The Golden Book of Chinese Music Theory

Richard Cohn

In 1978, archaeologists working in Hubei Province, China, uncovered a royal tomb from 433 B.C. Among the twenty musical instruments is a set of sixty-five bronze bells suspended from a wooden support. Each bell is almond-shaped and emits two distinct pitches depending on the strike point. They have low inharmonicity and rapidly self-damp, making them ideal for accompanying voices and other instruments (Bagley 2005, 54–55). The middle registers contain twelve distinct pitches per octave. The pitches divide the scale more-or-less equally. Pairs of pitches separated by 3, 4, or 7 units form intervals that sound consonant, without fitting any standard European tuning system particularly closely (Lehr 1988).

Each strike point is cast with a gold-inlaid inscription classifying its fixed pitch. Four root labels are identical to modern pentatonic ones: gong (^1), shang (^2), zhi (^4), and yu (^5). The fifth modern label, jue (^3), appears as well, but does not directly refer to an additional root four units above gong. Instead, jue is a suffix that indicates a transformation, in the Lewinian sense: it raises any of the four roots to which it attaches by four units. Labels for the remaining four chromatic pitch classes are generated by a second suffix, zeng, which maps those same roots upward by an additional four units. The generation of the chromatic system as a cross product of four roots and three suffixes (ø, jue, zeng) is isomorphic with the generation of the same system by transpositional combination of an all-combinatorial [0257] tetrachord with an [048] augmented triad.

The inscriptions also report a range of relative functions for each pitch. The surfaces of the larger bells, where writing space is sufficient, indicate a range of pentatonic functions for both of their constituent tones. Isomorphic to those inscriptions would be the Western understanding that, for example, the E bell functions as ^1 of the E scale, ^2 of the D scale, ^3 of the C scale, ^4 of the A scale, and ^5 of the G scale (where the scales are pentatonic). An analogous range of pentatonic functions is reported by the inscriptions on a set of 41 chime stones, also twelve to an octave, found in the tomb. 

I first learned of the Zeng bells from two articles (1979-80) by Yuan-Yuan Lee in Chinese Music, a publication of the Chinese Music Society of North America, and then subsequently from an archaeological monograph and a collection of metallurgical essays (von Falkenhuasen 1993; Chen et Al. 1994). In 1997, I was invited to participate in a plenary session for the annual meeting of the Society for Music Theory. Rightly guessing that this would be the biggest live audience I would ever have the opportunity to address, I picked up what I thought was a big stick, and waved it around in a slightly obnoxious way that I thought would focus some sustained attention. “One might expect,” I puffed, “that the level of interest that such a discovery might arouse in a scholarly community that identifies its domain by conjoining the terms ‘music’ and ‘theory’ might be tantamount to, say, that of a community of astronomers upon the discovery of a new moon for Jupiter. What does it say about our discipline that, for the last twenty years, we collectively yawned at or slept through this discovery, leaving its exploration to the archaeologists and materials scientists?” (Cohn 1998, par. 23). I waited for a response. But my bell rapidly self-damped, and my home field carried on with its hibernations.

Two recent developments make the Zeng bells newly relevant a quarter-century later, prompting me to what I hope is a better timed and more effective intervention. First, there is interest in responding to the global turn in the humanities, of which any reader of this blog will be keenly aware. Second, I discovered a 2005 article by Robert Bagley, a Princeton professor (now emeritus) of Chinese archaeology. If Google Scholar is to be trusted, The Prehistory of Chinese Music Theory has received as yet zero citations by music theorists. Hence my only slightly ironic boast of having made a “discovery,” rather than of having merely read an article that I downloaded onto my laptop.

Bagley evocatively describes the inscriptions as “a book about musical scales with a demonstration CD tucked inside the back cover” (2005, 58). As such, they are “the earliest texts about music theory presently known from China” (41). The inscriptions indicate that Zeng theorists were interested in the chromatic universe as a repository for twelve (notionally) equally distributed transpositions of the pentatonic scale, each comprised of definite pitches with well-defined functions. For a modern-day music theorist trained in Western music, this last phrase rolls off the pen so naturally that it takes work to see the teeming heap of concepts, mostly independent of one another, that it compresses. Bagley does this work, unpacking the claim into what are, by my count, seven sub-claims: (1) definite pitches having (2) well-defined functions with respect to (3) twelve distinct (4) pentatonic scales, (5) co-related by transposition, and (6) evenly distributed across a gamut of (7) octave-equivalent pitches representing twelve pitch classes (72). None of this can be taken for granted, as the way that musical systems were bestowed by nature.

Bagley situates the Zeng bells as an ostentatious culmination to a 1,500-year-old bell-forging culture. The pointed-ellipse technology was already perfected around 2,000 B.C. Early bells were created one at a time for functional purposes, such as tracking cattle or raising alarms. No later than 1100 B.C., single bells began to be gathered to court “from the field” in order to anchor the tuning of instrumental and vocal ensembles, eventually forming small musical consorts that were acoustically matched to each other, but visually motley. One consort, dated to the 11th century B.C., chromatically filled a half-octave, suggesting an early standardization of the chromatic reservoir. Assuming that the documentary evidence from the fifth century BC also applies to bell consorts six centuries earlier, we can imagine what priorities guided the matching of bell frequencies to form pentatonic scales: maximization of acoustic consonances, certainly, but also the transposability by substitution of a single bell one unit away, for example {CDEGA} => {CDFGA} => {CDFGBb}. There is no reason to believe that pentatonic modulations occurred mid-piece, and Bagley shows that, at least in the case of the chime stones, such modulations would not have been practical. The twelve distinct pentatonic transpositions, each bell serving as the gong of its own scale, likely responded to a range of cosmological, political, or social considerations.[i]

Bagley (2005; 2015) argues that the closure of the 12-tone chromatic reservoir results from the fixed-pitch properties of bells.  By comparison, although the seven diatonically tuned pitches of the Mesopotamian harp afford the same chain of fifth-related transpositions, by incremental retuning of single strings (Rahn 2022),  each string’s infinitely continuous tuning creates no incentive to circumscribe the pitch universe and close it back to its origin. A more complicated comparison is presented by the Greek system of tonoi, first described a century after the Zeng bells were entombed, which affords at least twelve distinct transpositions, and close back to their origin (Hagel 2009, 44). Andrew Barker (1987, 107; 1989/2, 26) has suggested that this system may have arisen in response to the increasingly central position of the aulos, whose pitches are fixed like bells, but are also to some extent varied by embouchure and air pressure, partial-hole fingering, and eventually mechanical attachments (see also Hagel 2009, 337). However, knowledge of these systems is assembled indirectly, from spotty documentary evidence, most of it 500 years after the fact, supplemented by poorly preserved musical instruments, and iconography.[ii] By contrast the aural and documentary evidence of the Zeng bells is unimpeachable, backed as it is by robust metallurgical collateral, due to a 2,500-year life underground and underwater.

I am grateful to Robert Bagley and David Cohen for suggestions and information.


Bagley, Robert. 2005. “The Prehistory of Chinese Music Theory,” Proceedings of the British Academy 131: 41–90.

——————. 2015. “Ancient Chinese Bells and the Origins of the Chromatic Scale.” Zhejiang University Journal of Art and Archaeology 2: 57–81.

Barker, Andrew. 1987. “Text and Sense at Philebus 56a,” Classical Quarterly 37.1: 103–109.

——————–. 1989. Greek Musical Writings, Volume 2: Harmonic and Acoustic Theory. Cambridge: Cambridge University Press.

Chen, Cheng-Yih et Al., eds. 1994. Two-Tone Set-Bells of Marquis Yi. Singapore: World Scientific.

Cohn, Richard. 1998. “Music Theory’s New Pedagogability.” Music Theory Online, 4.2.

Hagel, Stephan. 2009. Ancient Greek Music: a new technical history. Cambridge: Cambridge University Press.

Lee, Yuan-Yuan. 1979. “An Amazing Discovery in Chinese Music,” Chinese Music 2.2: 16–17.

——————— 1980. “The Music of the Zenghou Zhong,” Chinese Music 3.1: 3–15.

Lehr, A. 1998. “The Tuning of the Bells of Marquis Yi,” Acustica 67.2: 144–48.

Lynch, Tosca. 2018. “‘Without Timotheus, Much of our Melopoiia would not exist; but without Phrynis, there wouldn’t have been Timotheus’: Pherecrates’ twelve strings, the Strobilos and the Harmonic Paranomia of the New Music.” Greek and Roman Musical Studies 6.2: 290–327.

Nowacki, Edward. 2020. Greek and Latin Music Theory. Rochester: University of Rochester Press.

Rahn, Jay. 2022. “Was Mesopotamian Tuning Diatonic? A Parsimonious Answer.” Music Theory Online 28.1.

von Falkenhausen, Lothar. 1993. Suspended Music: Chime-Bells in the Culture of Bronze-Age China. Berkeley and Los Angeles: University of California Press.


[i] Robert Bagley writes, in recent private correspondence, that this speculation is not backed by any available documentary evidence.

[ii] Skepticism concerning the documentary evidence is expressed by Nowacki (2020, 28). Hagel (2009, 327) summarizes the condition of the preserved auloi. For an extraordinary recent harvesting of iconographic evidence from vase painting, see Lynch (2018, 310).

Colonial Organology and Ornithology in Richard Ligon’s Acoustics of Anthropological Difference (Part II)

Andrew J. Chung

[…] Continuation of Part I […]

Music theoretical judgments help to articulate Ligon’s understandings of the human as a category also in a somewhat later portion of his book devoted to careful empirical documentation of local flora and fauna. Describing an evidently thrush-like bird, he indulges some musings about quarter tones:

[It is] the colour of a Feldefare [fieldfair, Turdus pilaris], but the head seemes too big for her body, and for that reason they call her a Counsellor; her flying is extream wanton; and for her tune, ‘tis such as I have not heard any like her, not for the sweetnesse, but the strangenesse of it; for she performes that with her voice, that no instrument can play, nor no voice sing, but hers; and that is, quarter notes, her song being composed of five tones, and every one a quarter of a note higher then other. Mr. John Coprario, a rare composer of Musick, and my dear friend, told me once, that he was studying a curiosity in musick, that no man had ever attempted to do; and that was, of quarter notes; but he not being able to go through with it, gave it over: But if he had liv’d to have gone with me to the Barbadoes, this bird should have taught him.

(1657, 60)

For Ligon, the Counsellor bird’s quarter tonal singing seems at first to imply a notion of species difference. The musically knowledgeable (then, just as now) could have easily refuted him, but Ligon describes the Counsellor’s quarter tonal song as that which human instruments cannot play, nor human voices sing.

But what began as an observation of putatively inhuman ability transfigures itself by the time the passage quoted above concludes with mention of the composer John Coprario. Ligon ventures that perhaps Coprario could have developed quarter tonal abilities if he could have just voyaged to Barbados to study with the Counsellor bird. An interesting rhetorical substitution has taken place. While Ligon’s description of the Counsellor bird’s quarter tonal song began stationed at the notion of the bird’s inhuman abilities, it ends by betraying a rather different notion of quarter tonal scales and intervals as merely non-English rather than non-human. But for colonial powers in the early modern Atlantic, the non-human and the non-European were intertwined categories.[1] Thus, in Ligon’s narrative, the concept of quarter tonal sound polices species, geographical, and emergent racial boundaries; and his description of the Counsellor bird alludes further to certain early modern European attitudes, which held that non-Europeans like Macow were notionally animal until proven otherwise.

