University of Cincinnati
Date: 5/24/2004
I, Tamara A. Tidd, hereby submit this original work as part of the requirements for the degree of Master of Music in Music Theory.
It is entitled: Theory and Practice: Rameau’s Fundamental Bass Applied to the Contemporary French Overture.
Student's name: Tamara A. Tidd
This work and its defense approved by:
Committee chair: Robert Zierolf, Ph.D. Committee member: Miquel Roig Francoli, Ph.D. Committee member: Mary Sue Morrow, Ph.D.
Last Printed:10/3/2019 Document Of Defense Form
THEORY AND PRACTICE: RAMEAU’S FUNDAMENTAL BASS APPLIED TO THE CONTEMPORARY FRENCH OVERTURE
A thesis submitted to the
Division of Research and Advanced Studies Of the University of Cincinnati in partial fulfillment of the requirements for the degree of
MASTER OF MUSIC
In the Department of Composition, Musicology, and Theory Of the Cincinnati-Conservatory of Music
by Tamara A. Tidd
B.M., Belmont University, 1994
Committee Chair: Dr. Robert Zierolf
ABSTRACT
Music theorists at the turn of the eighteenth-century focused much of their energy introducing new theoretical methods for musical composition. As a result the field of music theory grew into several important areas. Jean-Philippe Rameau (1683-1764) first presented many of the ideas that form our modern analytical practice. In Traité de l’harmonie, Rameau established a system of harmonic principles currently in use today. These include: constructing chords in a series of thirds, the formation of the major triad from the overtone series, the relationship of chords to a tonal center, the theory of chordal inversions, and the theory of fundamental bass. Although Rameau first intended his theory of fundamental bass to be used as a pedagogical tool, the function of the fundamental bass developed into revealing the foundation or root of each chord. The purpose of the chordal root was to serve as an early theoretical and analytical perception later interpreted by Roman numerals.
The purpose of this Thesis will be to present an analysis of Rameau’s fundamental bass theory as it is applied to the music of the French overture style. In addition to Rameau’s overtures, some by Lully and Telemann were chosen to allow comparison both chronologically and nationally. Pieces selected include Alceste, Cadmus et Hermione, and Amadis by Lully;
Hippolyte et Arcie, La Princesse de Navarre, and Castor et Pollux by Rameau; and Suite in D,
Overture in D minor, and Orchestral Suite in F minor by Telemann. Rameau’s theory of fundamental bass was a theoretical revolution. It provided a new model to indicate not only the origin of harmonies, but how these harmonies progressed in music over real time. His theory also verified the interpretation of a succession of harmonies to be a process of motion. The essence of this Thesis is to demonstrate that the fundamental bass theory developed by Rameau
is a practical description of music from that time and beyond.
ACKNOWLEDGEMENTS
To my family: for their unfailing love and support.
To Dr. Robert Zierolf: my eternal gratitude for giving the opportunity to come to CCM and to be apart of such a wonderful institution.
To the other the faculty and staff at CCM for making this an experience I will never forget.
CONTENTS
Introduction ...... vii
Chapter
1. Theorists ...... 1
A. Theorists before Rameau.
2. Johann David Heinichen.
B. Rameau's contributions.
2. Theory of fundamental bass ...... 24
3. Analysis of Corelli's Sonatas ...... 48
4. Fundamental bass analysis of overtures by Lully,
Rameau, and Telemann ...... 70
5. Conclusions ...... 91
Bibliography ...... 93
Appendices ...... 98
vi
INTRODUCTION
Seventeenth-century theorists in France contributed to the wide variety of European theoretical literature. They were concerned with many theoretical and compositional issues such as: an ornamentation classification system for performers; the reconstruction of theory manuals to include all levels of pedagogy; establishing clear definitions of all theoretical terminology; the documentation of early music history; and distinguishing between specific theories of thoroughbass, counterpoint, and a formal organization of music.1 By the late seventeenth century French music theorists faced a substantial amount of diverse theoretical concepts concerning music theory and composition. For example, major/minor keys overlapped with different modal systems.
Empirical thoroughbass theorists constructed chords but could not associate them with a limited number of pitches. Other theorists insisted upon explaining the fundamentals of music by acoustical science, which conflicted with those theorists still using numerical ratios.
By the turn of the eighteenth century, theorists focused on introducing even more new theoretical methods for musical composition. As a result, the field of music theory grew into several important areas. For example, in Gradus ad Parnassum (1725), Johann
Joseph Fux (1660-1741) codified a species approach to counterpoint.
1Albert Cohen, “17th-Century Music Theory: France,” Journal of Music Theory 16 (1972), 16-35.
vii
Johann David Heinichen (1683-1729) provided information on the thoroughbass method in his treatise Der General-Bass in der Composition, (1728). These two traditions prepared the way for Jean-Philippe Rameau (1683-1764), who first presented many of the ideas that form our modern analytical practice. In his Traité de l'harmonie (1722) and other treatises that followed, Rameau established a system of harmonic principles then in use. These included: constructing chords in a series of thirds; the formation of the major triad from the overtone series; the relationship of chords to a tonal center; the theory of chordal inversions; and the theory of fundamental bass.
Rameau first intended his theory of fundamental bass to be used as a pedagogical tool to simplify the instruction of composition and thoroughbass. The fundamental bass reveals the foundation or root of each chord. Identification of the root was necessary to determine chordal progressions. These chordal roots were not intended to be performed; instead, their purpose was to serve as a theoretical and analytical perception later interpreted by Roman numerals.
Although Rameau revised his theory of fundamental bass, he did not extensively apply this theory to his own music. Theorists did, however, applied fundamental bass to music years later. The purpose of this thesis will be to present a test case study and analysis of Rameau's fundamental bass theory as it is applied to the music of the French overture styles. French overtures included a variety of harmonic and rhythmic styles, homophonic and polyphonic textures,
viii and a contrast between tempi. Overtures in France were divided into two parts: a slow section in duple meter with dotted rhythms followed by a faster fugal section often in triple or compound meter. At the end a return to the opening material is often found, allowing this form to be a representative type of binary or rounded binary form with harmonically contrasting parts. The French overture was established as the standard type in France during the reign of Louis XIV and quickly spread to Germany and England. In addition to Rameau’s overtures, those by Lully and Telemann, representing France and
Germany respectively, were chosen for this study to allow comparison both chronologically and nationally. Pieces selected include Alceste, Cadmus et Hermione, and Amadis by Lully; Hippolyte et Aricie, La Princesse de Navarre, and Castor et Pollux by Rameau; overtures from Suite in D, Overture in D minor, and Orchestral Suite in F minor by Telemann.
Rameau’s theory of fundamental bass was the most important theoretical revolution of the eighteenth century. It provided a new model to indicate not only the origin of harmonies but how these harmonies progressed in music over time. His theory also verified the interpretation of a succession of harmonies in music to be a process of motion. The essence of this thesis is to examine how the fundamental bass theory developed by Rameau is a practical description of music from that time.
xi
CHAPTER I
Johann Joseph Fux (1660-1741) and Johann David Heinichen (1683-1729) contributed vital information on species counterpoint and thoroughbass methods, respectively, during the early eighteenth century, thus providing a foundation for Rameau and his theory of fundamental bass. Fux, an Austrian composer and theorist, decided on a career in music during his early childhood. By 1698 he was appointed court composer for Emperor Leopold I. During his lifetime Fux held a variety of positions including
Vice-Kapellmeister, Kapellmeister, and Principal Court Kapellmeister for three Habsburg emperors.
Fux wrote secular and sacred works including trio sonatas, masses, Te Deum settings, oratorios, and operas. His Gradus ad Parnassum (1725) was quickly regarded as one of the most important counterpoint manuals and remains so today. Written in
Latin, Gradus was translated into German, Italian, French, and English, and influenced musicians including Beethoven, Haydn, Mozart, and Schubert. This treatise was constructed in the dialogue style, in which Fux disguised himself as the pupil Josephus.
Fux’s greatest influence, Palestrina, was the wise teacher Aloysius. Throughout the treatise Aloysius introduced Josephus to counterpoint principles using the species approach along with exercises for him to master. Josephus worked through the exercises and remained under constant surveillance from Aloysius, who corrected his exercises and answered his questions.
Joel Lester, in his book entitled Compositional Theory in the Eighteenth
Century, gave a detailed description of Fux’s treatise. Fux began the treatise by listing
1 2 the voice-leading rules for five types or species of two-part writing and consonances needed for species counterpoint. First species created counterpoint using whole notes above or below a cantus firmus in whole notes. Second species used half notes against the cantus firmus. Third species used quarter notes; fourth species featured suspensions; and fifth species combined the possibilities from the preceding species. These concepts were then introduced in three- and four-part writing followed by imitation, fugue, and invertible counterpoint.
Although Fux illustrated his points through exercises, he gave only the information needed to know to complete that specific exercise, which resulted in some confusion for readers. In one exercise Aloysius corrected the leap F-B to F-C. However, the leap F-A was changed to F-B-flat by Josephus two exercises later. Why was B-flat mentioned here and not in the previous exercise? With the first exercise in the E mode and the second exercise in the F mode, B-flat was more appropriate in the second exercise. Fux chose not to explain this situation because it consisted of a complicated discussion concerning contrapuntal and modal issues.2 It is clear that Fux wanted the student to face the reality of compositional problems and to learn to make choices.
Gradus endured due to Fux’s understanding of basic voice-leading principles by which a student can master the compositional styles of the eighteenth and nineteenth centuries.
Within this pedagogical framework, Fux recognized the prima practica traditions passed on from Zarlino. Although he was against innovations and new ways of thinking established by the Enlightenment in the eighteenth century, his treatise educated students
2Joel Lester, Compositional Theory in the Eighteenth Century (Cambridge: Harvard University Press, 1992), 33.
3 in counterpoint and composition. Fux’s work was the culmination of Germanic Baroque music in Austria and became the foundation of Viennese Classicism.
Johann David Heinichen, German composer and theorist, began his music career by composing and conducting sacred music. After completing a law degree from Leipzig
University, Heinichen traveled to Venice and Rome, where his reputation as a composer grew. This enabled him to win the post of Kapellmeister in 1717 to the court in Dresden.
By the beginning of the eighteenth century, Heinichen had composed in every form and established himself as a major theorist. His contemporaries regarded him as “the Rameau of Germany.”3
While in Venice Heinichen wrote his theoretical masterpiece Der General-
Bass in der Composition (1728). This treatise consisted of 960 pages with musical examples and is divided into two sections: Part One covered thorough-bass principles;
Part Two explained harpsichord accompaniment. As Lester explains, thoroughbass writers, including Johannes David Heinichen (1683-1729), Friderich Erhard Niedt (1674-
1708), Francois Campion (1685-1747), and C.P.E. Bach (1714-88), clarified how to read figured bass symbols with the bass becoming the foundation of all harmony and chords, and each explained procedures to follow for solving unfigured bass lines. Their treatises revealed views toward composition that valued an improvisational approach more than the traditional contrapuntal methods.4
3George Buelow, “Heinichen’s Treatment of Dissonance,” Journal of Music Theory 6 (1962), 218.
4Lester, 52.
4 Nevertheless, Der General-Bass was the most accomplished treatise on thoroughbass methods. This document transcended the other Baroque treatises with numerous examples of thoroughbass techniques. Heinichen, as well as other thoroughbass writers following the Zarlino tradition, built harmonies above the bass and explained root- position triads and consonant chords followed by dissonant chords. Root-position chords were defined as a fifth and third over the bass and did not need figures in order to be recognized. Heinichen further encouraged the performer to play root position chords in three different right-hand positions, which he called the “three principal chords” (drey
Haupt-Accorde).5 Heinichen then discussed other consonant chords, such as 6/3, and the principle of inversion. Lester suggested that Heinichen’s addition of theories on inversion after 1728 may have been influenced by Rameau.
The second part of this treatise reflected Heinichen’s tonal and harmonic views.
Lester broke down his discussion of unfigured basses and lists his three methods to assist performers. His first showed how to construct chords based solely on the intervals between the solo and bass parts. His second method, which consisted of standardized intervals regardless of key, was supplemented by his third method, is labeled Special
Rules. These Special Rules enumerated the position of miscellaneous chords within particular keys. They specify the necessary notes in major and minor keys and their modulations. Heinichen covered all 24 major and minor keys by using a circle that revealed their relationships as we see in Example 1.6
5Ibid., 53.
6Lester, 78.
5
Example 1: Buelow, 275. Heinichen’s twenty-four major and minor keys using a circle revealing their relationships.
One moved in either direction on the circle to an opposite neighboring position or to a skipped position. Heinichen explained that major keys modulated to their third, fifth, and sixth while minor keys modulated to their third, fourth, fifth, and seventh.7 In Der
General-Bass, Heinichen expanded the six Special Rules into eight General Rules discussed in the theatrical or operatic style. Due to its free treatment of dissonances,
Heinichen chose theatrical style rather than church or chamber styles. On page 587 of
Der General-Bass Heinichen explained why he wanted to regulate dissonant treatment:
Normally [in the theatrical style] no chord or progression can be considered correct that is not followed by a correct resolution of the dissonance, whether it occurs before or after the inversion of harmonies, in the upper, middle, or lowest part. If the chord passes this test, it is fundamental; when it does not, it is incorrect and without a very important reason to the contrary can not be allowed.8
7Ibid., 78-79.
