Mathiesen, Thomas J.

English

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Book Reviews 
Thomas Christensen. Rameau and Musical Thought in the 
Enlightenment. Cambridge Studies in Music Theory and Analysis, vol. 
4. Cambridge: Cambridge University Press, 1993. 
Review by Thomas J. Mathiesen 
Matthew Shirlaw, the first scholar of this century to engage in a 
painstaking analysis of the treatises of Jean-Philippe Rameau, 
concluded: "Rameau was a real theoretical genius. He was not only 
one of the greatest theorists of his time, but one of the greatest of all 
the theorists who have at any time endeavoured to elucidate the 
mysteries of harmony, and to discover its laws."l Rameau himself 
would surely have agreed with this assessment, yet his theories have 
had a checkered history. In his own lifetime, his treatises were 
carefully and sympathetically read by such intellectuals, scientists, and 
musicians as Louis-Bertrand Castel, Jean Le Rond d' Alembert, Denis 
Diderot, and even Jean-Jacques Rousseau. But by the end of his life in 
1764, all these men had rejected his work, in some cases with 
considerable asperity. Beginning with d' Alembert' s Elemens de musique 
theorique et pratique suivant les principes de M. Rameau (1752) and 
extending through the later eighteenth century and the nineteenth, 
Rameau's theories were simplified, adapted, expanded, criticized, and 
modified by theorists such as F. W. Marpurg, J. P. Kirnberger, F. -J. 
Fetis, Simon Sechter, H. L. F. von Helmholtz, Hugo Riemann, and 
others to such an extent that the tradition began to be mistaken for the 
theory itself. This unfortunate state of affairs was only aggravated by 
the fact that Rameau's treatises became increasingly scarce,2 and even 
IMatthew Shirlaw, The Theory of Hannony ... (London: Novello & Co., 1917; 
reprint, New York: Da Capo Press, 1969), x. 
2"It is perhaps significant that not one of Rameau's treatises underwent a second 
edition, in striking contrast to many less important theoretical works of the early 
eighteenth century." Jean-Philippe Rameau, Treatise on Hannony, trans. and with an 
224 Indiana Theory Review, Vol. 16 
had they been widely available, their density and prolixity would have 
discouraged all but the most diligent readers. Moreover, because 
Rameau's theory evolved over the nearly forty years separating the 
Traite de ['harmonie (1722) from the Code de musique pratique (1760), 
even a diligent reader can be overwhelmed by the inconsistencies, 
ostensible contradictions, and especially in the later treatises, various 
subtexts. 
At the beginning of the twentieth century, Rameau found a new 
champion in Shirlaw, who devoted the greater part of his Theory of 
Harmony to a detailed explication of the treatises themselves. Shirlaw 
recognized the difficulty of his task: 
. . . even the most complete acquaintance with all the books of 
the Traite would not entitle us to assume that we were familiar 
with Rameau' s theory of harmony. Rameau has embodied the 
results of his reflections on the subject, not in one only, but in 
several important theoretical works, a fact not always 
remembered by his commentators. His ideas on the subject of 
harmony were in a state of constant flux, and of continuous 
development. For this reason it would be a somewhat difficult 
task to give a synopsis of Rameau's theories on half a sheet of 
notepaper. 3 
To show the evolution of Rameau's thought, Shirlaw began with 
two preliminary chapters-one on figured bass and the classification of 
chords and the other on Zarlino and Descartes (with some reference to 
Mersenne)-and then took up the treatises one at a time, carefully 
tracing their theoretical premises while at the same time introducing 
various objections raised by Rameau's contemporaries, by later critics 
such as Hector Berlioz, Fetis, and Riemann, and by Shirlaw himself. 
This approach has the advantage of providing the reader with two 
senses of the theory: in terms of its conception, content, and 
introduction and notes by Philip Gossett (New York: Dover Publications, 1971), v. 
3Shirlaw, xi-xii. 
Book Reviews 225 
construction as the work of an individual intellect; and in terms of its 
place within a larger unfolding theory of harmony. 