I am interested, ultimately, neither in condemning Ligon for being a person of his time who acquired, chafed sometimes against, and participated in its prejudices—nor in excusing him for that very fact. One point I am interested in making concerns how music theoretical knowledge and its categories, for Ligon, were part of his rhetorical machinery for reiterating some of his prejudices. But I am certainly uninterested in endorsing what I would consider to be the trite conclusion, which I shall merely describe: that Ligon, laden with the anthropological condescension customary to people like himself, nevertheless articulated a limited form of recognition towards an enslaved African and alluded to an alternate possibility to the racial animus of the colonial project. The most reflection-worthy and vexing takeaway from Ligon’s True and Exact History is not the lesson about reading historically distant subjects in proper view of their historical distantness, but a rather more disquieting possibility with eminently 21st-century relevance: that the seemingly recuperative idioms of liberal, humanist recognition can function both as explicitly benevolent judgments and implicitly as mechanisms that in fact help to advance rather than counteract projects of domination—there is actually no contradiction between these.[2] As Columbus once wrote, in his own explicitly recuperative gesture of proto-liberal humanist recognition, the intelligence he discerned in the Indigenous Taíno he met at landfall in 1492 attested for him to their potential as “good and intelligent servants.”[3] For Ligon, likewise, his admiration for Macow’s abilities was continuous his belief in the viability of enculturating enslaved people into English norms (and into English Christianity as well). One broader discursive effect of Ligon’s narrative and its musical observations is that they acted to police lines of anthropological difference that rendered non-Europeans as sub-humans or non-humans by nominating individuals like Macow as exceptions to that colonial principle, thereby presuming that ontological demarcation in the process. As music theorists continue unearthing colonial concepts in music theoretical texts and their circulation, it is worth remembering as well to excavate how music theoretical concepts circulated in colonial texts to advance colonial dominion.


BIBLIOGRAPHY

Charry, Eric. 1996. “Plucked Lutes in West Africa: An Historical Overview.” The Galpin Society Journal 49: 3–37.

Coulthard, Glen Sean. 2014. Red Skin, White Masks: Rejecting the Colonial Politics of Recognition. Minneapolis: University of Minnesota Press.

Epstein, Dena J. 1975. “The Folk Banjo: A Documentary History.” Ethnomusicology 19 (3): 347–71.

Field, Christopher D. S. 1974. “Musical Observations from Barbados, 1647-50.” The Musical Times 115 (1577): 565–67.

Greenblatt, Stephen. 1991. Marvelous Possessions: The Wonder of the New World. Chicago: University of Chicago Press.

Harrison, Peter. 2005. “‘Fill the Earth and Subdue It’: Biblical Warrants for Colonization in Seventeenth Century England.” Journal of Religious History 29 (1): 3–24.

Hartman, Saidiya. 1997. Scenes of Subjection: Terror, Slavery, and Self-Making in Nineteenth-Century America. Oxford: Oxford University Press.

Hu, Zhuqing (Lester). 2021. “Chinese Ears, Delicate or Dull? Toward a Decolonial Comparativism.” Journal of the American Musicological Society 74 (3): 501–569.

Ligon, Richard. 1657. A True & Exact History of the Island of Barbados. London: Humphrey Moseley.

Nunn, Erich. 2016. “‘A Great Addition to Their Harmony’: Plantation Slavery and Musical Exchange in Seventeenth-Century Barbados.” The Global South 10 (2): 27–47.

Parrish, Susan Scott. 2010. “Richard Ligon and the Atlantic Science of Commonwealths.” The William and Mary Quarterly 67 (2): 209–48.


[1] For explorations of how early modern English thought conceptualized non-Europeans in terms of animality, see, for instance, Peter Harrison, “‘Fill the Earth and Subdue It’: Biblical Warrants for Colonization in Seventeenth Century England,” Journal of Religious History 29, no. 1 (2005): 3–24.

[2] Theoretical elaborations of this point regarding the perhaps counterintuitive intimacies of recognition and domination can be found in Saidaya Hartman, Scenes of Subjection: Terror, Slavery, and Self-Making in Nineteenth-Century America (Oxford: Oxford University Press, 1997); Glen Sean Coulthard, Red Skin, White Masks: Rejecting the Colonial Politics of Recognition (Minneapolis: University of Minnesota Press, 2014); and in music studies in Zhuqing (Lester) Hu, “Chinese Ears, Delicate or Dull? Toward a Decolonial Comparativism, Journal of the American Musicological Society 74, no. 3 (2021): 501–569.

[3] This passage from the diary of Columbus’s first voyage is quoted by Stephen Greenblatt, Marvelous Possessions: The Wonder of the New World (Chicago: University of Chicago Press, 1991), 90.

Colonial Organology and Ornithology in Richard Ligon’s Acoustics of Anthropological Difference (Part I)

Andrew J. Chung

Among early modern colonizers’ narratives of the invasion and expropriation of the so-called New World, a great many and perhaps most devoted some space to documenting the musical and performance customs among the Indigenous people they encountered there and the enslaved Africans they brought there. Occasionally, even (indirect) music theoretical judgments surfaced in colonizers’ writings and their translations. For instance, ideas of Indigenous musics being poorly tuned and inharmonious helped their authors articulate broader societal and ontological judgments of non-Europeans—whose musicking always carried metaphysical, social, theological, extramusical significances to European ears.

Not counting the many musicians who arrived in the Americas to establish colonial churches, one of the most musically learned authors who documented the project of advancing European settlement in the Americas was surely Richard Ligon, whose A True and Exact History of the Island of Barbados (1657) offers the 17th century’s most detailed window onto the English colonial project in the Caribbean. A royalist, he left England in 1647 during its period of civil wars and bought a 50% stake in a sugarcane plantation in Barbados. Ligon was no musical slouch: he rubbed shoulders with those involved in the musical life of the crown, and was a close friend and, eventually, estate executor to the composer John Coprario (1570–1626)—a favorite of the royal family.[1] He even brought a theorbo (a long-necked lute) to Barbados.

Among scholars within and outside of music studies, one of Ligon’s most cited discussions concerns his musical encounter with a West African man named Macow (also spelled “Macaw” in the literature) enslaved on the plantation, whom he refers to as the “chiefe musition” and keeper of the plantain grove on the plantation. About the aforementioned theorbo, Ligon records that one day:

He [Macow] found me playing on a Theorbo, and sinking to It which he hearkened very attentively to; and when I had done took the Theorbo in his hand, and strooke one string, stopping it by degrees upon every fret, and finding the notes to varie, till it came to the body of the instrument; and that the neerer the body of the instrument he stops, the smaller or higher the sound was, which he found was by the shortning of the string, considered with himselfe, how he might make some trial of this experiment upon such an instrument as he could come by, having no hope ever to have any instrument of this kind to practise on. (1657, 48–49)[2]

Scholars have noted how Ligon assumed, in a prejudiced trope that persists today, that Africans do not practice musics involving deliberate pitch, counterpoint, and harmony.[3] In an ambivalent moment of both explicit admiration and implicit assumptions of Macow’s benightedness as a non-European, Ligon interpreted Macow’s encounter with the instrument as a demonstration of his technical ingenuity with an instrument utterly foreign to him. Ligon was unaware that West African musical cultures have used many such instruments, like the kora, gunbri, and seperewa.[4] Macow, however, as an expert practitioner of the traditions he belonged to was demonstrating an ingenuity of a completely different kind than what Ligon imagined, because he would have recognized the general principle of the theorbo’s construction from past sonic experiences on the continent he was born on.

            This passage is noteworthy in a music theoretical sense because of how it alludes to quadrivial musica speculativa and its own instrumentarium. For the musically knowledgeable among the readers of his text (such as, perhaps, his friends among royal musical circles), the image of Macow stopping and striking a single string of the theorbo at various intervals would have recalled traditions of monochord experimentation and the high prestige of speculative canonics. Perhaps Ligon himself, with his own musical knowledge, pictured Macow as the musicus calculating string lengths and interval ratios before the monochord. The allusion to speculative music theoretical discourses of tuning and monochord experiments here functions to render Macow’s behavior legible within staunchly European regimes of comprehensibility.

            The next episode in Ligon’s narrative is equally remarkable for its early modern crossing of anthropological judgments with music theoretical understandings of scales, solmization, and tuning and temperament. A day or two later, Ligon finds Macow in the plantain grove building a wooden idiophone. Macow was:

sitting on the ground, and before him a piece of large timber, upon which he had laid crosse, sixe Billets, and having a handsaw and a hatchet by him, would cut the billets by little and little, till he had brought them to the tunes, he would fit them; for the shorter they were, the higher the Notes which he tried by knocking upon the ends of them with a sticke, which he had in his hand. When I found him at it, I took the stick out of his hand, and tried the sound, finding the sixe billets to have sixe distinct notes, one above another, which put me in a wonder, how he of himselfe, should without teaching doe so much. I then shewed him the difference between flats and sharpes, which he presently apprehended, as between Fa, and Mi: and he would have cut two more billets to those tones, but I had then no time to see it done, and so left him to his own enquiries. I say this much to let you see that some of these people are capable of learning Arts.

(1657, 49)

There are numerous music theoretical conditions of possibility for how Ligon developed this passage. Ligon had to draw on understandings of hexachordal solmization to probe Macow’s hearing, understanding, and craftsmanship. Believing that Macow had no prior understanding of melodic instruments, Ligon was astonished because he thought that showing Macow his theorbo just one or two days earlier instantly enabled Macow to grasp the pitch domain of musical sound itself. Susan Scott Parrish’s analysis of this passage holds that Ligon believed Macow was mimicking the gamut of the theorbo, meaning that Ligon judged the intervallic dispositions and temperament of Macow’s instrument to be  similar enough to that of his theorbo—if he indeed was interpreting the situation as Parrish describes.[5] Macow, however, was instead executing an instrumental design familiar to him perhaps to reciprocate Ligon’s organological show and tell. Ligon’s backhanded admiration for Macow and the seemingly benevolent gesture of pronouncing Macow as an exception to certain assumed “rules” about the character, abilities, and cultures of African societies is premised upon Ligon’s inability to understand musical pitch variation as a meaningful possibility among African musical practices.[6] It was with the help of music theoretical judgments that Ligon skeptically and provisionally extended some measure of anthropological inclusion and human recognition to Macow in the passage quoted above.


[1] As reported by Christopher D. S. Field, “Musical Observations from Barbados, 1647-50,” The Musical Times 115, no. 1577 (1974): 565.

[2] In this essay, I quote a handful of passages from Ligon’s original text. Orthographically, I have preserved 17th century spelling and punctuation, but I have converted instances of the long “s” (ie. “ſ”) to the standard “s.”

[3] See Erich Nunn, “‘A Great Addition to Their Harmony’: Plantation Slavery and Musical Exchange in Seventeenth-Century Barbados,” The Global South 10, no. 2 (2016): 34–35.

[4] Ligon was evidently unaware of work by Richard Jobson who, in 1623, published observations of stringed instruments in Gambia, as recorded by Dena J. Epstein, “The Folk Banjo: A Documentary History,” Ethnomusicology 19, no. 3 (1975): 350. Eric Charry notes that “Lutes have been played in West Africa since at least the fourteenth century, when both Al-‘Umarī and Ibn Battūta noted that they were used in royal ceremonies in old Mali” in Charry, “Plucked Lutes in West Africa: An Historical Overview,” The Galpin Society Journal 49 (1996): 3.

[5] See Susan Scott Parrish, “Richard Ligon and the Atlantic Science of Commonwealths.” The William and Mary Quarterly 67, no. 2 (2010): 239.

[6] This elevation of pitch over the time domain of music, of course, persists in all Euro-Western music theory curricula (though not without challenge in at least some classrooms).


[…] Continuation: Part II […]

Arabic Music Theory and Manuscript Studies: Greek Notation in al-Fārābī’s Great Book on Music?