8George Buelow, “Heinichen’s Treatment of Dissonance,” 219, quoting Johann David Heinichen, Der General-Bass in der Composition (Dresden, 1728), 587.
6
Heinichen demonstrated the resolutions of dissonances by dividing them into eight categories called General Rules. These General Rules expanded the six Special Rules and covered many major and minor situations. Heinichen used a solo cantata by
Alessandro Scarlatti to demonstrate these rules as Example 2 illustrated. Here Heinichen used scale-step rules for the accurate chord choice over the first eight notes (see Example
2).9
Example 2: Lester, 79; Heinichen 1728; Buelow 1966a, p. 231-32, mm. 1-3.
The realization is according to Buelow, page 282. Lester's comments paraphrase
Heinichen’s text.
The first note implies the key of B minor; but the cadence (B to E) indicate E minor with an incorrect signature. Conclusion: never judge the key from the first note but rather from the first cadence.
Each B, as scale-step 5, carries a major third. The C in measure 1 carries a sixth, being the sixth degree skipping to the fourth degree.
9George Buelow, Thorough-bass Accompaniment According to Johann David Heinichen, 2nd ed. (Los Angeles: University of California Press. Ann Arbor; UMI Research Press, 1986), 231-32.
7 The note D#, the leading tone, carries a sixth. The note G, scale-step 3, carries a sixth.
The note F#, as scale step 2, could have a major sixth. But when 2 immediately precedes a cadence, it is more beautiful to retain a seventh over it.
The B's at the cadence could have 5/4-#; 6-5/4-#; or just a major third. Remember, this cadence pattern because it is very common.10
Lester explained that Heinichen’s choice of chords was based on the appropriate harmony for each scale degree. Scale-step and cadence patterns were of primary importance in this example.
Der General-Bass contained a wealth of knowledge concerning thorough-bass practice and composition. Heinichen wanted to organize harmonic principles using the theatrical style of music to teach his students the art of composition using thoroughbass methods. One of his most important contributions was clarifying the use of dissonances in the theatrical style. Unlike other Baroque theorists, Heinichen freely admits that he can not classify every harmonic situation into one of his eight categories. Heinichen’s treatise earned him the praise and respect of his contemporaries and a permanent place among the most influential theorists of the Baroque era.
In 1722 Rameau’s treatise, Traité de l'harmonie, contributed a new vision of harmony. As a music theorist Rameau presented music as a scientific process with harmonic principles provided by nature. Thomas Christensen, in his book entitled
10Joel Lester, Compositional Theory in the Eighteenth Century, (Cambridge: Harvard University Press, 1992), 79-80, quoting George Buelow, Thorough-bass Accompaniment According to Johann David Heinichen, 2nd ed. (1986), 282.
8 Rameau and Musical Thought in the Enlightenment, described his early years as a composer.
Legend has it that Rameau’s formal musical education did not include theory. However, in his treatise Démonstration du principe de l'harmonie (Paris, 1750), Rameau explained how his attention became occupied with theory: “drawn since my youth by a mathematical instinct to the study of an art for which I found myself destined, and which has singularly occupied me my entire life.”11 At the age of seven or eight Rameau explained how he “sensed that the tritone should be resolved by the sixth and I made this into a rule.”12
Christensen, on page 30 of his book Rameau and Musical Thought in the
Enlightenment, summarized the state of music theory in France during the 17th century.
Theorists such as Marin Mersenne (1588-1648) and Rene Descartes (1596-1650), influenced by the musica theorica tradition, were mainly focused on the interrelationships between the origin and nature of musical material such as pitches, intervals, modes, prolations, and tunings. Discovering solutions for such problems as mode classifications, the mathematical generation of intervals, and the evaluation of tuning systems at first eluded them. Nevertheless, these theorists contributed to advancements in revising consonant hierarchy, temperament, and modal theory, and with their work established a turning point in the way of thinking about the musica theorica tradition.
The musica practica or musica attiva tradition largely dominated the second half
11Thomas Christensen, Rameau and Musical Thought in the Enlightenment, (New York: Cambridge University Press, 1993), 22, quoting Jean-Philippe Rameau, Démonstration du principe de l'harmonie (Paris, 1750), 110.
12 Ibid., 23, quoting Jean-Philippe Rameau, Génération harmonique (Paris, 1737), 223.
9 of the seventeenth century. Branching away from the philosophical, French music theory became more practical. Texts by Guillaume Nivers (1632-1714), Etienne Loulie (1654-
1702), Marc-Antoine Charpentier (1643-1704), and Michel L’ Affilard (1656-1708), ranged from singing treatises to thorough-bass primers, methods for transpositions, and dictions. Rameau bridged the gap between these two traditions. He acted both as a speculative theorist, by offering explanations, and as a practical theorist determined to produce results. His basse fondamentale principle was both theoretical and practical: theoretical in the sense of finding the origin of musical material and used as a practical way of describing music to musicians. Rameau, unlike seventeenth-century theorists, united the two traditions, speculative theory and practice, into one.13
The information on the following four pages is derived from Joan Ferris’s article,
“The Evolution of Rameau’s Harmonic Theories,” pages 231-33. Ferris’s article chronologically summarized Rameau’s theoretical treatises published throughout his career. Rameau’s theoretical system was based on several fundamental principles found in his first and most provocative work, the Traité de l'harmonie Reduite a ses Principles
Naturels, which first appeared in 1722. This treatise presented a theoretical system founded upon the senario, the first six partials of a vibrating string. Rameau illustrated how intervals and chords in their fundamental positions or inversions and chord successions were generated from the senario. A more comprehensive study of his harmonic theories from this treatise will be presented in chapter two.
Four years later, after becoming acquainted with the acoustical studies of Marin
Mersenne (1588-1648), Rameau wrote his next treatise, the Nouveau Systême de musique
13Ibid., 30.
10 théorique (1726). From these studies Rameau observed how overtones originating from the harmonic divisions of a string are also produced by a resonating body. Other advancements in this treatise included labeling the fourth scale degree subdominant and defining its role pertaining to the theory of double-employment. Dissertation sur les differentes métodes d'accompagnement (1732), his next treatise, was a practical description of how fundamental harmony can explain the basic mechanics of music.
Although the theoretical concepts found in Nouveau Systême are not improved upon,
Rameau constantly practiced and expanded his theoretical viewpoints. In 1737,
Génération harmonique was written, which focused on his latest experiment. He thought he had discovered how similar properties of the resonating body were achieved by the co- vibration of strings with lengths that are multiples of the original pulsating string.
Thirteen years later, in Démonstration du principle de l'harmonie (1750) Rameau realized this experiment found in Génération and obliterated the idea of the fundamental being the lowest tone of a partial series. The pulsating string's length caused only portions of the long string to vibrate in conjunction with the unison of the pulsating string. This discovery led to the demise of the subdominant. Rameau then theorized on the origins of the subdominant as the product of nature and art.
In 1752 he wrote his next treatise, Nouvelles réflexions de M. Rameau sun la
Démonstration du principle de l'harmonie, which explained new experimental discoveries. Rameau tried to discover a natural relationship between music and architecture, and he experimented using brass instruments, proving that the first six
partials are in tune. Rameau further advanced his study of the subdominant and concluded that it was out of tune due to its location in the partial series, which in turn
11 proved the superiority of the tonic and dominant over the subdominant.
Observations sun notre instinct pour la musique (1754) expanded upon his concept of melody arising from harmony and how harmony was second nature to man.
Rameau then described the physical effects such as the effect on the ear and the emotional effect harmony creates. Code de musique pratique (1760) was a practical treatise divided into two parts. In part one Rameau sorted through ambiguous points and presented an accurate statement of his theories. He addressed conflicting issues such as the construction of chords by added thirds versus the harmonic generation of chords.
The second half of this treatise articulated Rameau's theories for the last time. He dismissed his ideas concerning undertones and that chords came into existence as a product of art. Confirming his original theory of one single source generating everything in music, Rameau attempted to construct a sensible system of music.
In Origine der Sciences, published in 1762, Rameau examined the philosophical and emotional effects of the tonic sound, melodic inflection, and fundamental harmony on people. As a theorist, Rameau remained loyal to several primary concepts. He insisted that harmony is the foundation for all music. Contrary to other views on harmony, he claimed that it does not occur at random but is firmly established by concrete evidence. After studying the senario, the division of a string with the fundamental sound depicted as unity, he studied the harmonics produced by a resonating body and established the idea of a single musical sound containing partials within itself.14 Throughout his works Rameau reduced music to a science using
14Joan Ferris, “The Evolution of Rameau's Harmonic Theories,” Journal of Music Theory 3, (1959), 231-33.
12 mathematics. Although he was immersed in the intricacies of his theoretical methods, he exalted musical experience over then, thereby threatening the stability of his theoretical system by looking for other explanations. As a product of the Enlightenment, Rameau endlessly searched for faults and ways to improve his theories in pursuit of establishing universal harmonic principles.
At age 39 Rameau wrote his first and monumental treatise, Traité de l'harmonie.
One of the most important concepts Rameau articulated was the basse fondamentale, the fundamental bass. In his book Rameau and Musical Thought in the Enlightenment,
Thomas Christensen gave a brief synopsis of Rameau’s theories, which are as follows:
Rameau established the structure of music as harmonic in nature and as generated from a single fundamental source. This source began as the string divisions of the monochord and in later works was the physical base of the corps sonore, a vibrating body generating the harmonic upper partials. The ratios and proportions produced by the monochord and the corps sonore enabled Rameau to summarize harmonies (chords).
He also categorized all chord-root motion as the cadential formula of a dissonant seventh chord resolving to a consonant triad, thus proving how chord successions and ratios mirror each other. Dissonant progressions resembled the basic fundamental bass progression of a dissonant seventh chord resolving down by a perfect fifth to a consonant triad by new ideas such as the generative fundamental, inversional identity, and supposition. Therefore, this acoustical source accounted for musical syntax, terminology, and components such as melody, counterpoint, and rhythm of all tonal music. In his subsequent treatises Rameau eagerly sought to prove his theories worthy enough to be
13 seen as a scientific system.
Rameau’s theories were often compared by his contemporaries to Newton’s and
Descartes’. Newton’s Philsophiae Naturalis Principia Mathematica (1687) scientifically unified theories from his predecessors, Galileo and Kepler, which proved how earthly material bodies and planetary motion behaved identically. By presenting a theoretical system using mathematical principles Rameau united dissonant treatment rules and thoroughbass chordal formulations. Rameau often found himself called the “Newton of
Music” by his colleagues.15 Rene Descartes (1596-1650), in his Discours de la methode, changed the way of thinking when searching for the truth on any subject. Descartes’ method dismissed previously existing facts regardless of how long they existed. After clearing your mind of all preconceptions, one investigated the subject, formed principles, then tested these principles against a methodological foundation based upon mathematics.
Rameau relentlessly searched for theories to replace the unorganized quantity of principles of counterpoint and thoroughbass. In the Preface to the Traité, Rameau expressed this view:
Music is a science which should have certain rules; these rules should be drawn from an evident principle; and this principle can not really be known to us without the aid of mathematics.16
Rameau was very clear in stating his beliefs that a single source, the monochord and corps sonore combined with mathematics, produced an entire theoretical system of music. Jean Benjamin de Laborde, music lexicographer, historian, and
15Christensen, 8.
16Thomas Christensen, Rameau and Musical Thought in the Enlightenment (New York: Cambridge University Press, 1993), 11-12, quoting Jean-Philippe Rameau, Treatise on Harmony, trans. by Philip Gossett. (New York: Dover Publications, Inc., 1971), xx.
14 contemporary of Rameau, compared him correctly to Newton and Descartes.
One can say that Rameau was both Descartes and Newton, Since he did for music what these two great men together did for philosophy. Like Newton, he began with what existed in practice in order to find the principle. And like Descartes, he began with nature herself (that is to say, the phenomenon known as the corps sonore) in order to deduce along with all its consequences the principles and individual rules. By his efforts [music theory] has become elevated to a practical science whose mechanical operations are at once the most plausible and simple.17
Regardless of what label his colleagues bestowed upon him, Traité de l'harmonie is an incredible accomplishment. The information on the following three pages has been paraphrased from Christensen’s book, pages 24-29, Rameau and Musical Thought in the
Enlightenment, where he gave a brief history of Rameau’s sketches and professors before he published his Traité in 1722. Rene Suaudeau, a former professor of music at the Ecole
Nationale De Musique in Clermont-Ferrand, described Rameau's original exercise, sketches, and notes from his second Clermont residence for the Traité in a monograph.
The original notes for this treatise were lost. According to Suaudeau’s study, he established the main ideas from the Clermont notes. Rameau borrowed ideas then shaped them to appropriately reinforce his own.
The fundamental bass idea can be traced from new individual sources in the seventeenth century. His intention for the fundamental bass was to serve as a teaching tool. Using thoroughbass theory for his background, Rameau began by establishing the
17Thomas Christensen, Thomas Christensen, Rameau and Musical Thought in the Enlightenment (New York: Cambridge University Press, 1993), 18, quoting Jean Benjamin de Laborde, Essai sur la musique ancienne et moderne, 4vols. (Paris, 1780), III, 466-67.
