Volume 22, Issue 2

During the Late Antiquity and the Early Middle Ages, different strategies of visualizing music were adopted. In this article the history and the development of music-related diagrams is put into the larger context of a cultural history of visualization. The philosophical discussion on notational iconicity and diagrammatology, known as ‘Schriftbildlichkeit’, supplies a theoretical background for the description of the music diagrams offered here. The basic question is how visuality and musical graphic (diagrams and notation) interact focusing on a specific visual logic related to musical issues. After a short introduction to Sybille Krämer‘s concept of diagram and after working out some main characteristic of medieval diagrams, a selection of music related diagrams is depicted. The sources presented range from ancient Greek and Latin descriptions of musical diagrams (Aristoxenus of Tarentum, Phaenias of Eresus, Bakchios and Vitruvius) to the wing diagrams of Aristides Quintilianus and Martianus Capella, the structural graphics by Boethius and concludes with the notational diagrams in the Carolingian music treatises (Musica and Scolica Enchiriadis).

The present study adverts to a newly found manuscript and reclassifies the diagrams of the ‘Mainauer Naturlehre’ in the context of the Latin tradition. Thus, a deficit of research concerning the astronomic technical literature in Middle High German can be closed. The Basle vernacular manuscript that is discussed here shows a very strong relationship between the text and its diagrams, which is examined as a special kind of diagrammatical act, whose intratextual function lies primarily in the realm of historical semantics: the diagram generates a notion of scientific specialization in vernacular. In contrast to this, the York manuscript confronts text and diagram in a contrapunctual way and supplements the vernacular text with an appendix of Latin diagrams. This relation between German prose and Latin diagrammatic tradition might well be a reflection of a pragmatic background.

The ‘Geometria Culmensis’ (around 1400), the most ancient German educational book on practical geometry, tries to instruct lay surveyors as well as experts in the art of field measurement. The oldest existent manuscript transmits the Latin text together with the German adaption. Both texts show a similar albeit not equal set of diagrams illustrating the geometric and arithmetic problems proposed in the texts. The article tries to explore the ambivalent reference of the diagrams and shows how the ‘Geometria’ itself discusses their status as diagrammatic model and instrument.

R. Shlomo Yitṣḥaki (Hebrew: שלמה יצחקי), generally known by the acronym Rashi, was a medieval French rabbi who lived between 1040 and 1105 in Troyes (Champagne). Rashi was the author of two comprehensive commentaries on the Talmud and on the Tanakh. His commentary on the Talmud, which covers nearly all of the Babylonian Talmud (a total of 30 tractates), has been included in every edition of the Talmud since its first printing by Daniel Bomberg in the 1520 s. His commentary on the most books of the Tanakh – especially on the Chumash – is still an indispensable exegetical tool to almost all students of the Hebrew Bible. This perush al ha-Torah supplemented almost all printed Hebrew Bibles or Chumash Editions and initiated more than 300 super-commentaries, which analyze and elucidate Rashi’s choices of exegesis, grammar, variant readings, Masora and midrash citations. The manuscript editions of his commentary were augmented with various map diagrams of Erets Israel, which disappeared in the printed editions of the Rashi commentary. Abraham Berliner mentioned this loss and recent scholarship is rediscovering these Rashi diagrams and maps. This paper elucidates the so-called Numeri 34 map-diagrams in the oldest extant manuscripts of the Rashi commentary, and their refinement and recycling within the Masora (figurata) of Ashkenazi bible manuscripts.

The Bibliothèque nationale de France in Paris (BnF, MS Latin 5184) holds a fragment of the ‘Manipulus florum’ of Galvanus Flamma. This copy of a milanese urban chronical dates back to 1340. In addition to a modified version of the text, it contains 118 geometrical schemata covered in text. The article focuses mainly on the circular representations of the city and – while exploring their variety – discusses the semantic field of these diagrams.

The article shows the impact of diagrammatic thought and pattern in the transformation of ‘what has been seen’ into more or less systematic sketches, using the example of Villard’s de Honnecourt ‘Portfolio’ (Paris, BnF, Ms. fr. 19093, c. 1240). Rather than discussing the later use of the ‘Portfolio’, the focus is on Villard’s initial use of basic geometrical operations to understand, construct and amend his environment through the process of drawing. Analyzing his approach can thus contribute to the understanding of knowledge organization not only concerning the architecture of the 13 th century but also to an understanding of knowledge organization in general.

Abstact Subject of this essay is the question of how the invisibility of God can be visualized. The ‘Regia Carmina’ of Convenevole da Prato (London, British Library, Royal 6 E IX) serves as an example. They are designed through allegorical iconotexts. Convenevole’s reflection consists basically of a mental image and a painted picture. This essay deals with two questions: 1) How are the mental image and the painted picture arranged to initiate a thought process regarding the relation of the painted picture to God in a diagrammatic transfer? The thought process aims to gain knowledge about the figurative representation of God. 2) Is the iconotext only modelled as a medium of insight or can it also be seen as a figure of reflection of a diagrammatic way of thinking, in which the possibilities and limits of pictorial and verbal signs are defined? In this example the fundamental and productive connection of allegorical and diagrammatic method becomes apparent. On the one hand the diagrammatic way of thinking is influenced by allegory. On the other hand the process of allegorisation that is based on a diagrammatic point of view becomes evident.

Starting from the concept and definition of littera in the Grammar treatises of the Late Antiquity and the Early Middle Ages, the contribution analyzes common graphic elements which were used by the scribes to create initials, ornamental patterns and the layout of the manuscript page. These elements and their functions were partly described in encyclopaedic works, e. g. of Isidor of Sevilla and Martianus Capella in the chapters about Geometry. Not only were these features well known through the study of the Artes , they also represented useful tools for the invention and production of medieval diagrams.

How and where do relationships arise that can be rendered diagrammatically? Do they emerge through the process of human reasoning or through the act of drawing on surface? Or do they unfold in the dynamic processes at play in observable reality? The following article argues that the latter is the case, making recourse to the philosophy of Charles Sanders Peirce. As a case study, it explores Galileo Galilei’s investigation of free-fall motion and examines both printed texts and manuscripts in order to understand how Galilei arrived at his conclusions. While the published diagrams present his results in graphic traditions that date back to the 14th century, Galilei’s handwritten sketches and notes demonstrate the difficult process of hypothesis formation. In these documents we can observe Galilei grappling with adapting the forms of older diagrammatical notation to his experiments. Through close observation of the phenomena in front of him, Galileo tries to comprehend clearly which parameters of motion can be measured and correlated on the inclined plane.