In the late 1960s and early 1970s, interest in re-examining the 
theory of Rameau was stimulated by the publication of a facsimile 
edition of his complete theoretical writings, edited by Erwin Jacobi;4 
the revised and enlarged edition of Cuthbert Girdlestone's Jean-Philippe 
Rameau: His Life and Work; 5 Philip Gossett's translation of the 
complete Traite de l'harmonie into English;6 and several important 
dissertations and articles. 7 In 1985, Thomas Christensen completed his 
Yale dissertation on d' Alembert's critique of Rameau, which was 
followed by the publication of several interesting articles exploring 
specific aspects of Rameau's theory. Now, in his new book, Rameau 
and Musical Thought in the Enlightenment, published as part of Ian 
Bent's series Cambridge Studies in Music Theory and Analysis, 
Christensen expands upon his earlier work and provides the reader with 
the first comprehensive study of Rameau as music theorist since 
Shirlaw's Theory of Harmony. 
The studies of Shirlaw and Christensen naturally invite comparison. 
In fact, Christensen himself anticipates this comparison by describing 
Shirlaw's treatment as "probably the most systematic and sympathetic 
reading Rameau has ever received." He regards the result as "a 
richly-detailed exposition that reveals much of the power and originality 
4Erwin R. Jacobi, ed., The Complete Theoretical Writings of Jean-Philippe Rameau, 
6 vols., Publications of the American Institute of Musicology: Miscellanea, ser. 3 (n. p.: 
American Institute of Musicology, 1967-72). 
5Cuthbert Girdlestone, Jean-Philippe Rameau: His Life and Work, rev. and enl. ed. 
(New York: Dover Publications, 1969). 
6See n. 2 above. 
7The book under review (Thomas Christensen, Rameau and Musical Thought in the 
Enlightenment, Cambridge Studies in Music Theory and Analysis, vol. 4 [Cambridge: 
Cambridge University Press, 1993]) contains a very good bibliography (pp. 313-20); see 
also the extensive bibliography for the entry "Jean-Philippe Rameau" in David 
Damschroder and David Russell Williams, Music Theory from Zarlino to Schenker: A 
Bibliography and Guide, Harmonologia, no. 4 (Stuyvesant, NY: Pendragon Press, 1990), 
251-60. 
226 Indiana Theory Review, Vol. 16 
of Rameau's thought, as well as its obvious shortcomings" but 
concludes in the end that it makes "a frustrating read."8 Various 
readers will no doubt differ in their summary assessments of the earlier 
work, but all will surely discern certain parallels in the organization of 
the two works, while at the same time noticing distinctive differences. 
Both take a chronological approach, for the most part; both include 
excurses on the objections of Leonard Euler to Rameau's theory of 
"octave identity," followed immediately by considerations ofRameau's 
disputes with the philosophes of the Encyclopedie;9 and both provide 
systematic explanations and demonstrations of the theoretical principles. 
Shirlaw's treatment, as already noted, is placed in a fairly broad 
historical context, extending from Zarlino to nineteenth-century English 
theorists such as Alfred Day, Sir John Stainer, and Ebenezer Prout, but 
except for a brief reference to Descartes (in Chapter Two) and passing 
references to a few scientific figures (in Chapter Three), it is 
exclusively musical. Christensen's study is in one sense much more 
narrowly focused, concentrating almost entirely on figures of the 
seventeenth and eighteenth centuries, but in another sense, it is much 
broader in scope, since it views Rameau's theory within the context of 
the compelling scientific and philosophical controversies of the 
Enlightenment. Christensen also makes use of manuscript materials 
such as the so-called "Clermont notes," "Art de la basse 
fondamentale," and the "Opera Memoire," unknown to Shirlaw, to 
provide a much fuller view of the actual development of Rameau's 
theory. 
Christensen organizes his book in ten chapters, preceded by a brief 
introduction. In the first chapter, he considers Rameau as a figure 
responding to the various intellectual forces of Cartesianism, 
Newtonianism, Lockean sensationalism, and Malebranchian 
occasionalism, in short, the competing intellectual forces of the 
Enlightenment. In Christensen's view, this was not a simple 
Enlightenment "consisting of an intrepid troop of secular materialists, 
8Christensen, 2. 
9Shirlaw, 274-76 and 276-83; Christensen, 245-47 and 247-51. 