15 necessary consonant framework of music as being the major and minor triads. Then he further clarified the three fundamental chord types: the accord parfait (consonant triad); the accord de grande-sixte (added-sixth chord); and the accord de 7e de dominante (seventh chord). For example, F-major and G-major triads, according to Rameau, complemented and reinforced C major as the tonic. The addition of dissonances of the F- and G-major triads, he illuminated their function and classified them as representing one of the three fundamental chord types. He labeled the bottom note of each of these chords, what we call today the root, as the basse fondamentale.
He also discussed how the fundamental bass of the chord remained the same despite the inversion (renversement) in which a chord appears. Rameau’s Clermont notes offered explanations of ninth and eleventh chords by suppositions, discussions of added- sixth chords, and the concept of double employment (double emploi). Furthermore,
Rameau accomplished two very important tasks in these Clermont notes. First, he diminished the multitude of figured-bass signatures to a few fundamental types; second, he revealed how composition is much easier by following his chord succession rules.
These principles in the “Clermont notes,” according to Suaudeau, were his most important ideas which lead to the development of his scientific theory of music found in
Traité.18
Traité de l'harmonie was the first treatise to recognize the needed separation of harmony from counterpoint as a compositional tool. In this treatise Rameau narrowly defined the subject of harmony in four books. Book 1, titled “On the Relationship between Harmonic Ratios and Proportions” outlined the underlying framework for
18Christensen, 24-29.
16 chords, ratios, proportions, and their existing relationships with each other. He demonstrated how chords are generated from a single source, that being the monochord. Through string divisions Rameau used the monochord to produce all of the ratios needed to build any chord. Next he labeled the consonant triad and the dissonant seventh chord as the two fundamental chord types, with all other chords originating from these two.
He emphasized the important role the monochord plays in providing the foundation for those chords that control all harmony and music.
In Book 2, “On the Nature and Properties of chords and Everything which May
Be used to Make Music Perfect,” Rameau introduced the fundamental bass (basse fondamentale). This book interpreted the chords found in Book 1 using the fundamental bass. Rameau’s most significant discovery was how the monochord and the fundamental bass produce similar interval ratios, which controlled both chord construction and succession. Book 3, “Principles of Composition” and Book 4, “Principles of
Accompaniment,” provided a detailed discussion of the text found in Book 2. Rameau claimed that composition and accompanying became easier if one used the fundamental bass.
Even after a brief survey of Traité it became clear that Rameau spent many years investigating and fine-tuning his theories. This treatise presented his ideas in the most inventive and creative form. It contained a substantial amount of his most important and fundamental principles including chord generation and inversion, the fundamental bass, supposition, and the obvious relationship between melody and harmony. Although these ideas were presented with little organization or structure, Traité consequentially was his most important treatise because it represented his debut into the theoretical community.
This same treatise, however, was criticized because many of the individual
17 elements originated from sources other than Rameau. Christensen highlighted the fact that the ideas leading up to the development of the fundamental bass were found in seventeenth- century theory, including speculative and practical texts. Many thoroughbass and compositional treatises of the seventeenth-century provided “informal guidelines that
Rameau could use as a starting point” for the fundamental bass.19 Even though Traité was hailed as the first complete theoretical treatise on harmony, Rameau may not have cared to admit his degree of dependency upon his predecessors.
At the beginning of the seventeenth century, the triad rapidly gained prominence in many treatises. Theorists such as Joachim Burmeister (1564-1629) and Johannes
Lippius (1585-1612) faithfully followed Zarlino and labeled the major triad as the most concrete and stable structure in music. They based their belief on Zarlino’s arithmetic division of the octave and fifth in his senario. By mid-seventeenth century, French theorists were divided by different styles. For instance, some theorists leaned towards the simplification of triads with even more emphasis on tonal characteristics. Opposing this was the style of exploiting dissonances in the name of expression, which permitted a subtle breakdown of tonality. French music theorists displayed characteristics from both of these styles in their thoroughbass treatises.
Thoroughbass practice became popular in France by the mid-seventeenth century.
If the thoroughbass practice had not transformed French triadic theory, Rameau might never had discovered the fundamental bass. Thoroughbass led Rameau to the realization of harmony as having been broken down into temporal units by a dominating bass line.
In Nouveau systême, Rameau wrote: “the shortest and surest means for becoming
19Christensen, 43.
18 properly sensitive to harmony is by accompanying on the harpsichord or organ, since one will always hear a most regular succession of full harmonies.”20 Through accompaniment he heard the bass line producing harmonic successions continually. As a result Rameau focused on accompaniment as the most important method to illustrate his fundamental bass theory. Moreover, he staunchly believed the complexities of accompaniment were greatly reduced and simplified by using the fundamental bass.
Before we continue our study of the fundamental bass, a brief discussion of
Rameau's harmonic and triadic theories found in Books 1 and 2 of his Traité will be presented here. Rameau begins Book 1 of his treatise by quoting this passage from
Descartes’ Compendium Musicae:
That all the consonances are determined by the first six numbers; for the sounds produced by the whole string and its different divisions correspond to the notes C,c,g,c,e,g,(if C be taken to represent the sound produced by the entire string) in which, if the Octave c be added, all the consonances will be found; for this reason all the force of harmony has been attributed to number.
That the origin and degrees of perfection of these consonances are determined by the order in which the numbers arise. Thus the Octave is the most perfect consonance; after it comes the Fifth, which is not so perfect as the Octave, then the Fourth, and so on.
That the sounds which arise form these divisions of the string give, when heard together, the most perfect harmony that one can imagine.
That all these sounds are generated for the whole string, or from its parts; but just as numbers must be related to Unity, which is the source of numbers, so must the different divisions of the string be related to the entire string in which they are contained; and the
20Thomas Christensen, Rameau and Musical Thought in the Enlightenment, (New York: Cambridge University Press, 1993), 51 quoting Jean-Philippe Rameau, Nouveau systême (Paris, 1726), 91.Christensen, 43.
19 sounds arising from these divisions must be considered as being generated from the first or fundamental sound, which is therefore the source and foundation of all other sounds. The harmony therefore resulting from the consonant intervals produced by the entire string and its divisions is not perfect unless this fundamental sound is heard below the other sounds; for this sound must appear as the principle or source of these consonances, and of the harmony which they form; it is the base and foundation.21
Shirlaw explained how important the octave is to Rameau’s theories. By defining an interval as being the difference or distance between a lower and an upper sound, the octave, with the 2:1 ratio located between the first and second partials, was Rameau's most important interval. As a result of being the most perfect consonance, the octave now functioned as the outer perimeter for all other intervals to measure against. By understanding the mathematical and physical principles of the octave, it provided him with the foundation of his harmonic theories: harmonic generation (generation harmonique), harmonic inversion (renversement), and fundamental bass (basse fondamentale). Rameau then concluded by saying the octave, being the most perfect consonant interval, was a replica or repetition of this sound.22
Referring back now to Joan Ferris’s article, “The Evolution of Rameau’s
Harmonic Theories,” Ferris showed how the concept of the octave allows Rameau to develop his theory of inversion for both intervals and chords. This first distinguishable interval to be heard after the octave, which later was established by Rameau as the backbone of harmony, was the fifth (3:2). Rameau then illustrated his principle of
21Matthew Shirlaw, The Theory of Harmony, (London: Novello & Company, Limited, 1955), 66, quoting Jean-Philippe Rameau, Traité, (1725) Bk. I, Ch. 3.
22Matthew Shirlaw, The Theory of Harmony (New York, 1969), 66.
20 inversions by explaining the interval of the fourth. As the second replica of the fundamental, the fourth (4:3) was located by finding the difference between the fourth partial and the fifth. It was seen as merely as a by-product of the fifth. Rameau continued along these same lines by using the principle of inversion to explain the minor sixth and the major third, and the major sixth and its inversion the minor third. The minor third, however, plagued Rameau throughout his career. He could not justify it because it can not be traced directly back to the fundamental or a replica of the fundamental.23 In Traité, he simply dismissed this problem by saying “the principle of the minor third seems to be different from that of the major third.”24 Consequently Rameau's three essential consonances were the fifth and the two thirds. His secondary consonances were the fourth and the two sixths.
Rameau stated that primary consonances cannot be seen as the inversion of secondary consonances; likewise, secondary consonances were totally defined by the primary consonances. However, Rameau had tremendous difficulty defining dissonances. He began by establishing the major tone (9:8) by subtracting the fourth (4:3) from the fifth
(3:2). By using mathematical concepts such as adding, cubing, and squaring, Rameau constructed other dissonant intervals. He devised other methods of establishing dissonant intervals such as chromatically altering consonances. One dissonant interval, the seventh, gave Rameau much concern. He wrestled with the possibility of the seventh actually
23Ferris. 233.
24Joan Ferris, “The Evolution of Rameau’s Harmonic Theories,” Journal of Music Theory 3, (1959): 234, quoting Jean-Philippe Rameau, Traité, trans. By Philip Gossett, (New York: Dover Publications, Inc., 1971), 13.
21 being classified as an interval. Later he abandoned the labeling of the seventh as a dissonance interval and renamed it a fundamental interval in connection with his fundamental bass concept.25 For Rameau the presence of the fundamental sound in the bottom part of the interval was not necessary because it was still considered to be the generating tone or root. He had now clearly established both consonant and dissonant intervals from the senario. Rameau continued by listing the characteristics that define a chord:
1. The chord is not to exceed the range of an octave. 2. The foundation of all chords is the fifth (is the most significant harmonic component of music). 3. Chord construction can be determined by the major or minor thirds.26
Rameau limited chords to only two basic types: the consonant accord parfait, or perfect chord, and the dissonant accord de la septieme, or seventh chord. The perfect chord, also known as the major triad, was the only chord that directly comes from the senario. He reduced all chords to either a perfect chord, a seventh chord, an inversion of either of these, or a specific type of seventh chord produced by supposition or by the addition of a sixth. When Rameau encountered chords without a perfect fifth, such as augmented or diminished chords, he viewed them as being incomplete. Chords such as ninth or eleventh chords were explained by supposition (accords par supposition).
Rameau’s intentions when discussing the basic chord types was to clarify and reduce thoroughbass harmonies. Throughout this treatise Rameau focused on thoroughbass figures and methods. His theory of inversion was designed to show every
25Shirlaw, 68.
26Joan Ferris, “The Evolution of Rameau’s Harmonic Theories,” Journal of Music Theory 3, (1959): 235, quoting, quoting Jean-Philippe Rameau, Treatise on Harmony, trans. by Philip Gossett. (New York: Dover Publications, Inc., 1971), 32.
22 chord in its primary, or fundamental, form, proving how chords may be inverted using the same process as when inverting intervals. Shirlaw summarized Rameau’s inversion theory as follows:
In the major harmony (as c-e-g), which is represented by the numbers 4:5:6, if we place 4 an Octave higher we obtain the first inversion of the harmony, that is, a chord of the Sixth (e-g-c), represented by the numbers 5:6:8. If in the same way we place 5 an Octave higher, we obtain the second inversion of the harmony, a chord of the Fourth and Sixth (g-c-e), represented by the numbers 6:8:10. We can not however here carry the process of inversion further, for if we place 6 an Octave higher, we get a chord represented by the numbers 8:10:12. But this proportion is the same as 4:5:6, and indeed represents the original harmony itself. The first chord is called Perfect; the two chords derived from it are called Imperfect; for in the case of these derived chords the fundamental sound, c, is not in this bass; it is transposed, and represented by another sound, namely its Octave.27
Rameau has thus demonstrated the intervals generated over the fundamental, that being the perfect fifth and major third, and he justified the perfect fourth and minor sixth as being complements of the fundamental. Furthermore, Rameau tried in vain to assign a relationship between the minor third and major sixth parallel to that of the perfect fifth and major third: “Since all intervals were generated by the octave and begin and end there, so should the minor third. It should not be found indirectly, between the major third and the fifth, but related directly to the fundamental sound or its octave.”28 He
27Matthew Shirlaw, The Theory of Harmony (London: Novello & Company, Limited, 1955), 68, quoting Jean-Philippe Rameau, Treatise on Harmony, trans. by Philip Gossett. (New York: Dover Publications, Inc., 1971), 40.
28Ibid, 67, quoting Jean-Philippe Rameau, Treatise on Harmony, trans. by Philip Gossett. (New York: Dover Publications, Inc., 1971), Bk. I, Ch. 3, Article 5.
23 failed to illustrate the fundamental generating the minor third and as a result diminished the possibilities of major and minor chords being related.
Although Rameau could not justify the origin or inversion of the minor third, his inversion principle alone transformed the role of the interval or chord without nullifying its harmonic use or foundation. The theory of inversion allowed him to arrange and categorize consonant and dissonant intervals. In fact, Rameau's principles of harmonic generation, fundamental bass, and the inversion of chords were very closely interrelated.
