This is Your Brain on Hexachordal Solmization

Megan Kaes Long

Recently, I posed a question on Twitter: what kind of solmization system(s) were you brought up on, and to what extent did solmization shape your understanding of pitch space? The responses ran the gamut of systems — some folks grew up on fixed do, others on moveable do with la-based minor, others developed idiosyncratic systems based on their instruments, others learned hand signs. But one theme was consistent in all of the responses: whatever system we learned as young musicians, it profoundly shaped the way we hear and understand music, because it helped us build out our personal mental map of musical space. But how?[1]

Over the last few years, I’ve learned how to sing Renaissance music using hexachordal solmization (with the help of user-friendly resources by Anne Smith (2011) and Elam Rotem). My hope was that learning this skill would help me understand sixteenth-century music better, and indeed solmization has completely changed how I hear, sing, and interpret this repertoire. The hexachord system comes with its own assumptions and opportunities that are distinct from those of contemporary fixed and moveable do, and I’ve found that hexachordal solmization just makes sense when I’m singing a Lasso motet from parts, or, more anachronistically, analyzing a Marenzio madrigal in score.

Some scholars (e.g. Mengozzi 2010) have critiqued the application of rudimentary sixteenth-century pedagogy to sixteenth-century repertoire. Professional musicians surely did not sight read music on syllables, so why should we assume that syllables were compositionally meaningful? I believe that our internalized sense of tonal space shapes how we hear and play, regardless of whether or not we explicitly (or mentally) articulate syllables in our own professional practice. Indeed, some 16th-century music theoretical sources confirm the centrality of this kind of implicit knowledge in contemporary thought. For instance, Italian music theorist Giovanni Maria Lanfranco (1533), paraphrasing Gaffurius, noted:

Any piece can be sung in three ways. The first is to solfa, and to utter the name of the notes, that is, ut re mi fa sol la, as schoolboys do. The second is just to utter the sound and the note conceived in the mind, leaving out the name of the syllables, as musical instruments do. The third, which pertains to singers, is the application of the words of the songs to the sounds conceived in the mind by means of the six singable syllables. (qtd. in Dean 1996)

Lanfranco’s testimony suggests that the act of “conceiving music in the mind” is indeed the work of conceptualizing the relationships of the solmization syllables, and using the scalar context they provide to accurately render notated music audible.[2]

But what kinds of affordances does implicit knowledge of hexachordal solmization provide? What follows are a few reflections on how hexachordal solmization illuminates the nature of sixteenth-century tonal space.

First, solmization systems interact in productive ways with the diatonic environments they are designed to teach. If contemporary moveable do solfege reflects the seven-note diatonicity of the major scale and its capacity for transposition around the circle of fifths (via the doctrine of key signatures), then hexachordal solmization reflects the more flexible diatonicism of the Guidonian gamut, which is not a seven-note system but an eight-note system, where both B fa and B mi (that is, B-flat and B-natural) are viable diatonic pitches. The principles of mutation (and the mutation shortcut of fa super la) ensure that both B-flat and B-natural are equally accessible under the cantus durus system (with no signature); one is not a substitute for or alteration of the other. Composers often strategically exploit the contrast between these degrees for text expressive or formal ends (Long 2023). The multivalence of B fa B mi is also reflected in the distinct structure of modal collections—specifically, the ways that certain degrees, like the sixth in the Dorian mode, tend to be treated flexibly. The hexachords, the gamut, and the modes emerge as three distinct yet interconnected ways of thinking about pitch relations in sixteenth-century music, and we often need to triangulate them to get a full picture of the structure of a particular motet or mass movement.

Second, hexachordal solmization and the Guidonian gamut are tied to the notation of specific pitches—Renaissance musical thought is firmly rooted in the dual systems of cantus durus and cantus mollis (the void and one-flat systems), and the hexachords on G, C, F, and B-flat that support these systems. The hexachord system is not infinitely transposable (the existence of fictive, chromatic hexachords notwithstanding); my capacity to solmize (and indeed my conception of Renaissance tonal space more broadly) is inseparable from the notated pitch levels of Renaissance sources (regardless of the actual frequencies at which these works were performed). This kind of “notational absolute pitch” (for want of a better term) has significant ramifications for the tonal structure of Renaissance music. For instance, flats and sharps are not treated the same under hexachordal solmization. In most accounts, flats are solmized “fa” automatically; on the other hand, sharps don’t affect solmization at all (Berger 1987). Accordingly, Renaissance musicians sang, felt, and understood that the “intermingled” sharps that created cadences (leading tones and Picardy thirds) were different in kind from the more structural flatward mutation that motivated rules-of-thumb like fa super la (cf. Baragwanath 2020). A related phenomenon involves the notion of “tonal compass” (Crook 1998). We tend to assume that the pitches available to composers are regulated by the limitations of keyboard instruments tuned in meantone temperament. But they are also regulated, conceptually, by solmization. The mutations required to introduce flats mean that motets and mass movements seldom include more than one flat beyond the signature. But composers will use up to four sharper notes—so works in cantus mollis (the one-flat system) tend to extend no further flatward than E-flat, but as far sharp as G-sharp.