Marcel Camprubí

Arabic music theory from the Abbasid period (750–1258) is a rich and sophisticated tradition that incorporates ancient Greek thought into autochthonous Arabic musical theorization and practice. Extant Arabic theoretical writings on music, which survive from the 9th century onwards, were penned by theorists mainly active in Baghdad. [1] Al-Fārābī (d. 950), author of the mighty Great Book on Music and two smaller works on rhythm, is arguably the most prominent theorist from the period.[2]

The last decade has been rightly characterized as a silver age in Arabic manuscript studies. Numerous studies have investigated the history of reading practices and knowledge transmission in the Arabic context through close scrutiny of details and paratextual information in handwritten sources.[3] The increasing digitization of Arabic manuscripts in European, North American, and Middle Eastern collections has undoubtably contributed to this trend. A correlative phenomenon has been the revalorization of the historische Hilfswissenschaften, the technical disciplines such as paleography employed to make historical evidence legible and thus, meaningful. This arsenal of techniques, once dismissed as ancillary due to being applied with naïve positivism, is being reclaimed as central to the historical project.[4]

My research focuses on the use of notation in Arabic musico-theoretical works, an area that is not well served by the existing printed materials.[5] Due to silent editorial interventions, modern editions and translations of early Abbasid writings on music present notated examples through means other than those appearing in the manuscripts. My contribution here draws attention to the kind of insights that can be gleaned when engaging with the manuscripts themselves.

Greek Notation in al-Fārābī’s Great Book on Music?

Jamāʿa (جَماعة), a note collection or “scale,” is one of the topics that al-Fārābī addresses in the last section of his Great Book on Music. Twelve such collections, employing different genres of tetrachords within the framework of a double octave, known today as the Greater Perfect System, are visually presented in twelve double tables: the first table lists the fifteen notes of each collection and its particular intervallic configuration; the second indicates the consonances and dissonances among the pitches of the collection.[6]

While there is much to be said about this passage of the Great Book, I want to focus on a detail that appears in just one of the extant manuscripts of al-Fārābī’s magnum opus: Istanbul, Köprülü Kütüphanesi, ms. 953; the surviving copy with the most reliable readings.[7] I present here the first table for the first jamāʿa or collection in the manuscript (Figure 1) alongside a rendering in English (Figure 2).

Figure 1 Istanbul, Köprülü Kütüphanesi, ms. 953. Facsimile in Neubauer, Kitāb al-mūsīqī al-kabīr, 350.
Figure 2 English rendering of first table in Istanbul, Köprülü Kütüphanesi, ms. 953

Al-Fārābī’s jamāʿa tables work as follows: the first column consists of letters from the Arabic Abjad alphabet assigned to each note or scale degree; the second gives the name of such notes; the fourth numerically represents the pitches in the collection; and the fifth displays the intervallic relationships between consecutive notes as ratios. What distinguishes manuscript Köprülü’s rendering from that of other copies of the Great Book is the third column, featuring what appear to be modified letters from the Greek alphabet.

These signs in al-Fārābī’s Great Book resemble the notation signs of vocal music employed in the treatises of Greek theorists such as Alypius, Aristides Quintilianus, Gaudentius, and Bacchius (3rd and 4th century CE).[8] A tentative interpretation of the signs in al-Fārābī’s table may be as follows: the signs in rows 4–11 appear as a reversed psi (ψ), chi (Χ), pi (Π), reversed phi (φ), sigma (Σ), omega (ω), mu (μ), and reversed tau (Τ); in row 2 a delta (δ); rows 14–15 could be a modified omicron (ο) and epsilon (Ε). Yet, while a few individual signs can be matched to those appearing in Greek sources, al-Fārābī’s set of signs does not coincide with the ones featured in Greek notation tables. (See Figure 3 for an illustration of such tables).

Figure 3 One of the notation tables in Gaudentius’ Harmonic Introduction. Paris, Bibliothèque Nationale de France, ms. Grec 2456, f. 270a. The signs in the right double column correspond to vocal (left) and instrumental notation (right).

Despite the elusive relationship between al-Fārābī’s and Greek notation tables, Gaudentius’ Harmonic Introduction (῾Αρμονικὲ εἰσαγωγἐ) suggests that this is a possibility worth entertaining. Al-Fārābī’s numerical representation of pitches—column 4 in the table (see Figure 1 and 2)—has a precedent in Chapter 15 of Harmonic Introduction, in which Gaudentius describes this very same procedure to introduce two diagrams that are unfortunately absent in the extant manuscripts.[9]

Yet, divergences between Gaudentius and al-Fārābī might outweigh their ostensible similarities. Gaudentius, in the section of his Harmonic Introduction devoted to ancient Greek musical notation, argues that there cannot be a single notation sign for each note, i. e.  proslambanomenos, hypate hypaton, etc. Given that different tetrachordal configurations produce dissimilar pitches, one requires a unique sign to specifically represent each of them.[10] Yet, what we find in al-Fārābī’s Great Book is precisely the opposite: all the jamāʿa tables in the Köprülü manuscript present the same identical set of signs, no matter what kind of tetrachord is employed. Therefore, in al-Fārābī’s tables these signs do not represent pitches, but rather act as a shorthand for notes as scale degrees, a function that the Arabic letters in column 1 already fulfill.

The letter-like signs in al-Fārābī’s Great Book appear as a puzzling vestige of his Greek sources. Yet, precisely identifying and substantiating al-Fārābī’s intellectual debts to specific ancient Greek writings is no simple task. While I continue working on this, I would very much welcome thoughts and feedback (camprubi@princeton.edu). Get in touch!


Bibliography

Manuscript and editions

Istanbul, Köprülü Kütüphanesi, ms. 953.

Facsimile: Neubauer, Eckhard. Kitāb al-mūsīqī al-kabīr: MS 953, Köprülü Library, Istanbul. Publications of the Institute for the History of Arabic-Islamic Science, series C 61. Frankfurt am Main: Institut für Geschichte der Arabisch-Islamischen Wissenschaften, 1998.

Paris, Bibliothèque Nationale de France, ms. Grec 2456.

Al-Fārābī, Abū Naṣr. Kitāb al-mūsīqā al-kabīr, edited by Ghaṭṭās ʿAbd al-Malik Khashaba. Cairo: Dār al-kātib al-ʿarabī, 1967.

Erlanger, Rodolphe. La musique arabe, volume 2, Al-Fārābī, Livre III du Kitābu l-mūsīqī al-kabīr. Paris: Librairie orientaliste Paul Geuthner, 1935.

Quintilianus, Aristides. On Music: In Three Books, edited and translated by Thomas J. Mathiesen. New Haven: Yale University Press, 1983.

Secondary literature

Blum, Stephen. “Foundations of Musical Knowledge in the Muslim World.” In The Cambridge History of World Music, edited by Philip V. Bohlman, 103–24. Cambridge: Cambridge University Press, 2013.

Jan, Karl von. Musici scriptores graeci: Aristoteles, Euclides, Nicomachus, Bacchius, Gaudentius, Alypius et melodiarum veterum quidquid exstat. Leipzig: B. G. Teubneri, 1895.

Mathiesen, Thomas. Greek Views of Music. Vol. 1 of Source Readings in Music History, edited by Oliver Strunk and Leo Treitler. New York: W. W. Norton, 1998.

Neubauer, Eckhard. “Arabic Writings on Music: Eight to Nineteenth Centuries.” In The Garland Encyclopedia of World Music. Vol. 6, The Middle East, edited by Virginia Danielson, Dwight Reynolds, and Scott Marcus, 363–86. New York: Routledge, 2002.

Rudolph, Ulrich. “Abū Naṣr al-Fārābī.” In Philosophy in the Islamic World. Vol. 1, 8th–10th Centuries, edited by Ulrich Rudolph, Rotraud Hansberger, and Peter Adamson, 526–654. Leiden: Brill, 2017.

Rustow, Marina. The Lost Archive: Traces of a Caliphate in a Cairo Synagogue. Princeton: Princeton University Press, 2020.

Wollina, Torsten. “Tracing Ibn Ṭūlūn’s Autograph Corpus, with Emphasis on the 19th–20th Centuries.” Journal of Islamic Manuscripts 9 (2018): 308–40.

Zanoncelli, Luisa. La manualistica musicale greca. Milan: Guerini, 1990.


[1] To name a few, al-Kindī (c. 800–c. 870), Yaḥyā ibn al-Munajjim (856–912), the Brethren of Purity, Ibn Sīnā (980–1037), al-Ḥasan ibn Aḥmad (fl. late 10th c.) and Ibn Zayla (d. 1048). For a magisterial exposition of the main topics addressed in these works, see Blum, “Foundations of Knowledge.” For an overview of the sources, see Neubauer, “Arabic Writings.”

[2]  Rudolph, “Abū Naṣr al-Fārābī,” provides a comprehensive overview of al-Fārābī’s works in all disciplines, his biography and intellectual context, and secondary scholaship.

[3] Wollina, “Tracing Ibn Ṭūlūn’s Autograph,” 309–10. The Journal of Islamic Manuscripts documents this phenomenon, providing a snapshot of the directions in the field.

[4] Rustow, The Lost Archive, 8–10.

[5] Preparing critical editions as well as translations that would facilitate access to these materials for non-Arabic speakers remain fundamental tasks for the advancement of the field. The launch in 2020 of the project Saramusik—“Sources arabes sur la musique” (المصادر العربيّة للموسيقى)— by the Tunisian musicologist Anas Gharab (أنس غراب), a site that aims to host digital editions of Arabic theoretical works, is a phenomenal recent development. Saramusik: https://saramusik.org (accessed March 13, 2021).

[6] Al-Fārābī, Kitāb al-mūsīqā, 880–958; Erlanger, La musique arabe, 2:2–17.

[7] Facsimile in Neubauer, Kitāb al-mūsīqī, 343–65. This manuscript was copied in 654H [1256 CE] according to its colophon. The title page contains an ownership statement from Ibn al-Sarrāj al-Qalānisī, an eminent astrologer mostly active in Aleppo, dated 748H [1347 CE]. The manuscript was part of the initial collection of Köprülü Library in Istanbul, which opened its doors in 1678.

[8] Greek texts in Jan, Musici scriptores graeci and Zanoncelli, La manualistica (with Italian translations). English translations in Quintilianus, On Music, tr. Mathiesen; and Mathiesen, Greek Views, 47–85.

[9] Jan, Musici scriptores graeci, 343–44; Mathiesen, Greek Views, 76–7. The procedure is straightforward: taking the Proslambanomenos as starting point and assigning a certain number to it, one proceeds to allocate numerical values to the rest of scale degrees according to the specific interval ratios. The caveat is that one needs to choose an integer for the Proslambanomenos that is large enough to allow for all subsequent divisions without resulting in fractional numbers. A plain example in the table above is the octave relationship (2:1) between Proslambanomenos (1620), Mese (810), and Nete hyperbolaion (405).

[10] Mathiesen, Greek Views, 79.

Watching the Ether: An Irreplicable Experiment on Pitch-Pipes (Part I)

Sheryl Chow

In 1672, on the twelfth day of the eighth month of the eleventh year of the Kangxi reign (r. 1662–1722), the emperor issued an edict abolishing a practice of musico-cosmological observations, known as houqi, which lasted for more than a thousand years in China: “The method of houqi has long been lost. It is hardly credible and reliable.”[1] Before the practice was abolished, it had been performed to detect the annual arrival of the vernal equinox (chunfen 春分) in the second lunar month by the Astronomical Bureau. Translated as “watching the ether,” houqi 候氣 involves filling with reed ashes twelve pitch-pipes (lüguan 律管), each producing one pitch of a chromatic scale, then burying them in the soil. It was believed that at each of the twelve major solar terms (e.g., the equinoxes and solstices) in each month, the ashes inside the corresponding pitch-pipe would be blown forth from below owing to the movement of qi 氣 (commonly translated as “ether” or “vital force”) pertaining to the solar term (Figure 1).[2] For instance, the ashes inside the reference pitch pipe of huangzhong 黃鐘—akin to the Western middle C—would be blown forth from below at the winter solstice in the eleventh lunar month.