Furthermore, the inversion of intervals or chords could not exist without having been previously founded in theoretical concepts such as harmonic generation and the fundamental bass. Shirlaw pointed out the obvious lack of appreciation for Rameau's theories. Many musicians and music theorists alike refused to acknowledge a “purely acoustical phenomena science as the basis of harmony.”29 Whether we as musicians and theorists acknowledge it or not, we have accepted Rameau's principles of harmonic generation and the fundamental bass when we utilize his theory of inversion.
29Shirlaw, 75.
CHAPTER II
Rameau’s fundamental bass principle, found in the second book of
Traité, was his best attempt to simplify harmonic theory. Two leaders in the theoretical concepts of Rameau’s fundamental bass are Matthew Shirlaw and Thomas Christensen.
The information presented in this chapter has been compiled from Thomas Christensen’s book, Rameau and Musical Thought in the Enlightenment, and Matthew Shirlaw’s book,
The Theory of Harmony. The fundamental bass concept actually distinguished two distinct basses for the perfect chord: an actual sounding bass note found in the basso continuo and the fundamental bass. The fundamental bass or fundamental note (basse- fondamentale, son fondamental), known as the root, was used by Rameau to justify harmony as a real science controlled by laws of harmonic succession. This fundamental bass provided the harmonic principles overseeing the progressions of one harmony to another. The fundamental bass was the foundation of the harmony and the sole determining factor on which harmonic succession depends. As Shirlaw pointed out,
Rameau emphasized his view by saying:
Zarlino has compared the bass to the earth, which serves as a foundation for all other elements. It is called the bass of the harmony, because it is the basis and foundation of it. If the foundation were to fail, that would be as if the earth were to fail: all the beautiful order of Nature would fall into ruin; every piece of music would be filled with dissonance and confusion.
24 25
When one wishes to compose a bass, it is necessary to proceed by movements somewhat slow and separate. The higher parts may move more quickly and in diatonic [conjunct] progression.30
The fundamental bass principle was based upon the mathematical division of the monochord. Rameau states: “the string with its divisions furnishes us with a perfect harmony, the bass of this harmony resulting from the entire string, which is the source and foundation of all the other sounds.”31
Although the idea of the monochord can be traced back to both Zarlino and
Descartes, Christensen explained how Rameau utilizes the monochord in different ways.
The main function of the monochord in the past was to measure intervals. Rameau’s dilemma was producing a combination of intervals resulting in the chords he wanted.
With his theory of the son fondamental or fundamental sound, he attempted to prove how intervals are generated by separate sounds. Chords as a result were produced by the combination of intervals with the same fundamental sounds. The main purpose of the monochord was for the monochord string itself to generate intervals and chords that later functioned as the most natural resource of his harmonic principles.32
Accepting the monochord or senario as the basis for his theories, Rameau must solve the problem of generating dissonant chords. The following information was
30Matthew Shirlaw, The Theory of Harmony (London: Novello & Company, Limited, 1955), 98-99, quoting Jean-Philippe Rameau, Traité, (1725), Bk. II, Ch. I.
31Ibid., 99.
32Christensen, 90-91.
26 paraphrased from Chapter 4 of Christensen’s book entitled, Rameau and Musical
Thought in the Enlightnment, where Christensen explains Rameau’s theories of generating dissonance. Previously, Rameau controlled mathematical ratios in order to produce consonant and dissonant intervals. Since the major-minor tonal system became standard by 1722, he naturally reduced consonant chords to two fundamental triads.
Rameau solved his problem by declaring the dominant-seventh chord as the dissonant source. He came to this conclusion by the combination of appropriate thirds. This process was defined as combining major and minor thirds in ways resulting in the most commonly used chords. Rameau explained this process by stating:
To make matters simpler, we could consider thirds for the time being as the sole elements of all chords. To form all dissonant chords, we must add three or four thirds to one another. The differences among these dissonant chords are only from the different positions of these thirds.33
Rameau built chords by adding major or minor thirds above or below major and minor triads. Seventh chords produced the dissonant figures 6/4/2, 6/4/3, and 6/5/3 by using inversion. He justified all dissonant chords and their inversions using the fundamental seventh chord.
Next he explained how ninth and eleventh chords are produced by supposition. In the seventeenth century the term supposition identified non-harmonic tones and appoggiaturas sounding against consonant harmonies. Rameau, however, used supposition in a different way. Non-harmonic tones resonated against the
33Thomas Christensen, Rameau and Musical Thought in the Enlightenment, (New York: Cambridge University Press, 1993), 98, quoting Jean-Philippe Rameau, Treatise on Harmony, trans. by Philip Gossett. (New York: Dover Publications, Inc., 1971), 39.
27 fundamental seventh chord because of thirds placed beneath the fundamental bass. In
Example 3 one can see how the given ninth chord is a seventh chord on G with E functioning as a supposed bass.34
Example 3: Christensen, 99; Gossett, 89; Rameau, Traité, 76. A ninth chord with a “supposed” bass.
Dissonant suspensions were also explained by supposition. In Example 4 the 4-3 suspension illustrated how a seventh chord on D can have a supposed bass a fifth below on G.35
Example 4: Christensen, 100; Gossett, 89. Rameau, Traité, 76. A chord of suspension with a “supposed” bass.
Later in this chapter Rameau’s theory of supposition and the fundamental seventh chord will be discussed in depth.
34Christensen, 99.
35Ibid., 100.
28 Rameau’s concept of reducing harmonic theory to only two chord types, the dissonant seventh and the consonant triad, with a single generating source for both was extraordinary. This source justified all alterations of the two fundamental chord types including suspensions, added notes, and inversions. This theory proved indispensable as an aid for composers who were trying to simplify the complex musical language of harmonic theory. The background for his theory of the fundamental bass was thoroughbass. Keeping with current practices, Rameau encouraged music students to practice thoroughbass by accompanying.
Originally, the fundamental bass was meant to assist in realizing chords above the continuo bass. Accompanying was simplified by proving the relationship that exists between figured-bass signatures and using identical right-hand fingerings. Reducing all chords to specifically only two types, the consonant triad and the dissonant seventh chord, provided any accompanist the ability to realize any signature while knowing beforehand how to correctly place the corresponding triad or seventh chord with the appropriate bass note.
Christensen, on page 53 in Chapter 2 of his book, Rameau and Musical Thought in the Enlightenment, found an example taken from “Carte générale de la basse fondamentale,” which represented a brief synopsis of his fundamental bass theory. In this example Rameau produced 32 individual chords by employing the consonant triad and three different seventh chords.
29
Example 5: Christensen, 53; Rameau, Traité, 409. Rameau’s “General Table of the Fundamental Bass.”
Summarizing page 52 of Christensen’s book, the fundamental bass written below the basso continuo part showed the foundation of each chord.36 The fundamental bass in the first three chords illustrated the tonic triad. The chords located in part two were built on scale degree two from a dissonant minor-seventh chord. These twelve chords resulting from varying basso continuo notes included complex, chromatically altered chords
36Ibid., 52.
30 such as a “French” augmented-sixth chord in the minor mode and a secondary dominant chord in the major mode. Another exceptional one is the chord figured as 4.
Rameau explained this chord by using supposition; although G is in the basso continuo part, this chord was a seventh chord built on D. The third and fourth groups of chords described both dominant-seventh chords. The process of accompanying was now improved by reducing the number of required chords in the right hand down to only four, and voice leading now only entailed knowing how to prepare and resolve only four chord types. Christensen described how Rameau now established his two rules:
(1.) the seventh of each dissonant chord (the “minor” dissonance as he calls it) is usually – but not in all cases – prepared as a consonance in the previous chord and resolves downwards by step. (2.) the leading tone of a dominant-seventh chord and diminished- seventh chord at a cadence (the “major” dissonance) resolves upwards by step to the tonic note. 37
In this next example Rameau uses a succession of dissonant seventh chords to illustrate the consonant preparation and the downward consonant resolution of the seventh.
37ThomasChristensen, Rameau and Musical Thought in the Enlightenment, (New York: Cambridge University Press, 1993), 54, quoting Jean-Philippe Rameau, Treatise on Harmony, trans. by Philip Gossett. (New York: Dover Publications, Inc., 1971), 432.
31
Example 6: Christensen, 55; Rameau, Traité, 419.
In m.7 Rameau resolved the added-sixth chord upward by step to the third of the next triad. He justified this resolution by claiming that the added sixth was a “major” dissonance and therefore followed in the footsteps of the leading tone by resolving upward. Christensen explained that what Rameau was trying to prove through this example was the consolidation of voice-leading rules by using the fundamental bass.
Although the possible numerical combinations above the basso continuo may appeared to be endless, Rameau explained how there were actually very few fundamental chord progressions possible. He was not as concerned with the treatment of dissonance necessarily found in the thoroughbass treatises of the day. On the contrary, he
32 was specifically concerned with how a fundamental seventh chord was related to dissonant progressions.38 Christensen stressed that the importance of this example was to act as a reference for the fundamental bass of chords in sequential patterns.
This fundamental bass theory was not only an explanation of the fundamental note of harmony for sequential chord patterns it explained music in a scientific and mechanistic way. During the seventeenth century scientists were using the idea of mechanical motion to interpret all sciences ranging from metaphysics to biological processes. Fundamental bass was the result of Rameau’s efforts to find a mechanistic explanation for the motion of music. He was determined to prove how musical entities impact one another just as material bodies do in mechanics. He accomplished this by devoting the entire Book 2 of the Traité to the concept of fundamental bass and proving how chords connect with one another while acting as the catalyst of such motion.39
The information on the following six pages is paraphrased from Thomas
Christensen’s book, Rameau and Musical Thought in the Enlightenment, pages 105-08 and 114-16. Beginning with the fundamental bass progressions, he looked for connections between every fundamental bass note. He first discovered how these chord fundamentals naturally progress: “by those consonant intervals obtained from the first divisions of the string,” that being the perfect fifth, major and minor thirds and their inversions.40 He continues:
38Ibid., 54.
39Ibid., 106.
40Ibid.
33 Without abandoning the principle that has just been enunciated, then, we shall strengthen it even more by adding to it the principle of the undivided string. The latter contains in its first divisions those consonances which together form a perfect harmony. Thus, when we give a progression to the part representing this undivided string, we can only make it proceed by those consonant intervals obtained from the first divisions of this string. Each sound will consequently harmonize with the sound preceding it.41
Christensen emphasized that until Rameau, intervals were hierarchically ranked according to how frequently they (the intervals themselves and their respective inversions) appeared. Rameau dismissed the hierarchy idea by dividing intervals into two distinct categories: consonance and dissonance. All tonal music was reduced to consonant and dissonant intervals with the latter acting as the propelling force that disrupted the consonant intervals representing a perfect state of repose and tranquility.
He then added to this theory propositions from a physics text by Ignance-Gatson Pardies, a popular seventeenth-century Cartesian physicist. These two propositions stated that:
A moving body meeting another body which is at rest gives the body at rest all its motion and remains immobile itself. A hard body which strikes an immovable body will be reflected together with all of its motion.42
41Thomas Christensen, Rameau and Musical Thought in the Enlightenment (New York: Cambridge University Press, 1993), 106, quoting Jean-Philippe Rameau, Treatise on Harmony, trans. by Philip Gossett. (New York: Dover Publications, Inc., 1971), 59-60.
42Thomas Christensen, Rameau and Musical Thought in the Enlightenment (New York: Cambridge University Press, 1993), 107, quoting Oeuvres du R.P. Ignace-Gaston Padries, 2 vols. (Lyons, 1709), Book 2: Un discours du movement local, Proposition 18, 155; Proposition 23, 161.
34 Rameau established a connection between musical dissonances and colliding bodies and the similarities of each in their behavior. In Example 7 he illustrated his theory of colliding consonances and dissonances.43
Example 7: Christensen, 108; Rameau, Traité, 419; Gossett, 80. Perfect cadences.
By the time the dissonant suspension G found in mm. 1-2 of line 2 resolved to F, the consonant note G in line 1, m. 2 collided with it. In the last two measures we found the next collision. The consonant note G found in line 1 remained motionless after colliding with the dissonant note F in line 2, which returned to E in the last measure. Although this example provided a mechanistic analysis of the suspension, it left some questions concerning mechanistic motion unresolved. To exist as an authentic mechanistic model for music, every note must be continuously in motion by transferring the roles of consonance and dissonance back and forth. If this were the case the motion would never cease, and music would be unable to come to a resting point or stop. Another important unresolved question was how does one know where to place the first dissonant note in order to create harmonic motion? Although this example of mechanistic musical motion was far from perfect, it did provide a vision of actual musical notes colliding with
43Christensen, 108.
35 one another in temporal space.
Christensen, on pages 111-115 gives a detailed overview of how Rameau established the seventh as the fundamental dissonance and the crucial role it would play in cadential sequential patterns. The following information on the next four pages is paraphrased from Christensen’s text. Having accepted the role of dissonances as the instigator of all musical motion, Rameau now needed to explain how dissonances are generated by a single fundamental seventh harmony. Sevenths were only constructed after consonant intervals such as the perfect fifth and minor third were added together.
He desperately searched for an explanation for his theory of the seventh being a fundamental dissonance.
