Music, Myth, and Metaphysics: Harmony in Twelfth-Century Cosmology and Natural Philosophy by Andrew James Hicks A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Centre for Medieval Studies University of Toronto c Copyright by Andrew James Hicks (2012) ABSTRACT Music, Myth, and Metaphysics: Harmony in Twelfth-Century Cosmology and Natural Philosophy Andrew James Hicks Doctor of Philosophy, 2012 Centre for Medieval Studies University of Toronto This study engages a network of music, myth, and metaphysics within late-ancient and twelfth- century music theory and cosmology. It traces the development, expansion, and demise of a (natural-) philosophical harmonic speculation that stems largely from an a priori commitment to a harmonic cosmology with its deepest roots in Plato’s Timaeus. It argues that music theory not only allowed twelfth-century thinkers to conceptualize the fabric of the universe, but it also provided a hermeneu- tic tool for interpreting the ancient and late-ancient texts that offered detailed theories of the world’s construction. The twin goals of this study are thus philosophical and musicological: firstly and philosophically, to analyze and re-assert the importance of musical speculation in the writings of the self-styled physici, who probed the physical world and its metaphysical foundations during the ‘Twelfth-Century Renaissance’; secondly and musicologically, to document the sources and scope of this musical speculation and to situate it within the larger tradition of ‘speculative music theory.’ The first part of the thesis (chapters one and two) disentangles the knotty question of sources for and connections between the late-ancient texts (by Calcidius, Macrobius, and Boethius) that form the background of twelfth-century thought, and it sketches the proper domain of musical thought by tracing the expansion of music’s role in quadrivial and natural-philosophical contexts from late- ancient encyclopedism though various twelfth-century divisiones scientiae. The second part of the thesis (chapters three through five) assembles and analyzes the direct evidence for twelfth-century harmonic theory. These chapters, heuristically organized around the Boethian tripartition of music, present an anagogic ascent per aspera ad astra. Chapter three (musica instrumentalis) highlights the occasional and perhaps surprising employ of practical, technical music theory in cosmological con- texts, and focuses on the epistemological foundations of hearing and the ontological status granted to the sonorous ‘objects’ of hearing. Chapter four (musica humana) targets the anthropological, psycho- logical, and ethical implications of musical relations in and between body and soul. Finally, chapter five (musica mundana) outlines the cosmological framework, the anima mundi in particular, that underpins the concordant machinations of the machina mundi in all its manifestations. ii ACKNOWLEDGEMENTS Aestuante aestiuo in Leone sole, iaciente iacula numquam beneuole, dedi has primitias messas magna mole magnifico magistro dicens ‘lege, tolle!’ Laetabundus, subito onere leuatus, deo egi gratias, summe eleuatus, renouatus animo, carne fatigatus, quoniam ab arduis rebus feriatus. Si in istis uobis est quid utilitatis, laudes celeberrimae nunquam erunt satis, omnes quas ad magistros meos offeratis. Nullum donum maius est quam humilitatis. Quorum eloquentia me locupletaui, quorum et acumine me acuminaui, eos coram omnibus ego liberaui a quocumque uitio quod hic perpetraui. Nam si egi prudenter de Boethianis, si nil forte dixi quo reueler inanis, tunc hoc totum debetur studiis humanis mi consiliarii, magistri Iohannis. Si umquam de musica commode tractaui, fecit hanc concordiam (cum labore graui) Gabriela magistra, docens uoce suaui λείµµατος subtilia et sesquioctaui. Abelardus mihi est semper submolestus; causa est insomniae, causa indigestus. Qui (mireris) medicus tandem est suggestus? Quidam rex eruditus multumque modestus. Totam philosophiam uerbis tectam densis docuit me sapiens senex Carnotensis, cui quoque domus est urbs Atheniensis, per quem mundo notus est glossator Conchensis. iii Acknowledgements Et Latinas regulas (ignoscat offensis!) docuit me peritus uir Lancastriensis. Ille est dignissimus laudibus immensis, quippe qui sic clueat uir Latiniensis. Apud scholam inclitam Cantabrigiensem commoratus dulciter circa Maiam mensem lectione fructus sum, didicique sensim animum acuere ut acutum ensem. Vnde ago gratias alteri Iohanni, ad quem nos contulimus quasi Porretani; transfretani uenimus atque transmontani, umeris gigantium insidentes nani. Adeo contortus est scholae apparatus ut se possit soluere nemo implicatus, nec mi esset libertas multos post conatus, si non essem gratia Gratiae saluatus. Quondam dixit sapiens uoce cum superna: ‘poculis accenditur animi lucerna.’ Sic amicis soluatur gratia aeterna, ut qui lucubrauerint mecum in taberna. Meaeque familiae numquam obliuiscor, qua suffultus firmiter finem adipiscor; totius prosapiae laete reminiscor dum ad res scholasticas ego proficiscor. Hoc complecti nequii uerbis manifestis sine beneficio feminae caelestis, immo caelestissimae, et sit Deus testis: ea est uxorcula meaque Alcestis. Vxori meae hoc opus libens laetusque do atque dedico. iv CONTENTS Acknowledgements iii Contents v List of Figures vii Abbreviations viii Preface 1 1 Prolegomena: Platonic musicology in late-ancient thought7 1.1 A Platonic triptych.................................... 8 1.2 Timaean harmonic theory................................ 11 1.3 Pythagorean and Aristoxenian harmonic theory .................... 15 1.4 Boethius.......................................... 17 1.5 Timaean Arithmetic in Boethius’ De institutione musica . 19 1.6 Calcidius ......................................... 32 1.7 Macrobius......................................... 36 1.8 Back to Boethius: conclusions .............................. 40 2 Defining the domain: musica and the diuisiones scientiae 44 2.1 Boethius.......................................... 46 2.2 Martianus Capella..................................... 54 2.3 Calcidius and Macrobius................................. 57 2.4 Cassiodorus and Isidore.................................. 59 2.5 Bernard of Chartes and the Glosae Colonienses super Macrobium . 63 2.6 William of Conches.................................... 66 2.7 Bernard Silvestris..................................... 68 2.8 Hugh of St. Victor and related texts........................... 72 3 Musica instrumentalis: sound and system 76 3.1 References to contemporaneous practice and theory .................. 78 3.2 Boethius on sense perception and hearing........................ 87 3.3 Boethius on acoustics................................... 98 3.4 Twelfth-century views on perception and hearing....................104 3.5 Vox, sonus, et auditus apud grammaticos . 109 3.6 Vox, sonus, et auditus apud physicos ............................115 3.7 Appendix I ........................................119 4 Musica humana: anthropological harmony 129 4.1 Quantumque per uocem utilitatis capitur ex musica . 131 4.2 The ethical utility of music in the twelfth century ...................137 v Contents 4.3 Soul: being harmony, having harmony .........................142 4.4 Psychological harmonies: per similitudinem . 148 4.5 Somatic harmonies: the corpus organicum . 154 4.6 ‘Psychosomatic’ harmonies: the union of body and soul . 162 5 Musica mundana: cosmological harmonies 170 5.1 The Boethian framework of musica mundana . 179 5.2 Musica elementorum ....................................185 5.3 Anima mundi et harmonia: the late-ancient reception..................190 5.4 Anima mundi et harmonia: the twelfth century.....................193 5.5 Musica caelestis .......................................211 5.6 Appendix I ........................................220 5.7 Appendix II........................................225 5.8 Appendix III .......................................229 Bibliography 234 vi LIST OF FIGURES 1.1 Boethius’ proof that a minor semitone (mST) is larger than three commas (c) but smaller than four (Inst. mus. 3.14). .................................. 20 1.2 Barbera’s counterproof that a fifth is larger than two tones but smaller than three (1981, 31). .............................................. 21 1.3 Functional equivalences within Boethius’ method. ..................... 23 1.4 Geometric and arithmetic series: large vs. small ratios.................... 23 1.5 Comparison of actual values and approximate values in the computation of sequential tones (T) against a fifth..................................... 24 1.6 Comparison of actual values and Boethius’ approximate values in the calculation of se- quential commas (c) against a minor semitone (mST)..................... 25 1.7 Comparison of actual values and Boethius’ approximate values in the calculation of se- quential commas (c) against a minor semitone (mST), major semitone (MST), and whole tone (T)............................................. 26 1.8 Boethius’ partition of the monochord of the netai hyperboleon through three genera (Inst. mus. 4.6). ........................................ 29 1.9 Eratosthenes’ enharmonic tetrachord (according to Ptolemy, Harm. 3.14). 41 2.1 divisio philosophiae iuxta Boetium ............................. 47 2.2 divisio philosophiae iuxta Guillelmum de Conchis..................... 67 2.3 divisio musicae iuxta Hugonem de Sancto Victore ..................... 72 2.4 divisio musicae iuxta Tractatum de philosophia