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).
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