. Nan rectus dicitur ad differentiam alicujus rectae, quae langae et breves rectae sumuntur debita modo prima, et principaliter. In nan recto vera sumitur longa et brevis in primo modo, sed ex contingenti. Organum autem nan rectum disitur quidquid prafer- tur per non rectam mensuram, ut dictum est superius. Et ejus equipollentia tantum se tenet in unisono usque ad finem alicu- jus puncti, ut secum canvenit secundum aliquem cancordantiam. Organum is spoken of in many ways, both generally and specif- ically. Organum taken generally was discussed above, and n6w it ‘ must be discussed specifically. Organum taken specifically is de- scribed in two ways, either per. se or cum alio. Organum per se is said to be that which proceeds according to a certain modus rec- tus or non rectus. Rectus modus here means that by which discant proceeds; non rectus is described in distinction from modus rectus, especially where correct longs and breves are taken as in the first mode. In non rectus the long and breve are taken as in the first mode, but coincidentally. And so organum is said to be non rectum when it proceeds by non recta measurement, as was said 112 Et hac sufficit dici organa quantum ad discantum. Longae et breves in organa tali mada dignascuntur, scili- cet per cansonantiam, per fig— uram, et per paenultimam. Unde regula: omne id quad accidit in aliquo secundum virtutem cansonantiarum, dicitur langum. Alia regula: quicquid figuratur langum secundum ar- gana ante pausatianem vel loco consanantiae, dicitur langum. Alia regula: quicquid accipitur ante langam pausa- tionem vel ante perfectam cancordantiam, dicitur esse langum. above. And only equipollentia holds it together until the end of any punctus, so that it agrees with the rules of consonance. And this is sufficient for or- ganum, just as for discant. In organum the longs and breves are distinguished in this way, namely by consonance, by the figures (manner of notation), and by the rule of the penultimate. Whence the rule: whatever occurs by virtue of consonance is said to be long. Another rule: whatever is written as a long during the or- ganum and before a rest is said to be long. Another rule: whatever occurs before a long-rest or before a perfect consonance is said to be long. 113 Sequitur de tripli- cibus Triplum est cammixtia trium sonarum secundum habitudinem VI concordantiarum, scilicet uni— sonus, diapasan, etc., et hac in eodem tempore. Et ista est communis descriptio. Speciali- ter autem sic describitur: triplum est cantus proportion— atus aliquis canveniens et can- cordans cum discantu. Et sic est tertius cantus adjunctus duabus. Unde prima regula: triplum specialiter sumptum debet ex re- moto concordare primo et secunda cantui, nisi fuerit concordantia insimul per sonum reductum, quad sibi equipollet. Proprium est diapasan et infra, rematum est triplex diapason et infra usque XII. Concerning organum triplum Triplum is the joining of three voices according to the placement of the six consonances, namely the unison, octave, etc., and this is at the same time. This is the general description. Specifically, however, it is de- scribed thus: the triplum is a voice proportionally fitted to and consonant with discant. Thus a third voice is added to two. Whence the first rule: understood specifically, the EEEET lgm_should be placed so as to be consonant separately with the first and second voices, unless there be a concordance with both at the same time because they are equivalent to each other. The octave or less is called proprium 114 ad diapason, remotissimum est triplex diapason et infra usque ad duplex diapason. Diapason dicitur dupla, diapente cum diapason dicitur tripla, bis diapason dicitur quadrupla, diapente cum bis diapason sex- tupla, triplex diapason, quad vix reperitur nisi instrumentis a flatu, dicitur octupla. Et ista prabatur maxime per magnam figuram musicalem. Multa in praedicti dimisi- mus, quae partim cantinentur in triplicibus nunc praepositis et partim in quadruplicibus post- positis. Primum est de errors, secundum de eorundem calare, tertium est de positiane brevium in propriis locis, quartum est de nobilitate soni, quintum est dissonantia, ut sit cancordantia, (proper), the double octave down to the octave is called remotum, and the triple octave down to the double octave is called remotissi— mum, The octave is used for dupla, the twelfth for tripla, the double octave for quadrupla, the double octave and fifth for sextupla, the triple octave, which is hardly ever found except for wind instruments, for octupla. And this is shown chiefly by large musical figures. We have Spoken of many things, partly involved with the triple now under consideration, and partly with the quadrupla to be dealt with below. First we consider errors in the triplum; second, the gglg£_of that same voice; third, the proper placement of breves: fourth, the nobility of 115 sextum est de capulatione soni. Error tertii soni, quando ordinamus sonas male conven- ientes, quad per quatuor regulas cognascimus, quarum prima talis est: quatiens ascendimus per tanas integras et pastea jungenda semitonium in tonum, canvertitur et ul- timus tonus in semitonium. Quad fit mediante synemmenon, ut patet in exempla: 100. ,f _ the music; fifth, dissonance, so that there might be concordance; sixth the copula. There is an error in the triplum when we arrange the notes so that they fit together badly. We understand this by means of four rules, of which the first is: whenever we ascend by whole-tones a semitone must be added on afterward, so that the last whole-tone is changed to a semitone. This is done through synemmenon, as is shown in the example: 0) Alia regula de eodem est hic: si descendimus tonum et tertium tonum ascendimus, ibi Another rule concerning the same thing is this: ,if we de- scend a whole-tone and then 116 similiter per synemmenan fiet subtracta toni vel soni, ut hic: ascend a whole—tone, here like- wise, through synemmenon, there is a subtraction of a semitone, as here: _____£l____ 101. filth—— (bwchlnfiHM‘ Alia regula de eodem: quotiens ascendimus et iterum descendimus, ascensus largiatur. Et hac fit aliquotiens per synemmenon, aliquotiens autem non, ut hic: Another rule concerning the same: whenever we ascend and then descend, let the ascent be This is sometimes broadened. done through synemmenon, and sometimes not, as here: 102. I I T geafa noéllf Quarta regula est: cantin- uatio sonorum, 51 post semitonium fit vel tonus, et convaniens fit super quietam, penultima‘ The fourth rule is: If a continuation of a voice is made after a semitone or whole-tone, and is made so as to fall near praportia minuitur, sive fuerit semitonium vel tonus: 4%) a rest, the penultimate propor- tion is made smaller, whether it be a semitone or a whale-tone: 103. 'E—___—_HJ7___—__ __._1r I Istae regulae tenentur in cantu plana, sed aliquotiens re- stringuntur in discantu propter habitudinem cancordantiae ipsius discantus, quia subtilis debet cantum suum conformare respectu superioris cantus vel inclinare vel acuere, ut melius conforme- tur cancordantiae, in quantum poterit supradictas regulas observando. Color est pulchrituda soni vel abjectum auditus, per quad auditus suscipit placentiam. Et fit multis madis, aut sana These rules are observed in plainchant, but are often limited in discant because of the place- ment of the consonances, because a good cantus ought to/conform with respect to the upper voice, whether to be lowered or raised, so that it might be more fitting in consonance, as much as is pos- sible within the observation of the above rules. Eglg£_is the beauty of the melody or the object of the ear, through which the ear experiences pleasure. This is done in many 118 ordinata aut in flarificatiane soni aut in repetitiane ejusdem vacis vel diversae. In sana ordinata fit du- plex, aut respectu unius secun- dum praportionem infra diapente, ut hic: 104. Aut respectu plurium infra diap- ason proprie, ut patet in exem- ‘pla, et per abundantiam usque ad triplum, et tali ardinatiane utimur in instrumentis triplici- bus et quadruplicibus. In flarificatiane vocis fit color, ut cammixtia in conductis simplicibus. Et fit semper ista ccmmuxtio in sonis canjunctis at ways: either by patterned sounds, or by the ornamentation of sounds, or by repetition in the same voice or in different voices. Patterned sounds are made in two ways, either with respect to one note according to the propor- tion of the lower fifth, as here: or with respect to several notes properly at the lower octave, as in the example, especially in the triplum, and we use such pattern- ing in instrumental triple and quadruple. Eglg£_is made by the ornamen- tation of the voice, as in the melismata of simple conductus. And this kind of melisma is nan disjunctis, ut hic 119 always produced with conjunct, apparet: not disjunct notes, as it appears here: 105. . o “‘43:; Repetitia ejusdem vacis est color faciens ignatum sanum esse notum, per quam natitiam auditus suscipit placentiam. Et ista modo utimur in rondel- lis et cantilenis vulgaribus. Repetitia diversae vocis est idem sonus repetitus in tempore diversa a diversis vacibus. Et iste modus reperi- tur in triplicibus, quadruplici- bus et conductis et multis aliis ut patet in exempla subposita: Repetition in the same voice is éélér which causes an unnoticed sound to be noticed, and the ear thereby receives pleasure. This device is used in rondelli and secular songs. Repetition in different voices is the same sound repeated at a different time in a differ- ent voice. And this device is found in tripla, quadrupla, con— , ducti, and others, as is shown in the example below: 106. Positio brevium in primo modo est, quad ipsa brevis debet sic poni in concordantia sive discordantia, ut habeat ordina- tianem suam cum sono anteposita et postposita, et per viam ali- cujus coloris, sive fuerit in eadem voce sive in diversis. Et sic intellige de partibus The placement of breves in the first mode is this, that it should be placed in consonance or dissonance, so that it might have a proper arrangement with the preceding and following notes according to some 3219;, whether in the same voice or in different voices. And this 121 vacis in aliis modis. Nobilitatia soni est aug- mentatia ejusdem vel diminutia per madum superbiae, in augmen- tatiane, ut melius videatur, in grassitudine, ut bene audiatur, in fictiane, ut melius appeta— tur, in dimissiane, ut spiritus recurventur. Dissanantia ut sit cancor- dantia est inter duplex diapason et diapente et diapason una dis— sanantia vel duplex bene concor- dat, ut hic: 107. is also to be understood for the other modes. The nobility of the music is its augmentation or diminution according to the demands of excel- lence; in augmentation, so that it is better seen, in greater vol- ume, so that it is better heard, in construction, so that it is better appreciated, and in per- formance, so that the spirit is moved. A dissonance, if it is to sound well, may be placed between two octaves or between a fifth and an octave, and one or two dis- sonances will sound well, as here: 122 Copula duplex est, una quae The copula is understood in est medium inter organum purum two ways: first, that which 18 between organum purum and discant, et discantum, altera est quae . . . . and the other, that which is pro- fit in abSCiSSiane sanarum aut d c d b the cutt'n off f th sumenda tempus post tempus aut u e Y 1 g 0 e , sound, or taking a rest after a tempora post tempera. Et iste . . . single note or several rests modus sumitur flaialis. Et after several notes. This de— aliqui vacant haquetum madum , vice is what is meant by flaio- istum. -——-—- lis. Others call this device hocket. 123 Sequitur de quadru- plicibus Sanis praepositis at prae- positis at praeparatis quartus superveniens in debita quantitate ordinatus, et ista modo quadrup- lum nuncupatur. Et sciendum quad duplex est via quadrupli, una est secundum viam prapriam, alia secundum viam cammunem. Et ad hoc bene percipiendum talis est noster processus. Proprius situs primi dici- tur diapason et infra, praprius situs secundi est in duplici diapason et infra, praprius situs tertii est in duplici diapason et infra cum cammix- tione VI cancordantiarum sive in simplicitate sive in compos- itiane ad utrumque. XIII. Concerning organum quadruplum When (three) voices have been set down and prepared a fourth is arranged above them in proper quantities, and this is called the quadruplum. Let it be known that there are two manners for quadrupla, one is according to the proper way, and the other according to the common way. And thus it is to be understood that such is our system. The proper range of the first voice is the octave and below; the proper range of the second is the double octave and below; the proper range of the third voice is also the double octave and below, with the ob- servance of the six consonances 124 Proprius situs quadrupli in triplici diapason et infra, quad vix in apere ponitur, nisi in instrumentis, ita quad lon- gae in primo modo concordant cum omnibus praedictis, scilicet tribus cantibus praepositis, sive in concordantia simplici w Sed proprietas sive campasita. praedicta vix tenetur in aliqui- bus, quad patet in quadruplici- bus Magistri Perrotini per ta- tum in principia magni volumin- is. Quae quadruple optima re- periuntur et proportionate et in calore canservata, ut mani- feste ibidem patet. Sed quadruplum cammuniter sumptum, de qua ad praesens in- tendimus, madum tripli in alti- tudine et gravitate recepit, quamvis aliquantum excedat in with one or both of the other voices; the proper range of the fourth voice is the triple octave and below, and this is difficult to perform, unless it is done by instruments; it is done such that the longs of the first mode are consonant with all the others, namely the three voices already written, whether in consonance with one or all together. But this propriety of composition is achieved only with difficulty, as is clear in the quadruple of Magister Perrotinus, all in the beginning of his