Book Reviews 227 
fighting all the superstition, prejudice, and intolerance ... with the 
weapons of British empiricism" 10 but rather a "dialectical struggle 
between rationalist and empiricist tendencies," that is, "an intellectual 
tourbillon. ' '11 
The second chapter concentrates on Rameau' s theoretical method 
(insofar as a single method can be identified), "a dialectic in which 
Rameau was constantly attempting to mediate between the empirical 
appearances of musical practice and the synthetic demands of 
theoretical systematization. "12 The focus here is on the Traite; the 
evidence of the "Clermont notes," written apparently in the seven 
years prior to his move to Paris in 1722; the influence of Cartesianism; 
and the competing theoretical and practical traditions apparent in earlier 
French music theory, represented on the one hand by Marin Mersenne 
and Rene Descartes himself and on the other hand by figures such as 
Etienne Loulie and Michel L' Affilard. 
The third chapter, "Precursors of Harmonic Theory," provides a 
brief consideration of French thorough-bass practice as represented in 
a number of treatises published in the seventeenth century, with 
particular focus on the important regIe de I 'octave13 and the way in 
which the art of accompaniment became "the key that has opened to 
him [Rameau] the most secret sanctuaries of music. "14 Two other 
elements important to the development of Rameau' s theory are also 
introduced here: first, the new conception of dissonance as a means of 
defining harmonic progression, and second, a rising awareness of 
JOChristensen, 15. 
!lIbid., 19. Christensen credits the dialectical analogy to Ernst Cassirer. 
12Ibid., 40. 
J3This is essentially a pattern of root-position triads (on the first and fifth notes of a 
diatonic scale spanning an octave) and first-inversion triads or seventh chords (on the 
other degrees of the scale). As Christensen describes it (ibid., 50), "By knowing which 
particular sixth chord belongs to which scale degree, one has a means of harmonizing 
every diatonic scale progression." 
14Prom L.-B. Castel's review in the]ournal de Trevoux (1722), quoted in ibid., 51. 
228 Indiana Theory Review, Vol. 16 
inverted chords as equivalent to their perfect disposition, not merely as 
derived from that disposition. In order for this "equivalence" to be 
logically (and perhaps empirically) acceptable, it was necessary to 
identify and recognize a "generative fundamental," and this is the 
subject of the fourth and fifth chapters. 
Christensen provides in Chapters Four and Five a useful summary 
of the various mathematical principles described by "canonists" (as he 
calls them) such as Johannes Kepler, Athanasius Kircher, Robert Fludd, 
and Mersenne, concentrating however on the ways in which these 
principles were expounded by Zarlino and especially Descartes in his 
Compendium musicae. All these principles had been explored earlier by 
various Greek musical writers, who had observed the interesting 
correspondence between arithmetic ratios such as 1 :2, 1 :3, 1 :4, 2:3, 
and 4:3 and the musical consonances of the octave, twelfth, fifteenth, 
fifth, and fourth, not to mention much more complex ratios and 
intervals, which were also examined in some of the treatises. 15 As these 
principles were rediscovered and applied by later theorists, they were 
eventually adapted by Rameau for his theory of chordal generation, in 
which two basic types of chords, the consonant triad and the dissonant 
seventh, and all their compounds and inversions could be generated 
from a single source. But the adaptation went beyond this, for Rameau 
also saw that the harmonic relationships inherent in each chord were 
also inherent in the movement of the underlying fundamental bass from 
chord to chord, thereby explaining "how music was a fully dynamic 
process that unfolded over real time." Thus, "music is a coherent and 
intelligible succession of directed harmonies over real time that can be 
both defined by and modeled with the fundamental bass." 16 
151 note here in passing that a number of Christensen's observations on the 
manipulation of the monochord and the ways in which monochord theorists actually 
viewed their findings (see especially pp. 78-83), while perhaps true for Zarlino and 
Descartes, should not be taken as generally true for earlier theorists of the canon, who 
show considerable variety in their conception of the construction of this instrument, their 
ways of measuring the intervals on multiple strings or on a single string, and their 
understanding of the results (in terms of frequency, string length, or pure number). 
l6Ibid., 132. 
