Tuning the World: Pitch Lessons for the History of Music Theory

Fanny Gribenski

Last January, I published a book entitled Tuning the World: The Rise of 440 Hertz in Music, Science, and Politics (1859–1955) (Chicago: University of Chicago Press). Surprisingly—or perhaps, unsurprisingly, given the separation between my own subfield of historical musicology and music theory—I never thought of this work as a contribution to music theory. Following the invitation to contribute to this blog, however, I realized that this publication resonates with current conversations within this field, and in the history of music theory in particular.

To sum it up briefly, the history of concert pitch—first fixed at A 435 vibrations, or Hertz, by the French government in 1859, and later redefined as A 440 in the United States and internationally in 1939—is one that reveals the contradictions between abstract, mathematical conceptions of pitch and the reality of social, material, and environmental conditions involved in producing sound. In this post, I summarize some of the lessons of this history for music theory, showing especially the value of science and technology studies for materialist approaches to music’s core concepts. As an abundant literature across various fields of the social and human sciences has analyzed, standards offer unique sites to analyze the fabric of social life (Yates & Murphy 2019; Lampland & Starr, 2009; Brunsson & Jacobson 2002). While “the story of A” has been told from a philological perspective with the aim to “historically inform” performance practice (Haynes 2002), my book draws on science and technology studies to unpack the social and political significance of 440 Hertz—crucially, to ask what it means to try and impose a single frequency as a universal point of reference for musicians across the globe, or to “tune the world.”

A conceptual mess

Before they could agree on a single frequency, actors in these debates first had to determine what constituted “pitch.” In a recent article, Bryan Parkhurst and Stephan Hammel (2015) have sketched a materialist approach to the concepts of “note,” “tone,” and “pitch.” As part of this program, they have drawn attention to the “terminological messiness” that surrounds these notions. Adding to the “conceptual unruliness” they identify, unpacking the history of concert pitch uncovers the many layers of contingencies that it, too, holds. To begin with, the expression “musical pitch” lacks a clear equivalent in French, German, and Italian. In all these languages, the notion has at least two possible translations. While the words “diapason,” “Kammerton,” and “corista” have historically referred to the standard pitch in use at different times or places, the words “ton,” “Tonhöhe,” and “tono” have generally designated the perception of a lower or higher pitch. What is more, in the nineteenth century, the French word “diapason” referred not only to abstract standards in use for musical practice and instrument building—the “convention by which one attributes the name of a certain note to a certain sound” (Lasalle 1858, 335)—but also to the physical devices that embodied such standards (increasingly, but not exclusively, steel tuning forks), as well as to the ambitus of a given voice or instrument (the range of sounds extending from the lowest to the highest note that can be produced).

Ways to quantify, categorize, and represent pitch varied far beyond linguistic fluctuations. Before the general acceptance of electro-acoustical procedures for sound measurement in the interwar period and the use of the Hertz as a uniform unit beginning in 1960, sound measurements depended on diverse cultural contexts.[i] For example, in France the use of single vibrations to indicate frequency prevailed, whereas double vibrations predominated in Germany, Britain, and the United States. Pitch was also subject to temperature variation, measurements of which had to be converted between degrees Celsius and Fahrenheit.[ii] Due to the relationship between duration and frequency (the latter being inversely proportional to the former), determining pitch was further inseparable from counting time, and the second itself was not a universally agreed upon unit of measurement.[iii]

In addition, pitch quantification was inseparable from the various material and cultural contingencies of the objects and techniques it employed: to secure the validity of their measurements, acousticians had to describe at length the method and apparatus they used to produce them. It was only over the course of pitch negotiations that scholars started to detach pitch data from the specific contingencies of their production, as part of their project to “tune the world.” This process of unification, however, made it virtually impossible to implement a standard as it overlooked the importance of materiality in the production of pitch. Given the combined impact of environmental conditions and the materiality of musical instruments on pitch, in particular, securing uniformity in the realm of frequency required far more than the design of precise measurement techniques and technologies. In implementing their reforms, standardizers (including musicians, scientists, instrument makers, engineers, and diplomats) thus ended up measuring the importance of local material conditions on the production of pitch.

An expanding but shrinking territory

My empirical approach to the history of concert pitch ultimately reveals a dual, contradictory movement of expansion and contraction. On the one hand, due to the combined effect of globalization and imperialism, and of the development of ever-more encompassing measurement procedures, the geographical territories that adopted concert pitch radically expanded between the beginning of the nineteenth century and the late twentieth century. The impulse to standardize pitch was a proxy for the imperial ambitions of Western nations: throughout the negotiations, the standardizers’ world grew from a single musical site in the first years of the nineteenth century—the Paris Opera—to entire nations in the second half of the nineteenth century (such as Great Britain, Austria, Belgium, Italy, Russia, and Germany), to internationalist projects from the 1880s onwards. At first limited to Europe, this impulse came to span the Global South, first in the context of colonialism, then with the emergence of global modes of governance after World War II. In parallel, the standardizers’ focus went from measuring the “initial frequency” of musical instruments or tuning forks outside any musical context, to the analysis of pitch over the course of an entire work of music. With the emergence of broadcasting technologies, acousticians became able to measure pitch live all across the technologized world.