great book. These quadrupla are found to be very well-proportioned and re- strained with respect to 29195, as is manifestly plain. But quadruplum understood commonly, about which we now 12S aliquibus locis. Et sic tale quadruplum cum tribus sibi assa- ciatis ab aliquibus duplex can- tus nuncupatur, quia duo invicem nunc cum uno nunc cum reliquo audientibus, tanquam esset du- plex discantus. Percipitur ta- men instrumentis maxime cam- pletis. Situs praprius prime infra diapason, ut superius. Situs vera secundi est infra duplex diapason et simplex diapason. Tertius in triplici usque in duplici. Quartus in quadru- plici et infra usque in trip— lici, et tamen in adjutaria. Si enim aliquis cantus trans- cendat per acutum et grave suum diapason respectu soni infimi, unus intrahat alium per viam accommodatianis secundum quad speak, is done in the manner of the triplum in height and depth, although it exceeds it in some places. And so the quadruplum, when three voices are added to it, is called by some the duplex cantus, because when two voices are heard now with one voice, now with another, it is as if it were two-voice discant. However, this is understood especially when performed with instruments. The proper range of the first voice is the octave and below, as above;. that of the second voice, the octave to the double octave, that of the third voice in triple the double oc- tave to triple octave; that of the fourth voice in gpgggppla the triple octave to quadruple octave, and so on. If any voice 126 necesse fuerit. Sed quia vox humane ad talia non ascendit, idea quiescamus infra duplex diapason, si possibilitas sit in voce, et pracedamus in prae- dicta quadrupla per ejus regu- las. Unde prime regula est, quad si sit de primo modo, po- nendae sunt amnes longae in con- cordantia cum omnibus longis trium subpositorum ut diximus sua modo. Alia regula: si ascendis cum una vel descendis una pro- pertione, vel dues ascende postee vel descende cum reliqua, et sic mutanda descensionem vel ascensionem nunc cum uno nunc cum reliqua, danec veniat ad Et eodem modo intellige finem. de omnibus aliis. goes beyond its proper octave, whether above or below, with respect to the bottom voice, then one voice enters the range of another by the way of accom- modation, according to what may be necessary. But because the human voice cannot ascend to such a range, it should remain beneath the double octave if possible, and proceed according to the above-stated rules of quadruple. The first rule is, if it be in the first mode, all longs should be placed in consonance with the longs of the three voices written below, as we have said, in their proper manner. Another rule: if you ascend or descend with one voice, after- ward ascend with two or descend 127 Tertia regula est: pon- calores loco sonorum proportion- aliter ignotorum, et quanta magis calores, tanta sonus erit magis notus. Et si fuerit no— tus, erit placens. Item loco coloris in regione cujuslibet pone cantilenam notam copulam vel punctum vel descensum vel ascensum alicujus instrumenti vel clausam lay. Haec positio Johannis dicti de Garlandia, de musica mensurabili. with all the rest, and thus the ascent and descent must be var- ied now with one and now with the rest, until the end is reached. And in this manner understand the arrangement of all the voices. The third rule is: place colores in a place of relatively plain sounds, and the greater the color, the more memorable will be the sound. And if it is memorable, it will be pleasing. Likewise, in the place of gplpp in any passage, place a copula or punctum or the ascent or de- scent of some instrument, or a clausam lay, This is the treatise of Johannes, surnamed de Garlandia, on mensural music. COMMENTARY , Chapter I Garlandia here states that he has previously written a trea- tise on plainchant and the ecclesiastical modes (species). This is apparently the De plana musica, one version of which exists along with the shorter version of the present treatise in the Vatican manuscript (see Introduction). It includes sections on hexachords, mutation of hexachords, and modes, along with some information on the notation of plainchant. The concept of common and proper modes requires some explana- tion. Common mode is non-modal rhythm, that which does not utilize definite repeated patterns. This generally applies to syllabic music, particularly the motet and conductus, written in single (non-ligated) notes, and it may also have some reference to earlier organum duplum (organum purum), which was relatively rhythmically free. Proper mode, on the other hand, refers to the more recent organum, written in pat- terns of ligatures (that is, groups of two or more connected notes) which assumed rhythmic significance more according to their context than their physical appearance. 128 129 All the treatises of the time are essentially in agreement concerning the six modes except for that of Magister Lambertus (Pseudo-Aristotle, Tractatus de Musica, Coussemaker, I, pp. 251-281), whose system consisted of nine modes. Though this treatise is some- what obscure and confused, the modes are as follows: I. JPJMJ mm H J. NJ. M M u. MNMJ. v. J. J. J. WWW mam: mm M? mffifii 17f! The explanations of these patterns are fairly clear. Lamber- tus gives an example of each, and then the durational value of each note. For example, the passage on the fourth note is as follows (Coussemaker, I, p. 274): 130 The first note of the binaria extends one tempus, the second two tempore; the first note of the ternaria extends one tempus, the second, two tempore, the third, three tempore, accord- ing to the ordering of the fourth mode. It can be seen that Lambertus' third mode is Garlandia's (and everyone else's) fourth, whereas the normal third mode is present only as a variant: here, Mode IV which could also be viewed as little more than a variant of mode II. Likewise, the normal form.of the sixth mode is only approximated by Lambertus' ninth. The sixth, seventh, and eighth are problematical, but may be considered variants of modes I and II. Though it may seem unlikely, the binary interpretation of modes VII and VIII here cannot be rejected out of hand (see below). The treatise of Walter Odington gives an example of a mode consisting of long, breve, breve, long (Jay Huff, trans., Walter Odington, De speculatione musicae, Part VI, 1973, p. 14); this is explained as a combination of modes I and II, a variant of one or the other of them. Many such variants existed from time to time. Ernest H. Sanders ("Duple Rhythm and Alternate Third Mode in the Thirteenth Century," Journal of the American Musicological Society, XV, 1972, pp. 249-291) sees evidence that the third mode, especially when used in combination with the first, sometimes took the pattern [ J. J b ]. Though not explicitly supported by the theorists, this interpretation 131 seems to have been necessitated by the demands of consonance and dis- sonance in certain instances. Such a rhythm was not otherwise pos- sible to notate as a modal pattern in Garlandia's system, except for brief appearances in mode I (see below, extensio modi). Of the theor- ists, Anonymous IV is the most helpful regarding irregular modal pat- terns (De mensuris et discentu, Chapter VII, Coussemaker, pp. 361- 364). Sanders also discusses evidence that binary rhythm.was occas- ionally used (mode III = J n ), at least in England. The terms in plenitudine vocis, sub voce cassa, and sub voce amissa are obscure. In the Vatican manuscript the terms per vocem rectam, per vocem cassam, and per vocem omissam occur in the course of the explanation of the concept of tempus, but are not explained clearly. The passage is as follows: The recta brevis is that which contains one tempus. Thus it is possible to explain how one tempus is understood. One tempus, as this is understood, is that in which one recte brevis should be placed. Whence the recta brevis should be placed into a time- value such that it is indivisible; but this tempus is done in three ways. Sometimes per vocem rectam, sometimes per vocem cassam, sometimes per vocem omissam. The recta brevis is placed in the first tempus, that is to say, p25, vocem rectam. It should be known, moreover, that two such breves which are thus written make up one recte longa. On the basis of this confusing passage, perhaps these terms can be clarified. If per vocem rectam means that situation in which 132 a single tempus is represented by a single breve, then it may.be that per vocem cassam (cassam = empty or hollow) indicates that a tempus falls on a later part of a note-value, e.g., the second half of a. longa recte. It would then follow that per vocem omissam refers to a tempus occurring at a rest. This seems to imply some sort of con- cept that the tempus was like a continuous underlying pulse, something more than a hypothetical standard against which the durations were measured. William Waite, however, takes the opposite view. Though the tempus was a time-unit against which noteevalues were measured, it probably should not be construed in the modern sense of a "beat.“ Waite (The Rhythm of Twelfth-Century;Polyphony, 1954, pp. 31-32) has explained that the modes apparently had some connection with the met- rical feet of classical verse, though there is no hint of that here. There had been a practice of indicating these feet with hand motions; thus, each foot included one upward motion and one downward motion. Any metrical foot contained two motions or pulses; but the modal pat- terns contained from three to six tempore, and so the tempus could not be conceived of as an underlying beat, since the relationship of tempus to the hand-motions varied from mode to mode. For example, mode I would have a downward motion of two tempera and an upward motion of one tempus, whereas mode III would have equal motions of three tempore. 133 Garlandia's definition of tempus as the smallest possible time-unit must also be qualified, because it was possible to divide the tempus still further by the use of semibreves. Longa recta translates literally as "correct long.“ Though the long could have two, three, or more tempore, that of two tempore was considered by Garlandia to be the normal type. Likewise, the breve was considered "correct“ when it contained one tempus, and "altered" (though this term is not used here) when it contained two tempore. The term ultra mensuram is more commonly encountered in contemporary treatises than is "oblique.“ Indeed, the latter is sel- dom used even in the latter parts of this treatise. Longs of three or more tempore and.semibreves of less than one tempus were consid- ered "beyond measurement." The treatises of Odington and Lambertus reverse Garlandia's concept, so that the long of two tempore was termed "imperfect," as distinct from the “perfect“ long of three tempore. This is the terminology which survives in the Franconian system and afterward. Garlandia: : (4' duplex longa = J 0 longa ultra mensuram = J q 7 1 longa recta 134 I J (brevis altera) J) brevis recta . Odington and Lambertus: 1 (I (J- duplex longa .1 J. 1.... perfect. .1 J 1.... 1......ct. I J brevis altera lb brevis perfecta It should also be noted that other treatises, such as Walter Odington's, restrict the value of the dpplex longa to two longae rectae; that is, six tempore. But Garlandia was apparently aware of the many instances in the rhythmically free organa dupla of the Notre Dame school in which strictly measured note-values were interspersed with those which were somewhat indeterminate. In such cases, the exact duration of a duplex longa might have to be determined by alignment or by the syllabification of the text. The long "which bends itself toward sharpness or gravity“ is obviously the plica longa, in which the stem on the right side of the note indicates an unwritten pitch, usually a second from the written note, in the direction of the stem (see below). The next passage, after the explanation of the concept of perfect and imperfect modes, is quite confused. The three rules 135 rules for determining the length of non-ligated notes also appear in the Vatican manuscript, but here they are inserted in the middle of an unrelated paragraph. The final five paragraphs of this chapter are probably a spurious addition. It is very likely that the copyist adapted this material from Anonymous IV, where the example showing the process of converting a chant fragment into a modal melody appears verbatim. Also, the term_p£dp, meaning the single pattern of a mode, is used extensively in Anonymous IV, but only seldom in this treatise. Most references to the term are in Chapter II, where it refers to the rhythmic position of longs rather than to the modal patterns themselves. The concept of "reduction" does appear else- where in the Positio, but it also figures in the writings of other theorists. This passage is absent from the Vatican manuscript. In the final two paragraphs it is stated that the rests in the fifth and sixth modes vary;in value. This is problematic, in that specific examples are not given. In the illustrations later on in the treatise, the rest in mode V appears always to be long, that is, three tempore. But, as will be seen, the example of mode V given in chapter IV is unclear; juxtaposition with another voice clears up the confusion in most cases. The situation is more con- fused with respect to the sixth mode. The prOper procedure is clear when this mode is used with mode I or II: the final note has the 136 same value as the simultaneous note in the other voice; but when it is used with the third or fourth mode, there is some question..The examples in the eleventh chapter show these combinations, but only in their perfect forms. For example, when the third and sixth modes are used together, the final note of each voice is a long of three tempore and a long of two tempore, respectively. Thus, the voice in the sixth mode would require a brevis recta rest plus an addi- tional longa ultra mensuram rest, unless it were clear from context that there should be an overlapping of phrases intended: we 1. M J. >. 