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1

DYER, JOSEPH. "The Place of Musica in Medieval Classifications of Knowledge." Journal of Musicology 24, no. 1 (January 1, 2007): 3–71. http://dx.doi.org/10.1525/jm.2007.24.1.3.

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ABSTRACT Medieval classifications of knowledge (divisiones scientiarum) were created to impose order on the ever-expanding breadth of human knowledge and to demonstrate the interconnectedness of its several parts. In the earlier Middle Ages the trivium and the quadrivium had sufficed to circumscribe the bounds of secular learning, but the eventual availability of the entire Aristotelian corpus stimulated a reevaluation of the scope of human knowledge. Classifications emanating from the School of Chartres (the Didascalicon of Hugh of St. Victor and the anonymous Tractatus quidam) did not venture far beyond Boethius, Cassiodorus, and Isidore of Seville. Dominic Gundissalinus (fl. 1144––64), a Spaniard who based parts of his elaborate analysis of music on Al-Fāārāābīī, attempted to balance theory and practice, in contradistinction to the earlier mathematical emphasis. Aristotle had rejected musica mundana, and his natural science left little room for a musica humana based on numerical proportion. Consequently, both had to be reinterpreted. Robert Kilwardby's De ortu scientiarum (ca. 1250) sought to integrate the traditional Boethian treatment of musica with an Aristotelian perspective. Responding to the empirical emphasis of Aristotle's philosophy, Kilwardby focused on music as audible phenomenon as opposed to Platonic ““sounding number.”” Medieval philosophers were reluctant to assign (audible) music to natural science or to place it among the scientie mechanice. One solution argued that music, though a separate subiectum suitable for philosophical investigation, was subalternated to arithmetic. Although drawing its explanations from that discipline, it nevertheless had its own set of ““rules”” governing its proper activity. Thomas Aquinas proposed to resolve the conflict between the physicality of musical sound and abstract mathematics through the theory of scientie medie. These stood halfway between speculative and natural science, taking their material objects from physical phenomena but their formal object from mathematics. Still, Thomas defended the superiority of the speculative tradition by asserting that scientie medie ““have a closer affinity to mathematics”” (magis sunt affines mathematicis) than to natural science.
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2

Fast, Susan. "Bakhtin and the discourse of late medieval music theory." Plainsong and Medieval Music 5, no. 2 (October 1996): 175–91. http://dx.doi.org/10.1017/s0961137100001145.

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In his lucid discussion of genre in medieval treatises on music, Lawrence Gushee states that: The main part of Gushee's discussion is taken up with documents written up to the thirteenth century; for that reason he pays only a brief visit to treatises written thereafter, recognizing, however, a generic category in ‘works of the later thirteenth and fourteenth centuries which can be classed together merely by virtue of their size and synthetic character’. Among these he counts the treatises of Jacques de Liège, Walter Odington, Engelbert of Admont, Marchettus of Padua and Jerome of Moravia. One could add a few others to this list, such as the Tractatus de musica of Magister Lambertus and the work largely derived from that one, the Quatuor principalia musicae. These are ‘synthetic’, to use Gushee's word, in that they attempt a comprehensive treatment of their subject – they cover both theoretical and practical aspects of pitch and rhythm, and usually begin with a mythic/historic overview of music and a classification scheme that situates it within the sphere of other disciplines.
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3

Polo Pujadas, Magda. "Philosophy of Music: Wittgenstein and Cardew." Philosophy of Music 74, no. 4 (December 30, 2018): 1425–36. http://dx.doi.org/10.17990/rpf/2018_74_4_1425.

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The article focuses on the experimental music that emerged after the Second World War and in graphic musical notation. He has a special interest in the influence exercised by the reading of the Tractatus Logico Philosophicus in the musical work Treatise by Cornelius Cardew. The isomorphism between language and reality and the different types of propositions formulated by the first Wittgenstein represent a new conception of music in the composer.
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4

Parsons, Laurel. "Music and Text in Elisabeth Lutyens's Wittgenstein Motet." Canadian University Music Review 20, no. 1 (May 16, 2013): 71–100. http://dx.doi.org/10.7202/1015648ar.