Rameau constructed the seventh chord by affixing a third to the major triad. The third then acted as the origin of dissonance with all seventh chords and their derivations resulting from the additions of thirds to triads. Rameau then classified these thirds as the
“major dissonance,” that being the lower major third of the seventh chord, and the “minor dissonance,” which was the upper minor third added above the triad. Although Rameau's scientific reasoning for producing the seventh as a single unit was often misunderstood, his motives were honorable. His intentions were to find the secrets of motion in music, which he discovered through the cadence parfaite.
In the seventeenth century the cadence was a topic of particular importance for
French theorists. Rameau interpreted mainly in two ways: Cadence represented a specific ornamentation or trill on the penultimate note of a phrase; or, a cadence represented a structural closing dependent upon specific scale degrees corresponding with the bass voice or the interval produced by the bass voice moving. This second
36 cadential definition was broken down further into three separate categories: cadence parfaite, cadence rompue, and the cadence imparfaite. The cadence parfaite, or perfect cadence, was defined as the bass voice and the fundamental bass voice moving to the final of a key (motion down by a fifth; from dominant to tonic). The cadence rompue, or broken cadence, also known as the interrupted cadence, described a cadential ending that avoided a perfect cadence. Finally, the cadence imparfaite, or imperfect cadence, was simply the reverse of the perfect cadence (motion up by fifth; from tonic to dominant, or from the fourth degree to the tonic).
During the seventeenth century, French theorists such as Guillaume Nivers
(1632-1714), emphasized the importance of the cadence in their theoretical treatises.
This view concerning the cadence greatly influenced Rameau in his own writings. In
Traité Rameau summarized the beliefs of his predecessors about the cadence when he exclaimed how music is an imitation of cadential motion. However, he expanded the definition of the three cadential categories by applying his own harmonic principles and connected it to his theory of harmonic motion. The cadence was the epitome of consonance and dissonance or pressure and release in music. The penultimate chord of the cadence naturally represented the pressure or dissonance that further accentuates the calming effect of the consonant chord once it resolves. The cadence parfaite or perfect cadence became his prototype. Consequently, the perfect cadence was defined as a seventh chord resolving downward to a perfect chord in which the fundamental bass progressed from the dominant to the tonic. Rameau explained the process by stating:
37
It appears natural that the penultimate chord should be distinguished by something which renders it less perfect; for if two perfect chords follow one another in a Perfect Cadence, one is unable to judge which of these chords is the true chord of repose.44
Prior to Rameau, French theorists thought about the seventh not as the catalyst of harmonic motion, but rather as a passing tone on a weak beat or as part of the 7-6 suspension. Nonetheless, the perfect cadence represented the most basic component of harmonic motion and provided the model for all other cadential progressions. In a later treatise, Code de musique pratique, Rameau clarified his views on the cadence by stating:
The single perfect cadence . . . is the origin of the diversity that may be introduced in harmony. This cadence may be inverted, broken, interrupted, imitated, and avoided, from which all variety in harmony is drawn.45
Rameau had several different cadential types. In Book 2, Chapter 5 of Traité he provides a detailed discussion of this cadence parfaite that comprises three necessary factors:
(1.) a fundamental bass descending a perfect fifth from the dominant to the tonic; (2.) a dissonant seventh ("minor" dissonance) above the dominant that must resolve downwards to the third of the tonic triad; and (3.) the leading tone ("major" dissonance) above the dominant that resolves upward to the tonic note. In Rameau's Example 8 he illustrates the perfect cadence.46
44Matthew Shirlaw, The Theory of Harmony (London: Novello & Company, Limited, 1955), 111, quoting Jean-Philippe Rameau, Traité, (1725), Bk. II, Ch. 2.
45Thomas Christensen, Rameau and Musical Thought in the Enlightenment (New York: Cambridge University Press, 1993), 115, quoting Jean-Philippe Rameau, Code de musique pratique, (1761), 93.
46Christensen, 115.
38
Example 8: Christensen, 116; Gossett, 66. The “perfect cadence.”
On pages 116-17, Christensen gave an excellent description of the cadential types perfect and broken. The penultimate chord of this cadence parfaite was labeled by Rameau as the dominant-tonic, meaning the tonic chord was defined by its dominant. This cadence occurred on other scale degrees as well and followed the same descending fifth pattern, earning the label dominant-tonic.
Although not all seventh chords resolve downward by a perfect fifth, Rameau justified this behavior by labeling this action as subordinate cadences that included the cadence rompue and the cadence irreguliere. The cadence rompue, or “broken cadence,” described an alteration in the progression of a perfect cadence resulting in an interrupted cadence. The fundamental bass now moved upward diatonically one degree to the sixth degree of the scale. This upward motion of the fundamental bass was the only component that separated the perfect cadence from the interrupted cadence; the other remaining notes above the dominant seventh chord resolved correctly. Examples 9 and
10 are good representations of the broken cadence.47
47Christensen, 117.
39
Example 9: Christensen, 117. The “broken cadence.”
Example 10: Christensen, 117. Rameau’s analysis of the “broken cadence.”
Rameau substantiated the chord resolution of this cadence by claiming it is an inverted tonic triad substituting the sixth for the dominant note of the tonic triad. He explained by saying:
The progression of the bass in the Interrupted Cadence is due to a license. A dissonance can be resolved only by the Fundamental bass descending a Fifth; if then the bass descends a Seventh or, which is the same thing, rises a Second, it is only by means of a license that this can be effected. For this interval of the Seventh owes its origin more to good taste than to nature, since it is not found among the sounds arising form the division of a string; it is this interval of the Seventh which gives rise to such a license
40 [and as a result produces an interrupted cadence].48
Although the logic behind his interpretation of this cadence contradicts itself, for example denying that the resolution chord is a submediant chord built on the sixth scale degree versus a tonic triad with a note of substitution, Rameau was more concerned with the fundamental bass cadential model.
Paraphrasing Shirlaw on page 112 of his book, The Theory of Harmony, we found the definition of the cadence irreguliere, which was the last category of cadences
Rameau describes. This cadence was simply the perfect cadence in reverse; instead of the progression being from dominant to tonic, it was from tonic to dominant. The sixth, although consonant, became dissonant against the fifth of the chord, thereby producing a chord of the “Added Sixth.” The resolution of this chord was not at all like the seventh; it resolved upwards, hence earning the name irregular (see Example 11).49
Example 11: Christensen, 118; Rameau, Traité, “Supplement 7”; Gossett, 81. The “irregular cadence.”
48Matthew Shirlaw, The Theory of Harmony (London: Novello & Company, Limited, 1955), 111-12, quoting Jean-Philippe Rameau, Traité, (1725), Bk. II, Ch. 6.
49Ibid.
41 He debated the role of the added-sixth chord continuously throughout Traité. At one point he described it as a dissonant structure coexisting alongside the dissonant seventh chord. This view, however, conflicted with his previously established theory proclaiming the seventh as the only source of dissonance. Rameau’s primary goal with this intense discussion of the addition of a sixth above the subdominant chord was to establish a predetermined progression of a tonic resolution. For Rameau, the added-sixth chord also represented the first inversion of the seventh chord on the supertonic. Actually, the added-sixth chord gave the impression of the subdominant harmony resolving to the dominant. In Example 12 the chord f-a-c-d was resolved two different ways: first as an irregular cadence found in (a); and (b) representing another resolution to first the dominant then the tonic.50
Example 12: Shirlaw, 114, Rameau, Traité, Bk. 2, Ch. 7.
Although Rameau labeled the first resolution as a “correct” resolution for the added-sixth chord, the second example may actually be the more “natural” resolution of this chord. If this is true then he has not met his main objective of a direct
50Ibid., 113.
42 tonic resolution and has weakened his own theories of tonal stability. In his later writings, specifically in the Génération harmonique, Rameau was able to decipher his unresolved issues by clarifying his views on mode and modulation.
These cadences established by Rameau represented the mechanistic motion of the fundamental bass and regulated the treatment of dissonant chords. The motion from a dissonant seventh chord resolving to a consonant triad by the fundamental bass motion of a fifth was his perfect replica of all motion in music.
The cadences (in turn) prove that there are but two chords which are essential and fundamental, namely, the Perfect chord and the chord of the Seventh; and that all the rules of harmony are based on the progressions natural to these two chords. It is from the Perfect Cadence that the principal and fundamental rules of harmony are derived.51
Referring back now to Christensen’s book, Rameau and Musical Thought in the
Enlightenment, the following information was paraphrased from pages 120-24. One of
Rameau's most celebrated analyses illustrating his theory was the famous monologue from Lully's Armide. Rameau examined this in three of his treatises: Nouveau systême,
Observations sur notre instinct pour la musique, and Code de musique pratique. In
Nouveau systême he wanted to illustrate the concept of modulation. Modulation was defined as the cadential models accentuating related scale degrees. In Example 13 a harmonic progression modulated from E minor to G major using an irregular cadence.52
51Matthew Shirlaw, The Theory of Harmony (London: Novello & Company, Limited, 1955), 114-15, quoting Jean-Philippe Rameau, Traité, (1725), Bk. II, Ch. 7.
52Christensen, 120-24.
43
Example 13: Opening of Rameau’s analysis of the monologue from Lully’s Armide. Christensen, 121, Rameau, Plate 5.1, 80-81. .
Rameau's modulation process began in m. 3 using a cadence parfaite to confirm G major as tonic. The music progressed through a series of modulations using the cadence parfaite from G major to A minor, B minor, C major, and D major. The fundamental bass made it clear that these cadences were produced from a succession of dissonant dominant-tonic chords resolving to the tonic. In order to explain why some of the dominant-tonic chords did not resolve directly to their appropriate consonant triad,
Rameau introduced the idea of evaded cadences.53 In this next example he illustrated a variety of cadences that were forced into motion by the additional dissonant note
53Thomas Christensen, Rameau and Musical Thought in the Enlightenment, (New York: Cambridge University Press, 1993), 122, quoting Rameau, Nouveau systême, Plate 5.1, 80-81.
44 found in the chord of resolution.
Example 14: Christensen, 123. Rameau’s chain of “evaded cadences.”
In (this) example we find two evaded perfect cadences (AB, GH), an evaded irregular cadence (FG), and four “broken cadences” (BC, CD, OP, RS). In between we find three properly resolved perfect cadences (HJ, LM, TV), a “passing” tonic (N), as well as sequential chains of simple (diatonic) dominants (AAA, DEF, QR, ST).54
Through this example Rameau clearly demonstrated the urgency of dissonant chords wanting to resolve. Rameau explained all other dissonant chords, including ninths, elevenths, and suspension chords as being generated by the seventh. As Christensen explained, Rameau was fully aware “that suspensions were melodic retardations
54Christensen, 122-23.
45 of consonances.”55
Christensen also stated that “chords by supposition serve only to suspend sounds which should be heard naturally.”56 He searched for an even better explanation of the suspension process by using supposition. Christensen summarized Rameau's inquiry concerning supposition when he wrote:
In essence, Rameau observed that all suspensions behave suspiciously like the minor seventh, that is, they each normally prepare and resolve in identical ways. He suspected that the seventh might indeed be the source of the suspension if one allows that the continuo bass "supposes" the true fundamental of the chord that actually lies above it. The argument is not, as it is often made out to be by historians [such as Shirlaw], simply that the octave is the "boundary" of all intervals. While Rameau indeed made this point, the real issue for him was that dissonance should be reduced to a single source if at all possible, and the seventh seemed to serve as that source.57
In Example 15 Rameau illustrated how a fundamental bass can be “supposed” a third and fifth below the continuo bass.58
55Ibid., 123.
56Ibid.
57 Thomas Christensen, Rameau and Musical Thought in the Enlightenment (New York: Cambridge University Press, 1993), 124, quoting Jean-Philippe Rameau, Treatise on Harmony, trans. by Philip Gossett. (New York: Dover Publications, Inc., 1971), 299.
58Christensen, 123.
46
Example 15: Christensen, 124. Rameau’s illustration of “supposition.”
The perfect cadence was clearly indicated by the descending fifth fundamental bass pattern. Some of the obstacles Rameau faced when trying to explain this process included the chord of the augmented fifth (found in m. 3). Being rooted in both the
French Baroque and the eighteenth century, these chords presented him a wealth of problems, such as a chord possibly performing both tonic and dominant functions simultaneously (see m. 3), or the resolution of the chord actually being anticipated and therefore distorting the role or function of the chord (m. 4). In “L’ Art de la basse fondamentale”, Rameau attempted to clarify his views by stating:
The suspension is nothing but the retardation of what naturally be heard according to the most perfect fundamental succession by fifth. This suspension is frequently drawn from the same principle as supposition, but in practice it is better to consider the note which forms it as a note of taste. . .. This note of taste in principle is only a dissonant fourth or ninth. The fourth suspends the third, and the ninth suspends the octave.
Rameau continued by saying:
A suspended note is only a [product] of taste; it has no fundamental bass, and if one assigns one to it, it is only in order to satisfy oneself in seeing that its origin is most often to be drawn from the supposition.