8’ LID—ID— 8 d m When mode VI is used with the perfect form of the fourth mode, a final long of three tempore seems to be required: .6 #4— 8 W 8 If the sixth mode were to end with a brevis recta in this case, ii that voice would fall silent before the final perfect consonance were reached. Of course, this is primarily of theoretical interest, because the fourth mode was virtually unused in actual composition. 137 Chapter II This brief chapter concerns only the note-symbols and their physical appearance. Throughout the treatise, the term "figure".is used as a generic term for any note or ligature. In reference to ligatures, the concepts of propriety, perfec- tion, and apposite propriety are introduced. The basis of this is the idea that the neumes as used in square plainchant notation were to be considered the normal forms. They were then classified accord- ing to the ascent and descent of the first and final intervals- Since the neumes whose first intervals were ascending normally had.no.ini- tial stem, this was "proper,“ and the addition of a stem rendered the ligature "without propriety." The opposite was true for a de- scending ligature. Likewise, "perfection" referred to the form of the final interval. The plipg is a stem added to the right of a note or ligature, the direction of that stem indicating an unwritten pitch. It will be noted that since the longa simplex already had a stem to the right, a method for distinguishing the plicated long and breve was necessary; hence, there are two stems of different lengths. Though exact rhythmic values depend on context, the following will illu- strate the principle: 138 new 4-4.1? breves: P=J3 sz/j Chapter III The normal forms of ligatures, that is, those with propriety and perfection, were assigned rhythmic values. Thus, the binaria (two-note ligature) is breve, long. The normal ternaria (three-note ligature) is long, breve, long. For ligatures of more than three notes, the value of all those prior to the final two, total one long. Whether these longs are rectae or ultra mensuram must be determined from context. The second rule here presents some difficulty. As the Latin stands, it translates "any figure without propriety and with perfec- tion has the value of a figure with opposite propriety.“ This is contradicted elsewhere in the treatise, and so the passage as it appears in the Vatican manuscript is apparently correct: "oppositum“ instead of “opposite,“ resulting in the given translation, and the following: Pan45=liandrflandfi=ili 139 If this is the correct reading, the upward stems of the descending ligatures are copyists' errors. Garlandia's explanation of the rhythmic interpretation of ligatures with opposite propriety differs from those of other theor- ists. Whereas the method given here results in values less than half a breve, it was more common to let the first two notes of such a ligature each equal half a breve regardless of the total number of notes in the ligature. Whether Gardlandia's method was ever in general use is impossible to determine. The use of liquescent neumes (u) in the illustration of binary ligatures cum opposite proprietate is also unclear. Their rhythmic values are apparently no different from those of the first ligature of the example, and so the concept of perfection has no meaning in these cases. Perhaps these forms retained some of their Gregorian usage as pronunciation aids. The plipa_implies the sounding of an unwritten pitch. Willi Apel (The Notation of Polyphonic Music, 5th ed., 1953, p. 227) has termed the written pitch the "plica-note" and the implied pitch the "plica-tone." The plica-tone was performed according to the direc- tion of the stem, usually resulting in what we would now call a neighboring-tone or passing-tone. Thus, if'the first note of the following ligature were a repetition of the plica-note, the plica- 140 tone would be a second above or below, according to whether the stem be ascending or descending. Otherwise, the plica-tone often filled in the interval of a third, in the manner of a passing tone. Some- times, however, a larger interval appeared between the plica-note and the next written pitch. In these cases, it appears that there was no standared procedure, although a satisfactory result is usually obtained when the interval between the plica-note and the plica-tone is a second. Occasionally the plipg_occurred where the interval with the next written pitch was a second, and the same procedure seems to apply; the plica-tone then anticipates the following pitch. The following example illustrates these different uses of the REESE. as they might appear in Mode I. The rhythmic interpretation of the plica is not explicitly stated in this treatise, nor in those of Anonymous IV and Walter Odington. Magister Lambertus (Coussemaker, I, p. 269), however, treats the subject in some detail. Here it is said that the plica— note and the plica—tone together take the value normally given to 141 the plica-note if it were not plicated. In those cases where the plica-note would be a binary duration, such as a longa recta, there is little problem; the two notes each receive half of the total dura- tion. When the plica-note would have been a longa ultra mensuram, the plica-tone receives one-third of the total duration. In the transcriptions given here, only the former occurs, always in the sixth mode. The latter would appear in transcription as quarter-note, eighth-note. Thus, the plipa could be used in the first or second mode to produce a brief appearance of mode VI. In modes III and IV, the pliga, when attached to the altered breve, would also produce mode VI, but when attached to the long would produce the first mode. Model: r55“): =JJ5U’IJJWIJ :er: .. .wmmm ll ModeIII:1N MN =ioWlJfiJ|J Mode IV: “I: fi‘h =MJHINJHTU'N Note that the addition of the plipa_to the altered breve of mode III or IV necessitates the division of a ternary ligature. Garlandia gives no such examples, and the above examples of these modes are conjectural; however, they are consistent with the manner in which Garlandia breaks up ligatures for other reasons, in particu- lar pitch-repetition. 142 The final paragraph of this chapter is highly cryptic- It is an explanation of the syllabic notation (cum littera, as opposed to melismatic notation, called sine littera) used for conductus and mo- tets, in which passages whose rhythms would otherwise be written in ligatures often have to be broken up into smaller groupings or single notes, because only one syllable can be set to a ligature. The spe- cific rules given here, however, are contrary to the previously- stated principles of propriety and perfection. Thus, according to the first two sentences here, binariae with propriety and without perfection are equivalent to long, breve, while binariae without pro- priety or perfection are breve, long. According to the normal rules, these durations would be indicated by the binariae without propriety and with perfection, and with propriety and perfection, respectively. Thus, here: M N P orf=JP End \Orr but, above:.. or 9 = Jrand rt era It remained for Franco of Cologne to solve this problem by systematically manipulating both the propriety and the perfection of the ligatures, regardless of context. The short-long significance of the normal binaria was retained. The value of the first note be- came long for any ligature without propriety; likewise, the second 143 note was short for any ligature without perfection. In ligatures of more than two notes, the same rules apply to their first and last notes, and all the interior notes are breves unless written with a right-hand stem: Binariae: :or For for F“ Ternariae: aJhN=nJ pfix<=JN sits m pfxv H7 Quaternariae: fi=mJ The connecting link between the ligature systems of Garlandia . M U. )7 M [7}? H and Franco is Walter Odington, who insists throughout his treatise that any'ligature with propriety and perfection should begin with a .breve arui end with a long, regardless of context. Thus, he prescribes 144 a ternaria without propriety at the beginnings of ordines in mode I, because the first note is long. He goes on to say (Huff, p. 23); Others give the ternary ligature propriety in this mode along with the binary. Consequently, in a ternaria the propriety indicates a long, in a binaria, a breve, thus: 5 p I I H p I . . . and so they make both propriety and impropriety represent a breve, which is . . . improper. Odington explains the several variations of modal notation much as Garlandia does, but consistently dismisses them as "contrary to rea- son. According to this passage in the Positio, conductus was writ- ten exclusively in imperfect ligatures, and so a separate set of rules was necessary. Waite (p. 95) amends this passage to read: The rule is that every imperfect ligature, if it is with propriety, extends through a perfection of the first mode up to the first longa that follows it. If it is without propriety, it extends through a perfection of the second mode up to the first brevis that follows. And all this is understood in canductus (and motets) when they appear with a text, if they are notated in the proper manner. But if they are not notated prop- erly, in general all ligatures are to be taken as im- perfect, and this is to be understood in discant and wherever correct measurement appears. This version is much closer to the same passage in the Vatican manuscript (Coussemaker, p. 179): The rule is: any imperfect figure, if it is with pro— priety, extends up to the first following long; if it is without propriety, it is understood (to extend) up 145 to the first following breve. And all this is under- stood in conductus when it is written cum littera, if it is written in the proper manner. If it is written in an improper manner, all figures are generally taken as imperfect, and this is understood in discant and wherever rectus modus is used. This confirms that a different set of rules was used for syl- labic music, and that some copyists did not observe the custom of using imperfect ligatures exclusively; but the final phrase is still somewhat confusing. Apparently discant here means any measured music, and modus rectus is mentioned to clarify the point that syllabic no- tation was essentially a breaking up of regular modal patterns. This is explained with greater detail and clarity in Anonymous IV (Luther Dittmer, trans., Anonymous IV, 1959, pp. 38-40), where definite rules are given for equating groups of single notes to the various liga- tures. This entire problem was theoretically obviated only very shortly afterward by Odington and Franco. Odington's example of con- ductus (Huff, p. 31), however, has no text and utilizes a strict mode I pattern, thus ducking the issue. It would seem that Odington is more interested in saying how he thinks things should be done then in describing what actually was done. This entire chapter of the Positio must be taken as an explan- ation of the rhythmic values of ligatures when used apart from regular modal notation. The rules for binariae generally obtain in the modes 146 as well, but it can be seen that ternariae have different values in different model contexts. In these cases, there was no attempt to show those differences by varying the written forms of the ligatures. Thus, in mode I, the ternaria has the normal meaning of long, breve, long. But in mode III it is breve, breve, long (the second breve is, of course, altered to two tempera), and yet it is still written with propriety and perfection. There were cases, however, in which the propriety and perfection of the ligatures in modal writing were manip- ulated, as will be seen in subsequent chapters. This is precisely the confusion about which Odington complained. These unclarified differences between melismatic and syllabic notation are the.chief stumbling block to the thorough understanding of this treatise, and indeed of pre-Franconian notation as a whole. The marked differences in the views of the various theorists make it clear that notation was in a period of rather rapid change and local variation. One problem is that of precise chronology. It would be attractive to see a se- quence of development from Garlandia to Odington to Franco, but it appears that the treatise of Odington is the latest of the three. Perhaps this is an indication only of Odington's conservatism, and of the fact that developments on the continent were not necessarily paralleled or immediately imitated in England. 147 Chapter IV The six modes, as written in ligatures in melismatic (EEEE. littera) organum and discant, are presented here. It is necessary to clarify several points. First, it will be noticed that in modes I, II, and VI the ligatures retain their normal rhythmic significance according to their propriety and perfection. The second method for writing mode II supports the interpretation that only the propriety of a ligature need be changed in order to reverse all the note-values: In mode I, fl = JPJ In mode II, F- = bl} It was only later that both the propriety and the perfection of liga- tures were manipulated in such cases. Thus, in model notation nearly all ligatures are with perfection; this makes the use of imperfect ligatures in syllabic notation quite distinct from the usage of melismatic notation. Only the fourth mode here uses an imperfect ligature, because the final two notes of an ordo in this mode are both breves, even theough the second of these is altered to a dura- tion of two tempera. 