Figure 1. An illustration of the hypothetical mechanism of ‘watching the ether’ (houqi 侯氣). As the twelve pitch-pipes protrude into the ground at different depths, the rising qi reaches the longer pipes first and the shorter pipes later, blowing off the reed ashes inside each pipe at the major solar term of each corresponding month.

Although failed attempts to obtain valid and reliable results had cast doubt on the theory of houqi, the practice had been sustained for more than a thousand years. Existing studies tend to attribute the practice’s longevity to fraudulent procedures, fabricated reports, ad hoc explanations for inconsistent results, and its conformity to the Chinese correlative worldview.[3] By invoking Harry Collins’s concept of the “experimenters’ regress,” however, I would like to shift focus towards the nature of houqi as an experiment. An experiment is not just an empirical method to test a theory, but also a skillful practice whose validity is also subject to test. Rather than emphasizing the impossibility of verifying the houqi theory, I shall highlight the difficulty in falsifying it owing to the very nature of experiments. But before that, let’s retrace the history of the houqi practice and of the attempts to verify it.

The earliest detailed account of houqi is found in the Book of the Later Han (Hou Han shu 後漢書; Later Han: 25–220), where it is proposed as a method of tuning rather than of cosmological observation:

[Zhang Guang and his colleagues] could not determine the tensions [huanji, literally “slow and fast”] of the strings [of Jing Fang’s thirteen-string tuner]. Pitches cannot be written down and shown to others. Those who know [the pitches] do not have the means to teach about them even if they want to. Those who understand [the pitches] with their mind-hearts learnt about them through experience, not from a teacher. Therefore, official historians who could identify pitches became extinct. Only the approximate numerical values [of the pitches] and houqi could be transmitted.[4]

The reliance on houqi in determining an appropriate pitch standard arose from the difficulty in documenting absolute pitches without the knowledge of sound frequency. Although there were plenty of documents that recorded the length and diameter of the pitch-pipe generating the reference pitch huangzhong, it was difficult to obtain the actual dimensions without knowing the measurement standard. In the absence of a consistent measurement standard across different regimes and regions or a means to translate between different measurement systems, pitch standard could not be transported on papers. In other words, they could not be transformed into what Bruno Latour calls “immutable mobiles,” like the positions of the planets marked on a star chart, or the locations of places represented on a map.[5]

While it is uncertain whether the account on houqi in the Book of the Later Han was meant to be a report of an actual experiment or a description of the procedures and predicted results, the Book of Sui (Sui shu 隋書) did document some actual attempts. Whereas Xin Dufang 信都芳, a staff officer in the Northern Qi (550–577 CE), successfully observed the scattering of ashes from his pitch-pipes at the corresponding solar terms, Mao Shuang 毛爽 (fl. 589 CE), the mayor of Shanyang 山陽, together with his colleagues from the Ministry of Music, obtained irregular results from their observations in 589 CE: the ashes sometimes scattered early, sometimes late, sometimes in abundance, sometimes in scarcity. When asked by Emperor Wen of Sui 隋文帝 (r. 581–604 CE) for an explanation, Niu Hong 牛弘 (545–610 CE) associated the volume of scattered ashes with the quality of governance: when half of the ashes were blown forth, it indicated that there was good governance; when all of the ashes were blown forth, it indicated that the officials were too relaxed; when no ashes were blown off in response to the movement of qi, it indicated that the emperor was atrocious. On the ground that it was impossible for the state of governance to vary from month to month, the emperor rejected Niu’s explanation and asked Mao for a report. In his report, Mao mentioned the music minister Du Kui’s 杜夔 (fl. 188–226 CE) failure in “watching the ether” and Xun Xu’s 荀勗 (ca. 221–289 CE) identification of its reason. Xun compared an ancient bronze ruler with Du’s ruler and found that it was 4 fen 分 shorter than Du’s, concluding that Du’s failure in houqi was due to the wrong dimensions of his pitch-pipes.[6] Mao also mentioned that his ancestor Mao Qicheng 毛栖誠 (fl. 502 CE) succeeded in houqi only after he modelled his pitch-pipes on a jade pitch-pipe acquired from a tomb in Ji 汲 (near present-day Weihui 衛輝 in Henan).[7]

Rather than providing an ad hoc interpretation as Niu Hong did, houqi experimenters tended more often to attribute negative or inconsistent results to flaws in the procedures and apparatus. According to Li Shida 李世達 (1533–1599), the Ming prime minister Zhang Juzheng 張居正 (1525–1582) also attempted to watch the ethers to no avail, but succeeded after he had modified the procedures following Yuan Huang’s 袁黃 (1533–1606) advice, which includes adjusting the depth and thickness of the chamber walls, the directions in which the doors of the three chambers face, and the length ratios of the pitch-pipes.[8] Yuan’s advice filled in a lot of gaps in the procedures described in the Book of the Later Han, which consists of only forty-nine characters. Although it is stipulated—probably to prevent winds from affecting the results—that the pitch-pipes should be placed inside three layers of chambers with airtight doors and hung with reddish silk fabrics, there are no specifications with respect to the sizes of the chambers, the directions of the doors, etc. It is instructed that the twelve pitch-pipes, each supported by a wooden rack, should be placed at the corresponding directions, but the directions are not specified.[9] Yet even if these variables are stated, it is still difficult to reproduce the procedures from a written record, for there are always more gaps to be filled. Some experimenters even contested on the place of origin of the reed ash, that of the bamboos used to make the pitch-pipes, and that of the millet grains used to measure the volumes of the pitch-pipes.[10]


[1] 至飛灰候氣,法久不傳,難以憑信。Shengzu Ren huangdi shilu 聖祖仁皇帝實錄 [Veritable Records of the Kangxi Emperor] (Beijing: Zhonghua shuju, 1986), 39.26a.

[2] In the Chinese lunisolar calendar, a solar year is divided into four seasons (ji 季), further divided into twelve major solar terms (jie 節) and then twenty-four solar terms (qi 氣). The twenty-four solar terms are 15 degrees apart in terms of the ecliptic longitude of the sun, with the major and minor solar terms alternating with one another. The twelve major solar terms are vernal equinox (0°), grain rain (30°), grain buds (60°), summer solstice (90°), great heat (120°), end of heat (150°), autumn equinox (180°), frost (210°), light snow (240°), winter solstice (270°), severe cold (300°), and spring showers (330°), where the vernal equinox (0°), summer solstice (90°), autumn equinox (180°), and winter solstice (270°) mark the beginning of the four seasons respectively. There are usually a major solar term and a minor solar term in each lunar month, but in about every thirty months, there is a month in which there is no major solar term owing to the incomensurability between the solar and lunar cycles. That month is treated as an intercalary month.

[3] Derk Bodde, “The Chinese Cosmic Magic Known as Watching for the Ethers (1959),” in Essays on Chinese Civilization, ed. Charles Le Blanc and Dorothy Borei (Princeton: Princeton University Press, 1981), 351–372; Yi-Long Huang and Chih-ch’eng Chang, “The Evolution and Decline of the Ancient Chinese Practice of Watching for the Ethers,” East Asian Science, Technology, and Medicine 13, no. 1 (1996): 82–106; Dai Nianzu, Zhongguo shengxue shi 中國聲學史 [A History of Acoustics in China] (Shijiazhuang Shi: Hebei jiaoyu chubanshe, 1994), 503.

[4] ……猶不可定其弦緩急。音不可書以時[曉]人,知之者欲教而無從,心達者體知而無師,故史官能辨清濁者遂絕。其可以相傳者,唯大搉常數及候氣而已。 Fan Ye and Sima Biao, Hou Han shu 後漢書 [Book of the Eastern Han], vol. 11 (Beijing: Zhonghua shuju, 1965), 3015.

[5] Bruno Latour, Science in Action: How to Follow Scientists and Engineers Through Society (Cambridge, MA: Harvard University Press, 1987), 227–229.

[6] In Ancient China the length of a ruler represented the length of 1 chi 尺, which was subdivided into 100 fen 分. The exact lengths of these measuring units varied in different dynasties according to the measuring standard. In Xun Xu’s time, 1 chi was approximately 25 cm.

[7] Fan Ye and Sima Biao, Hou Han shu, vol. 11, 3016; Wei Zheng, Sui shu 隋書 [Book of Sui] (Beijing: Zhonghua shuju, 1973), 394–396.

[8] Bodde, “The Chinese Cosmic Magic,” 33–34.

[9] Fan Ye and Sima Biao, Hou Han shu, vol. 11.

[10] Huang and Chang, “The Evolution and Decline of the Ancient Chinese Practice of Watching for the Ethers,” 85.

[…] Continuation: Part II […]

Watching the Ether: An Irreplicable Experiment on Pitch-Pipes (Part II)

Sheryl Chow

[…] Continuation of Part I […]

In the last blog post, we have seen that officials who failed to obtain consistent results in their attempts at “watching the ether”—the reed ashes inside twelve half-buried pitch-pipes blown forth by the qi (ether) at the corresponding major solar terms of the corresponding months—tended to seek reasons in the procedures and apparatus rather than rejecting the houqi theory altogether. This attribution of experimental failures to procedures instead of theory constitutes what Harry Collins called the “experimenters’ regress,” a circular reasoning stemming from the interdependence between proper procedures and successful results. Collins gives the example of gravitational waves: If we want to prove the existence of gravitational waves, we need to build a good gravity wave detector, but we do not know if we have built a good gravity wave detector until it detects a gravitational wave, so even if the detector cannot detect any gravitational wave, it does not necessarily mean that gravitational waves do not exist; it can be due to an insensitive detector.[1] Pierre Bourdieu succinctly summarizes Collins’s argument:

When other scientists fail to ‘replicate’ an experiment, the original researchers may object that their procedures have not been correctly observed. In fact, the acceptance or rejection of an experiment depends on the credence given to the competence of the experimenter as much as on the strength and significance of the experimental proofs.[2]

By the same token, a pitch-pipe could fail to detect the qi because it has the wrong dimensions, because it is buried in the wrong way, or because the wrong reeds are used to prepare the ashes, not because the houqi theory is wrong. And to add to the circular reasoning, one needs to predict the time of a solar term accurately to know whether the corresponding pitch-pipe has the correct dimensions, and to have a pitch-pipe of correct dimensions to detect the arrival of qi associated with the corresponding solar term.

This does not mean that theories could not be falsified with experiments, but the falsification requires faith in one’s experimental procedures. Few conducted such extensive trials as the Ming prince Zhu Zaiyu 朱載堉 (1536–1611), who attempted to watch the ether with 384 pitch-pipes of different lengths. As no ashes were blown free in any of the pitch-pipes, Zhu concluded that the houqi theory is false.[3] Perhaps one would wonder why someone such as Yang Guangxian 楊光先 (1597–1669) still upheld the houqi theory given the abundant number of his failed attempts at observing the ash-blowing qi.[4] Some might find reasons in Yang’s refusal to deny his own belief, his conservative mentality, his proclivity for book learning instead of empirical learning, or his political struggle with the Jesuits, who rejected the houqi practice.[5]

However, it is also noteworthy that sometimes only a couple of successful experiments are needed to verify a theory even when myriads have failed. Of all the experiments done by Louis Pasteur (1822–1895) to prove that micro-organisms cannot arise from non-living matter—a statement that holds true today—less than ten percent of them were successful because of the harsh requirements for successful results—for example, everything inside the flask has to be sterilized and isolated from external interference.[6] Certainly, the difference between zero and one could be substantial. But for Yang Guangxian, successful results were provided in written reports, be they fabricated or not. When Georges Pouchet (1833–1894) failed to replicate Pasteur’s experiment and suggested that Pasteur was wrong, Pasteur defended himself by pointing out that the mercury used in Pouchet was contaminated with germs.[7] The problem of houqi lies as much in the impossibility of verifying it as in the difficulty in empirically falsifying it through experiments, as failures in replicating the results of monthly qi-blown ashes could be attributed to the unfulfillment of the stringent and complicated yet obscure requirements for successfully watching the ether, but it is precisely because of a similar difficulty that Pasteur’s theory about micro-organisms could not be easily disproved by experiments conducted with improper procedures.