47 But as this is of no use in practice, it is better to recognize the note of suspension as counting for nothing [by itself] and assigning it the fundamental bass of the consonance that it suspends and that immediately follows it.59
The distinction between the suspension and supposition plagued Rameau until 1760 when he wrote Code. The suspension differs from supposition in that the suspension chord was incomplete, meaning the seventh chord of the fundamental bass was not fully stated, while the chord of supposition was complete. The location of the dissonant note was also different for each situation: In a suspension the dissonant note occurred in an inner voice while the basso continuo sustained the fundamental note of the chord for its duration; on the other hand, in a supposition the basso continuo was always the dissonant (non- harmonic) tone.60 Of all his theoretical treatises, Rameau attempted to clarify his views on the suspension and supposition in the Code de musique pratique (1760). Although he attempted to clear up any confusion he created concerning this subject, there was one idea Rameau was very clear on: The dissonant seventh is the only true catalyst of all harmonic motion.
59Thomas Christensen, Rameau and Musical Thought in the Enlightenment (New York: Cambridge University Press, 1993), 125-26, quoting Jean-Philippe Rameau, Treatise on Harmony, trans. by Philip Gossett. (New York: Dover Publications, Inc., 1971), 90.
60Christensen, 128.
CHAPTER III
In Book III of Traité Rameau stated that "harmonic succession is nothing but a connected series (enchainment) of Tonics and Dominants."61
He applied his mechanistic theory to the nature of harmony as well, believing that harmony was an imitation of the perfect cadence with the fundamental bass descending a fifth or ascending a fourth. Having already established the need for the dissonant seventh to resolve to a consonant triad, he proved how all harmonic successions are simply cadences pressing onward toward a resolution. As Shirlaw pointed out, Rameau clearly illuminated his ideals of a perfect harmonic world: a sequence of dominant-tonics descending by a circle of fifths to the final tonic (see Example 16).
61Matthew Shirlaw, The Theory of Harmony (London: Novello & Company, Limited, 1955), 121, quoting Jean-Philippe Rameau, Traité, (1725), Bk. III, Ch. 27.
48 49
Example 16: Gossett, 408; Rameau, Traité, Bk. IV, Ch. 8. The progression of seventh chords and their derivatives by inversion.
Rameau described this as “the essence of the most natural harmony . . . to which we often become habituated before understanding it.”62 Shirlaw provided an excellent description of Rameau’s theories of harmonic succession summarized on pages 124-29 from his book entitled The Theory of Harmony. For Rameau, each consonant harmonic succession
62Thomas Christensen, Rameau and Musical Thought in the Enlightenment (New York: Cambridge University Press, 1993), 129, quoting Jean-Philippe Rameau, Treatise on Harmony, trans. by Philip Gossett. (New York: Dover Publications, Inc., 1971), 408.
50 depicted new tonics and fundamental basses. Consequently, Rameau was able to justify his use of dissonance and dissonant seventh chords by stating:
As soon as the leading-note appears in a dissonant chord it is certain that it determines a conclusion of melody, and therefore it must be followed by the “perfect” chord upon the key-note; where- as if the leading-note does not appear in a dissonant chord, the conclusion is not determined.63
The dissonant note had the authority to determine key, and, as previously stated, it compelled the dominant seventh to resolve to the tonic. The dominant-seventh chord contained both the major dissonance, which rises a semitone, and the minor dissonance, which descended a semitone or tone. Since every tonic chord represented consonant harmony, all other chords will be dissonant. He also stated that if the dissonant note was not literally present in the chord then it was to be assumed. He explained the tonic triad as a consonant chord that experienced a period of rest or complete repose. All other existing chords were labeled by Rameau as seventh chords. On the other hand, not all harmonic successions were simple dominant-tonic to tonic cadential chord progressions.
The inconveniences of “secondary” cadential progressions for example, subdominant to dominant, disturbed his notion of the fundamental bass descending a fifth. Eventually, regardless of the key, all non-tonic chords were assumed to be seventh chords even though the seventh scale degree was not present in the chord. This assumption caused
Rameau some difficulty when he refigured the basso continuo parts and added
63Matthew Shirlaw, The Theory of Harmony (London: Novello & Company, Limited, 1955), 124, quoting Jean-Philippe Rameau, Treatise on Harmony, trans. by Philip Gossett. (New York: Dover Publications, Inc., 1971), 410.
51 fundamental bass to works by Corelli. He attempted to explain mechanistic harmonic motion in Corelli’s Op. 5 Sonatas, where he found many inconsistencies with Corelli’s use of dissonant treatment ranging form individual chord progressions to key changes. In his treatise of accompaniment, the Dissertation sur les diférentes métodes d'accompagnement pour le clavecin (1732), Rameau refigured Corelli’s basso continuo notation. He assigned the continuo part new symbols and claimed these new chord symbols were used in any diatonic progression (see Example 17).64
Chord Symbol
Tonic Triad (C-E-G) C Dominant Seventh (B-D-F-G) X Minor Seventh (C-D-F-A) 2 Added Sixth (C-E-G-A) aj Four Three (C-E-F-A) 4/3 Four (C-D-G) 4 Seven (C-E-G-B) 7
64Christensen, 59.
52
Example 17: Christensen, 59; Rameau, Dissertation (1732). Rameau’s figured-bass notation for Corelli’s Sonata Op. 5 no. 3.
He proceeded by explaining his new theory of connecting chords by using all common tones between the chords with the right hand in close position while the outer voices move by stepwise and contrary motion. He furthered his discussion of Corelli’s Sonata in chapter 23 of the Nouveau systême de musique theorique, where he discussed the idea of key or tonality as related to the dissonances. He believed Corelli’s lack of essential dissonances distorts any perception of key and harmonic continuity. Therefore, he assigned himself the task of refiguring Corelli’s harmonies.65
Fundamental Bass Progressions
A detailed, annotated translation of Rameau’s critique of Corelli’s sonatas was found in
65Lester, 306.
53 Appendix 1, pages 305-19 of Joel Lester’s Compositional Theory in the
Eighteenth Century. The following information on pages 58–75 was paraphrased from his book. Rameau began his critique by reviewing his concept of fundamental bass progressions following the cadential patterns of a perfect cadence (descending-fifth root progression), an irregular cadence (ascending-fifth root progression), a broken cadence
(stepwise root progressions), and an interrupted cadence (descending root progressions by thirds). In Example 18 he assigned a fundamental bass progression.66
Example 18: Lester, Compositional Theory in the Eighteenth Century, Appendix I, 306. Corelli, Sonata No. I, First Allegro, m. 5; mm. 9-10.
In this same example Rameau discussed harmonic sources for these chords:
Since the source of the Harmony is the same in these two different progressions A-B and C-D, consequently the Notes A and C must be figured the same. But Corelli seems to have judged them only according to the Violin, which makes a Sixth and Fifth from Note A,
66A detailed annotated translation of Rameau's critique of Corelli’s sonatas is found in Appendix 1 of Joel Lester's Compositional Theory in the Eighteenth Century (Cambridge: Harvard University Press, 1992) 305-19.
54
while it only makes a Sixth from Note C. The same problem appears in numerous other passages in the same Allegro and elsewhere.67
He was puzzled by Corelli’s lack of consistency in his basso continuo. The descending- fifth root progression was the most appropriate choice for a dominant-seventh chord emphasizing Rameau’s strongest cadential motion, the perfect cadence. Corelli’s choice of stepwise root progression was inappropriate because it alludes to the subsidiary cadence rompue or broken cadence.
Six-Four Chords In the next few examples he criticized Corelli’s misuse of the 6/4 chord. Example 19 shows a 6/4 chord in the key of G major; however, the D-major key signature conflicted with this interpretation of the chord.
Example 19: Lester, 307; Rameau, Traité, 93.
67Joel Lester, Compositional Theory in the Eighteenth Century, (Cambridge: Harvard University Press, 1992), 306, quoting Rameau, Traité, (1725), 93.
55
He stressed the descending-fifth bass-line progression as being the more accurate progression when approaching a dominant chord. In the following examples Rameau continued his discussion of the 6/4 and 4/3# chords.68
Example 20: Lester, 307; Corelli’s Sonata No. I, first Adagio; Sonata No. I, first Allegro, mm. 29-30; Sonata No. I, first Allegro, mm. 38-39; Sonata No. I, second Adagio, mm. 23-24; Sonata No. 2, first Adagio, mm. 8-9; Sonata No. 3, first Allegro, m. 28; Sonata No. 10, first Adagio, m. 17.
He began by explaining:
6/4 must be figured above Note C to indicate the perfect Chord of the principal Tone, which must naturally follow the Dominant heard at Note B. This 6/4 is even more necessary because Note D is in the Chord of that principal Tone and not at all in the Chord of the Dominant. If Note L is figured correctly, then Notes G and J are figured incorrectly, since each of these notes has a different fundamental
68Lester, 307.
56 bass. Note L represents the principal Tone; Note G makes the Fifth of the Dominant [i.e., of a seventh chord], and Note J makes the third [of a Dominant]. Thus, each of these Notes must be figured in relation to the Chord of the fundamental Tone that they represent [i.e., in relation to the root of that chord], conforming to the style of figuring adopted by Corelli. Consequently, 6/4 must be figured for a Note a Fifth above a principal Tone [i.e., a fifth above the root of a chord], as at L; 4/3 for a Note which is a Fifth above a Dominant or a Third above a Subdominant [i.e., a fifth above the root of a seventh chord or a third above the root of an added-sixth chord], as N; and 6/5 for a note a Third above a Dominant, as at A in [Example 18].69
Rameau was expressing his distaste for Corelli’s chord choices. These examples explained why the triad was an unsuitable choice for the notes because they were not tonics.
Non-Harmonic Tones
In this next example Rameau discussed Corelli’s use of non-harmonic tones.
Example 21: Lester, 309; Rameau, Traité, 97. Corelli’s Sonata No. 9, second Allegro, m. 12.
69Joel Lester, Compositional Theory in the Eighteenth Century, (Cambridge: Harvard University Press, 1992), 307-08, quoting Rameau, Traité, (1725), 97.
57
The same error is found in [Example 21]. The Violin alone should have informed Corelli that Note Q carries no Harmony, and that on the contrary it is Note R that carries it. Consequently, the 7/5 figured on Note Q is worthless.70
Rameau was more concerned with how the tones that are assigned thoroughbass figures function harmonically. In this situation Note Q was interpreted as a non-harmonic tone and therefore does not merit thoroughbass figuration.
Chord Choices
Corelli’s Sonatas, Example 20, restated for reference.
70Joel Lester, Compositional Theory in the Eighteenth Century, (Cambridge: Harvard University Press, 1992), 309, quoting Rameau, Traité, (1725), 98.
58
When Corelli employed the harmony of an irregular Cadence from Note P [Example 20] (as can be recognized by the Sixth added to the perfect Chord of the Subdominant, which then descends immediately by a Fourth in the Fundamental Bass, he could well have anticipated that the same Cadence takes place from X to M in [Example 20]. But when one does not know the source of the Harmony, the figured Melody [Chant figure] sometimes disguises it so much that the Ear can be fooled, as one sees here.
And if one wished to go by the most perfect progression in the Fundamental bass at Note F in [Examples 20], one would see that Note F must instead be figured with a 9 rather than with a 7, since the Note stipulating the 9 would have been expressly written in the Fundamental Bass, while only a custos would have marked the note which stipulates the 7.
The 7 which the Fundamental bass stipulates at Note F introduces an imitation of the interrupted Cadence into [the piece], whereas the 9 that [the Fundamental Bass] stipulates there introduces an imitation of the perfect Cadence. Now this is not a Harmonic Connection where the Key changes, which must happen when interrupted Cadences are thus used [where there is no key change], this is done more by accident and involuntary than by knowledge.71
He refused to accept Corelli’s use of this cadence. An interrupted cadence was defined by Rameau as the ascending-fifth bass motion, whether from the tonic to dominant or from the fourth scale step to the tonic. Since cadential motions represented key changes, this progression moved downward by a third with no key changes present, and therefore does not fit his definition of an irregular cadence. Corelli’s use of quarter rests also displeased Rameau, as we can see from the following example.
71Joel Lester, Compositional Theory in the Eighteenth Century, (Cambridge: Harvard University Press, 1992), 309-10, quoting Rameau, Traité, (1725), 97.
59
Quarter Rests
Example 22: Lester, 312; Corelli, Sonata No. 6, first Allegro, m. 42.
There is another thing to take note of in this composer: when he uses some quarter-note rests in his Basso Continuo, he does not indicate the Chord that must be played during that rest [Example 22].
If the rest followed a principal Tone, there would be nothing to say in such a case. But since this rest is between two Dissonances, of which the first must be resolved and of which the second must be prepared, one can not then dispense with sounding the Harmony that exists during that rest.
Since it is up to the Accompaniment to furnish the source of the Harmony, it is absolutely obligatory always to make the necessary Connection felt there. Without this Connection a defective gap is found there, at least in a passage where the rest not only interrupts the necessary Connection but destroys it.
This is so because the [proper] manner of laying out a Basso Continuo can never suspend that Connection.72
This connection referred to the link found between individual chords produced by the thoroughbass. Putting a rest in the thoroughbass disrupted the flow of each chord progression and confused the harmonic organization of the phrase.
72Joel Lester, Compositional Theory in the Eighteenth Century, (Cambridge: Harvard University Press, 1992), 312-13, quoting Rameau, Traité, (1725), 100.
60
Double Employment Rameau covered several of his basic ideals such as double employment, unprepared minor dissonances, and evading cadences in this next example.