148 Second, the length of the rest-signs does not necessarily in- dicate exact duration in accordance with the later chapter on rests. That chapter is therefore apparently intended to refer chiefly to syllabic notation. In the examples here, the rests in mode I (one tempus) cover two spaces, while those in mode II (two tempore) cover three spaces. However, the rests in modes III, IV, and VI also cover three spaces, while their values range from one to three tempore. In connection with this point, the first example given here of the fifth mode requires comment. This mode was thought of as per- fect when the phrase contained an odd number of notes. Thus, like the third and fourth modes, it was apparently considered to have a modal pattern (perfection) of six tempore. The illustration, however, contains two phrases of two notes, as well as two shorter rests. According to Apel (pp. 245—253), two-note groupings in the fifth mode were often rendered as if the first note were a duplex longa; this was usually clear in juxtaposition with a simultaneous voice. Another transcription is possible, however. The first chapter states that rests in the fifth made were sometimes short in imperfect ordines. Also, the chapter on rests says that the length of rest- signs is an exact indication of duration only in the perfect modes. Though these statements may seem to be mutually exclusive in this instance, they do suggest that in the fifth mode the rest is 149 sometimes a breve. This in turn, of course, requires that the pre- ceding note be shortened to a lopga recta. Hence, the example could be transcribed: 8 However, the slightly later writings of Anonymous IV and Walter Odington make no mention of any variability of the rests in the fifth mode, except that Anonymous IV includes the cautionary note that, in the case of earlier music, more consideration must often be given to the vertical alignment of parts, because notational niceties were often unobserved (Dittmer, p. 21). The second method shown for writing mode V is identical to that used for the first p£dp_of mode I; hence the admonition that this is not strictly proper, but is the custom in tenors only. Even Odington, with his distaste for any variant rhythmic reading of lig- atures, approves this method (Huff, p. 26). We see here a pattern common in tenors of all types of polyphony at the time, and it would seem that this is the germ of the isorhythmic principle in the fourteenth-century motet. Third, ligatures must occasionally be broken up into smaller groupings or single notes in order to allow for pitch-repetition. 150 This seems to follow the rules for non-modal notation, in that a binaria of mode I or II becomes a long and a breve, and a ternaria in mode II may become a binaria without propriety followed by a long. This also holds true in mode IV, where a ternaria can become a breve followed by a binaria with propriety, or an imperfect binaria fol- lowed by a long: In modes I and II: r‘. or a z; a 1 '= )5) In mode IV: ‘H. :; "tn‘wf 'F’1 == {b4 Jo There are anomalies, however, such as in the second example of the sixth mode, where a ternaria becomes an imperfect binaria followed by a long (a breve would be more accurate), and in the second example of mode I, where the binaria with propriety must be read as long, breve. Fourth, the first example of mode II contains a ternaria in the middle of the second phrase. If a rest is supplied immed- iately thereafter, there is no abnormality. But if it is correct as it stands, then fractio modi is indicated. This is a concept not mentioned in the Positio, but it is covered thoroughly by Anony- mous IV and other writers. In cases such as this, the first note of the abnormal ligature takes half the value of the preceding note. 151 This results in a brief appearance of the sixth mode or, since the ternary ligature begins on the second of group of three tempore, it could be construed as the second mode. The same result could be achieved, but without the implication of mode II, by the use of a plica: app-.31 air-N31 minimum mwwgy L.._JL_.JL__._.:L_| Hans Tischler (“A Propos the Notation of the Parisian Organa," Journal of the American Musicological Society, XIV, 1961, pp. 1-8) disagrees with this interpretation. Tischler bases his opinion on motets which were made by simply adding text to the upper voice(s) of organum. Working from the assumption that the organum and.motet versions necessarily have identical rhythms, Tischler would preserve the long value of the last note preceding the abnormal ternaria, and then render the first two notes of the ternaria as semibreves: Mn.“ .-. WNW J7 m, This view is supported by many motets, but Tischler has not demon- strated the necessity of exact rhythmic correspondence between the organa and their motet versions. It would seem probable that small rhythmic alterations could have been introduced. This rhythmic ad- justment could have been the result of problems arising from the very process of adding a text in order to create the motet. For example, 152 if the above example were transcribed according to Anonymous IV, the following would result: mum» L_———JL_J Unless the abnormal ternaria were broken up, any new syllable would have to begin on the first note of the ternaria, thus producing a momentary shift to the accentuation of mode II, as indicated above. The nature of the text may have made this undesireable, and so semi- breves were introduced to preserve the trochaic pattern. If the ESE? papia_in question were otherwise broken up, confusion could result as to whether or not extensio modi were intended (see below). All of this is not to say that Tischler's interpretation is not valid for some cases, but the point is hardly settled. Since the treatises of Anonymous IV and Garlandia are essentially in agreement on most points, it seems reasonable to utilize the method described for fractio by Anonymous IV, even though Garlandia does not explic- itly condone it. It is also important to realize that nowhere does Garlandia admit the possibility of the introduction of semibreves into strict modal rhythms. His discussions of currentes and ligatures cum opposite proprietate, both of which use semibreves, are more in reference to syllabic or other essentially nonemodal passages, such as copulae. In some instances, principles of consonance and disson- ance may well dictate adjustments of the kind Tischler describes. Un— fortunately, Garlandia's polyphonic examples do not help us here. 153 From this standpoint, those which do utilize fractio modi are satis- factory by either rendering. It was also possible to introduce longer note-values into modal passages, a process called extensio modi by Apel (pp. 234-235). Thus: firm- 11.3 = JJ’JHJNJJJJJN This passage conforms to all the rules given previously: the long of the third ligature is extended to three tempera because it falls be- fore another long, and the final ternaria retains its normal reading according to its propriety and perfection. Finally, it should be mentioned that the end of the first illustration of the sixth mode is irregular, requiring the penultimate binaria to be read as two breves even though it is written with per- fection. The final ligature has also been transcribed in this way, although the normal reading, breve, long, would also be acceptable. As was discussed previously, Odington's treatise disagrees with the Positio on details of propriety and perfection of ligatures in the notation of the modes. His complete system is as follows: I. ternaria without propriety and with-perfection, binariae with propriety and perfection. II. binariae with propriety and perfection, single breve. 154 III. queternaria without propriety and with perfection, ter- nariae with propriety and perfection. IV. ternariae with propriety and perfection, binaria with propriety and without perfection (as Garlandia). V. single longs. VI. ligatures of any number of notes with propriety or oppo- site propriety, and without perfection. Garlandia's method of writing mode VI with plicated binariae is mentioned, but dismissed as being in reality mode II; the concept of "reduction" to another mode is absent here. Lambertus is essentially in agreement with Garlandia where the modes correspond, except that imperfect ligatures are used for mode V (Coussemaker, p. 275): ' 4 @312 Chapter V The imperfect modes are those in which phrases end with a note-value different from that of the initial note. The underlying 155 concept here is that the succession of durations basic to a particu- lar mode continues, with rests placed where a repetition‘of the ini- tial note-value would normally have occurred, thus causing the suc- ceeding phrase to begin in the middle of the modal pattern. It is in these imperfect modes that we see a great deal of manipulation of the propriety and perfection of the ligatures. In this chapter there are several problems with the original text. For example, in the explanation of the first method of writing mode III, the original states that the ternariae should be imperfect, whereas they are shown as perfect; inasmuch as the final note of a ternaria is long, it is more fittingly perfect, and so the text has been amended here. In the subsequent example, the explanation is in- complete. The full pattern is: long, imperfect binaria, rest, long, perfect binaria, rest, etc. In the illustrations of mode II, there are apparently missing rests; the third rest of the first example and the fifth rest of the second example have been added. The examples of the imperfect sixth made also require comment. It will be noticed that the ascending plicated binariae are written in imperfect form. This is apparently only a notational convenience, and it is mentioned by Odington (Huff, p. 22): “Occasionally an ascending ligature, without perfection, has the plica too; but in this instance the plica, according to some, changes the ligature from 156 imperfect to perfect.“ He then goes on to say that a plicated liga- ture can be rendered imperfect by use of the oblique stroke: M? In this case, the plica-note and plica-tone together would equal a breve, and so semibreves result. This explanation helps consider- ably in interpreting the examples of imperfect ligatures given near the end of the third chapter. In the second example of mode VI several of the binariae are separated into single notes because of pitch-repetition. The second note of each pair is written as a regular long, although according to the second chapter two stems are required for a descend- ing pligg, the one on the right longer than that on the left. Anonymous IV discusses the imperfect modes in much greater detail than does Garlandia, but Odington treats them even more briefly. It is true that they were hardly ever used in actual compo- sitions, and so are chiefly of theoretical interest. The correspond- ing passage in the Vatican manuscript is much abbreviated. Detailed explanations of the proper ligatures are absent, and many of the examples are obviously incorrect. For example, the following is given to illustrate the imperfect second made: i v 157 The first part of this example corresponds to the imperfect third mode as explained in the Positio, and the remainder has no counter- part there, though it is easily transcribed. Though the same chant sources are used, none of the examples in the Vatican manuscript occurs in the Positio in precisely the same form and location. Franco of Cologne, speaking about the imperfect modes, men- tions that the rest has the capacity to change the modes, so that the first mode becomes the second or vice versa. In the imperfect first mode, for example, the second phrase will begin with a breve, which was apparently not thought of as any sort of anacrusis. Thus, there was probably no concept of real accent or stress in this music, but rather a purely qualitative concept--a point of similarity with classical metrics (for further discussion of this point, see Waite, pp. 40-41 and passim). Anonymous VII (De musica libellus, Coussemaker, I, pp. 378- 383) also mentions changing modes within a phrase, but in a different way: And it should be known that the first mode, which proceeds with a long and then [a breve], merges with the fifth mode, which proceeds with all longs; for sometimes in a motet, after several longs, there immediately fol- lows a long and then a breve; and thus one mode is made from two by equipollentia and by such merging. The second mode merges with the third, for after a long or two breves in the third mode, a breve and then a long can immediately follow. And thus from the third and second modes one mode can be made by equipollentia 158 and by such merging. Similarly, the third.mode and the fifth merge in this [way], because after a long in the fifth made, two breves from.the third mode can follow: and thus, by Equipollentia and by such merging, one mode can be made from the third mode and the fifth. This seems to refer chiefly to syllabic music of the later part of the period in question, when the modes were not so strictly observed. The first paragraph of the passage, in particular, sup- ports the transcription of the conductus in the Appendix below; if the overall rhythm is considered to be that of mode V, then binariae are transcribed in mode I rather than mode II. The treatise of Anonymous VII is not long, and is, on the whole, consistent with the Positio. It does not cover notation in any depth, but discusses tgppus, the basic note-values, forms of notes and ligatures, intervals, and a few points concerning the ecclesiastical modes in antiphons and Psalm tones. Though the note-values are described as in Garlandia (e.g., the longa recte has two tempera , ligatures are treated somewhat dif- ferently. Here there is no reference to opposite propriety, and five- note ligatures cum proprietate have the initial upward stem: 5. w All ligatures of more than three notes are reduced to the value of the ternaria, which is long, breve, long: 159 JN =mJ LP: .6771 This example makes it clear that the concept of opposite propriety PI. is in force here, though unstated. This treatment of five-note ligatures is also similar to the interpretation of currentes or con- juncturae as presented by Anonymous IV and others: 577} The values for ligatures other than those with propriety and perfec- tion are not given. The passage immediately following that given above is also of interest, because it implies something similar to Garlandia's concept of reduction: It should be observed that the motellus [upper voice of a motet?], in whatever mode it may be, should be judged according to that mode in which the tenor is. And the reason is that the tenor is the foundation and more important part of the motet; and a thing should be identified according to the more important and more worthy. Therefore, if the motellus is in the first mode, as in Bone Compaigpie and p_quam sancta and many others, but the tenor is in the fifth mode, the motel- lp§_is said to be deemed in the fifth mode, for a long and a breve in the motellus are equivalent to a long in the tenor; for any long in the tenor has the value of a long and a breve in the first mode according to the rule given above. .