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Although Elisabeth Lutyens (1906-83) was a pioneer of British twentieth-century music, her work is relatively unknown in North America. This article begins with an introduction to her life and compositions, before going on to a detailed analysis of text-music relations in selected passages of her Motet, op. 27 (1953). The analysis forms the basis for a discussion of the concept of text as representation of music: Lutyens began to compose the music of the Motet first, and chose its text—excerpts from the Tractatus logico-philosophicus (1921) by the Austrian-born English philosopher Ludwig Wittgenstein (1889-1951)—because it seemed a fitting expression of the musical ideas that had already begun to develop.
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5

CLINE, DAVID. "Treatise and the Tractatus." Journal of the Royal Musical Association 145, no. 1 (May 2020): 119–66. http://dx.doi.org/10.1017/rma.2020.5.

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AbstractCornelius Cardew named his monumental graphic score Treatise after Ludwig Wittgenstein’s early philosophical masterpiece Tractatus logico-philosophicus, and this well-known fact has engendered speculation about whether there might be other connections between Cardew’s composition and Wittgenstein’s book. Previous commentaries have focused on possible allusions to the Tractatus in the visual imagery employed by Cardew, and this article includes further suggestions of this type. However, it concentrates on more general affinities between Treatise, as Cardew conceived of it prior to his involvement with the free improvisation group AMM, and the philosophy adumbrated in the Tractatus. Foremost among these is a striking concordance between Cardew’s initial enthusiasm for an isomorphic mode of interpreting Treatise and Wittgenstein’s picture theory of the proposition. The article also excavates traces of the picture theory in the numerological basis of Volo solo, a more conventionally notated by-product of the Treatise project.
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6

Seibert, Andrei Yur'evich. "The livre partition phenomenon in J.-G. Kastner’s oeuvre." PHILHARMONICA. International Music Journal, no. 6 (June 2020): 9–19. http://dx.doi.org/10.7256/2453-613x.2020.6.34651.

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In the 19th century, after a two-centuries oblivion, the interest in a medieval genre “danse macabre” reappeared. Dances of Death were embodied not only in pictorial art, literature and music, but also attracted the attention of scholars. The research subject of this article is one of such scientific works - “Les Danses des Morts” by J.-G. Kastner. Its uniqueness consists in the combination of a theoretical research and practical embodiment of its results in a piece of music. The genre of the tractate is defined by scholars as “livre partition” - a sheet music book. The article contains the biographical data of the life and creative work of the French scholar, music expert and composer, little-known in Russian musicology. Based on their own translation of the original text, the authors study the structure-content components of the tractate and define its specificity. J.-G. Kastner considers the genre “danse macabre” in the historical, philosophical and aesthetic contexts; traces back the interdependence of literary, decorative, and musical versions of the dances. The tractate of the French musicologist considers in detail the range of instruments of dance macabre (based on the collection of wooden engravings of a gothic Doten Dantz printed in the late 15th century). The authors define the features of J.-G. Kastner’s ideas which differ them from the thanatological views of his predecessors H. Peino and E.-H. Langlois.
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7

Page, Christopher. "A Treatise on Musicians from ?c. 1400: The Tractatulus de differentiis et gradibus cantorum by Arnulf de St Ghislain." Journal of the Royal Musical Association 117, no. 1 (1992): 1–21. http://dx.doi.org/10.1093/jrma/117.1.1.

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The historian John Keegan was one of the first to ask the simple yet searching question: what actually happens in combat? It is well known that English footsoldiers received a charge by French knights at the battle of Agincourt in 1415, but what took place when men and horses collided? Keegan gives his answers in The Face of Battle, and it may be time for musicologists to modulate the sonorous questions that he poses there for their own purposes. What actually happened, for example, when a motet by Johannes Ciconia was performed in northern Italy c 1400? When friends and associates gathered together to hear such music, what was the nature of their various musical aptitudes and interests? Did women participate in the performances? What was the role of instrumentalists? Some of these questions, no doubt, will never find an answer; there are no medieval chronicles devoted to musical gatherings as there are chronicles – and many other writings – devoted to battles like Agincourt. None the less, literary and iconographical sources are among those which may still have something to reveal about ‘the face of performance’ (to coin a phrase after Keegan's own), and the purpose of this article is to examine the contents of one that has been unjustly neglected: the Tractatulus de differentiis et gradibus cantorum by Arnulf de St Ghislain. This brief treatise classifies the kinds of musicians who performed or admired polyphonic music and is therefore quite exceptional among the works loosely classified as medieval music theory.
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8