Example 23: Lester, 313; Corelli, Sonata No. 7, first Allegro, mm. 26-31.
The first Fundamental Bass ends here in the Key of F major at A, and resumes immediately afterward in D minor at D, which is related to it. The second Fundamental Bass maintains the Key of D minor by means of an irregular Cadence between G and H. The third Fundamental Bass once again maintains the Key of D minor by means of an interrupted Cadence between J and L. Note here that one can cause a listener to confuse the irregular Cadence G-H and the imitation of the perfect [Cadence] L-M. The first Note of each of these Cadences (G and L) gives the same harmonic source. But by virtue of the Cadences that they announce, one can take either one or the other as fundamental. [Rameau labels this process as double employment.]
The first rest can be realized as is, because the [preceding] Connection ends there on the principal Tone. The other rests can not do without the source of the Harmony which must support the Connection there. In any case, if one could provide a Connection
61
during this example solely by means of the Chords that Corelli figured, we would be wrong to condemn him. But note well that according to the Connection of the Basso Continuo Melody and that of the Violin, only the Key [Modulation] of D can be understood, and that Key is absolutely destroyed by the Chord figured at N, which according to the Violin must impart to us the Key of F.
We do not insist on this source of the Key, if it could be brought about and followed by a Connection relative to that of the Melody. But on the contrary, one can not follow Corelli’s figuring thereby considering the Violin line without sounding some unprepared minor Dissonances [chord sevenths], or without imitating a broken Cadence, while the Melody gives no occasion for such a cadence.73
Rameau thought of cadential patterns as the only explanation of sequential progressions.
Measures 29-30 illustrated unprepared minor dissonances; the last beat of m. 29 was interrupted as a C dominant-seventh chord with an unprepared B-flat rather than an E- diminished chord. His ideas of a broken cadence originated from mm. 30-31with the C- seventh chord moving to a D-minor triad.74
73Joel Lester, Compositional Theory in the Eighteenth Century, (Cambridge: Harvard University Press, 1992), 313-14, quoting Rameau, Traité, (1725), 102.
74Ibid.
62
Suspension versus Supposition
Example 24: Lester, 316; Corelli, Sonata No. 5, second Adagio, mm. 10-11 and 25-26.
In these last two examples there is a Connection that terminates only the 6 that follows the 7 at Note G, as one can also learn from the melody of the violin in the Composer's score. The leading Tone which announces the end of this Connection is marked there precisely by a sharp or a natural; thus there must not be any Chords between that of the Dominant A and that of the principal Tone D. Nevertheless, Corelli figures one new [chord] between that of the Dominant A and that of the principal Tone D in the first passage, and two new Chords in the other. What does one conclude from such an error? If Corelli really meant to claim that the Chord figured with a 7 on the Notes labeled G was the same as the Chord on the Dominants at Notes A, he could have easily seen that this 7 in no way indicated such a Chord. Moreover, seeing as he was careful to mark the leading Tone everywhere with a sharp or with a natural (which must indicate the leading Tone), how would he have forgotten this here if he had been aware that the leading Tone must remain in the Harmony until the principal Tone, D at Note D?75
Rameau understood the source of these 7-6 suspensions was the supposed ninth chord.
75Joel Lester, Compositional Theory in the Eighteenth Century, (Cambridge: Harvard University Press, 1992), 315-16, quoting Rameau, Traité, (1725), 103.
63 As Lester clearly explained, the first chord functions as a D-seventh chord with a supposed B-flat followed by a G-minor triad resulting in implied parallel octaves in the bass.
Implied Dissonances
In her article entitled “The Development of Rameau’s Thoughts on Modulation and
Chromaticism,” Cynthia Verba provided a detailed discussion about Rameau’s implied dissonances in his harmonic analysis of the monologue from Lully’s Armide. The following information regarding implied dissonances on the next five pages of this thesis was paraphrased from both Verba”s , “The Development of Rameau’s Thoughts on
Modulation and Chromaticism” and Joel Lester’s, Compositional Theory in the
Eighteenth Century. In Nouveau systême and Observations sure notre instinct pour la musique, Rameau added a fundamental bass analysis and explained progressions by the addition of implied dissonances. Lully’s recitative Enfin il est en ma puissance, from
Armide, is presented in this next example.
64
Example 25: Verba, “The Development of Rameau's Thoughts on Modulation and Chromaticism,” p. 73- 74. Lully’s recitative Enfin il est en ma puissance from Armide.
In Nouveau systême Rameau analyzed the passage mm. 13-23 in the key of G major. See
Example 26.
65
Example 26: Lester, 137. Rameau 1726, p. 82-84. Basso continuo figures in brackets absent in Lully’s 1686 edition (facsimile in Verba, 74). Remarks below the fundamental bass paraphrase Rameau.
Rameau found an example of mechanistic motion, a perfect cadence by ascending fifth, beginning in m. 14 as the music progresses from G major to C major, A minor, E minor,
A minor, D major, and G major in m. 19. This passage ended with a brief circle of fifth progressions back to G major. The first example of Rameau adding an implied dissonance was found in m. 15 with the addition of a sixth to A resulted in the subdominant of E. In order to avoid stepwise motion of the fundamental bass, he placed an A in the fundamental-bass, which confirmed the A, dominant-tonic seventh chord moving to D major by an ascending fourth fundamental bass progression motion.
Finally, in m. 20 the music moved the E-minor ninth chord to the dominant-tonic on A
66 resulting in a circle of fifth progression back to G major.76
Twenty-eight years later in his treatise Observations sur notre instinct pour la musique (1754) Rameau analyzed this same passage in response to a challenge from
Jean-Jacques Rousseau (1712-78). Rousseau’s Lettre sur la musique française (1753) openly criticized this passage of music from Armide that Rameau hailed as a fine example of French music. As seen in this next example from Observations, Rameau built on his concept of implied dissonances.
Example 27: Verba, 80; Rameau, Observations, 98.
Rameau’s harmonic interpretation of this passage conflicted with Rousseau’s. Rameau viewed this portion of Armide as a series of expressive modulations paralleling the intensity of the text. This intensity was brought about by Rameau expanding his earlier concept of implied dissonances to explain non-tonic harmonies as dominant-tonics with accidentals included rather than ordinary seventh chords. The expressiveness of the text was a result of these added dissonances as the music modulated through keys G, C, D, and G. Rousseau viewed these modulations as disconnected, neutral, and a poor
76Lester, 137.
67 representation of the text. One interesting observation about this entire conflict over the effects of implied dissonances on harmonic content was the fact that Rameau reanalyzed this passage. His original analysis of this monologue, which appeared in the Nouveau systême, was quite different from the analysis we find in Observations.
Example 28: Verba, 80; Rameau, Nouveau, 94.
Rameau analyzed this passage in Nouveau systême as a non-chromatic and non- modulation progression in the key of G supporting the expressive text. During this time of his life, Rameau’s concept of modulation did not include the use of implied chromatics for rapid modulations. However, in Observations we found a shockingly different analysis of the same passage. Here Rameau used modulation and implied chromatics simultaneously to harmonically support the text.
By 1754 his idea of frequent modulation incorporated the concept of implied dissonances. The rapid modulations, beginning in m. 18 through the end of m. 21, corresponded with the emotionally changing text. Suddenly, the simple diatonic analysis found in Nouveau seems like a harmonically incorrect representation of this text. Which analysis correctly represented Rameau’s true interpretation? The answer was both. His concept of modulation with the use of chromaticism was born
68 in the Traité and continued to develop throughout most of his later works.
Minor Dissonances
Returning now to Corelli’s sonata, Rameau’s use of minor dissonances is the next subject of discussion found in Example 29.77
Example 29: Lester, 317. Corelli Sonata No. 8, first Allegro, mm. 12-14.
The Cadence is broken from G to A, or from G to H [in the Fundamental Bass], and the Cadence is irregular from J to L [both times]. We do not know if the faulty passage indicated here has been taken as a model, but many Musicians have fewer scruples about using it than they have about making two consecutive Octaves. Such a fault [moving to a 6 chord a step above a dominant seventh] may be excusable in one situation but not in another. For instance, whenever one can assume that the Notes carry no Harmony, or whenever one separates the Dissonance from the Harmony, provided that the natural progression of a minor Third does not suffer, in such cases the Sixth figured on Note A is good.78
77Lester, 317.
78Ibid., 317-18.
69
In this passage Rameau was trying to clear up the confusion caused by several dissonances. He focused on the progression from notes G-A, because the seventh of the dominant remains into the next harmony.
Rameau concluded his discussion of Corelli’s analysis by giving credit to the composer. He claimed that Corelli’s works did fall into the category of genius; however, the errors that he made were unacceptable for a man of his talents. If Corelli had correctly understood the rules of accompaniment, these thoroughbass errors would not have occurred. Acknowledging the compositional stylistic changes between Corelli’s music and the music of the 1720s, Rameau encouraged musicians to be more inspired by the rules for accompaniment rather than what their ear told them.
Throughout this entire analysis Rameau was acting in two contrary roles. First he wanted to prove how the omission of dissonances disrupted the flow of harmonic direction. Therefore, he replaced simple chords with more intricate and complicated dissonances and supposed chords. On the other hand, Rameau was intelligibly trying to act as speculative theorist by refocusing the harmonic direction of Corelli’s works.
Dissonances did function for Rameau as the catalyst for all mechanistic motion in music.
As we shall see in the following chapters, Rameau's theories will be tested even further by applying them to his own music as well as to Lully’s and Telemann’s.
CHAPTER IV
As previously stated, Rameau’s theory of fundamental bass was to be used as a pedagogical tool to simplify instruction in composition and thoroughbass. The purpose of the fundamental bass was to reveal the foundation or root of each chord. Although
Rameau continued to revise his fundamental bass theory throughout his treatises, he did not extensively apply this theory to his own music. The purpose of this chapter is to present a test case study and analysis of Rameau’s fundamental bass theory as it is applied to the music of the French overture style. In addition to Rameau’s overtures, those by Lully and Telemann, composers representing France and Germany, were chosen for this study to allow comparison both chronologically and nationally.
The application and analysis of Rameau’s theory of fundamental bass was accomplished by establishing specific categories. These categories represented a possible method for validating the practicality of his theory for music from that time. The categories were based on Rameau’s analysis of Corelli’s sonatas and my own research.
The analysis categories applied to each overture include: mechanistic motion, double employment, supposition, and transformation. The criterion for each analysis category was determined by Rameau’s own theories. Examples for each category are listed here in the body of the text. Other examples for each category are listed in the Appendix.
70 71
Mechanistic Motion
This was the principle of harmonic motion in music or how one chord moves to the next. He based this principle on the perfect cadence, the dominant-tonic moving to a tonic with a perfect fifth fundamental bass motion. In today’s terminology, these terms translate into a dominant-seventh chord and a tonic chord. The catalyst of this harmonic motion was the minor-seventh relationship of the dominant seventh chord; it was the presence of this dissonant note that caused motion in music. Seventh chords were his invention. Until Rameau, very little was said about how one chord moves to another.
There was much discussion about how melodies and single lines moved; however, the idea that harmony moved was a new and different idea for the time. Examples of mechanistic motion were easy to recognize in Rameau’s own music. In m. 65 of his overture Castor et Pollux we find an excellent example of mechanistic motion. The A- major tonic chord on beat one changes into a dominant-seventh chord by the addition of the seventh G on beat 2. Then the A dominant-seventh moves to the D-tonic chord on the downbeat of m. 66. It was the addition of this seventh that allowed the A-tonic chord to move (see Example 30).
72
Example 30: Rameau Castor et Pollux, mm. 64-67.
Mechanistic harmonic motion in the music by Lully and Telemann can be seen in
Examples 31 and 32. In mm. 8-12 of Telemann’s Ouvertüre D-Dür, the D tonic triad changes into a dominant-seventh chord with the addition of the seventh on the first beat in m. 9. The actual movement of the D dominant- seventh chord is prolonged until m.
11, where it moves to its tonic chord on A in the first half of beat 1. On the second part of beat 2 the process is repeated when the A-tonic chord added the seventh, G, becoming an A dominant-seventh chord that resolves in m. 12 to its tonic D-major.
73
Example 31: Telemann Ouvertüre, mm. 8-12.
Another example of mechanistic motion is found in mm. 6-7 of Lully’s Cadmus et
Hermione. The E triad became a dominant-seventh chord on the second part of the beat 3 in m. 6, which resolved to its tonic an A-major chord in m. 7.
74
Example 32: Lully, Cadmus et Hermione, mm. 6-7.
Although this model of mechanistic motion explained the majority of motion in music, it could not stand alone and account for every situation. Other principles such as double employment and supposition were added to this model to deal with musical situations that did not fit the model exactly the way he thought that they should.
Double Employment
Rameau introduced the principle of double employment in Traité and continued to develop it throughout his remaining treatises. With this principle he attempted to justify the motion of the subdominant to the dominant seventh. This progression presented a fundamental-bass succession by a second that
75 contradicted his idea of mechanistic motion model of music ascending or descending a perfect fifth in the fundamental bass.