--< 160 The fifth and sixth modes cannot, of course, and with a dur- ation different from the initial one, and so here the concept of perfection refers to the normal length of a modal pattern. In mode V, this was apparently six temppra, so that the final note of a perfect ppdp plus the necessary rest completed the final perfection. Thus, the imperfect form of this mode had an even number of notes, so that the rest occupied only the first half of a perfection. There is evidence that this was not a stable concept, however. When used with the first or second mode, the fifth mode may have been conceived as having a perfection of only three temper . The examples of mode VI make it particularly unclear as to whether the perfection was three or six tempore. There is no apparent difference between Gar- landia's examples of the perfect and imperfect forms of this mode, except that the ligatures fall in different rhythmic positions. The Vatican manuscript is also unclear on this point. The example of the perfect fifth mode has one p£gp_of five notes and one of ten; the imperfect example is correct, however; three ordines of four notes. The examples of mode VI are totally incoherent (Cousse- maker, p. 177): Exemplum sextae de modo perfecta: .1 are 161 Exemplum sextae de imperfecto modo: Sale- e—a! For the views of Odington and Anonymous IV on this problem, see below. Chapter VI The general rules presented here apply to both model and non- modal music. Most are fairly easily understood, and are consistent with preceding statements. Thus, the rule that ligatures of more than three notes are reduced to the value of three, holds true for the qpaternaria found in the sixth mode: a'n-‘iJaN and #1th Garlandia is careful to stress the point that these equivalences (quipgllentiae) depend on context, just as do the values of liga- tures in modi recti. The final paragraph, however, is quite difficult. Waite (p. 87) translates this passage, “Whenever there is a multitude of breves, 1.6., semibreves, they always share in the value of the preceding note, because the preceding note together with these semibreves is understood to have only such a value as the preceding note repre- sents." 'In practice, that preceding note was always a long, and so A | :‘ 162 we have here basically another type of fractio modi, usually referred to as currentes (“running.notes") or'conjuncturae, and these are per- haps the most difficult problem.in thirteenth-century notation. In Garlandia's example, it is difficult to recognize any model context, and so, without knowing whether the longs are rectae or ultra mensuram, no transcription is possible. After the rest, mode III may be in- tended, and this portion would then become: gm finfimm It seems probable, however, that the illustration is simply a group of representative ligatures of this type, rather than a measured passage. Anonymous IV is in agreement with Garlandia on the point that currentes share in the value of the preceding note. The most extensive presentation of this subject is in the Tractatus of Magister Lambertus (Coussemaker, pp. 275-278). According to this passage, either currentes (here called conjuncturae, although it should be noted that elsewhere Lambertus uses the term interchangeably with 'ligature“) or semibreves of a ligature cum oppgsitagprgprietate could imperfect the preceding note. Thus: JITJnglac. Wimp. 163 It is interesting to note that in the first example the EliSE. shortens the value of both notes of the binary ligature, rather than only that of the plica-note ( J m ). Lambertus is explicit in stating that the semibreves are equal. This final paragraph of Garlandia's chapter also brings out the point that the terms pppyg and semibreve were not completely fixed at this time. Sanders ("Duple Rhythm . . .," pp. 267-268) discusses this, pointing out the avoidance of the word "semibreve“ in Anonymous IV, and coming to the conclusion that "semibreve" can mean half of either a breve or a long. That is to say, if two shorter values take the place of a long, they can be called semibreves, although their value is that of a recta brevis. Lambertus, however, seems to use semibrevis exclusively in reference to divisions of the breve. Chapter VII There is little difficulty with this information on rests, except for some of the statements concerning the relationship of the rest to the preceding mode. The principle that a perfect mode con- tains an odd number of notes is obvious with respect to modes I, II, and V, but is not necessarily true for the others. It has been shown that there is no discernible difference between Garlandia's 164 illustrations of the perfect and imperfect forms of the sixth mode, and so the pertinent statements here are difficult to apply. Even if it is assumed that the perfection of the sixth mode is six Esm- pgpg, it can be seen that the second example given above of the sixth mode has an ppdp of twenty-two notes, an even number. It is probable that "even“ and “odd" here are in reference to the normal number of notes found in a particular pgdp, Thus, any multiple of three (or six) would be an “even“ number for mode VI, and likewise for modes III and IV. If this is true, then it would seem that Garlandia considered mode V to have a perfection of six tempore, and would thus require a duplex longa rest in some cases where the number of notes is even. However, this is difficult to square with the examples given elsewhere in the Positio. The other theorists are of little aid in clarifying this point. Odington (Huff, pp. 19-20) states that the sixth mode has a perfection of three temppra, but that it is sometimes considered to be six tempore when used with the modi pg; ultra mensuram. In the perfect form of the mode, therefore, there are groups of three notes followed by a single breve and then a rest of two tempore. The imperfect form has only groups of three: gimme) 165 This does not appear in Garlandia's examples, however. Anonymous IV (Dittmer, p. 23) describes a more complex repetitive pattern similar to Garlandia's second example of the imperfect first mode: gunman :m/n. Also, both of these theorists consider the perfection of the fifth mode to be only three tempore when used with modes I and II: this eliminates any concept of perfect and imperfect. The rule that the rest takes the value of the penultimate note of the preceding mode is also problematic; it is true only for modes I, II, and V. It is perhaps significant that these are also the modes which most often appear in compositions, and so this rule would apply to most instances encountered by the performers of the period. Garlandia seems to apply general rules to matters which simply cannot be so systematized; his method is typical of the often turgid scholasticism of the thirteenth century. Hence the rule that perfect rests (i.e., those used in the perfect forms of the modes) should be reckoned according to their length; but in his own examples this precept is not observed, even where the different versions of the treatise agree. The parallel passage in the Vatican manuscript is of some help with this chapter. It is important to note that it has demissio 166 for divisio in the second sentence: "A rest is the absence of sound made in a proper quantity." Chapter VIII The types of rests presented here are those found in both model and non-modal contexts. The finispunctorum roughly corresponds to a double bar placed at the end of a section, generally followed by a change of style; from strictly modal organal or discant style to the freer copula, for example. The divisio modorum is the rest placed between ordines in model passages, and its duration varies according to context, especially in the imperfect modes. The divisio syllabarum and suspiratio are not rests at all, properly speaking. The former simply marks changes of syllable in order to facilitate coordination of voices in melismatic passages. The latter is appar- ently only a breath mark for the singer or player. Thus, neither of these is a measured rest. Anonymous IV does not expand significantly on the information given here, although he does give some specific examples. Odington, however, anticipates the later punctus divisionis, calling it divisio View; modi: 167 Odington also introduces the semibreve rest, and differentiates be- tween the perfect, imperfect, and altered forms of longs and breves. Thus, the perfect long rest covers three spaces, the imperfect long or altered breve covers two, and so on, according to the number of tempora represented. The finis_punctorum is also included, but not the divisio syllabarum and suspiratio. The rests given by Lambertus are similar, but provide for two types of semibreve (one-third tempus and two-thirds tempus): perfect long rest, four spaces; imperfect long or altered breve, three spaces; brevis recta, two spaces; semibrevis major, one space, semibrevis minor, one-half space. These are named, reSpectively, perfecta pausa, pausula imperfecta, suspirium, semisuspirium majus, and semisusprium minus. The finis punctorum, divisio syllabarum, and suspiratio are not mentioned. This is essentially the same as Franco's system. Chapter IX Garlandia's classification of consonance and dissonance re- sults in the following ordering from most consonant to most dissonant: 1. unison, octave 2. perfect fifth and fourth 3. major and minor thirds 168 4. major sixth, minor seventh 5. major second, minor sixth 6. semitone, tritone, major seventh. The demonstration of compound intervals attempts to treat the subject with the techniques of Aristotelian logic (Garlandia was one of the scholars who persisted in teaching Aristotle in spite of the Papal ban then in force against most of Aristotle's writings). It is an interesting glipse into the scholastic method, but is hardly a cogent argument. The point being made can be deciphered thus: given an octave on G, a third above the upper note is consonant with both pitches of the octave, but a third above the lower G forms a sixth with the other, and so is consonant with one and dissonant with the other. The same argument is unsuccessful, however, when applied to the fifth, because a fourth and a fifth are formed, which are equally consonant according to Garlandia's classification. It is probable that this entire passage is a borrowing from another source, according to which the fourth was considered less consonant than the fifth. For example, Odington (Huff, pp. 28-29) considers the fourth a proper consonance within a piece, but states that the final interval should be a unison, octave, or fifth. 169 Chapper X This brief chapter presents the mathematical proportions of the various intervals. As explained in Anonymous IV (Dittmer, pp. 53-56), there were five types of proportions: multiplex, superpar- ticularis, superpartiens, multiplex supegparticularis, and multiplex superpartiens. In the multiplex variety, one number is a multiple of the other; thus, the octave, 2:1, is of this type. Superparticu- laris proportions are those in which the upper number is one more than the lower. For example, sesguioctava, or 9:8, falls into this category. Those proportions whose upper number contains the lower plus several fractions were termed superpartiens: superseptempartiens pppag means that the lower number is nine, and the upper is nine plus seven, i.e., lw:9. The final two types represent multiples of these, for example, multiplex superparticularis is a ratio in which the upper number is a multiple of the lower, plus one. Garlandia's ~ratios are those of Pythagorean intonation. That given for the minor sixth, however, is incorrect. The correct proportion for the sixths B-C, A—F, and B. G is 384:243 (in other words, CCLXII should be substituted for CCXLII in the manuscript). This is obtained by subtracting the major third from the octave. It should also be noted that Garlandia's ratio for the tritone, 729:512, is the augmented fourth, obtained by subtracting the perfect 170 fifth from the major seventh. The ratio for the diminished fifth, 1024:729 (obtained by subtracting the major seventh from the perfect eleventh) is omitted. The explanations given for the major and minor thirds are somewhat unclear. They are freely translated here, but perhaps an- other interpretation is possible. The given translation proceeds from the assumption that the statement literally says, “The major third is a lesser superpartiens than the minor third." That is to say, the upper number is proportionally closer to the lower, and so the ratio is closer to equality and the interval is more consonant. If, however, the term "lesser superpartiens" indicates a specific interval, a reading which also makes grammatical sense, then the statement would read, "The major third is greater than the minor third by the lesser superpartiens." That interval of difference is 2187:2048 (major third minus minor third, or 81:64 divided by 32:27), which in the Pythagorean system is also the difference between the whole-tone and the semi-tone. This was usually called the apotome, chromatic semitone, or semitonus major (because it is a larger inter- val than 256:243, the diatonic semitone). This interpretation, however, breaks down when we proceed to the explanation of the minor third, because it is incorrect to say that the minor third is greater than the next smaller interval by the 171 same difference:.uthe.minor third minus the major second (32:27 divided by 9:8)-equals 256:243, the diatonic semitone (or diesis, or semitonus minor).. It can be seen that Garlandia's explanation of intervals is, at best, incomplete. It is more a quick primer than a full exposi- tion. The rules for the placement of dissonance seem to be fol- lowed for the most part in the polyphonic examples in Chapter XI. The only real prohibition here is that a consonance should not be preceded by any of the three most dissonant intervals. However, it will be seen below that the tritone is occasionally found in a consonant position regardless of the theory. Chapter XI This section is arranged so as to present examples of all possible combinations of the six modes in two-voice discant. It begins with a general discussion, defining discant as the simul- taneous sounding of measured voices. It will be seen that this is in distinction to organum, in which the tenor was not measured (but organum is also generic for all polyphony), and copula, in which 172 rhythm was essentially free of modal patterns. §ppgg_is apparently the melody itself or the pitch of.an.individual note, whereas 253327 g2§g_refers to the arrangement of that melody into ligatures and rhythmic patterns so that the total duration will coincide properly with another voice. The third paragraph says essentially that longs in any mode ought to be consonant; literally, the statement refers to the odd- numbered notes, which are longs in the first mode. Thus, there was nearly always consonance in strong rhythmic positions. This does not necessarily mean that part of the measure which would be considered rhythmically strong today. In mode II, for example, the long is rhythmically strong merely because of its longer duration, though it falls on what would be called a weak position in the bar. This idea is immediately qualified by the statement that two notes equivalent to a long may be set against a long, and that either one of them.may be dissonant. There are many instances of this in the illustrations which follow; for example, this passage from example 75: 173 Many surviving organa (but none of Garlandia's examples) begin in this manner, with a strong dissonance at the initial attack: Octaves, fifths, and unisons, as is to be expected, are the most common consonances in these illustrations, but thirds and fourths are also fairly common, and there are instances of the tritone being used as a consonance (this is from example 63): sixths are here consistently treated as dissonant intervals. The examples in this chapter are arranged in the following order: first, modus rectus with modus rectus, then modus per ultra mensuram with modus per ultra mensuram, and then modus rectus with modus per ultra mensuram. Each of these groups has two divisions; either the modes are "in the same ordo“ or “in opposite ordines." In most cases, this concept is fairly clear. Two modes are said to 174 be "in the same pgdpf when the longs--that is, the parts of the pat- tern requiring consonance--fall simultaneously. Thus, when modes I and II or III and IV are used together, the longs fall in different rhythmic positions, and so the modes are said to be "in opposite ordines.“ Since the sixth mode contains no longs, it must be con- sidered as equivalent to either the first or the second mode, so that the note requiring consonance would be either the first or second of the pattern. When written as plicated binariae, the plica-note of each ligature was theoretically long, and so in this form the mode was considered equivalent to mode II for harmbnic pur- poses. When written in ternariae the sixth mode could reduce to either the first mode or the second. The fifth mode could also be thought of as reducing to either mode I or II. Therefore, when it appeared along with the third or fourth mode, the altered breve of the latter was often consistently consonant as though it were a longa.recta of mode II. Though this concept is not excessively difficult, it is often difficult to apply to the examples. In the case of examples 65 and 66, it is hard to see any difference from examples 60 and 61, though the former are supposedly on opposite ordines and the latter in the same gggp, There are other anomalies as well, most being obvious copying errors; for example, the listing of modes III and VI among combinations 175 of odd-numbered modes, whereas the examples are of modes III and V (examples 90 and 91). Near the end of the chapter, in the section concerned with combinations of modi recti and modi per ultra mensuram, the combination of‘modes I and'VI appears, though both are modi recti. Fractio modi is found in numerous instances in these examples (such as the final one, example 99), and there is one instance of what appears to be extensio modi. In example 84, a binaria is found in the sixth mode. It is here transcribed breve, long, in order to preserve the rhythmic placement of the following ligatures. However, the questionable use of a dissonance against the long in the upper voice suggests that the original is incorrect at this point. In many of the examples the value of rests is doubtful, expe- cially in combinations of modes whose final durations are different. The upper voice ends before the final consonance is reached in example 84, and an extra rest of three tempgra is necessary. There are numerous similar circumstances. A copula is a brief passage in no strict mode, usually occur- ring at the end of a main section of organum. The notation usually included numerous currentes and plicae (this is apparently what is meant by tractus, or “lines"; see waits, P. 116). There was often an underlying modal rhythm, but it was almost completely obscured both aurally and visually by the abundance of irregular groupings. 176 Odington describes the copula somewhat differently (Huff, pp. 31-33). Here, it is placed at the ends of sections and is always begun with an unmeasured long, and then proceeds in binary ligatures in either the first or the second mode. There is also the possibil- ity of writing copulae with all unligated notes, in which case they are apparently equal breves as in the sixth mode. Many copulae contain currentes of as many as nine notes, and several more or less satisfactory solutions are possible in most of these cases. Sometimes it appears that the ligatures have none of their normal rhythmic significance, and so one must proceed merely on the basis of consonance and dissonance. Garlandia's classification of organum into per se and gum alig_apparently refers to two- and three-voice writing, respectively. Two-voice organum could be either strictly modal or rhythmically free; this latter accounts for the great majority of early organum duplum, often referred to as organum purum. This was similar to the unmeasured organum of St. Martial, and apparently comes from a time when the ligatures were beginning to assume rhythmic significance, but were not yet systematized into modes. Most of the notes, however, were read as longs or breves as in mode I (rectae), and so it is to this that Garlandia is referring in the final passage of this chapter. Since longs and breves were not consistently differentiated by their 177 physical appearance in that early stage,.it was necessary to determine durations on the basis of consonance.and dissonance. This subject is treated much more thoroughly by Anonymous IV (Dittmer, pp. 71-72), where specific and exhaustive rules are presented. Chapter XII Just as the word organum is both generic and specific, the term triplum refers both to three-voice polyphony and to the third voice itself. This third voice was added to two previously composed, a process known as "successive counterpoint." The triplum.was re- quired to be consonant with only one of the other voices, and so there was often a much greater incidence of dissonance in tripla than in QEEQE' In the second paragraph, the listing of intervals proper to the various types of polyphony apparently refers to the maximum in- terval spanned by the other voices at any time rather than a general range limitation. The treble octave was apparently indicated by some special convention of notation ("large musical figures“), but the precise meaning of this is unclear. The four rules given for the adjustment of melodic intervals are essentially what was later known as musica ficta. Thus, there‘ 178 will be a B-flat in the first example, and an F-sharp in the second. The third rule is difficult to interpret; perhaps the “broadening" is some sort of rubato or ritard. This may have something to do with the perfonmance of chant, the kind of thing indicated by the episema in the editions of the Benedictines of Solesmes. The reference to synemmenon, however, also suggests some manipulation of intervals. Synemmenon was the process of adding a conjunct tetrachord in Greek theory, and in the Middle Ages the con- cept was applied to the theory of hexachords. In the first example, this means that whereas the beginning utilizes the "natural" hexachord C-A, the B-flat is provided by overlapping the "soft" hexachord F-D, with three notes common to both. In order to arrive at the F-sharp of the second example, it is necessary to use a hexachord on D, be- cause any hexachord had only one semitone, falling beteen the third and fourth notes. In the original Guidonian system, only the hexa- chords on C (“natural"), F ("soft"), and G (“hard“) were used, and so B-flat was the only possible accidental. The final rule here indicates that a C-sharp was supplied; thus providing a leading-tone to D. This was apparently done in plainchant as well as polyphony at the time. Garlandia's caution concerning this practice in polyphony is easily understood through this illustration (from chapter XI, example 96): 179 If F-sharp is supplied in the upper voice according to the second rule, then a diminished fifth occurs with the C in the lower voice. This would violate the rule in Chapter X that a perfect dissonance ought not immediately precede a perfect consonance. If the C in the lower voice is sharped as well, all the rules seem to be satis- fied. There are many instances in which this type of chromatic alteration is suitable on melodic grounds, but results in unaccep- table vertical sonorities. It is apparent that the so-called double leading-tone was a part of performance practice as early as the mid- thirteenth century, although in the example above it might be pref- erable to avoid chromatic alteration altogether. 22l2£.is a relatively vague term referring to ornamental effects. The examples here show sequence-like patterns and a repeti- tion of pitch which must have been some sort of vocal tremulando much as the distropha and tristropha (I I and III on a single syllable) may have been in chant. The statement concerning repetition in the same voice probably has reference to various secular song-forms which used refrains and other musical repetitions quite extensively. The 180 term.rondellus was sometimes merely the Latin form of rondeau, but was also used to mean a.type of polyphony similar to a round or canon, in which a melodic fragment was passed from voice to voice while the accompanying voice or voices were varied. Odington uses the term in this sense, and gives a complete example (Huff, pp. 29- 30). The next illustration shows a simple exchange of parts, now generally known as Stimmtausch. The notation is somewhat irregular. The plicated ligature should probably be perfect, and the descending currentes would be better expressed by a ternaria cum opposite pro- prietate. However, the other voice makes it clear that mode II is intended, and so the solution is arrived at through consideration of consonance and dissonance. It seems probable that the B-flat in the second measure of the lower voice and again in the third.measure, upper voice, should be performed as B-natural. The paragraph concerning the "nobility" of the music is cryp- tic. The exact usage of the term augmentation is unclear, and the ‘wordings of the editions of Coussemaker and Cserba are different. Cserba's version is given here, but neither his nor Coussemaker's is entirely satisfactory. The mention of hocket contains the only known occurrence of the term flaiolis, which has no readily apparent etymological 181 connection with any standard Latin or Greek term. Odington (Huff, pp. 34-39) gives a much.more thorough discussion of hocket, includ- ing an example in each of the six modes. He also mentions that when semibreves are used in hocket a small circle is used in place of the divisio modi, because the latter is identical with the semibreve rest. This does not appear to have been in general use, inasmuch as there is no mention of it by the other theorists. Anonymous IV and Odington also refer to various types of ornamentation. Anonymous IV uses the term.florata in describing the prolongation of a consonance at the beginning of a piece, and Oding- ton says that in ogganumjpurum the sustained tenor is “held tremulando, even when it strikes a dissonance“ ("Tenor autem tremule teneatur, et cum discordia offendit," Coussemaker, p. 246). Franco also mentions that there was some discretion left to the performer, but this is stated in the context of the preservation of consonance (Coussemaker, p. 135): Whatever is long, let it seek concordance with respect to the tenor; but if a dissonance should arise, let the tenor be silent, or shape itself into concordance. Later in the same passage the word floratura appears, describing how the notes should be sung when all the voices approach a unison. Garlandia was certainly acquainted with the term.aolor as it was used in rhetoric. and literature. This technical usage dates 182 back to a more or less figurative usage by Cicero and others; the terms flos (flower) and color could be taken to mean either an ornate style of writing or speaking, or a specific embellishment of diction. Seneca described rhetoric as consisting of three parts: sententiae, the ideas presented; divisio, the analysis and organization of those ideas; and colores, the