Book Reviews 229 
Chapters Six and Seven concentrate on Rameau's reconceptual-
ization of his earlier theory in terms of the corps sonore, or in other 
words, a vibrating body and its harmonic overtones. Christensen 
reviews some of the scientific treatments of overtones in the generations 
prior to Rameau, especially those of Mersenne and Joseph Sauveur, but 
the emphasis is on the development of Rameau' s new theories-in the 
Generation harmonique (1737) and his 1749 presentation to the 
Academie Royale des Sciences, preserved, as it seems, in an 
unpublished manuscript in the Bibliotheque-Musee de l'Opera, which 
Christensen calls the "Opera Memoire," and later published in a 
longer version as the Demonstration du principe de I 'harmonie 
(1750)-and reactions to them by scientists such as Dortous de Mairan, 
Castel, Euler, Daniel Bernoulli, and d' Alembert. Related to Rameau's 
new interest in the corps sonore was a fascination with the geometric 
proportion. This proportion could be used to explain the obvious 
harmonic force of the subdominant, which had previously been 
disregarded as a cadence point or a fundamental chord, and of greater 
importance, it could provide a new model of symmetrical musical 
relationships in place of the' 'rigorously mechanistic, directed chain of 
dominants found in the Traite. . . . The function of mode can now be 
understood as a kind of solar system, where the tonic represents a large 
body like the sun drawing smaller planets from all directions towards 
its own center. "17 These symmetries are particularly well summarized 
in Christensen's figure 7. 1, which shows the interlocking patterns of 
arithmetic, harmonic, and geometric proportions and their respective 
associations with the minor triad, the major triad, and the relationship 
among subdominant, tonic, and dominant functions. IS 
In the final chapters, Christensen explores the history of Rameau's 
association with the philosophes and his gradual estrangement from 
them, especially from his erstwhile champion d' Alembert. Christensen 
certainly does not discount basic personalities in trying to provide 
17Ibid., 185. 
18Ibid., 208. I should remark, however, that the note d'" is misplaced in the 
diagram. It should fall directly over the number 27. 
230 Indiana Theory Review, Vol. 16 
reasons for the controversies that became more and more acidulous in 
the last decades of Rameau's life, but he sees these hostilities primarily 
as the inescapable result of the various cultural, intellectual, and 
rhetorical positions competing for primacy in the course of the French 
Enlightenment. Christensen is apparently aware that his interpretation 
of Rameau's theory as consciously rhetorical may not sit well with all 
readers: 
The dependence of music theory-or really any kind of 
theory-upon political and rhetorical factors may strike some 
readers as a baleful situation, one the theorist ought to strive to 
mitigate as much as possible. I would argue, on the contrary, 
that such a dependence can be a virtue. Only to the degree that 
music theory responds to questions of pressing import of [i.e., 
to (?)] its time in a culturally-resonant language does it accrue 
vitality. Music theory for someone like Rameau was not a 
discipline standing outside his culture, but one intrinsically a 
part of it. Of course, a theory has the possibility of not just 
responding to cultural forces, but also of redirecting them. 19 
While this point of view seems to be used in modern criticism to reduce 
the individual to little more than a soulless package of tedious 
ideologies, Christensen does not take it to extremes. He clearly 
recognizes that Rameau' s theory is important and still of interest today 
precisely because it transcends the limitations of its time and culture, 
for at the end of his book, he writes: 
The truly revolutionary accomplishment of Rameau, I think, 
consisted in the overall reconceptualization of music and the 
music-theoretical enterprise he envisioned. Almost 
single-handedly, he redirected the focus of music theory to 
questions involving chordal generation, harmonic coherence, and 
19Ibid., 305. 
Book Reviews 231 
tonal identity, questions that still resonate today. 20 
The subject matter of Rameau and Musical Thought in the 
Enlightenment is often quite complex, and this is certainly not a book 
for the casual reader. Thomas Christensen, however, does his best to 
make the material as accessible as possible by writing in an effective 
and well-controlled style, with the footnotes unobstrusively providing 
solid and appropriate documentation (though here, I think the publisher 
should have used a somewhat larger type). Rameau and Musical 
Thought in the Enlightenment makes an impressive contribution to our 
understanding of his music theory and especially the intellectual ferment 
within which it was formed. If it is true that' 'no scholar of tonal music 
may remain ignorant of concepts such as the sonorous body (corps 
sonore) and fundamental bass (basse !ondamentale), regardless of his 
or her own theoretical orientation or reaction to these formulations,' ,21 
then it is also true that this is a book for all such scholars to add to 
their libraries. 
2°Ibid., 306. 
21Damschroder and Williams, 250. 



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