Athanasius Kircher's _Musurgia Universalis_ has sustained attention of diverse readers since its publication in 1650. Recently, it has been studied for its accounts of natural science and magic, _Affektenlehre_, and combinatorics in the European Republic of Letters (Gouk 1999, Murata 2000, Palisca 2006, Bianchi 2011, McKay 2012). Kircher's readers and correspondents were also situated around the globe, connected by the epistolary network established by Jesuits and other missionary orders. Yet, while some attention has been devoted to readers of Kircher's scientific works in New Spain (Findlen 2004), the precise role of the _Musurgia_ in colonial contexts has not been studied at depth. In this paper, I examine Kircher's books in the library of Sor Juana Inés de la Cruz (Finley 2019) and a compendium included in a previously unattributed manuscript issuing from Manila entitled _Observationes diversarum artium_ (Irving 2010) in order to address the import of Kircher's musical thought in a global context.


My paper situates the _Musurgia_ in the early modern/colonial period (Quijano 1992) by attending to its allegorical and practical inscription across the globe. I begin by examining what I call Kircher's 'cosmo-musico-politics' an allegorical account of the cosmos organized by a musical biding force (_vis harmosouza_) that serves to legitimize absolute rule as _imago dei._ I then examine how three of Kircher's overseas readers engaged this musical cosmopolitics in colonial contexts. In a 1654 letter to Kircher, Jesuit novice Gerardo Montiel informs Kircher that he has brought the first copy of the _Musurgia_ to the Indies for use by Jesuit fathers in the missions. From this same copy, friar Ignacio Muñoz compiled his _Observationes diversarum artium_ while in Manila before travelling to Mexico, and back to Madrid, serving as cartographer for the Spanish empire. Finally, I examine Sor Juana's critique of Kircher's Eurocentric cosmology through her own decentered musical cosmopolitics, as indicated in _Primero sueño_ and her nonextant musical treatise _El Caracol_ (the snail). As practical treatise and philosophical tract, I conclude, the _Musurgia_ travelled a different globe than it described _more musico_, as it disseminated Eurocentric musical thought during the early modern/colonial period.

Much has been made of Marchetto's division of the tone into five parts, both in our own time, and in his. While arguments have been made that he divides the tone equally, a close reading of the _Lucidarium_ shows that his interpretation, rather than being unique, aligns with Ciconia's and Tinctoris's notion that sharped notes could be raised by a quarter tone, implying a tradition spanning over a century of widened sharps. Simultaneously, we see in French and English theorists of the time a complete rejection of the idea that sharped pitches should be raised beyond their values in Pythagorean tuning.  While this disparity has led to a rejection of one tradition over the other on matters of tuning sharps, this paper seeks to place each theoretical tradition in their respective contexts by examining the sharp practices associated with repertoires separated by place and genre.  
The main problem of any system that widens the sharp is the B-F# fifth. While arguments could be made that the wide and narrow 3rds and 6ths were made pleasant by their resolution to perfect intervals, the same could not be said for the wide fifth. This interval is too sharp to give a sense of arrival on a cadence, so it is highly unlikely that pieces employing this system would conclude sections with the imperfect B-F# fifth. What this paper will demonstrate is that Italian polyphony of the period uses this interval significantly less often as a cadential sonority than French polyphony does, implying that Italian polyphony could more successfully use the raised sharp system than could French polyphony. This finding is particularly acute in the case of Ciconia who, in his sacred works employs B-F# as a cadential interval while he avoids it in the secular works, which could imply two divergent traditions of tuning delineated by genre occurring simultaneously.  Through examining the repertoires, we gain insight into which genres were more likely to use which tuning system and we expand what it means to hear with a period ear in the music of the late middle ages.

While Boethius' towering stature in music history remains unquestioned, the Boethius of musicology stands at a disconcerting distance from the Boethius known in other areas of historical inquiry. This can in part be explained as an issue of current musicological practice and disciplinarity. Musicologists (tend to) read only a few of Boethius' writings (Dyer, 2007), and these texts are little read elsewhere (Marenbon, 2009). This difference produces another in the characterization of Boethius' thought. Musicology's Boethius is a staunch Pythagorean, but this is only one of two different positions on number and mathematics that can be found among Boethius' writings (Hicks, 2017; Crialesi, 2020). The alternative, abstractionist position is better known to historians of logic and philosophy (de Libera, 1999; Marenbon, 2012).


Boethius' writings on mathematics and abstraction are nonetheless relevant to musicology. By reading these texts musicology might develop a more coherent understanding of the whole of Boethius' body of thought in general (after Marenbon, 2014). Yet the abstractionist writings are also specifically valuable to musicologists. Offering an alternative to the Pythagorean position, the abstractionist materials unseat the Pythagorean from its privileged position as an assumed default. Moreover the alterity of the abstractionist position introduces a critical distance through which the Pythagorean writings themselves can better be understood. The philosophical difference between the positions is not insignificant, and the careful handling of incorporeality (for example) in the abstractionist writings as well as the different terms in which mathematics is understood may provide a basis on which to nuance the description of Boethius' Pythagorean position.


In this paper I examine Boethius' writings on mathematics and abstraction, drawing from the full range of his logical and theological texts. I identify both the nature of mathematical objects and the characteristic activity of mathematics as it is understood in these writings. Finally by examining the points of contact between the Pythagorean and abstractionist positions I argue that the abstractionist writings are a legitimate object of musicological study in their own right as a participant in a common tradition of numerical inquiry.