Since the late nineteenth century, frequent defeats in wars with foreign powers had prompted China to reject many traditional beliefs as irrational and backward and adopt Western science as a rational and progressive force to modernize and fortify the nation. This left a mark on the historiography of Chinese music theory. Many Chinese music scholars tended to only embrace music theory that can exhibit China’s “progressiveness,” such as Zhu Zaiyu’s 朱載堉 (1536–1611) theory of equal temperament, and dismiss theories such as houqi and the correlation between pitches and calendar months because of their “unscientificity.”[8] But it is noteworthy that the houqi theory was not conclusively falsified by an experiment with agreed-upon procedures and widely accepted results. Rather, it lost its validity along with the abolishment of the correlative worldview that forms its theoretical foundation.


Bibliography

Shengzu Ren huangdi shilu 聖祖仁皇帝實錄 [Veritable Records of the Kangxi Emperor]. Beijing: Zhonghua shuju, 1986.

Bourdieu, Pierre. Science of Science and Reflexivity. Translated by Richard Nice. The University of Chicago Press: Chicago, 2004.

Collins, Harry M. Changing Order: Replication and Induction in Scientific Practice. London: Sage Publications, 1985.

Farley, John, and Gerald L. Geison. “Science, Politics and Spontaneous Generation in Nineteenth-Century France: The Pasteur-Pouchet Debate.” Bulletin of the History of Medicine 48, no. 2 (1974): 161-198.

Huang, Yi-Long, and Chih-ch’eng Chang. “The Evolution and Decline of the Ancient Chinese Practice of Watching for the Ethers.” [In English]. East Asian Science, Technology, and Medicine 13, no. 1 (05 Jul. 1996 1996): 82–106.


[1] Harry M. Collins, Changing Order: Replication and Induction in Scientific Practice (London: Sage Publications, 1985), 83–84.

[2] Pierre Bourdieu, Science of Science and Reflexivity, trans. Richard Nice (The University of Chicago Press: Chicago, 2004), 20.

[3] Yi-Long Huang and Chih-ch’eng Chang, “The Evolution and Decline of the Ancient Chinese Practice of Watching for the Ethers,” East Asian Science, Technology, and Medicine 13, no. 1 (1996): 89.

[4] Shengzu Ren huangdi shilu 聖祖仁皇帝實錄 [Veritable Records of the Kangxi Emperor] (Beijing: Zhonghua shuju, 1986), 27.11a, 27.18b.

[5] Huang and Chang, “The Evolution and Decline of the Ancient Chinese Practice of Watching for the Ethers,” 90–102.

[6] John Farley and Gerald L. Geison, “Science, Politics and Spontaneous Generation in Nineteenth-Century France: The Pasteur-Pouchet Debate,” Bulletin of the History of Medicine 48, no. 2 (1974): 191.

[7] Ibid.

[8] E.g. Yang Yinliu, Zhongguo gudai yinyue shigao [A Draft of Ancient Chinese Music History] (Beijing: Renmin yinyue chubanshe, 1981), 1011–1012.

Music Theory, Global Designs, and Modernity/Coloniality: Reading Athanasius Kircher’s Musurgia universalis in the “New World” (Part II)

Daniel Villegas Vélez

Part II. The Musurgia universalis in New Spain

[…] Continuation of Part I. Musicosmopolitics […]

The first copy of the Musurgia universalis (1650) found in New Spain arrived by way of Father François Guillot, a former colleague of Kircher’s at Avignon who had been living in Puebla since 1635 with the Spanish name of Francisco Ximénez (Osorio Romero 1993, xvii). Upon finding one of Kircher’s books, Ximénez ordered from Seville as many of Kircher’s works as could be found in the city. He then gave a copy of the Musurgia to Alexandro Favián—a criollo priest with polymath ambitions that rivalled Kircher’s own. As he writes in the first of many letters to Kircher, Favián built a lyre based on the scant bibliography. But the criollo scientist was unsure if “it conformed to those employed nowadays in your countries, which are the perfect ones.” One day, he relates, “the admirable Musurgia by Your Reverence arrived in this Kingdom, in which I have seen that [the lyre] I made was in all conformity with everything that Your Reverence teaches.”[1] Even if Favián judged it to be “harmonically correct” (which he was more than qualified to do), his criollo lyre still required authorization according to the standards of the center. Under the global design shared by Kircher and Favián, episteme trumps aesthesis.

Favián sent money and specimens for Kircher’s famous museum and built a Kircherian library in Puebla complete with a framed portrait of the Jesuit. In turn, Kircher ended up dedicating his 1667 Magneticum Naturae Regnum to Favián, but not before confirming that the criollo had Italian ancestry: 

I admired your multiple studies and the cultivation of all the fine arts in you, a native of the New World; yet, that in those foreign regions of America, in those parts of the heavens unknown to us, a man equipped with such aids of virtue and gifted by God’s prerogative with so many charismas could be found, I could not persuade myself of. Finally, through reciprocal epistolary exchange over some years, having dissipated all doubts, I learned that you were not of Indian origin but of the Illustrious Family of the Fabians from Genoa—higher than any exceptions—of stock inserted into Spanish lineage (Kircher 1667, 5-6).[2]

Renowned for his credulity, Kircher could only believe in a polymath if he was not native, but a transplanted European—if he was Kircher’s equal.[3] The asymmetry between Favián and Kircher clearly illustrates the ambiguous position criollo intellectuals occupied in the global Republic of Letters. Alienated from the Indigenous world by reason of their settler position, criollos were also marginal to those of the metropolis, who did not recognize them as equals because their “mixed blood”—a result of rape and forced marriage of Indigenous women with Spaniards—marked them as intellectually and ontologically inferior to white Europeans (Bauer and Mazzotti 2012). From this position, they had few choices but to reproduce the same global designs that marked them as exterior to the epistemic and cultural centers.

Perhaps no one was more aware of the conflicting body-political demands of the global design than Sor Juana Inés de la Cruz, another criolla whose racial otherness was re-marked by her gender (Martínez-San Miguel 2017, 15). Yet, while Sor Juana explicitly questioned the idea that femininity—for her, the exterior difference of an otherwise genderless soul—was a hindrance to intellectual accomplishment, her broader output was nevertheless aligned with the Catholic global design where, as Yolanda Martínez San Miguel puts it, “the argument of human equality among criollos and Europeans is developed to further incorporate the Americas into Catholic religion and the western episteme” (Martínez-San Miguel 2017, 15). A voracious reader, Sor Juana’s fascination with Kircher is well attested in her works and in a well-known portrait by Juan de la Miranda and its copy by Miguel Cabrera, both of which place volumes titled Kirkerii opera among the philosophical and theological works in her famous library (Paz 1982, 309; Lyon 2017). She summed up her enjoyment of Kircher’s book with the playful neologism “to Kirkerize” (kirquerizar), which an early scholar glossed as “to imitate the famous mathematician of her time, Athanasius Kircher” (de la Maza 1952, 18)(Findlen 2004, 333). Her most celebrated poem, Primero sueño, is a metaphysical out-of-body reflection on the structure of the cosmos inspired more by Kircher’s Itinerarium extaticum (1656) than by Plato’s “Myth of Er.”

Miguel Cabrera, Retrato de Sor Juana Inés de la Cruz, c. 1750.  Oil on canvas, 281 x 224 cm. Museo Nacional de Historia, Castillo de Chapultepec, México. (CC BY-NC-ND 4.0) Credit: Instituto Nacional de Antropología e Historia, México.
Miguel Cabrera, Retrato de Sor Juana Inés de la Cruz, c. 1750.  Oil on canvas, 281 x 224 cm. Museo Nacional de Historia, Castillo de Chapultepec, México. (CC BY-NC-ND 4.0) Credit: Instituto Nacional de Antropología e Historia, México. (Detail).

Sor Juana was also a musician. In a 1688 poem dedicated to her former patron and Sapphic love object, the vicereine of New Spain María Luisa Manríquez de Lara y Gonzaga, Countess of Paredes, Sor Juana promises a music treatise where she would “reduce for easier handling” all the musical rules (Cruz 2009).[4] The most intriguing claim of the nonextant treatise is expressed in its very title, Caracol (Conch Shell). Since, as she writes in the poem,

En él, si mal no me acuerdo,

me parece que decía

que es una línea espiral,

no un círculo, la armonía;

              y por razón de su forma

revuelta sobre sí misma,

le intitulé Caracol,

porque esa revuelta hacía.

(Romance 21, vv. 116-128).

[In it, if I am not mistaken, I believe I said that harmony is a spiral line, not a circle. And because of its shape, turning around itself, I titled it Conch Shell, because of the turn it made.]

The precise meaning behind the intriguing notion of a spiral harmony remains a mystery. But it cannot refer to the lack of closure of the circle of fifths in Pythagorean tuning, as Robert Stevenson (1996) and, more recently, Mario Ortiz (2007) have argued, not least because the very notion of a closed circle of fifths and hence the condition to figure this excess as a spiral did not emerge until at least 1711 with Heinichen’s Neu erfundene und grundliche Anweisung . . . des General-Basses (Barnett 2002, 444; Lester 1989, 110-112).

The notion of “a spiral harmony” is more capacious, and likely cannot be circumscribed by a single paradigm. Sor Juana had a wealth of both spiral and circular images to engage: from the various spiral-shaped objects in Kircher’s Musurgia, which she obviously knew, to the (less likely) spiral in Bartholomé Ramos de Pareja’s 1482 Musica practica, as suggested respectively by Octavio Paz (1982, 316-17) and Rocío Olivares Zorrilla (2015). As Stevenson suggests, she must have also been familiar with the Aztec conch shell or quiquiztli and the spiral volutes that serve as the metonymic glyph for cuicatl or “song,” although nothing else in the poem suggests she was directly drawing on Indigenous elements to contest hegemonic notions of harmony (Stevenson 1996, 13; Finley 2014, 31).[5]

Less a contestation of the hegemony of the circle or its decentering (as in the ellipse analyzed by Cuban poet Severo Sarduy), the spiral is an affirmation of the center from the periphery, a tendency towards a center that is only reached by augmenting the distance from the origin (Sarduy 2013, 208). The spiral is thus an evocative baroque figuration of the position that criollo intellectuals like Favián and Sor Juana occupied with respect to the hegemonic (if idiosyncratic) discourse deployed by Kircher. The diversity of the body-politics of the Jesuit’s readership was thus caught in the darker side of the movement’s mission, a global (i.e., colonial) project of universalist ambition so successful that it almost engulfed its readers. Remarking their trace in the musicological canon is the task of the global musicologies of today.

Coda

The most immediately “colonial” element in the Musurgia universalis is the famous combinatoric system of composition, one of Kircher’s most celebrated inventions (Murata 2000; McKay 2012). The devices allowed even those untrained in music to write four-part counterpoint for a text in any language employing a series of tables and permutational rules, to produce the kind of compositions that Kofi Agawu identifies as instrumental in deploying “tonality as a colonizing force” (Agawu 2016). Indeed, Kircher writes,

Since the attraction of barbarians consists in the practice of music and the frequent praise of God, but they not always have printed books or even composers at hand, the Fathers believed that they could use this Musurgia very well in the future because they would be able to use it to produce songs not only in Latin but also in any given language, including those of the Indies, and in any barbaric language (MU B 3-4).

Montiel had this precise aim in mind when he carried the first copy of the Musurgia to the Indies. Muñoz must also have sensed its utility, as he devoted most of his Musicalia speculativa to carefully reproducing the various devices. Favián extolled one of such devices, the arca musarithmica, as “something as new and admirable that not enough human languages existed to praise it.”[6] Kircher’s interest in the use of music to “attract barbarians” is neither idiosyncratic musing nor bombastic sales pitch, but a concern for the Jesuits who were already deploying the affective power of music as a central weapon in their colonizing war against the Indigenous people of America.