HaCohen, Ruth. "Sounds of Revelation: Aesthetic-Political Theology in Schoenberg's Moses und Aron." Modernist Cultures 1, no. 2 (October 2005): 110–40. http://dx.doi.org/10.3366/e2041102209000082.

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Ruth HaCohen (Hebrew University) explores Modernism's artistic exploration of its relationship to theology by taking up Schoenberg's late, unfinished opera Moses and Aaron. Reading that opera as a theological-political-aesthetic Tractatus in the tradition of Spinoza, HaCohen draws out the theological implications of Schoenberg's radical rethinking of formal conventions as these organize the relationship between music and text.
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9

Dennis, Brian. "Cardew's ‘Treatise’ (mainly the visual aspects)." Tempo, no. 177 (June 1991): 10–16. http://dx.doi.org/10.1017/s0040298200013516.

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Cornelius Cardew's 193–page Treatise is the longest and most elaborate piece of Graphic Music ever made. Although it was intended for improvisation and realization, using as many or as few pages as required, and with no fixed rules of interpretation, the piece can be regarded as a graphic construction inspired by music – and with ‘music’, in the broadest sense, as its subject matter. It was influenced by the philosophy of Frege and Wittgenstein, and in particular the latter's exhaustive treatise Tractatus Logico-Philosophicus, which not only inspired the title but almost certainly the composer's economical approach to this endeavour and the rigorous development of his material. It was composed from 1963 to 67.
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10

Cowan, Robert. "Reich And Wittgenstein: Notes towards a synthesis." Tempo, no. 157 (June 1986): 2–7. http://dx.doi.org/10.1017/s0040298200022270.

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To try to establish a relationship between the terse linguistic philosophy of Ludwig Wittgenstein and the deceptively simple minimalist music of Steve Reich might at first seem a little ambitious, if not downright misguided. Yet a synoptic survey of the two men's work reveals a series of formal and conceptual correlations that is often quite striking. I hasten to add that my comparisons apply mostly to those of Reich's compositions where melodic and harmonic ideas are ‘phased’ and developed over the ground of a constant pulse, rather than to works such as The Desert Music where poetic texts substantially influence the form and design of Reich's music. I tend to draw more on Wittgenstein's later thought – especially the Philosophical Investigations than on his Tractatus Logico-Philosophicus, although Reich himself has quoted from the latter in discussing his own artistic style.
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11

Davis, Whitney. "The World Rewound: Peter Forgács's Wittgenstein Tractatus." Journal of Aesthetics and Art Criticism 64, no. 1 (January 2006): 199–211. http://dx.doi.org/10.1111/j.0021-8529.2006.00241.x.

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12

Fuller, Sarah, Philip Schreur, and Daniel Leech-Wilkinson. "Tractatus figurarum: A New Critical Text and Translation on Facing Pages." Notes 48, no. 2 (December 1991): 473. http://dx.doi.org/10.2307/942037.

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13

PIERAGOSTINI, RENATA. "Augustinian networks and the Chicago music theory manuscript." Plainsong and Medieval Music 22, no. 1 (April 2013): 65–85. http://dx.doi.org/10.1017/s0961137112000198.

