Conference Agenda

In the Carolingian period, diagrams were added for the first time to Pliny’s Natural History. We can possibly even date these additions to a specific event in 809: Charlemagne’s conference on computistical reforms. Among these diagrams was a type which Bruce Eastwood and Gerd Graßhoff have classified as ‘planetary intervals diagrams.’ This type of diagram exists in two forms - circular and list - and represents a blend of what we might think of as standard music and astronomical diagrams. Simple astronomic diagrams were already commonly associated with Macrobius’ Commentary on the Dream of Scipio, a text that incorporated the cosmic implications of music. With the reintroduction of Martianus Capella’s encyclopedic Marriage of Philology and Mercury later in the ninth century, more sophisticated diagrams appeared across the sections on mathematics, astronomy, and music. Both Boethius’ quadrivial treatises, De institutione musica and De institutione arithmetica, include diagrams that are indicated within the texts. Boethius’ music diagrams were occasionally extracted and included in manuscripts of astronomical texts, such as in the eleventh-century Paris, B.N. Lat. 8663. While music theorists have examined the theoretical implications of the Carolingian music diagrams and historians of science have examined the astronomical diagrams in detail, the interrelationality of astronomical and music diagrams remains understudied.

In this paper, I will examine early medieval astronomical and music diagrams together to understand how diagrams act as a way for quadrivial sources to translate and comment on their own interconnectivity. I will focus on ninth-, tenth-, and early eleventh-century manuscripts which include both music and astronomical diagrams, exploring how these diagrams transform across treatises and shape how one engages with their associated texts. My approach to diagrams draws on work done in medieval studies and art history by Mary Carruthers (1990 & 2020) and Jeffrey Hamburger (2022), and interrogates how diagrams shape a particular way of thinking and act in dialogue with their associated texts. Looking at diagrams quadrivially rather than by discipline illuminates how diagrams informed medieval people’s understanding not only of these texts but ultimately of their entire world.

One of the most distinctive features of Ṣafī al-Dīn al-Urmawī’s two treatises (Kitāb al-Adwār fi’l-mūsīqa, c1235, and al-Risāla al-Sharafiya fi’l-nisab al-ta’līfiya, c1267) is their frequent and varied use of diagrams. These treatises and their diagrams spread widely through the hands and pens of students, copiers, and commentators, resulting in a varied manuscript network spanning centuries, regions, and languages. While certain aspects of al-Urmawi’s diagrams remain relatively stable in transmission, many others do not. This paper reflects on the types of variation and transformation that these diagrams underwent at three stages of the treatises’ lives: their composition, their Arabic transmission, and their translation in 'Abd al-Qādir al-Marāghī’s early 15th-century Persian commentary on the Kitāb al-Adwār.

Some changes are purely in mis en page: al-Marāghī’s choice to put all of the circular diagrams of consonance on the same page for easy comparison creates a layout which does not exist in the diagrams’ Arabic transmission and directs a reader’s attention in novel ways. Some changes involve a revision of the diagram’s graphic structure. The manuscript Süleymaniye Fatih 3662, which Owen Wright has characterized as a preliminary version of the Kitāb al-Adwār (Wright, 1995), shows al-Urmawī’s initial attempts at a circular gamut. These would be restructured into his now famous diagrams in the earliest copies of the treatise, like Nuruosmaniye Kütüphanesi 3653. Some restructurings are more subtle: the circular diagram of shared pitches between various octave cycles in Kütüphanesi MS 3653 has an extra space for the pitch an octave above the lowest one, while all later sources remove it to create a visual representation of pure octave equivalence. Other changes introduce new visual techniques to existing diagrams. This can be seen in the range of approaches taken in depicting the species of octave cycles or their component tetrachords throughout the treatises’ Arabic transmission and al-Marāghī’s commentary. When taken together, the many visual transformations found in this manuscript network attest to the continued (re)negotiations of visual communication and diagrammatic techniques that al-Urmawī, as well as the individual students, scribes and commentators that followed him, engaged in.

The tradition of using diagrammata in the field of ancient Greek music theory is well attested from very early sources on, although it is not always easy to define what these diagrammata looked like. Most of the time, they are not very likely to constitute actual diagrams, according to the contemporary understanding of this kind of objects. The earliest extant example of an extensive use of diagrams starts with Ptolemy’s Harmonics, under the general influence of mathematics. This is not to say that mathematical harmonics started with Ptolemy, but that he initiated, as far as we know, a tradition of depicting arithmetical and acoustic properties by using the resources and habits of geometrical figures. What can we learn from Ptolemy’s diagrams ? What could have been a quite simple investigation turns out to be more difficult to answer, as the extent to which one can access Ptolemy’s figures today is under question. The oldest extant Byzantine manuscript (twelfth century) has lost every diagram, leaving blank spaces. Later manuscripts from the thirteenth century display most of the diagrams, raising the question about their origin: do they derive from a lost archetype, or should we ascribe them to Byzantine scholars, who tried to reconstruct the diagrams from a close reading of the text? The question thus turns to: can we gain access to Ptolemy’s diagrams at all?

By comparing the oldest evidence, I will argue in favor of a long-lasting influence of Byzantine diagrammatic practices in the field of music theory. Not only did they shape later Byzantine treatises, as in Pachymeres’ Quadrivium and Bryennios’ Harmonica; they also set standards for later manuscript production, influenced their western European reception, and even our modern reading of these diagrams, as modern editors and translators usually relied on the visual manuscript evidence and only sought adequacy to the text’s reading, if they gave diagrams any thought at all. Ancient Greek Musical diagrammatic practices have mainly come down to us, in a nutshell, through the lenses of Byzantine scholars.