“Arca Musarhitmica” in MU B 185

Whether Jesuits did arrive to employ Kircher’s musicolonial war machines in the reducciones, we will never know. After all, the compositions produced with the combinatorial systems were designed to be ephemeral objects, not lasting “works.” They were conceived in order to exploit human musicking capacities to “domesticate”—as one Jesuit put it—the untold number of Indigenous peoples who inhabited the reducciones between 1549 and 1776.[7] From Montiel and Muñoz we know that Kircher’s contemporaries understood the mechanism and found it useful for these very purposes. To see these and other devices solely as musical (or music-theoretical) works, scientific objects, or even mere curiosities and not as affective weapons of colonization is, sadly, another symptom of the white frame of music studies.


Agawu, V. Kofi. 2016. “Tonality as a Colonizing Force in Africa.” In Audible Empire: Music, Global Politics, Critique, edited by Ronald Michael Radano and Tejumola Olaniyan, 334–355. Durham: Duke University Press.

Barnett, Gregory. 2002. “Tonal Organization in Seventeenth-century Music Theory.” In The Cambridge History of Western Music Theory, edited by Thomas Christensen, 407–455. Cambridge: Cambridge University Press.

Bauer, Ralph, and José Antonio Mazzotti. 2012. “Introduction: Creole Subjects in the Colonial Americas.” In Creole Subjects in the Colonial Americas, edited by Ralph Bauer and José Antonio Mazzotti, 14–78. Chapel Hill: University of North Carolina Press.

Camenietzski, Carlos Ziller. 2004. “Baroque Science between the Old and the New World: Father Kircher and His Colleague Valentin Stansel (1621–1705).” In Athanasius Kircher: The Last Man Who Knew Everything, edited by Paula Findlen, 311–328. New York: Routledge.

Cruz, Juana Inés de la. 2009. Obras completas I: Lírica personal. Edited by Antonio Alatorre. México: Fondo de Cultura Económica.

Findlen, Paula. 2004. “A Jesuit’s Books in the New World: Athanasius Kircher and His American Readers.” In Athanasius Kircher: The Last Man Who Knew Everything, edited by Paula Findlen, 329–364. New York: Routledge.

Finley, Sarah. 2014. “Acoustic Epistemologies and Aurality in Sor Juana Inés de la Cruz.” PhD diss., University of Kentucky.

Gumilla, Joseph. 1946 [1745]. El Orinoco ilustrado. Vol. 3. Madrid: M. Aguilar.

Kircher, Athanasius. 1650. Musurgia universalis, sive Ars magna consoni et dissoni. 2 vols. Rome: Haeredum Francisci Corbelletti/Typis Ludovici Grignani. Reprint, Facsimile edition: Hildesheim: G. Olms, 1970 ed. Ulf Scharlau.

———. 1667. Magneticum naturae regnum sive Disceptatio physiologica. Rome: Ignatii de Lazaris.

Lester, Joel. 1989. Between Modes and Keys: German theory 1592-1802. Stuyvesant: Pendragon Press.

Lyon, J. Vanessa. 2017. “‘My Original, A Woman’ Copies, Origins, and Sor Juana’s Iconic Portraits.” In Routledge Research Companion to the Works of Sor Juana Inés de la Cruz, edited by Emilie L. Bergmann and Stacey Schlau, 91–106.

Martínez-San Miguel, Yolanda. 2017. “The Creole Intellectual Project: Creating the Baroque Archive.” In Routledge Research Companion to the Works of Sor Juana Inés de la Cruz, edited by Emilie L. Bergmann and Stacey Schlau, 12–22. New York: Routledge.

McKay, John Zachary. 2012. “Universal Music-Making: Athanasius Kircher and Musical Thought in the Seventeenth Century.” PhD diss., Harvard University.

Murata, Margaret. 2000. “Music History in the Musurgia universalis of Athanasius Kircher.” In The Jesuits: Cultures, Sciences, and the Arts, 1540–1773, 190–207. Toronto: University of Toronto Press.

Olivares Zorrilla, Rocío. 2015. “El modelo de la espiral armónica de sor Juana: entre el pitagorismo y la modernidad.” Literatura Mexicana 26 (1): 11–39.

Ortiz, Mario A. 2007. “La musa y el melopeo: Los diálogos transatlánticos entre Sor Juana Inés de la Cruz y Pietro Cerone.” Hispanic Review 75 (3): 243–264.

Osorio Romero, Ignacio. 1993. La luz imaginaria: epistolario de Atanasio Kircher con los novohispanos. México, D.F.: Universidad Nacional Autónoma de México.

Paz, Octavio. 1982. Sor Juana Inés de la Cruz o las trampas de la fé. Barcelona: Seix Barral.

Powell, Amanda. 2017. “Passionate Advocate: Sor Juana, Feminisms, and Sapphic Loves.” In Routledge Research Companion to the Works of Sor Juana Inés de la Cruz, edited by Emilie L. Bergmann and Stacey Schlau, 63–77.

Saldívar, Gabriel. 1934. Historia de la música en México. México: Publicaciones del Departamento de Bellas Artes.

Sarduy, Severo. 2013. “Barroco.” In Obras III. Ensayos, 129–224. Mexico: Fondo de Cultura Económica.

Stevenson, Robert. 1996. “Sor Juana Inés de la Cruz’s Musical Rapports: a Tercentenary Remembrance.” Inter-American Music Review 15 (1): 1–21. https://iamr.uchile.cl/index.php/IAMR/article/view/52869/55465.

Trabulse, Elías. 1998. “El tránsito del hermetismo a la ciencia moderna: Alejandro Fabián, Sor Juana Inés de la Cruz y Carlos de Sigüenza y Góngora.” Calíope 4 (1/2): 56–69.

Villegas Vélez, Daniel. 2022. “Apparatus of Capture: Music and the Mimetic Construction of Social Reality in the Early Modern/Colonial Period.” CounterText 8 (1).


[1] Alejandro Favián, Letter to Athanasius Kircher, Puebla, February 2, 1661. Kircher’s correspondence with Favián was reconstructed by Ignacio Osorio Romero (1993).

[2] Translation in Trabulse (1998, 58)

[3] On the epistemological basis of Kircher’s “credulity,” see Camenietzski (2004, 322)

[4] I follow Amanda Powell’s choice of the term “Sapphic” to indicate both the presence and the irreducibility to modern notions of lesbian love in Sor Juana’s textual personae, inscribed in between sexuality and literary construction (Powell 2017).

[5] While intriguing, the thesis that the spiral was a critique of Zapotec composer Juan Mathias rests on tenuous evidence and is more likely the product of Gabriel Saldívar’s elevation of sor Juana as the Mexican national heroine above Indigenous musicians (Saldívar 1934, 130).

[6] Alejandro Favián, Letter to Athanasius Kircher, Puebla, May 9, 1663. (Osorio Romero 1993, 30)

[7] “It has been experimented in the Missions we have founded how much they are attracted and domesticated by music, how much they appreciate it and how proud they are those whose children have been destined by the missionary for music school.” (Gumilla 1946[1745], 515). For the role of mimetic musical performance in the reducciones and the Jesuit notion of the human, see (Villegas Vélez 2022)

Music Theory, Global Designs, and Modernity/Coloniality: Reading Athanasius Kircher’s Musurgia universalis in the “New World” (Part I)

Daniel Villegas Vélez

Part I. Musicosmopolitics

Few music treatises circulated in the early modern/colonial period as broadly and efficiently as Athanasius Kircher’s Musurgia universalis (1650).[1] Of the 1500 printed copies of the Musurgia, 300 were given to Jesuit missionaries who distributed it around the globe: “et in Africam, Asiam et Americam distracta fuerunt.”[2] The copy in the Biblioteca Nacional de Colombia, Bogotá (which has housed the library of the Jesuit College since its 1767 expropriation), is registered as “Ex-libris: ms. Provincia Novi Regni donum authoris.”[3] The book reached readers across the globe, in particular those in the Spanish colonies, where Kircher would become a point of reference in late-seventeenth century scientific circles (Trabulse 1998).  In this post, I draw from my forthcoming manuscript, Mimetologies: Mimesis and Music 1600–1850 (Oxford University Press) to examine how three of Kircher’s readers—situated at different points of racial and gender spectrums—responded to the Jesuit’s works: Ignacio Muñoz, a Spanish Dominican friar; Alejandro Favián, a criollo priest from Puebla; and Sor Juana Inés de la Cruz, the most notable intellectual of her time.

The global circulation of the Musurgia universalis was, in a sense, already inscribed in the universalist ambitions of its title, which translates roughly to “the musical performance of the universe.” In the Musurgia, music is not merely a subdiscipline of mathematics or a humanist craft, but a way of understanding the universe. In Kircher’s idiosyncratic brand of Hermetic Neoplatonism, the universe or kosmos is organized musically and in “perfect imitation” of the Creator, so that understanding the empirical manifestations of music across the globe constitutes true knowledge of God. A sentence attributed to Hermes Trismegistus inscribed in the frontispiece of the second volume puts it succinctly: “Musica nihil aliud est, quam omnium ordinem scire.” [Music is nothing else than knowing the order of everything].

If few music treatises have such universalist ambitions, it is even more rare to find the political implications of these ambitions made explicit in the work itself. In the dedicatory to Archduke Leopold William of Austria, Governor of the Spanish Netherlands and brother to Emperor Ferdinand III, Kircher evokes the bitter memories of the Thirty Year’s War as he introduces the Musurgia as that art by which the Prince “restores customs to the harmonious tranquility of peace in the most dissonant times of the Christian Republic” (MU B 366).[4] More than a conventional turn of phrase, Kircher expands on the claim in book X through a detailed analysis of the forms of government according to the theory of musical means, going on to declare Christian monarchy (a harmonic proportion in which the sovereign distributes everything among the best people according to their virtue and merits) as the best form of government. According to Kircher, one studies music not simply to “know everything,” but to know how to rule everything according to such knowledge.

I adventure the (admittedly baroque) term “Musicosmopolitics” to describe this blend of (musical and cosmological) knowledge and politics. I suggest that most music treatises contain such a blend of knowledge and politics, even when the political consequences of their epistemic claims are—purposefully or not—hidden from view. This, I believe, is what Philip Ewell (2020) means when he speaks about music theory’s “white frame.” While the Musurgia is not unique in this respect, it is a fruitful text to examine from this perspective because it is explicit about its musicosmopolitics. Kircher took the term “universal” seriously: the Musurgia integrates, in a single narrative of Catholic revelation and salvation, all forms of music-making from antiquity to his time. For this, he draws from the library of the Collegio Romano as well as two epistolary networks of which Kircher himself was a central node: the European Respublica literaria and the missionaries of the Society of Jesus stationed in China, Japan, India, South East Asia, Africa, and America. The Musurgia is conceived as an ars politica—a means to command and control the mores of the people through harmony. More precisely, the Ars consoni, et dissoni explains the mutual belonging of consonance and dissonance as an all-pervasive ontological condition, a universal principle: “Consonum sine dissono, dissonum sine consono subsistere nequaquam posse Deus, Natura, Politice, docet” (MU A [IX]). [God, Nature and Politics teach that neither consonance without dissonance nor dissonance without consonance can subsist.] Thus seen, the Musurgia was “a global design,” to use Walter Mignolo’s formulation, an account of how the world is and how it should be organized, written in such a way that the provinciality of its Eurocentric, Catholic enunciations are obscured under a presumed universality that simultaneously delegitimizes alternate conceptions—hence a uni-versal (Mignolo 2021, 184). Attending to its diverse readers allows us to appreciate the scope and limitations of the Musurgia’s global design.