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ABSTRACTThe manuscript Chicago, Newberry Library 54.1, copied in Pavia in 1391 by an English friar, has been the object of attention of scholars for some time now. Because of the presence of Senleches's song La harpe de melodie (famously notated in the shape of a harp), and of the earliest known dated copy of the Tractatus figurarum (which reflects late fourteenth-century developments in the notation of complex rhythms), the Chicago manuscript has often been cited in support of the historiographical hypothesis which sees the Visconti court of Pavia–Milan as the main centre of production of Ars subtilior repertory in Italy. In the absence of records on the scribe ‘G de Anglia’ and the context in which he worked, it has been almost inevitable thus far to associate the compilation of the manuscript with the Visconti court and the city university (founded and supported by the Visconti). A recently identified document, however, provides some clues to the identity of the scribe of Chicago 54.1, who can now be identified as an Augustinian Hermit. This is confirmed by various elements in the manuscript that also indicate Augustinian connections, placing the compilation of the manuscript in the context of the Augustinian house of Pavia. These elements help to shift the focus of attention to other cultural contexts that may have played a role in the compilation of the manuscript, and invite a reassessment of the hitherto assumed connections with the Visconti court and secular university.
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14

Regelski, Thomas A. "Tractate on Critical Theory and Praxis: Implications for Professionalizing Music Education." Action, Criticism, and Theory for Music Education 19, no. 1 (May 2020): 6–53. http://dx.doi.org/10.22176/act19.1.6.

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15

Meyer, Christian, Prosdocimo de' Beldomandi, and Jan Herlinger. "Brevis summula proportionum quantum ad musicam pertinet; and Parvulus tractatulus de modo monacordum dividendi (...)." Revue de musicologie 73, no. 2 (1987): 270. http://dx.doi.org/10.2307/928951.

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16

Ellsworth, Oliver B., and Jill M. Palmer. "Tractatus et compendium cantus figurati. (Mss. London, British Libr., Add. 34200; Regensburg, Proskesche Musikbibl., 98 th. 4 degrees)." Notes 50, no. 2 (December 1993): 554. http://dx.doi.org/10.2307/898450.

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17

Somavilla, Ilse. "Wittgenstein’s Ambivalent Attitude toward Science and Culture." Wittgenstein-Studien 9, no. 1 (February 21, 2018): 13–29. http://dx.doi.org/10.1515/witt-2018-0003.

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Abstract:Wittgenstein’s ambivalent attitude toward science (and philosophy) can be observed as early as in the Tractatus – both in the preface and toward the end, e. g. on 6.52, 6.54 and also implicitly inherent in his final sentence “Whereof one cannot speak, thereof one must be silent.” Thus, despite his analytical method and apparently high appreciation of science, he was aware of its limits – as well as of its dangers. This awareness becomes increasingly obvious in the course of the later years, among others marked by a shift from analysis to description and a turning to other ways of knowledge than scientific ones: Ways of showing instead of saying viz. verbal and scientific explanations. These alternatives he saw in literature, art and music. However, even as concerns these fields, he sometimes holds a critical attitude toward culture, above all within the development of the civilization of his century. His resentment of the gradual moral and intellectual decline at the turn of the 20th century leads to a highly suspicious attitude toward any progress in the fields of culture and science, which he clearly expresses in his preface to the Philosophical Remarks, distancing himself from the so-called typical western scientist, whose spirit he considers “alien & uncongenial’ to his”. (Cf. CV 1998: 8e)
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18

Meyer, Christian. "Un témoin de la réception méridionale des traditions d'enseignement du Nord aux XIVe et XVe siècles : Barcelona, Biblioteca de Catalunya, M. 883." Anuario Musical, no. 58 (December 30, 2003): 9. http://dx.doi.org/10.3989/anuariomusical.2003.58.69.

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[fr] Le recueil de traités de musique conservé à la Bibliothèque de Catalogne à Barcelone sous la cote M. 883 réunit les principales matières de l'enseignement de la musique -chant liturgique, "música plana" et polyphonie (organum et déchant)- à l'exception des théories mathématiques de la "música speculativa". Il représente des traditions d'enseignement répandues dans une aire géographique comprise entre Seine et Rhin : le milieu parisien y occupe une place prépondérante (tradition d'enseignement de Jean de Garlande, Lambertus), mais on y distingue également des cultures monastiques, en particulier celle de l'ordre de Cîteaux et des Frères prêcheurs. Ce recueil, qui pourrait avoir été constitué à la faveur ou dans un milieu proche de la papauté d'Avignon (peut-être sous le pontificat du pape cistercien Benoît XII), a connu une large diffusion en Italie au XVe siècle et révèle à cet égard un aspect singulier des processus d'acculturation dans les domaines de la pratique et de la théorie de la musique en Italie depuis la fin du XIVe s. et au siècle suivant. Vers 1474, à Mantoue, Franchinus Gafurius puisa dans cette collection de traités l'essentiel de son Tractatus brevis cantus plani.
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19

