The Journal of Seventeenth-Century Music

Volume 31 (2025) No. 1

Tuning and Temperament: Practice vs Science 1450–2020. By Patrizio Barbieri. Rome: Gangemi Editore, 2023. [592 pp. ISBN 978-88-492-4601-8.]

Reviewed by Loren Ludwig*

1. Overview

2. Contributors across Europe, Mersenne, Frescobaldi

3. Disciplinary Approaches

References

1. Overview

1.1 Patrizio Barbieri’s Tuning and Temperament: Practice vs Science 1450–2020 is an essential and monumental contribution to English-language scholarship on the diverse history of the subject in its European contexts. The study of tuning and temperament is necessarily trans-disciplinary, requiring expertise in the history of musical instruments, surviving repertoire, science (particularly physics, acoustics, and mathematics), and the social and institutional spaces in which music was composed, performed, and studied. Barbieri, who passed away in January 2024, was a rare scholar with technical and historiographic expertise in these diverse areas.

1.2 Tuning and Temperament is the last of several recent, self-curated anthologies of Barbieri’s publications.^[1] The current volume includes material published as early as 1980. With the help of translators Ken Hurr and Hugh Ward-Perkins, Barbieri presents a wide-ranging collection of articles originally published in English, French, Italian, and German, now “revised, restructured, partly rewritten, expanded (in some cases radically), and … translated.” While the materials offered in Tuning and Temperament do have some overlap with earlier volumes (such as Barbieri’s discussions of harmonic and acoustic theories in eighteenth- and nineteenth-century Venice or the chapter on the history of equal temperament in Enharmonic Instruments), the writings offered in Barbieri’s latest volume largely complement, rather than duplicate, the preceding anthologies. Tuning and Temperament, like the earlier collections, provides a detailed Table of Contents with section headings for each chapter. This latest volume also includes a very useful set of extended abstracts of each chapter, a feature that complements the overall highly systematic organization of complex historiographic and bibliographic materials. An extensive bibliography and index of names (though not, unfortunately, subjects or terms) contribute to the volume’s usefulness.

1.3 While Barbieri’s work in Tuning and Temperament extends from the fifteenth century (a previously unknown treatise on organ building and tuning) through the twenty-first (how inharmonicity has shaped piano tuning practices), this review will focus on his substantial discussion of the subject in Europe ca. 1500–1700. Tuning and Temperament’s twenty-one chapters include eleven that deal substantively with seventeenth-century (and earlier) material, including discussions of the development of mathematical, organological, and musico-theoretical approaches to equal temperament; tuning and temperament “conflicts” between keyboard, fretted, and non-fixed-pitch instruments; and important “epiphonomena” to the study of tuning, including historical uses of mathematical instruments like the mesolabe and sector, evolving understandings of beat frequency ca. 1630–1860, and the inharmonicity of musical strings. While Barbieri’s volume has much to offer the history of equal temperament, he avoids advocacy for any particular historical solution to the problems of commas (Pythagorean or syntonic) and the resultant teleological pitfalls so familiar from earlier histories of the subject. Readers seeking detailed historical information on the use of meantone and circulating temperaments on keyboards and fretted instruments will encounter a wealth of unfamiliar and fascinating material. By and large, the translations and adaptations of earlier publications manage to preserve Barbieri’s arguments and examples while standardizing technical language and minimizing redundancy. That said, frequent consultation of the author’s own entries in his extensive bibliography and a bit of guesswork is required to trace some current material to its earlier published antecedents.

2. Contributors across Europe, Mersenne, Frescobaldi

2.1 Italian interlocutors and sources are a particular strength for Barbieri, who offers a great deal of regional specificity in chapters such as “Instrument tuning in Tuscany: 150 years of proposals and disputes, from V. Galilei to Cristofori c. 1580–1730” and those focused on seventeenth-century Perugia, Rome, and Prague. Additionally, he provides discussions of numerous important contributors  to the history of tuning and temperament who have been largely overlooked, especially in Anglophone scholarship. For example, in 1630 Johann Faulhaber (1580–1635) published specifications for a monochord of equal temperament that may have been calculated using logarithms. (Faulhaber must not have known the work of the Flemish-born mathematician Simon Stevins, whose values for equal temperament, calculated first in the 1580s using square and cube roots, languished in manuscript until the nineteenth century.^[2]) Spanish polymath Juan Caramuel Lobkowitz (1606–1682) used logarithms to calculate equal temperament and designed keyboard instruments for Holy Roman Emperor Ferdinand III. In his Sistema Musico (1666) the Perugian philosopher, mathematician, astronomer, and music theorist Lemme Rossi (1602–1673) offered “the first printed treatise on music theory to adopt logarithms to calculate Equal Temperament” (Barbieri, p. 285). Mathematician and engineer Jean Gallé (fl. ca. 1620) instructed several French instrument builders and musicians in equal temperament and provided Mersenne with one set of values for equal-temperament  string lengths. And the Roman composer, theorist, and poet Pietro Francesco Valentini (1570–1654) demonstrated an equal-temperament monochord and designed various equal-temperament  keyboard instruments. While several of these names might ring bells for cognoscenti, Barbieri’s discussion of them in Tuning and Temperament adds substantially to English language discussion of these important contributors to tuning and temperament in sixteenth- and seventeenth-century Europe.