imaginative expression of ideas (see Charles Sears Baldwin, Ancient Rhetoric and Poetic, 1959, pp. 97-100). According to James J. Murphy (Rhetoric in the Middle Ages, 1974, p. 189), Eplp£_was by the middle of the eleventh century a technical term meaning a figure of speech. By the time of Garlandia, most treatises on rhetoric referred to figures of speech as colores verborum. Garlandia‘s own treatise, De arte prosayca, metrica, et rithmica, lists forty-three colores verborum and eighteen colores sententiarum (figures of thought). The relationship of this to the musical use of the term he- comes apparent when this list is examined: the first three entries under colores verborum are repetitio, or anaphora, the repetition of a word at the beginnings of successive lines; conversio, or EEEEET trophe, the repetition of a word at the ends of lines; and complexio, or interlacement, a combination of the other two. Garlandia's examples of gplpp in music are also largely concerned with forms of repetition. Thus, it seems that musical expression was considered, 183 at least in some quarters, to be parallel to rhetorical expres- sion. By the following century, this technical usage of the term color had faded. Colores rhetorici in the fourteenth century came to mean simply "figurative language" in a general sense. In the Canterbury Tales, Chaucer mentions "colours of rethoryk" almost sarcastically, implying that stereotyped figures of speech have no place in good narrative (see Charles Baldwin Sears, Medieval Rhet- oric and Poetic to 1400, 1959, pp. 289-292; other studies of rhet- oric which make reference to Garlandia and the colores are listed in the Bibliography). Chapter XIII This final chapter is in large part a repetition of the re- marks in the previous chapter, but now applied to a fourth voice. The comments concerning range are puzzling, because actual examples seldom exceed the double octave in total range. It is possible that instruments sometimes played an octave higher than written. Likewise, the term duplex cantus is unclear. Duplex discantus would seem to make more sense, but would still have little meaning in the context of the entire passage. 184 The second of the three rules given near the end of the chapter is in.reference to contrary and oblique motion. This point is also stressed by Odington (Huff, p. 29). In the third rule, the terms copula and punctum.are virtually synonymous. Clausam lay is unclear, but it may have a similar mean- ing as well, and perhaps simply means a closing section. The refer- ence to instruments seems to imply that there were sometimes intru- mental passages within vocal compositions. There are none clearly called for in Notre Dame organum, but since this chapter is probably an addition to the treatise, it may refer to motets and other pieces of the period around 1300, which often include melismata apparently intended for instrumental performance. The question of the use of instruments in thirteenth-century music is one which deserves investigation. Many of the conducti of the period include melismata which may have been for instruments, and many writers mention the use of instruments in support of the voices. This would seem to be a matter of obvious practicality in the case of the sustained tenors of organum_purum. There is even considerable doubt as to precisely what instru- ments were in general use. One of the instrumental (i.e., textless, and therefore presumed to be instrumental) motets of the Codex Bam- berg is entitled "In seculum viellatoris," indicating performance 185 by viols, but aside from a little pictorial evidence, further infor— mation is lacking. The Codex Bamberg This is a collection of one hundred motets and conducti which includes several textless pieces at the end. The notation used here corresponds closely to that explained by Garlandia in the Positio. The one major difference is that rests, which here always indicate precise durations, are somewhat different. The semibreve rest covers one space of the staff, and the brevis rest covers two. Likewise, the lopga recta rest covers three spaces, and the longa ultra mensuram four. There are other minor variations. Sometimes two notae cur- rentes are immediately followed by a breve. This is simply read as two semibreves followed by a brevis recta; the entire grouping thus has twice the value of a group of three notae currentes: ”0 :57 0.. :5] There are also instances of currentes appearing in connection with single longs or with ligatures whose last notes are long. It is apparent from context that the currentes must be read as separate 186 semibreves in these cases, rather than sharing in the value of the previous note. Thus, in the textless motet Neuma (Aubrey, I, folio vo 62 ): r... : J5) fl rather than ml Garlandia's remarks apparently are valid only for the-earlier organum. However, Anonymous IV also states that currentes should share in the value of the last note of the preceding ligature. It is therefore probable that the older practice survived longer in England than on the continent. There are tenors in modes I, II, III, and V, as well as rhythms which combine modal patterns. Mode V is always written in longs; consequently there is no confusion with mode I. The rules for propriety and perfection of ligatures as described by Garlandia 7ro) are observed faithfully here; for example (Aubrey, I, folio 2 o I — CE The cum littera notation of the upper voices are nearly de- void of all but imperfect ligatures. Perfect ligatures appear only at the ends of phrases where final longs are required. Nearly all 187 of the upper voices can be construed as utilizing variants of mode I, II, or III, altered mainly through the use of the plica, ligatures cum opposita proprietate, or groups of two or three semibreves. Some of the tenors in mode V include two-note ordines, as in Garlandia's example discussed above. In these cases it is apparent from the context of the other voices that the first of the two must be read as a duplex longa, and many of them are written as such vo . (e.g., Aubrey, I, folio 8 ). The only instances of the breve rest being used inrmode V are in tenors which use a mixed mode (Aubrey, I, V folio 8 0): From the notation used in this manuscript it was only a short step to the system of Franco of Cologne, which served as the basis of mensural notation through the sixteenth century. Franco's innovations resolved most of the problems of syllabic notation and systematized the use.of ligatures as well, thus theoretically free- ing notation from the modal patterns which had been predominant for 150 years. Garlandia's treatise represents an intermediate 188 stage in that development, and is among the earliest attempts to formalize any kind of non-modal rhythmic notation. APPENDIX APPENDIX I Here are presented transcriptions of examples of the three main forms of thirteenth-century polyphony. First is the organum triplum "Descendit de caelis," from the manuscript Wolfenbfittel 1206 (Helms vo ro stedt 1099), folio 7 -8 . The greater part of this composition presents few problems of transcription. Modes I, II, and III are used, with fractio modi occasionally appearing through the use of plicae. The difficulties are in the copulae which appear before each change of syllable. The first three of these are relatively brief, whereas the final one is extended. Except for the three-note liga- tures in the final copula, currentes are here most satisfactorily rendered by the method of splitting the value of the preceding long. The sequence of ternariae which makes up the second half of the second system of folio Bro must be interpreted differently, however; each ternaria is equal in value, because there are the same number of ligatures in the two voices. This is in spite of the fact that the same melodic shape is sometimes written in the form of currentes and sometimes not. In this transcription, these ternariae have been read as long, breve, long; the second long is ultra mensuram because 189 190 it falls before another long. It also appears likely that equal breves would afford an acceptable solution to this passage. Another problem is the transcription of the tenor at the word "de." Something approximating the fifth mode seems to be intended here, but some notes must be read as duplices longae or even longer values in order to produce a satisfactory harmonic result. This passage thus falls curiously between the discant and organal styles. The suspiratio is used here after the initial long, and the divisio syllabarum appears at each change of syllable. These should not be confused with the divisio modorum, which indicates a rest, even though their appearance is identical. No distinction is made between these signs in this manuscript despite the descriptions of the theorists . The second example is the two-voice conductus "Presul nostri temporis" from the same manuscript (folio 92:0-93ro). This partic- ular piece contains an unusual amount of melismatic writing; each line of the text is set off by melismatic sections, whereas it was more common to include melismata only at the end and perhaps at the beginning of conductus. This transcription follows as much as pos- sible Garlandia's rules for gpp_1ittera notation: written longs are transcribed as such, a ligature is given the total value of a long through the principle of eggipollentia, and ligatures are considered 191 imperfect even though most are written with propriety and perfection. Thus, the overall rhythm is that of mode V with frequent fractio; binariae are transcribed long, breve, and ternariae are rendered as equal breves. The general style of this piece corresponds to that termed "longa-fractio" by Gordon A. Anderson ("The Rhythm of cum littera Sections of Polyphonic Conductus in Mensural Sources," Journal of the American Musicological Society, XXVI, Summer, 1973, pp. 288-304). Anderson defines three other styles: modal-syllabic, in which mode I or II predominates, with very little fractio utilized, and indicated either by the differentiation of longs and breves on the page or simply by the rhythm of the text; longa-syllabic, in which each syl- lable takes the value of a long, with virtually no use of shorter values; and melismatic-text, in which syllables extend longer than three tegpora. Anderson agrees that modal renderings are to be pre- ferred whenever possible, and that the style often changes within a piece, often with deliberate and dramatic purpose. In several of the melismatic sections of this piece a modal interpretation seems most successful, and so ligatures of identical form are transcribed in varying ways in many instances. Also, the values of rests appear to be variable, with little or no visual dif- ferentiation. Principles of consonance and dissonance provided the 192 basis for these judgements, and it is recognized that this transcrip- tion is but one of many possible solutions. The end of the piece is especially curious. As presented here, it is highly unsatisfactory from a harmonic standpoint, but no harmonically satisfactory solution seems to make rhythmic sense. The alternate ending is offered with the recognition that, while it is better for the final three long- WPMJ 1' values, the preceding beat is still a problem. Other versions are, of course, possible, but have their own serious drawbacks. The manuscript Wolfenbfittel 677 (Helmstedt 628) contains a three-voice version of this conductus (a top voice has been added to the two given here). This version is essentially the same, except that the final passage is significantly longer; it is thus possible that the two-voice version is incomplete. At any rate, the three- voice version is of no aid in determining the correct reading of the passage in question. ' The third example is a motet from the Codex Bamberg, folio 23ro. There are very few problems with the transcription here; in this manu- script the rests always indicate exact durations, and the side-by- side lines of the upper voices are durationally equivalent. It will be noticed that notes written as lozenges are always semibreves, never currentes. The note values used for the other transcriptions have here been doubled for easier reading; it appears to be immaterial 193 whether 2 or 2 is used, although the tenor utilizes patterns of six tempora, and so the latter has been preferred. Aubrey's transcriptions of the motets of this manuscript essen- tially agree with that given here except for one important point. Aubrey transcribes all semibreves as ternary sub-divisions of the 1 breve. It is clear from the Positio that when more than two semi- E l: breves replace a breve, the last of these must be longer; this results En. in the duple division of the breve which is used here. The tenor voice, as is true in many of the Bamberg motets, uses a repeated rhythmic pattern combining modes I and V. This is one of the cases mentioned earlier in which the breve-rest and lppg2_£ggp§_ appear in the fifth mode. This tenor contains an exact repetition beginning with the tenth ordo. 194 {a , .,.\ :5“ gig i ”.1 ‘d ..—-_V.. '.v_... _&‘..:-_. .- J' . 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Brevis (pl. breves). The shorter of the two basic rhythmic values of modal music. Its normal form, the brevis recta or "correct breve," was half of a longa recta and contained one tempus, the theoretical i rhythmic unit against which all durations were measured. In some cases, e.g., in the third and fourth modes, a brevis could contain two tempore. Garlandia does not specifically mention this, but it was called by other theorists brevis altera ("altered breve"). 2. Conductus. A polyphonic piece utilizing no plainchant and set to a rhymed, metrical Latin text which was sacred or semi-sacred. The setting was usually more or less syllabic, with occasional melis- mata at beginnings or ends of lines. 3. Copul . A brief section in organum occurring at the end of a main section, usually followed by a change from organal to discant style or vice versa. The copula generally utilized non-modal rhythms, and was always melismatic. 