Wästberg, Per, Lars Palm, Gunnar Harding, Lars Palm, Lars Palm, Tomas Venclova, Rimas Uzgiris, and Regina Derieva. "All Saints/Tractatus Musico-philosophicus/(before we were so rudely interrupted)/Three O'Clock At Night On The Sea/Seven Russian Songs In Bethlehem." Poem 2, no. 2 (January 2014): 9–18. http://dx.doi.org/10.1080/20519842.2014.11415446.

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20

Soulez, Antonia. "Phrases musicales." Circuit 17, no. 1 (December 7, 2007): 27–47. http://dx.doi.org/10.7202/016772ar.

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L’auteure examine ici la portée du paradigme musical dans la philosophie de Wittgenstein. Le cadre de cet examen est l’approche à partir de Wittgenstein de ce que les philosophes ont aujourd’hui à dire de la signification musicale. Deux styles d’approche sont suggérés, l’un projectif bien marqué par l’idée de « musikalische Gedanke » dans le Tractatus et révélateur d’une filiation à laquelle appartient Wittgenstein, et l’autre horizontal suivant l’axe grammatical du rapport esthétique d’appropriation du geste de l’oeuvre à travers une écoute active. Cette conception intègre une exploration de la résonance des aspects, dans une troisième phase qui ne sera pas développée. Comment Wittgenstein remplit-il certains critères d’appartenance à ce que Lydia Goehr appelle « la quête formelle de l’autonomie du musical » est une question qui conduit l’auteure à re-situer le nouage musique et société chez Wittgenstein, par contraste avec Adorno, en mettant en relief les conditions auxquelles une compréhension interne d’un « contenu formel » (Granger) peut se combiner ici avec le contexte d’une pratique. Soulez met donc l’autonomie musicale selon Wittgenstein à l’épreuve du contexte des formes de vie, dans une phase où dominent les « jeux » d’une grammaire comparative motivée par l’analogie de la compréhension d’une phrase du langage avec celle de la compréhension d’une phrase musicale. Mettant l’accent sur le caractère actif de la compréhension, doublée d’une performance, l’auteure entend montrer comment Wittgenstein pense la musique avec la société autrement qu’Adorno, donc sans référence dialectique. La clef est une connexion inédite entre immanentisme de la signification musicale à l’échelle d’une phrase, comme le pense Wittgenstein et ses contemporains de l’École de Vienne, et un schéma esthético-pragmatique de « context-dependency ». De là s’ensuit une forme d’autonomie compatible avec la sphère extramusicale. Si « tout un monde se tient dans une phrase musicale », comme le dit Wittgenstein, c’est bien au sens où un motif répercute certains aspects d’un « monde » auquel nous contribuons en le « faisant ».
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21

Chica Pérez, Víctor Hugo. "La solución de Wittgenstein al problema del "concepto caballo", o de cómo hablar acerca de la estructura del lenguaje según el Tractatus." Co-herencia 15, no. 29 (August 2018): 153–77. http://dx.doi.org/10.17230/co-herencia.15.29.6.