The Musurgia arrived in the Philippines just four years after its publication, transported by one of Kircher’s pupils, Giovanni Montiel. For the young missionary, the Musurgia was “of great usefulness to the Fathers of the missions, where music is taught publicly.”[5] Ten years later, Ignacio Muñoz, a Dominican friar then stationed in Manila, began copying lengthy passages from the Musurgia into a manuscript volume titled Observationes diversarum artium (Muñoz 1662-77; González Acosta 2001, 220; Bordas, Robledo, and Knighton 1998, 408).[6] Muñoz—who was employed as a royal hydrographer responsible for updating the navigation charts employed by Spanish merchants, colonizers, and slave traders—devoted more than a hundred manuscript pages to a section titled Musicalia speculativa.

Under close examination, the section on music reveals itself as a copy of the Musurgia, organized by books and summarized into postulates, diagrams, and tables that synthesize its contents. Lacking in Muñoz’s version, however, is the entire musicosmopolitical framework of Kircher’s work: with its redactions and its focus on the technical aspects of music-making, Observationes comes to resemble more traditional music handbooks of its time. This is not to say that Muñoz’s copy is less universalist than Kircher’s. Rather, his careful efforts at copying the Jesuit’s work reveals how close the Musurgia was to Muñoz’s own project of charting the globe to facilitate Spanish domination. The globe Kircher described more musico was certainly not the same globe Muñoz measured more geometrico, yet the two found themselves co-inscribed in the pages of the Observationes where they shared the common task of deploying the colonial global design of Catholic Spain in the so-called “New World.”


Bordas, Cristina, Luis Robledo, and Tess Knighton. 1998. “José Zaragozá’s Box: Science and Music in Charles II’s Spain.” Early Music 26 (3): 391–413. https://doi.org/10.2307/3128699.

Ewell, Philip A. 2020. “Music Theory and the White Racial Frame.” Music Theory Online 26 (2). https://doi.org/10.30535/mto.26.2.4.

Feagin, Joe R. 2010. The White Racial Frame: Centuries of Racial Framing and Counter-Framing. New York: Routledge.

Fletcher, John Edward. 2011. A Study of the Life and Works of Athanasius Kircher, ‘Germanus Incredibilis’: With a Selection of His Unpublished Correspondence and an Annotated Translation of His Autobiography. Leiden and Boston: Brill.

González Acosta, Alejandro. 2001. “Buenas nuevas para los estudiosos: hallazgos bibliográficos mexicanos en Europa y Estados Unidos.” Boletín Millares Carlo 20: 219–229.

Irving, David R. M. 2009. “The Dissemination and use of European Music Books in Early Modern Asia.” Early Music History 28: 39–59.

Kircher, Athanasius. 1650. Musurgia universalis, sive Ars magna consoni et dissoni. 2 vols. Rome: Haeredum Francisci Corbelletti/Typis Ludovici Grignani. Reprint, Facsimile edition: Hildesheim: G. Olms, 1970 ed. Ulf Scharlau.

Mignolo, Walter. 2021. The Politics of Decolonial Investigations. Durham: Duke University Press.

Muñoz, Ignacio. 1662-77. “Observationes diversarum artium.” Biblioteca Nacional de España. MS 7111.

Trabulse, Elías. 1998. “El tránsito del hermetismo a la ciencia moderna: Alejandro Fabián, Sor Juana Inés de la Cruz y Carlos de Sigüenza y Góngora.” Calíope 4 (1/2): 56–69.


[1] Kircher, Athanasius. Musurgia universalis, sive Ars magna consoni et dissoni. 2 vols. Rome: Haeredum Francisci Corbelletti/Typis Ludovici Grignani, 1650. Facsimile edition: Hildesheim: G. Olms, 1970 ed. Ulf Scharlau.

[2] Kircher to Joannes Jansson, n.d., Kircher MS 561, fol. 79r., Archivio della Pontificia Università Gregoriana, Rome. Quoted in (Fletcher 2011, 417)

[3] Biblioteca Nacional de Colombia, RG 4019.

[4] I follow the convention of referring to the volumes of the Musurgia as MU A and B respectively, followed by page numbers.

[5] Giovanni Montèl [Montiel], Letter to Kircher, 15 July 1654, Archivio della Pontificia Università Gregoriana, Rome APUG 567, fol. 155r. Accessed through the Stanford University’s Kircher Correspondence Project. Translation in (Irving 2009, 46; Fletcher 2011, 219)

[6] The section on music was first identified as a digest of the Musurgia by David Irving, who attributed it to an anonymous Jesuit (Irving 2009). Muñoz, however, was a Dominican and had no teaching appointments at the Jesuit College in Manila. He was briefly appointed to the chair of Mathematics in Mexico before returning to Spain. It is unclear if he ever took the post.

[…] Continuation: Part II. The Musurgia universalis in New Spain […]

Madame de Pompadour as Music Theorist

Callum Blackmore

The Querelle des Bouffons[1] was a music-theoretical dispute that took place in France between 1752 and 1754. The dispute was, at face value, about the relative merits of French and Italian opera, sparked by the arrival of a troupe of Italian players at the Paris Opéra.

It has been difficult for historians to gauge the contributions of women to the Querelle des Bouffons. All of the pamphlets published during the Querelle were penned by men. This is not to say that women did not make profound and lasting contributions to the dispute. But these contributions were often ephemeral – conversations in a salon or personal correspondences between friends.[2] This presents us with a distinct historiographical problem: how do we discuss the gender politics of the Querelle when the contributions of women are so conspicuously absent from its published record? The answer, I suggest, is that we must expand our definition of what constitutes a “music-theoretical” document vis-à-vis the Querelle and, more broadly, what constituted “music theory” in eighteenth-century France. The Querelle des Bouffons was never simply a “music-theoretical” dispute: rather, because it concerned the relationship between music, the listening subject, and the monarchical state, the Querelle was viewed as a broader philosophical disagreement with grave implications for French national politics.[3] As such, it was discussed in many documents that were not music-theoretical pamphlets or treatises, many of which were penned by women.

In this blog post, I will focus on the writings of one woman: Madame de Pompadour, the official royal mistress to Louis XV. Historians have long acknowledged Madame de Pompadour’s stake in the pamphlet war: in many ways, she was the most powerful player in the dispute due to the amount of cultural influence the King had bestowed upon her. However, because she left no music-theoretical treatises or pamphlets, and because her operatic patronage was so mired in paradox,[4] historians have found it difficult to pinpoint Madame de Pompadour’s position on the key issues of the debate, leading to a number of misunderstandings and misconceptions about her musical attitudes.[5]  

Madame de Pompadour did, indeed, write about the Querelle des Bouffons, but she did so only by means of a personal anecdote in her memoirs. The anecdote in question concerns Madame de Pompadour’s first encounter with Rousseau, who had been invited to the mistress’s toilette at the height of the Querelle by her brother.[6] Rousseau and Madame de Pompadour did not immediately hit it off: to the favorite, he seemed “devoured by pride,” with a “sly gaze which viewed everything with a distrustful attention.”[7] But they gradually warmed to each other, and the visit culminated with Rousseau sitting down at the harpsichord to perform excerpts from his opera, Le devin du village, written as an exemplar of the Italian style. 

Rousseau’s performance prompted considerable reflection from Madame de Pompadour. She recalled Rameau’s writings in the Querelle, remembering his contempt for Rousseau’s operatic writing. She suggested that Rameau objected to importing the Italian style – with its highly ornamented ariettas – into French music because the French language “does not lend itself to this piling-up of roulades, to this luxury of notes pressed against one another.”[8] Madame de Pompadour quietly scoffs at this argument, however, suggesting that it causes Rameau to “grimace with impatience” at even the “most beautiful” aria by Jommelli or Pergolesi.[9] In this statement, Madame de Pompadour distinguishes herself from many members of the French camp, who argued for a direct correlation between language and style that precluded musical cosmopolitanism.

Yet, despite acknowledging the “agreeableness” of Italian music, Madame de Pompadour ultimately asserts the superiority of the French style. The central issue with Italian music, she argues, was its “poverty of harmony.”[10] For Madame de Pompadour, the harmonic syntax of Italian music was almost entirely incomprehensible:

When the Italians […] produce harmonious effects, they lose their footing, and they produce nothing but noise. This is because, for our ear to be able to grasp the chord, it must be prolonged and, above all, well-marked, which cannot happen in a musical system that is too overburdened with notes.[11]

Madame de Pompadour’s gripe with Italian music concerned the cognitive effect of its melodic excesses on the ear’s ability to comprehend harmony. For Madame de Pompadour, the cognition of harmony took precedence over the appreciation of all other musical features. Musical style, she suggests, must be oriented towards the accentuation of harmony, even if it comes at the expense of melodic beauty. In this way, Madame de Pompadour’s was much closer in her music-theoretical ideology to Rameau (whose primary concern was the power of harmony as a “natural” force and its primacy in French music) than to the broad majority of the French camp, who generally disliked Italian music on nationalistic grounds.

Madame de Pompadour’s contribution to the Querelle des Bouffons is vital for a number of reasons: firstly, it brings an interesting flavor to the Querelle’s debates over melody and harmony by viewing this issue primarily in terms of musical texture, warning of the dangers of a melodic language which crowds out the harmonic grammar, rendering it unintelligible, “noisy.” In this way, her writings constitute a truly unique view on the cognitive relationship between melody and harmony. Her theories certainly warrant more investigation for this, and this alone. Secondly, Madame de Pompadour was one of the most prolific operatic patrons of the Enlightenment: her views on harmony were not just theory, but shaped the aesthetic profile of French opera in the eighteenth century.

My short blog post has had two goals: to show that Madame de Pompadour held a unique music-theoretical position within the French camp of the Querelle des Bouffons; and, to demonstrate that, in order to unearth this position, we need to look beyond those genres of historical text traditionally considered to be “music-theoretical.” Madame de Pompadour outlines an idiosyncratic theory of musical style as an afterthought to a personal anecdote about a rather socially awkward encounter with Rousseau. It is a quotidian anecdote in her sprawling, two-volume memoirs – easily missed amongst talk of global politics and court intrigue. Yet, neglecting these pithy, fragmentary, liminal writings necessarily means losing sight of the ways in which women shaped this landmark music-theoretical debate.


[1] Roughly “the quarrel of the comic actors.”

[2] Jolanta T. Pekacz, “Gender as a Political Orientation: Parisian Salonnières and the Querelle des Bouffons,” Canadian Journal of History 32, no. 3 (1997): 405–14.

[3] Indeed, as this complex pamphlet war raged on, it soon became about so much more than the dangers and benefits of musical cosmopolitanism. The Querelle expanded to encompass a range of interlocking debates: whether harmony was more expressive than melody; which aspects of music were “naturally” occurring and which were socially constructed; and whether or not music functioned as a mimetic force within the operatic diegesis.

[4] From 1747 to 1753, Madame de Pompadour ran a private opera house for the enjoyment of the monarch and his inner circle and also exerted considerable control over the menus plaisirs, the organization responsible for all official royal entertainment. During the Querelle itself, Madame de Pompadour deployed this patronage to seemingly contradictory ends: on the one hand, she commissioned Mondonville’s Titon et l’Aurore, which would become a landmark work for the French camp; on the other hand, she premiered (at her private theater) the full version of Rousseau’s Le devin du village, an opera written to emulate the melodiousness of the Italian style.

[5] Notably, scholars have asserted (incorrectly) that Madame de Pompadour disliked Rameau and his music, primarily based on gossipy, second-hand accounts that contradict Madame de Pompadour’s own writings.

[6] At that time, Madame de Pompadour had already performed his “charming” opera, Le devin du village, at her private theater, and so was familiar with his musical output. However, she confessed to only having heard second-hand of Rousseau’s work as a man of letters.