211 212 4. SEE littera and ging_littera. "With text" and "without text," and thus syllabic and melismatic, respectively. These two styles required somewhat separate notational rules because of the fact that more than one syllable could not be set to a single ligature. Garlandia's system provides for the virtually exclusive use of imperfect ligatures in cum littera notation. rfl“fir=:nr~——- 5. Discant. This term refers to polyphony in which all voices are measured, as opposed to the organal style, in which the tenor con- sists of unmetered notes whose durations are determined by simple alignment in the score. 6. Divisio modorum (pl. divisiones). A vertical line indicating a rest at the end of a phrase (ordo) in modal passages. In some manu- scripts its value is determined according to context; in others, its length indicates its value. 7. Divisio syllabarum. A vertical line, usually spanning less than one space on the staff, indicating a change of syllable and thus aiding the coordination of the voices. This was necessitated by the practice of writing the text only under the lowest voice of the score. 213 8. Equipollentia. The principle of equivalence according to which the rhythmic values of ligatures were determined, mainly in syllabic music. The total duration of a four- or five-note ligature was thus equated with that of a three-note ligature. This term could also refer to the correspondence of rhythmic values between voices in modal contexts. F 7.67“ 6; “‘4- .—_ 9. Extensio modi. A term coined by Willi Apel for the process by which longer-than-normal values were introduced into modal passages. Though it figures in a few of his examples, it is not discussed by Garlandia. 10. Figure. Garlandia's generic term for any single note or ligature. 11. Finis punctorum (p1. fines). A vertical line spanning all the lines and spaces of the staff, used at the ends of pieces and of sections. Its modern equivalent is the double bar. 12. Flaiolis. Garlandia's term for hocket, not found in other sources 0 214 13. Fractio modi. The process of introducing smaller note-values into modal passages. Though Garlandia does not explain this device, it figures in several of his examples. 14. Hocket. A technique whereby one voice has a note and another voice has a rest, and vice versa, in alternating fashion. The term r—“_.'.3\ii.fibf '. is used both of the technique and of pieces which use it extensively. 15. Ligature. A term meaning "tied together," used for any group of connected notes. A two-note ligature is a binaria (pl. binariae), one with three notes is a ternaria, and so on(qgaternarig, 3315f ternaria). 16. Egggg_(pl. longae). The longer of the two basic note-values of modal music. The 122g3_£ggtg_("correct long") contained two tempora, and was thus twice the value of the brevis 53333. The lgggg_could also contained three tempera, and was then called 21t£§_mensuram ("beyond measurement"). The duplex lgnga_(pl. duplices longae) was most often equivalent to two longae 31££3 mensuram (six tempera), but could, according to context, be an indeterminate duration of more than six tempora. 215 17. Medium. The term used by Garlandia for the classification of intervals which are neither the most nor the least consonant or dis— sonant. The perfect fifth and fourth are the medium consonances, and the whole-tone and minor sixth are the medium dissonances. 18. Modus (pl. modi). For Garlandia, this term is often equivalent I to “rhythm." The modern confusion resulting from multiple uses of L: the word "mode" is avoided by calling tonalities species. Garlandia subdividies m2§2§_in two ways. First there is "common mode," or rhythm which does not conform to regular repeated patterns; and then there is "proper mode," i.e., the system of six standard rhythmic patterns. PrOper mode is then divided into mgggg_rectus, which uses only longae rectae and breves rectae; and modu§_pgrnu1trg_mensuram (or, occasionally, m9§2§_ngn_rectus), which uses other values. Thus, modes I, II, and VI are mggi_£ggti, and II, IV, and V are 229$.EEE. ultra mensuram. l9. Opposita proprietas. Literally, "opposite propriety." This is a characteristic of a ligature whose first notes are to be inter- preted as semibreves, and it is indicated by an ascending stem on the left of the ligature's first note. 216 20. Qggg (pl. ordines). Literally, "row," "line," or "order." Its most common meaning, which is not stressed by Garlandia, is a phrase in modal music, containing a certain number of pattern-repetitions and ending with a rest. In the treatise of Anonymous IV, for example, the phrase in which the modal pattern is stated once is termed "first ordo," one in which the pattern appears twice is called "second 25921" and so on. Garlandia also uses the term to indicate the rhythmic relationship of simultaneous voices. When two voices are written so that the longs coincide, they are said to be "in the same grdg," When the longs fall in different rhythmic positions, the two voices are "in opposite ordines." 21. Organum (p1. organa). The generic term for polyphony, also used to indicate the style of writing over an unmetered tenor, as opposed to discant style, in which all voices are metered. Garlandia also mentions the term organum‘pgggm, used for the earlier two-voice writing of the Leonin style, a type predating the systematization of the six modes, but in which mensural notation began its development. Organum duplum, triplum, and quadruplum. refer to two-, three-, and four-voice writing, respectively. 22. Perfectus and imperfectus. Of modes: A mode was "perfect" when an ordo ended with the duration with which it began, and it 217 was "imperfect" when the first and last durations of an gggg_were different. In modes V and VI, however, these terms referred to the number of notes in an 9522, Of ligatures: ligatures whose final' two notes were written according to the standard forms of plainchant notation were considered "perfect," and ended breve, long (except in a few modal contexts). This rhythmic interpretation could be changed by altering the form of the ligatures, thus rendering them ”imper- fect." Sometimes the noun perfectio was used rather than the adjective (cum perfectione and.§ing_perfectione). Shortly after Garlandia's time, singie notes, i.e., the long of three temera and the breve which was divisible into three semibreves, were also called "perfect." Of intervals: Garlandia's classification of the most consonant and most dissonant intervals. The perfect consonances are the unison and actave, and the perfect dissonances are the tritone, minor second, and major seventh. Likewise, "imperfect" was said of the least consonant and least dissonant intervals in each class. The imperfect consonances are the major and minor thirds, and the imperfect dissonances are the minor seventh and the major sixth. 23. Plica (pl. plicae). Literally, "fold," but with the figurative meaning of "hint," as in "implication." This is a stem added to the right of a note or ligature. It calls for the performance of an 218 unwritten pitch a second above or below the pitch of the note to which it is attached; this is determined by the direction of the stem. The implied.pitch (plica-tone) assumes a portion of the rhythmic value of the written pitch (plica-note). 24. Proprietas. "Propriety." Ligatures cum proprietate ("with pro- priety") are those whose first note is written in the standard form for plainchant notation. This requires that the first pitch is a breve in a binaria, and that the first two pitches are long, breve in a ternaria. In Garlandia's system, writing a ligature 3132,2527 prietate reverses the rhythmic values of all the notes of the ligature. 25. Punctus (pl. puncti). Term used by Garlandia to mean a note, a phrase, or an entire section. 26. Quadruplum (pl. quadruple). Either a piece written in four voices or the fourth (top) voice itself. 27. Rondellus (pl. rondelli). A genre in which a phrase is passed from voice to voice, resulting in a type of imitation, usually at the unison. The voice(s) accompanying the repeated material were usually varied, and so this was distinct from the device Stimmtausch, 219 in which two voices were exchanged intact. This term was also occa- sionally used to mean a secular rondeau, sometimes with Latin text. 28. Semibrevis (pl. semibreves). In Garlandia's system, any sub- division of the breve, usually one-half. Like the long of three tempora, the semibreve was considered ultra mensuram. 29. Suspiratio (pl. suspirationes). "Sigh" or "breath." A ver- tical line similar to a short rest, indicating a breath for the singers, but having no definite duration. 30. §ynemmenon. Literally, "hook." The Greek term for the con- junct joining of hexachords, mainly to allow for the introduction of accidentals or the extension of melodic range beyond a sixth. 31. Tempus (pl. tempora). A theoretical durational unit against which notes and rests were measured. There is some question as to whether this can be considered analogous to the modern concept of heat or pulse. 32. Triplum (p1. tripla). Term for three-voice polyphony, also used of the third voice. 220 33. Ultra mensuram. "Beyond measurement," a term for note-values longer than two temEre or shorter than one w, also used in reference to the modes using these values, i.e., modes III, IV, and V. BIBLIOGRAPHY BIBLIOGRAPHY Anderson, Gordon A. "Motets of the Thirteenth-Century Manuscript LEDClayette: A Stylistic Study of the Repertory," Musice Discipline, XXVIII, 1974, pp. 5-37. . "Motets of the Thirteenth-Century Manuscript §2_Cleyette: The Repertory and its Historical Significance," Musica Disciplina, XXVII, 1973, pp. 11-40. "The Rhythm of cum littera Sections of Polyphonic Con- ductus in Mensural Sources," Journal of the American Musi- cological Society, XXVI, 2, 1973, pp. 288-304. . "A Troped Offertorium—Conductus of the Thirteenth Century," Journal of the American Musicological Society, XXIV, l, 1971, Pp. 96-100. Apel, Willi. The Notation of Polyphonic Music, 900-1600, fifth ed., The Mediaeval Academy of America, Cambridge, Mass., 1953. Aubrey, Pierre. Cent Motets du XIIIe Siécle, 3 vols., A. Rouart, Le Rolle, & Co., Paris, 1908. Baldwin, Charles Sears. Ancient Rhetoric and Poetic, Peter Smith, Gbuoester, Mass., 1959. . Medieval Rhetoric and Poetic to 1400, Peter Smith, Gloucester, Mass., 1959. Caplan, Harry. "Classical Rhetoric and the Medieval Theory of Preaching," Historical Studies of Rhetoric and Rhetoricians, Raymond F. Howes, ed., Cornell University Press, Ithaca, N.Y., Clark, Donald Leman. Rhetoric and Poetry in the Renaissance, Russell & Russell, New York, 1963, pp. 45-52. 221 222 Coussemaker, Charles Edmond Henri. Scriptorum de musica medii aevi, Vol. I. Crocker, Richard L. "Discant, Counterpoint, and Harmony," Journal of the American Musicological Society, XV, 1, 1962, pp. 1-21. Cserba, Simon M. Ed., Hieronymus de Moravia, O.P.: Tractatus de Musica, Verlag Friedrich Pustet, Regensburg, 1935, pp. 194- 229. Dalglish, William E. "The Hocket in Medieval Polyphony," Musical Quarterly, LV, 3, 1969, pp. 344-362. Dittmer, Luther. Trans., Anonymous IV, Institute of Medieval Music, Brooklyn, N.Y., 1959. . "The Ligatures of the Montpellier Manuscript," Musica Falck, Robert. "Rondellus, Canon, and Related Types Before 1300," Journal of the American Musicological Society, XXV, 1, 1972, pp. 38—57. Fox, John. The Rhetorical Tradition in French Literature of the Later Middle Ages, University of Exeter, 1959. Gallo, F. Alberto. "Tra Giovanni di Garlandia e Filippo da Vitry," Musica Discipline, XXIII, 1969, pp. 13-20. Huff, Jay A. Trans., Walter Odington: De Speculations musicae, Part VI, American Institute of Musicology, 1973. Husmann, Heinrich. "The Origin and Destination of the Megnus Liber Organi," Musical Quarterly, XLIX, 3, 1963, pp. 311-330. Karp, Theodore. "Towards a Critical Edition of Notre Dame Organa Dupla," usical Quarterly, LII, 3, 1966, pp. 350-367. Le Clerc, Victor. "Jean de Garlands, Poets et Grammarien," Histoire Litteraire de la France, Vol. VIII, Paris, 1868, pp. 83-98. __ WM 223 Levy, Kenneth. "A Dominican Organum Duplum," Journal of the American Musicological Society, XXVII, 2, 1974, pp. 183-211. Murphy, James J. Rhetoric in the Middle Aggs, University of Cali- fornia Press, Berkeley, 1974. Paetow, Louis J. The Life and Works of Johannes de Garlandia, as Vol. IV, No. 2 of Memoirs of the University of California, 1927. Parrish, Carl. The Notation of Medieval Music, W. W. Norton & Co., New York, 1957. Rasch, Rudolph A. Johannes de Garlandia, Institute of Medieval Music, Brooklyn, N. Y., 1969. Reaney, Gilbert. "The Question of Authorship in the Medieval Treatises on Music," Musica Discipline, XVIII, 1964, pp. 7-17. Reese, Gustave. Music in the Middle Ages, W. W. Norton & Co., New York, 1940. Reimer, Erich. Johannes de Garlandia: De musica mensurabili, Vols. 10 and 11 of Beihefte zum.Archiv fflr Musikwissenschaft, Wiesbaden, 1972. Sanders, Ernest H. "Duple Rhythm and Alternate Third Mode in the Thirteenth Century," Journal of the American Musicological . "Peripheral Polyphony of the Thirteenth Century," . Journal of the American Musicological Society, XVII, 3, 1964, pp. 261-287. Sandys, Sir John Edwin. A History_of Classical Scholarship, Vol. 1, Hefner Publishing Co., New York, 1958, pp. 549-551. Tischler, Hans. "A Propos a Critical Edition of the Parisian Organa Dupla," Acte Musicolggice, XL, 1968, pp. 28-43. . "A Propos of a Newly Discovered Organum," Journal of the American Musicological Socigty, XXVIII, 3, 1975, pp. 515-526. 224 . "A Propos the Notation of the Parisian Organa," Journal of the American Musicological Society, XIV, 1, 1961, pp. 1-8. . "A Three-Part Rondellus in Trent MS 87," Journal of the American Musicological Society, XXIV, 3, 1971, pp. 449-457. Waite, William G. The Rhythm of Twelfth-Century Polyphony, Yale University Press, New Haven, 1954. Wright, Thomas. Ed. , "The Dictionarius of Jean de Garlande," 1_\_ Volume of Vocabularies, London, 1857, pp. 120-138. l-n. “11111111111111