2.2 Among the more familiar figures who appear in Tuning and Temperament are Marin Mersenne and Girolamo Frescobaldi; each receives detailed treatment that advances (if not resolves) persistent historiographical questions. In the case of Mersenne, Barbieri offers translations of some notoriously ambiguous passages on equal temperament, informed by careful analysis of the writings of Mersenne’s many interlocutors (such as the aforementioned Gallé) as well as a thorough check of the accuracy of the relevant tables of figures. (Barbieri finds recurring patterns of errors, typically in the final couple units of various 5- and 6-digit string lengths.) After an illuminating discussion of a tuning method offered by Mersenne that Barbieri identifies as a very likely candidate for equal temperament, Barbieri charmingly concludes: “Although elsewhere he appears to contradict himself, we may definitely conclude that [Mersenne’s] attitude to equal temperament in organs and harpsichords is one of most prudent possibilism and benevolent abstention.”

2.3 A survey of Barbieri’s decades of scholarship on Frescobaldi reveals his attempts to make sense of what Frescobaldi’s compositions might reveal about tuning practices in Italy during the first half of the seventeenth century and, conversely, whether contemporaneous debates about temperament can inform how we tune (and hear) Frescobaldi. Complementary chapters B (“Equal temperament on keyboard instruments: proposals and rebuttals 1530–1680,” and particularly the subsection “The introduction of equal temperament in Rome: Doni, Frescobaldi, and O. Castelli, 1639–1641”) and C (“Tonality expansion in keyboard compositions at the time of Frescobaldi: with late-17th-century developments toward circulating temperaments”) take up this question in detail. Barbieri’s account is anchored by an anecdote recounted by Giovanni Battista Doni in De Praestantia (1647). In a story that appears to have fascinated Roman musical litterati around mid-century, Doni describes (in Barbieri’s translation) an “old man in a wretched state who recently came to this city, who only knew how to play the harpsichord a little. This person passed off—as a new and highly useful discovery—that equality of semitones usually, but wrongly, attributed to Aristoxenes and believed, also wrongly, to be found in instruments with a neck divided into frets; and this he used to tune his instrument, causing considerable controversy.” Barbieri documents various versions of the story and its reverberation among such cognoscenti as Mersenne (whom Doni warned about equal division of the tone), Pietro della Valle, and Ottaviano Castelli, who, to the irritation of his colleagues, was evidently quite taken with the “wretched” old man’s equal temperament. This section of the chapter exemplifies Barbieri’s capacity to read arcane sources against each other to bring paleographic and historiographic details into useful focus, and in this case, to establish useful ante and post quem dates for the appearance of Doni’s “old man” in Rome. Barbieri manages to reveal the aesthetic, cultural, and institutional complexities of the controversy while also establishing a useful chronology. The episode, Barbieri concludes, occurred only after Frescobaldi had published his most tonally adventurous works, which, by virtue of their tendency to stay within the compass of E♭–G♯, would have obviated the need for equal temperament.

3. Disciplinary approaches

3.1 Historians, organologists, and performers of Renaissance and early Baroque music will find much of use in this collection, including Barbieri’s answers to longstanding controversies in the historiography of tuning and temperament. These include questions such as whether/how/when meantone tunings were used with fretted instruments like lutes and viols; whether/when/how circulating and equal temperaments displaced keyboards with split keys over the course of the seventeenth century; when (and where) circulating temperaments appeared prior to their popularization by German theorists ca. 1700; and how various families of instruments might have reconciled the different, incompatible tuning systems ascribed to them by several sixteenth- and seventeenth-century writers. Barbieri’s penchant for larding chapters with chronological lists of (often largely unfamiliar) exempla makes many sections of Tuning and Temperament particularly useful. These numerous annotated lists appear in nearly every chapter and include, for example, “Circulating temperaments in late-Seicento Italy” or “Historical sectors provided with a Scala musica” or “Artificiose counterpoint compositions involving equal temperament” (in which Barbieri provides an illuminating reinterpretation of many of the very same pieces initially described in Edward Lowinsky’s Secret Chromatic Art in the Netherlands Motet of 1946). More broadly, Barbieri’s collection offers perspectives on tuning solutions available for particular instruments at particular historical moments and how these might shape practical and expressive dimensions of performance; how instruments as objects are intertwined with ideas about mathematics and the physics of sound (the domain of Natural Philosophy and its cognates in the sixteenth and seventeenth centuries); and how preferences and practices around tuning and temperament coalesce around narratives of nationality and identity (with a particular strength in Italian sources).

3.2 But there is also material relevant to the histories of science and technology, a field into which Barbieri (originally trained as an engineer) has made many forays over the last four decades. Tuning and Temperament contributes to histories of mathematics, physics, and acoustics (as in “Mesolabe and sector: musical applications of two mathematical instruments, 1558–1790”). Barbieri’s  focus on the materiality of instruments reveals the complex dynamics between technological development and emergent knowledge about the scientific principles that inform them (as found in chapters including “The beat-frequency calculation of tempered consonances: a long-standing physical-mathematical enigma, 1630–1860” or “The inharmonicity of musical string instruments, 1543–2020”).

3.3 Tuning and Temperament’s structure as an anthology precludes an overarching historical narrative (unlike those found in earlier English treatments of the subject by Murray Barbour, Mark Lindley, or Ross Duffin, for example) or governing argument. But such apparatus likely wouldn’t be of much use to the volume’s intended readers—scholars, performers, and organologists seeking detailed information on the diversity of historical approaches to tuning and temperament. Rather, Barbieri’s extensive analyses of less (or un-) familiar sources and thoughtful engagement with questions that have bedeviled the last century of historiography promise to substantially advance how we think about the history of tuning and temperament in early modern Europe.