[7] Jeanne Antoinette Poisson, marquise de Pompadour, Mémoires de madame la marquise de Pompadour, vol. 1 (Paris: Mame et Delaunay-Vallee, 1830), 412.

[8] Ibid. Naturally, this is a gross simplification, and, perhaps, a gross misrepresentation of Rameau’s position.

[9] Ibid.

[10] Marquise de Pompadour, Mémoires de madame la marquise de Pompadour, 1:413.

[11] Ibid.

Should We Burn the Pianos?: Introducing A Collaborative Project Focused on Building “New Instruments for Theory” 

Daniel Walden

Enter just about any room of a Western-style conservatory or music department, and you will probably stumble into a piano.  Nearly everyone on the teaching and research staff has a use for them. Composers, improvisers, and performers employ them in searching for new artistic possibilities. Theorists use them to work out the properties of musical harmony. And pedagogues are almost certain to employ them when teaching students the laws of harmony, as well as for developing aural skills, score reading, and critical listening. In short, the piano keyboard is a classic example of what Alexander Rehding (2016a and 2016b) calls an “instrument of theory,” shaping how we conceive and interpret music, and playing an integral role in defining the discourse networks by which musical knowledge is stored, transmitted, and reproduced.[1]

But challenges have arisen to the sovereignty of the keyboard. Consider recent developments in music theory pedagogy.  Departments across the US and UK (and perhaps Europe?) have started removing keyboard skills, once considered foundational, from their undergraduate curricula. Just this year at Oxford, Keyboard Skills was converted from a compulsory course into an optional one; at Harvard, it was eliminated as a requirement several years earlier; at Durham University, it has been absent from the formal curriculum for decades, at least. (These are the institutions I have been a part of and can thus speak about from personal experience, but I am sure they are not the only ones.) Driving these curricular adjustments are a set of social, political, and institutional concerns: for the advantage it gives to students of means who were able to afford private training on the keyboard; for the marked gender inequalities in grading outcomes, seemingly indicative of unconscious bias; for the possibility that it might act as a deterrent to prospective students; and so forth. 

Yet another affront has been mounted from the side of theoretical research. In my own work (2019), I have examined how the keyboard acted as a filter in the investigation of non-Western and Indigenous music—not only because it quantized pitch values to a one-size-fits-all scale of twelve divisions per octave, but also because it was instrumentalized as a training device that would tutor musicians in how to pay attention to certain highly valued parameters (i.e., pitch) over others of supposedly secondary value (timbre). I am not the only one to raise these sorts of questions. Bryan Parkhurst and Stephan Hammel (2020) have issued a bracing Marxist critique of the piano (and piano-making firms) for its historical role in instantiating the exploitative paradigms of capitalism. And Martin Scherzinger (2016) has written about how the lion’s share of computer software remains grounded in “claviocentric digital patterns,” with MIDI logic creating a “path dependencies” in both collaborative and interpretative settings.  The pitch sequences of the world, the notes, are “gradually coalescing around the MIDI standard” of twelve-tone equal temperament—leading him to paraphrase the software engineer Xavier Serra in speculating as to whether keyboard-based digital protocols might constitute “a kind of colonialism.”

Anxieties about the social and cognitive effects of the keyboard are not exactly new. Legend has it that harpsichords were scorned as relics of elite culture during the French Revolution, and were eventually rounded up and chopped into firewood by the hundreds. So should we emulate the sans-culottes and burn all the pianos? As a pianist myself, my answer is obviously “no” (although there may be a few practice room pianos out there that would be better as kindling). But the lessons of curriculum redesign and recent keyboard studies clearly suggest that it is worth questioning its legacy and enduring centrality, and that we should begin applying our energy to the development of new instruments of theory that are designed to highlight our current path dependencies as musical researchers, pedagogues, and creators and to offer new ones. By “new,”I don’t necessarily mean “original” or “as yet unseen” (although instruments that are new in that sense would also be welcome). In fact, many of the “new” instruments of theory I have in mind are historical. I would nevertheless call them “new” because they are capable of jolting scholars and pedagogues out of their “path dependencies,” and into new modes of thinking and communicating that are more flexible, creative, and socially inclusive. 

What might such an instrument of theory look like? Perhaps like the instrument you see in figs. 1 and 2—almost like a piano, but not quite. This is the “Demonstration Harmonium,” built by Oskar Walcker for the Japanese music theorist Tanaka Shōhei in 1892—and then neglected for over a century, until it was restored to playing condition by the builder’s great-grandson, Gerhard Walcker, for the inventor’s grandson, Dr. Tanaka Tasuku. This instrument features not twelve equal divisions of the octave, but twenty divisions tuned in just intonation and distributed across split sharps and naturals. This makes it impractical for performance—it only works in C Major, for one thing—but its purpose was not for practice but for pedagogy and research. As Tanaka outlines in a four-page advertisement that accompanies the instrument, explaining its objectives and providing a sample pedagogical program for young pupils, the goal of the harmonium was to break intellectual habits formed by the piano and encourage new ways of listening and thinking, sensitive to the significance of microtonal discriminations of intonation and the alterity of tonal relations within unequal pitch spaces. It is extraordinarily effective to that end, as I discovered five years ago when I had the chance to try the instrument myself, and put myself through Tanaka’s pedagogical program. I found it a defamiliarizing experience, in the sense that it introduces minute alterations to the acoustical and haptic feedback one would expect from a keyboard instrument, and those alterations ultimately challenged me to rethink in productive ways all that was familiar to me from daily practice on the piano. 

Figure 1: “Demonstration Harmonium,” built by Oskar Walcker for the Japanese music theorist Tanaka Shōhei in 1892. Photo Credit: Daniel Walden, 2016.
Figure 2: “Demonstration Harmonium,” built by Oskar Walcker for the Japanese music theorist Tanaka Shōhei in 1892. Photo Credit: Daniel Walden, 2016.

I found that tonic triads, for example, required a subtle pronation of the wrist so that the pinky lands correctly on the back split G; the requirement to pronate every time I returned to the tonic served as a tactile reminder of the peculiar geometries of a just-intonation system, in which fifths and thirds are tuned by separate chains. Progressing further through Tanaka’s pedagogical program, I discovered that virtually every harmonic function had some sort of small peculiarity built into it, and that this choreography was guiding me towards carving new and alternative “paths” through tonal space, breaking my dependencies upon those I had inscribed through piano practice and theory training. Once I completed Tanaka’s pedagogical program, I continued to learn simply through play with the instrument, following the pleasure that accompanied the discovery of new types of harmonic relations (what is the sound of a limma + a major third?) and tactile sensations (what is the best hand position for a just diminished ninth?).[2]

This is why I would call the Demonstration Harmonium a “new” instrument of theory—even though it is of course old, in the sense that it is historical.  There are doubtless many other “new” instruments we could identify through historical research, with different affordances for different areas of theory: monochords, tuning pipes, sirens, rhythmicons, etc.  And as every instrument has its limitations—Tanaka’s keyboard may break path dependencies, but could it free us from claviocentrism?—it seems to me that it would be quite useful to start identifying and reconstructing such instruments in order to develop a new theoretical instrumentarium. And so, with support in the form of a Small Research Grant from the British Academy and Leverhulme Trust, I have begun assembling an interdisciplinary laboratory I call NIFTY—after New Instruments for TheorY—that will bring together theorists, instrument builders, and computer scientists interested in the research and development of new instruments of theory modelled after both historical and entirely original designs. My objective for NIFTY is to make these instruments as widely accessible as possible, by ensuring that all digital instruments are open-source and available as free downloads, and that all acoustical/analog instruments can either be 3D printed or constructed from simple DIY kits using cheaply available materials.  In this way, I hope to remove as many constraints as possible on the potential for these new instruments to have a meaningful impact on the ways we teach and research theory.[3]       

NIFTY will start in the coming year with a series of workshops. Attendees will have the opportunity to select a new instrument of theory—one they have discovered in their research, or one they have conceived themselves—and work closely with the other participants in determining potential research and pedagogical applications for the instrument, as well as a plan for how to render that instrument as broadly accessible as possible. In future stages of the project, we will start to build those instruments, and develop a website to host them. My own focus will be on developing digital reproductions of the just-intonation and microtonal instruments of theory I have discovered through my research—ranging from Tanaka’s instrument to the Euharmonic Organ of Henry Liston, built in 1817 for St. Andrew’s Presbyterian Church in Calcutta, to the “Oriental Piano” built in the 1930s by Lebanese musician Abdallah Chahiné to demonstrate the Arab maqām system. I expect these instruments to take the form of a software application that can take input from any standard MIDI keyboard, as well as a set of guitar pedals, and output the intonation systems to which these historical instruments were tuned. But I am hopeful that other projects will take very different forms. I am currently looking for new collaborators—so please get in touch with me if you might be interested in being part of this project!

A final thought about how this project may prove useful for assistance in other projects underway in the discipline, focused on decolonial and anti-racist ends (see for instance Jade Conlee and Tatiana Koike’s recent post on this site): if music theory is stuck within the “path dependencies” of colonial ideology and the white racial frame, the problems music theory face must lie as much with the mediums as the message. How then can we ever seek to effect substantial changes in music theory discourse, if we allow the current discourse networks to remain unaltered?


Bibliography

Conlee, Jade and Tatiana Koike.  “Reimagining Formalism for an Antiracist Music Theory,” Part I and Part II.  Blog for the History of Music Theory SMT Interest Group & AMS Study Group, dated 8 March 2021 and 18 March 2021.  Accessed 17 October 2021.  Link here

Dabin, Matthew, Terumi Narushima et al. “3D Modelling and Printing of Microtonal Flutes.” Proceedings of the 16th International Conference on New Interfaces for Musical Expression (NIME 2016), 286-290. Brisbane, Australia: Queensland Conservatorium Griffith University, 2016.

De Souza, Jonathan. Music at Hand: Instruments, Bodies, and Cognition. Oxford: Oxford University Press, 2017).

Dolan, Emily. “Toward a Musicology of Interaces.” Keyboard Perspectives 5 (2012), 1–13.

Eidsheim, Nina.  “The UCLA PEER Lab.”  Accessed 17 October 2021.  Link here

Moseley, Roger.  Keys to Play: Music as a Ludic Medium from Apollo to Nintendo.  Berkeley: UC Press, 2016.

Gawboy, Anna.  “The Wheatstone Concertina and Symmetrical Arrangements of Tonal Space.”  Journal of Music Theory 53/2 (2009): 163–190.

Rehding, Alexander. “Instruments of Music Theory.” Music Theory Online 22/4 (2016). Link here.

Rehding, Alexander. “Three Music Theory Lessons.” Journal of the Royal Musicological Association 141/2 (2016), 251–282.

Scherzinger, Martin. “Software Physiognomics: Adorno’s Radio Analytics Today.” New German Critique 43/3 (2016): 53–72. 

Sonevytsky, Maria.  “The Accordion and Ethnic Whiteness: Toward a New Critical Organology.”  The World of Music 50/3 (2008), 101–118.

Parkhurst, Bryan and Stephan Hammel, “Pitch, Tone, and Note,” in The Oxford Handbook of Critical Concepts in Music Theory (2020).  Link here (paywall).

Walden, Daniel.  “Pitch vs. Timbre.”  In The Oxford Handbook of Timbre, ed. Emily Dolan and Alexander Rehding (Oxford: Oxford University Press, 2019).  Link here (paywall).


[1] See also Sonevytsky 2008, Gawboy 2009, Dolan 2012, De Souza 2017.

[2] My idea of creative “play” as a valuable research method is shaped by Moseley 2016 as well as Nina Eidsheim’s work with the UCLA Practice-based Experimental Epistemology Research (PEER) Lab (click here for more info).

[3] This is not the first project of its kind. See for instance Terumi Narushima’s collaborative project focused on 3D printing of microtonal flutes, described in Dabin/Narushima et al. 2016.