On the other hand, the standardization of pitch involved a complex combination of legal, bureaucratic, social, and aesthetic efforts. Given the different jurisdictions governing diverse aspects of the process, pitch was at once highly mutable and stubbornly immobile. What is more, after World War II,new scientific approaches to pitch started to emphasize the subjective character of the standard. Drawing on psychology, acousticians increasingly differentiated between the phenomenon of frequency and its perception, and they began to insist on the impossibility of reducing concert pitch to its techno-scientific specifications. By the time the standardization process was complete, the standard proved applicable in only a fraction of the situations for which it had initially been thought useful. Crucially, when the International Organization for Standardization (ISO) adopted the standard in 1955, standardizers renounced the idea of certifying the conformity of instruments to A 440, arguing that pitch was ultimately the product of an interaction between an instrument and a player. The aesthetic, subjective aspects of pitch have ultimately exercised an equal, if not opposing power to the gradual triumph of standardization.

Conclusion

Rich with a long history, concert pitch A 440 still resonates with the voices and actions of those—human and nonhuman—who are involved in the making of this standard. Today, growing conspiracy theories spread online about concert pitch reveal how contested the standard continues to be, while its lack of application in large portions of the globe shows the limitations of this “universal” point of reference.[iv] Beyond highlighting an overlooked episode in the history of sound and politics, Tuning the World shows how empirically rich approaches inspired by science and technology studies can help us rethink the core concepts of music theory. Ultimately, the history of concert pitch reveals the limits of techno-scientific authority over music. Given the fact that the production of pitch always requires the cooperation of musical parties and involves complex interactions between an instrument, a player, and their environment, concert pitch did not follow the same path as that of other standards. What over a century of negotiations finally revealed was just how difficult it is to control and standardize pitch. Industry and commerce may have shaped pitch, but concert pitch, in turn, fine-tuned the way standardization happened in these realms.  And ongoing redefinitions of the standard in a broad array of musical cultures, including early musical performance, classical orchestral practice, and various subgenres of popular music—from pop to electronic dance music—show that the “story of A” continues, highlighting the complexity of networks that shape musical sounds.

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Bibliography

Brunsson, N. and Jacobson, B., eds. 2000. A World of Standards. Oxford: Oxford University Press.

CGPM. 1961. Compte rendu des séances de la 11^e conférence générale des poids et mesures. Paris: Gauthier-Villars.

Gribenski, F. 2021. “Nature’s ‘Disturbing Influence’: Pitch and Temperature in the Age of Empire.” In “Music and the Invention of Environment in the Long Nineteenth Century,” edited by Paige, K. Special issue, 19th Century Music 45, no. 1: 23–36.

Haynes, B. 2002. A History of Performing Pitch: The Story of “A.” Lanham, Mar., and Oxford: The Scarecrow Press.

Lampland, M. and Star, S. L. 2009. Standards and Their Stories: How Quantifying, Classifying, and Formalizing Practices Shape Everyday Life. Ithaca, NY: Cornell University Press.

Lassalle, A. de. 1858. “Chronique musicale: La question du diapason et sa prochaine solution officielle.” Le Monde illustré (20 Nov.): 335.

Parkhurst, B. and Hammel, S. 2015. “Pitch, Tone, and Note.” In The Oxford Handbook of Critical Concepts in Music Theory, edited by Rehding, A. and Rings, S. Oxford: Oxford University Press.

Rosenberg, R. E. 2021. “Perfect Pitch: 432 Hz Music and the Promise of Frequency.” Journal of Popular Music Studies 33, no. 1: 137–154.

Yates, J. and Murphy, C. N. 2019. Engineering Rules: Global Standard Setting since 1880. Baltimore, MA: Johns Hopkins University Press.

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[i] This unit was named after the German physicist Heinrich Hertz (1857–1894)—who made important scientific contributions to the study of electromagnetism—by the International Electrotechnical Commission in 1935. But it only became the official unit for the measurement of frequency on an international scale after the General Conference on Weights and Measures created the “International Unit System,” in 1960. CGPM 1961.

[ii] On the impact of temperature on pitch, see Gribenski 2021.

[iii] Historically, the second was defined in terms of the rotation of the earth, as 1/86,400th of a mean solar day. In 1956, however, it was redefined as a fraction of the rotation of the earth around the sun, before being based on the properties of atoms. Various pendulum clocks served as standards for timekeeping during the nineteenth century, before the generalization of quartz and, later, atomic clocks. Ironically, precision in timekeeping relied on that of tuning forks—as in the history of many other standards, there is a circularity at play in the history of pitch standardization.

[iv] On these controversies, see Rosenberg 2021.