In chapters 7 and 8 of the Micrologus (c. 1026–28), Guido d'Arezzo introduces the term “affinity” (affinitas). Although he does not provide a definition, one can infer from his discussion that he is describing a concept that corresponds to Hucbald's “comradeship” (socialitas) [1]. Essentially, both authors observe that certain intervallic patterns reoccur within the diatonic tone system at the interval of a fourth or fifth, creating pairs of related notes. For instance, Guido explains that from both a and E one descends by two tones and a semitone: a–G–F–E; E–D–C–B.

The problem nevertheless remains that Guido advances several observations pertaining to affinity but never explicitly delineates the concept, and it is not readily apparent how his different examples correlate. At one point, he explains that D and G descend similarly by a tone and a semitone. Yet the idea that two intervals suffice to produce affinity is incompatible with the claim that affinity occurs solely at the interval of a fourth or fifth, since the diatonic segment F–G–a–♮ contains adjacent pairs of tones: F–G–a and G–a–♮. Guido's inconsistent terminology poses an additional challenge. For example, “to have concordance” (habere concordiam) can signify either that notes are distant from each other by a consonant interval or that they have affinity—two relatable but distinct ideas. The elliptical rhetoric of chapter 8 in particular has led to differing interpretations. When Guido posits that all affinities are connected with “these three notes,” most scholars read C, D, and E; however, some argue for D, E, and F [2]. The diagram at the end of chapter 8 constitutes the summation of Guido's thoughts on affinity, illustrating all the combinations of affinity pairings. Thus, it provides an important clue to understanding the preceding discussion.

With this diagram forming the focal point of my presentation, I will outline its possible interpretations, notably that of Dolores Pesce [3]. Building on her conclusion, I will show that the entirety of Guido's thoughts on affinity at the fourth or fifth are encapsulated by the relation between the natural and hard hexachords. Although neither Guido nor Pesce overtly mention hexachords, this explanation allows to reconcile Guido's various remarks. Moreover, I will propose a complementary reading of the diagram and supporting text in which I claim that chapter 8 exposes the inversional properties of species of consonance within the hexachord and, more generally, within the tone system. According to this proposition, the Micrologus would be the first publication in the history of Western music theory to address species inversion.

[1] Dolores Pesce, The Affinities and Medieval Transposition (Indiana University Press, 1987), 19; Charles M. Atkinson, The Critical Nexus (Oxford University Press, 2009), 160.

[2] Marie-Noël Colette and Jean-Christophe Jolivet, eds, Micrologus (Institut de pédagogie musicale et chorégraphique, 1993), 42.

[3] Dolores Pesce, “A historical context for Guido d'Arezzo's use of distinction,” in Music in Medieval Europe, ed. Terence Bailey and Alma Santosuosso (Ashgate, 2007), 160–62.