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El artículo propone interpretar la distinción que ofrece Wittgenstein en el Tractatus entre conceptos ordinarios y conceptos formales como una respuesta a las dificultades que se originan en la distinción fregeana entre concepto y objeto, a las cuales la tradición se ha referido como las dificultades del “concepto caballo”. Se mostrará que las expresiones contradictorias y paradójicas que surgen tanto del ataque a dicha distinción (v. g. “el concepto caballo es un objeto”), como de su defensa (v. g. “el concepto caballo no es un concepto”), tienen su origen en la pretensión ilegítima de describir o caracterizar la estructura lógica de la proposición usando para ello otras proposiciones. La distinción entre conceptos ordinarios y formales permite aclarar, primero, en qué sentido esas expresiones son absurdos; segundo, que la distinción entre concepto y objeto solo puede reconocerse en el simbolismo por las características de los signos, pero no puede constituir objeto de descripción.
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22

Wallace, Richard. "J. Bofill I Soliguer: La Problemàtica del Tractat De institutione musica de Boeci. (Aurea Saecula, 8.) Pp. 116. Barcelona: Universitat de Barcelona, 1993. Paper." Classical Review 45, no. 2 (October 1995): 452–53. http://dx.doi.org/10.1017/s0009840x00294894.

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23

Hammond, Frederick. ""Brevis summula proportionum quantum ad musicam pertinent" and "Parvus tractatulus de modo monochordum dividendi" ("A Short Summary of Ratios Insofar as They Pertain to Music" and "A Little Treatise on the Method of Dividing the Monochord"). Prosdocimo de' Beldomandi, Jan Herlinger." Speculum 64, no. 4 (October 1989): 1026–27. http://dx.doi.org/10.2307/2852929.

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24

Nardini, Luisa. "Guy of Saint-Denis, Tractatus de tonis, ed. and trans. Constant J. Mews, Carol J. Williams, John N. Crossley, and Catherine Jeffreys. (Teams: Varia.) Kalamazoo: Medieval Institute Publications, 2017. Paper. Pp. liv, 287; many music samples and 1 table. $39.95. ISBN: 978-1-58044-254-1." Speculum 95, no. 4 (October 1, 2020): 1178–79. http://dx.doi.org/10.1086/710648.

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25

Rabe, August Valentin. "Witkowska-Zaremba, Elżbieta (Hg.) (2015), Tabulatura Joannis de Lublin. Ad faciendum cantum choralem; fundamentum; ad faciendam correcturam (= Monumenta musicae in Polonia: Seria C, Tractatus de musica, Bd. 3), übers. ins Polnische von ders., engl. Übersetzungen von Anna Maria Busse Berger, Warschau: Instytut Sztuki Polskiej Akademii Nauk." Zeitschrift der Gesellschaft für Musiktheorie [Journal of the German-Speaking Society of Music Theory] 17, no. 2 (2020). http://dx.doi.org/10.31751/1076.

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26

Zur, Uri. "The Amoraic controversy, halakha and authority in Bavli Eruvin 104a." HTS Teologiese Studies / Theological Studies 77, no. 4 (August 12, 2021). http://dx.doi.org/10.4102/hts.v77i4.6777.

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The Talmud Bavli presents in Tractate Eruvin (104a) a controversy between two Amoraim, Ulla and Rabbah. This controversy on the topic of producing a sound on the Sabbath is the context of the present study. According to Ulla, any production of sound on the Sabbath is forbidden, and according to Rabbah, producing a musical sound is prohibited on the Sabbath but producing a sound that is not musical is permitted. The purpose of the study is to present the two approaches to solving the controversy, where the dilemma is which of them should the halakha follow. The setting of the study is a comparative analysis of two different halakhic approaches. Accordingly, this controversy created two different fundamental halakhic approaches that have implications for the authority of the Talmud Bavli compared to the Talmud Yerushalmi, that is, which of these Talmuds has more authority than the other. The research methods of this article portray the various outlooks of the poskim and commentators, from amongst the first representatives to relate to this problem, where the results show that a relative majority of the commentators follow the approach of the Rif. The article’s conclusion is that the authority of the Talmud Bavli is greater than that of the Talmud Yerushalmi.Contribution: The contribution of the article is in showing the fundamental arguments that the poskim and commentators raised to solve this dilemma, which serve as a basic foundation for all the poskim and commentators who followed them and who advocated either the one approach or the other. Furthermore, the article also contributes by providing a source interpretation of the Hebrew and Aramaic text and rabbinic literature, which fits the scope of the journal.
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