Finally, hexachords provide a framework for navigating the diatonic system rooted in linear rather than vertical relationships. (One way to understand this distinction is to observe that octave equivalence is downplayed in hexachordal solmization: we might sing the G below middle C as ut and the G an octave above it as sol, acknowledging the distinct melodic contexts of these two degrees within the ambitus of their respective voice parts. The distinct solmization syllables we apply here do not compromise a composer’s capacity to treat a G ut/G sol simultaneity as an octave.) Attending to linear solmization patterns pays huge dividends in performance. For instance, the imitative exposition of a motet often involves a soggetto which appears at two (or even three) pitch levels with the same solmization—this technique was so common that Renaissance theorists even gave it a special name, fuga, as distinct from imitazione (Haar 1971, Long 2023). Such solmization patterns certainly facilitate group sight singing, but they also lay bare the contrapuntal structure of dense canonic passages in real time (and indeed facilitate the composition of such passages). But these patterns also help singers trained in solmization to internalize stock melodic patterns, to feel the unique characteristics of different modal collections, and to navigate melodic relationships that occur at multiple pitch levels without invoking unwieldy concepts like modulation or modal commixture.[3]

I’m fascinated by the unique affordances of hexachordal solmization as it was learned and practiced by sixteenth-century musicians, and how the hexachordal system exists in symbiosis with both modal theory and the polyphonic repertoire. And I’m struck by the staying power of this 1000-year-old pedagogical method, which has been modified and manipulated dozens of times to suit changes in musical style, from its initial conception in the eleventh century to the two-hexachord system advocated by sixteenth-century pedagogues (Mengozzi 2010) to the eighteenth-century solfeggio tradition (Baragwanath 2020) to the modern pedagogical drama between advocates of do-based and la-based minor. We have much to gain from considering in more detail how our solmization systems interact with and even shape their attendant musical styles and the ways that composers, singers, and other musicians navigate these styles.


Images

A Guidonian hand, from a fifteenth-century manuscript copy of Johannes Tinctoris, Expositio manus. Universitat de València, BH Ms. 0835, fol. 3v. (CC-BY-NC license)
A gamut diagram from Adam Gumpelzhaimer, Compendium musicae (Augsburg: Schönig, 1591), sig. B3r. Staats- und Universitätsbibliothek Dresden, MB.8.457,angeb.3. (public domain)

Works Cited

Baragwanath, Nicholas. 2020. The Solfeggio Tradition: A Forgotten Art of Melody in the Long Eighteenth Century. New York: Oxford University Press.

Berger, Karol. 1987. Musica ficta: Theories of Accidental Inflections in Vocal Polyphony from Marchetto da Padova to Gioseffo Zarlino. Cambridge: Cambridge University Press.

Crook, David. 1997. “Tonal Compass in the Motets of Orlando di Lasso.” In Hearing the Motet: Essays on the Motet of the Middle Ages and Renaissance, edited by Dolores Pesce, 286–306. New York: Oxford University Press.

Dean, Jeffrey. 1996. “Okeghem’s Attitude towards Modality: Three-Mode and Eight-Mode Typologies” in Modality in the Music of the Fourteenth and Fifteenth Centuries, edited by Ursula Günther, Ludwig Finscher, and Jeffrey Dean, 203–46. Neuhausen-Stuttgart: Hänssler-Verlag.

Edwards, Warwick A. 1970. “The Performance of Ensemble Music in Elizabethan England.” Proceedings of the Royal Musical Association 97: 113–23.

Haar, James. 1971. “Zarlino’s Definition of Fugue and Imitation.” Journal of the American Musicological Society 24, no. 2: 226–54.

Karpinski, Gary S. 2021. “A Cognitive Basis for Choosing a Solmization System.” Music Theory Online 27, no. 2.

Lanfranco, Giovanni Maria. 1533. Scintille di musica. Brescia: Lodovico Britannico.

Long, Megan Kaes. 2023. “Hexachordal Solmization and Syllable-Invariant Counterpoint in the Vocal Music of William Byrd.” Music Theory Spectrum 45, no. 2. Forthcoming.

Mengozzi, Stefano. 2010. The Renaissance Reform of Medieval Music Theory: Guido of Arezzo between Myth and History. Cambridge: Cambridge University Press.

Pike, Lionel. 1998. Hexachords in Late-Renaissance Music. Aldershot: Ashgate.

Rotem, Elam. 2017. “Solmization and the Guidonian hand in the 16th century.” Early Music Sources. YouTube video. https://www.youtube.com/watch?v=IRDDT1uSrd0

Smith, Anne. 2011. The Performance of 16th-Century Music: Learning from the Theorists. New York: Oxford University Press.


[1] Recent work at the intersection of cognitive psychology and music theory pedagogy, like Karpinski 2021, provides some insight on this question.

[2] See also Edwards 1970, Pike 1998, 15–16.

[3] Baragwanath 2020 has recently explored the extension of these affordances to the 18th-century solfeggio tradition.

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