Double employment explained those fundamental bass motions as descending by a fifth instead of ascending stepwise motion, therefore proving how all fundamental bass motions could be found within his perfect cadence mechanistic model of harmonic motion. To do this Rameau changed the harmonic function of the subdominant chord to be either a simple dominant or a subdominant with an added sixth. A simple dominant chord was defined as any minor-seventh chord that is not a dominant-seventh. The subdominant with an added sixth is simply an added-sixth chord built on the subdominant scale degree as the root.
When the subdominant chord was changed to either a simple dominant or an added-sixth chord, the fundamental bass progression of a second or stepwise motion was avoided. Stepwise motion in the fundamental bass does not make for a good harmonic progression. Rameau approached every chord as if it had an implied dissonance.
Dissonance made music move and was the source of all motion in music. Dissonance could be reduced to two types: the dominant-seventh chord and the added-sixth chord, which in a way was a mirror reflection of the dominant-seventh chord (see Example 33).
76
6/5 7
Example 33: McKinney
Example 33 presented C-F-G-C, a typical I-IV-V-I progression in the key of C. Rameau analyzed the fundamental bass progression as follows: the motion of C to F was a strong harmonic motion. The next motion from F to G (IV-V) was not a good harmonic progression. The F chord, FAC with the fundamental bass being F, must have had an implied dissonance in order to move. Thus the subdominant chord changed functions and became an added-sixth chord. The 6/5 above the F chord indicated the D that was implied. Then sometime before it moves on to the next chord we understand it in its next sense as a chord with the fundamental bass note D. Rameau wrote two fundamental bass notes even though there was only one bass note present in the basso continuo part. Now the D was not the dissonant note; C is. The 7 written above the D indicated that it was now a dominant-seventh chord with a proper dissonant note leading to G in the next bar.
This motion D to G was now a type of perfect cadence with the bass moving down by fifth. The two types of dissonances used included: the first one being the F chord with the D as the implied dissonance; the next interpretation was a D chord with C as the implied dissonance. This solved both problems. By using double employment a chord could be doubly employed, one type of dissonance going in and another type
77 going out.
A literal example of double employment in Rameau’s music was found in mm.
73-77 of La Princesse de Navarre. Here we find a clearly illustrated example of the relationship between the subdominant leading to the dominant via the implied dissonance, which was evidently spelled out rather than just implied. The progression C-
F-D-G-C is seen in mm. 73-75 and restated starting with the second half of m. 75 through m. 77.
Example 34: Rameau, La Princesse, mm. 73-77.
78
In Example 35 we find the similar chord progression, C-F-G-C, which illustrated
Rameau’s double employment principle in Lully’s Alceste.
Example 35: Lully, Alceste, mm. 36-38.
Double employment is seen again in Telemann’s Ouvertüre, mm. 89-90.
79
Example 36: Telemann, Ouvertüre, mm. 89-90.
After the G-tonic chord moved to the subdominant chord on C, the subdominant chord now added the necessary implied dissonance, A, in order to move to the D-dominant chord, thus producing a strong harmonic motion. More examples of double employment can be seen in the appendix.
Supposition
The principle of supposition, introduced in Chapter 2, was Rameau’s concept of all other dissonant chords, including suspension chords, as being generated by the seventh. Through supposition Rameau solved the resolution of suspensions by changing every descending suspension into a minor dissonance or chord seventh, and every
80 ascending suspension into a major dissonance or leading tone. At the end of Book II of
Traité, Rameau included his motet Laboravi in which examples of supposition can be found. In the penultimate measure, D-C# is a 4-3 suspension over the bass A (see
Example 37).
Example 37: Lester, 109; Rameau Traité Bk. 2, Ch. 10; Gossett, 358.
The D resolves as a seventh over E, with the bass A below that E. Now the D functions as the new seventh; the E is the fundamental bass over the supposed bass of A. Here was a perfect illustration of the supposed bass totally separate from the seventh chord resolving the dissonance. The first example of supposition I found in Rameau’s
81 music was in La Princesse located in mm. 7-8 (see Example 38).
Example 38: Rameau, La Princesse, mm . 7-8.
On the downbeat of m. 8 we find a 6-5/4-3 double suspension; Rameau analyzed this suspension as a cadential 6/4. There were two possible interpretations for this suspension. The first stemmed from the 6-5 suspension A-G over the fundamental bass
C. The A became the seventh scale degree over the new fundamental bass B-flat with C as the supposed bass (see Example 39).
82
Example 39: Rameau, La Princesse, mm. 7-8, fundamental bass analysis.
The second interpretation was the 4-3, F-E, suspension over the fundamental bass C. The fourth scale degree, F, was now the new seventh with G as the fundamental bass with C being the supposed bass (see Example 40).
Example 40: Rameau, La Princesse, mm. 7-8, fundamental bass analysis.
83 In Example 41 Rameau used supposition to explain ninth chords.
Example 41: Rameau, Hippolyte et Arcie, m. 45.
In m. 45 of Rameau’s overture Hippolyte we find an F ninth chord, F A G E, with F as the fundamental bass. Through supposition the ninth scale degree, G, became the seventh of an A-minor seventh chord with F as the supposed bass.
Examples of supposition were found in all of Lully’s overtures. Beginning with
Alceste in mm. 2-3 there was a 4-3 suspension, D-C, with A as the bass. Through supposition the D became the new seventh with A as the supposed bass and E as the fundamental bass (see Example 42).
84
Example 42: Lully, Alceste, mm. 2-3. In mm. 27-28 of Amadis another 4-3 suspension, D-C# over A, was found (see Example 43).
Example 43: Lully, Amadis, mm. 27-28.
85
The fourth scale degree, D, became the new seventh with E as the fundamental bass and
A as the supposed bass. The 9-8 suspension was found in Cadmus with B becoming the new seventh over C as the fundamental bass with A as the supposed bass (see Example
44).
Example 44: Lully, Cadmus, mm.17-18.
In the next two examples we found similar supposition examples in the overtures by
Telemann (see Examples 45 and 46).
86
Example 45: Telemann, Ouvertüre, mm. 3-4.
Example 46: Telemann, Ouvertüre, m. 27.
87 Rameau wants all dissonances to be understood as coming from the motion of the fundamental bass. In principle, Rameau wants us to understand the suspension as having its origin in supposition even if we did not think of the fundamental bass every time.Through supposition Rameau provided theoretical consistency for the resolutions of dissonances, therefore explaining what suspensions really are. With this discovery
Rameau boasted that for the most part all thoroughbass figures were now thought of in terms of seventh chords.
Transformation
The transformation theory is a subcategory of the Mechanistic Model. Transformation explained such instances as when a stable chord, such as a tonic, transforms into an unstable chord by adding a seventh that needs to move forward. A perfect scenario of the transformation category was illustrated when a major or minor triad becomes a dominant seventh then moves a fifth higher or lower. For instance, in example 47 we find in m. 65 an A-major triad on beat 1 that transformed into a dominant-seventh chord on beat 2, ultimately resolving to D in m. 66.
88
Example 47: Rameau, Castor, mm. 64-66.
Another example of transformation occurred in mm. 22-23 of Rameau’s Castor et Pollux.
This example, however, presents us with yet another way of achieving mechanistic motion.
89
Example 48: Rameau, Castor, mm. 21-23.
In m. 22 we find a C-minor triad on beat 1 that then transformed into a C-major triad on beat 2. This kind of unequivocal transformation continued by adding the seventh, B-flat, to yet again transform the C-major triad into a C dominant-seventh ultimately resulting in a resolution to an F-major triad in m. 23. Although significantly fewer examples of transformation were found in Telemann, one clear example was found in Lully’s Alceste.
90
Example 49: Lully, Alceste, mm. 1-2.
Once again we find in m. 1 an A minor triad transforming into an A major triad on beat 3.
In Summary
These categories best represented Rameau’s theories in music. Mechanistic Motion symbolized Rameau’s idea of perfect harmonic motion in music, root motion by fifth.
Double Employment existed as a means of fitting a common harmonic progression, such as a IV to V, into his model of root motion by fifth. Supposition existed to explain the motion of suspensions using the model of the perfect cadence. Finally, the
Transformation category took into account stable chords recreating themselves in order to allow the harmonic motion to continue. These categories and examples best exemplify
Rameau’s theories of harmonic motion in music.
CHAPTER V
The motive throughout Traité de l’harmonie, in particular Book 3, was the investigation of characteristic interrelationships between chords. The idea of music viewed as a scientific process reduced to mathematical equations for musical construction troubled Rameau throughout his career. Since Rameau was unable to identify a single source to generate more than one chord naturally in harmony, some theorists believed all his energy and efforts spent on his theory of chord generation was in vain. Rameau’s theory could not explain or correct all harmonic progressions found in works by Lully,
Rameau, and Telemann. Therefore, he created additional concepts of double employment and supposition to accommodate his situation. Rameau’s perceptions and hypothesis about chord generation and the fundamental bass were ahead of the time.
To summarize, Rameau’s fundamental bass was represented in a harmonic progression. It was initially intended to serve as an analytic device for root movements in chords and their inversions. The application of Rameau’s theory of supposition proved to have more success in explaining suspensions and suspension chains in works by all three composers. Despite these complications, Rameau’s theory of fundamental bass reinforced his main objective to think of music as a scientific process. The movement of one chord to another was now thought of as a foreordained consequence of musical law.
The significance of his fundamental bass theory was that it allowed Rameau to create hypotheses and through experimentation to discover “the laws which govern harmonic
91 92 succession; in essence, a real science of harmony.”79
Through fundamental bass the mechanistic model of musical motion was conceived, which in turn proved the abstract origin and logical successions of harmonic progressions. The mechanistic model of music was clearly established in the analysis of the overtures by Lully, Rameau, and Telemann due to fundamental-bass theory. To condemn Rameau’s theory for any confusion is a grave mistake. It was Rameau who fought his way through all of his current day theoretical struggles and reduced all harmonies to triads and seventh chords. In fact, he was a pioneer in theory of the vertical approach to harmony. Rameau provided a new model, a fundamental bass, which indicated not only the origin of harmonies but how these harmonies progressed in music over time. His theory of fundamental bass was the ammunition needed for the most important theoretical revolution of the eighteenth century and is an exceptional description of music from that time.
79 Shirlaw, The Theory of Harmony, 88.
BIBLIOGRAPHY
Anthony, James R. French Baroque Music. New York: W.W. Norton & Company, Inc., 1974.
Bernard, Jonathan. “The Principle and the Elements: Rameau’s Controversy with d’Alembert.” Journal of Music Theory 24 (1980): 37- 62.
Buelow, George. “Heinichen’s Treatment of Dissonance.” Journal of Music Theory 6 (1962): 216-74.
______. Thorough-bass Accompaniment According to Johann David Heinichen. Los Angeles: University of California Press. 2nd ed. Ann Arbor: UMI Research Press, 1986.
Boomgaarden, Donald R. Musical Thought in Britain and GermanyDuring the Early Eighteenth Century. New York: Peter Lang, 1987.
Christensen, Thomas. “Science and Music Theory in the Enlightenment; D’Alembert’s Critique of Rameau.” Ph.D. diss., Yale University, 1985.
______. “Rameau’s L’Art de la Basse Fondamentale.” Music Theory Spectrum 9 (1987): 18-41.
______. “Eighteenth-Century Science and the Corps Sonore: The Scientific Background to Rameau's Principle of Harmony.” Journal of Music Theory 31 (1987): 23-50.
______. Rameau and Musical Thought in the Enlightenment. New York: Cambridge University Press, 1993.
Cohan, Albert. “17th - Century Music Theory: France.” Journal of Music Theory 16/1-2 (1972): 16-35.
Dart, Thurston. The Interpretation of Music. London: Hutchinson & CO. LTD, 1964.
93 94 Dolmetsch, Arnold. The Interpretation of the Music of the XVII and XVIII Centuries. London: Oxford University Press, 1946.
Donington, Robert. The Interpretation of Early Music. New York: St. Martin's Press Inc., 1963.
______. Baroque Music: Style and Performance. London: Faber & Faber, 1982.
Ferris, Joan. “The Evolution of Rameau’s Harmonic Theories.” Journal of Music Theory 3 (1959 ): 231-56.
Gessele, Cynthia. “The Institutionalization of Music Theory in France: 1764-1802.” Ph.D. diss., Princeton University, 1989.
Girdlestone, Cuthbert. Jean-Philippe Rameau: His Life and Work. New York: Dover Publications, Inc., 1969.
Grant, Cecil Powell. “The Real Relationship between Kirnberger’s and Rameau’s Concept of Fundamental Bass.” Journal of Music Theory 21 (1963): 324-38.
Hargrave, Mary. The Earlier French Musicians. London: Kegan Paul, Trench, Trubner & CO., LTD., 1929.
Harman, Alec. Late Renaissance and Baroque Music. London: Barrie & Rockliff, 1959.
Hefling, Stephen E. Rhythmic Alteration in Seventeenth and Eighteenth Century Music. New York: Schirmer Books, 1993.
Heyer, John Hajdu. Jean-Baptiste Lully and the Music of the French Baroque. New York: Cambridge University Press, 1989.
Hyer, Brian. “Before Rameau and After.” Music Analysis 15 (1996): 75-100.
Keane, Sister Mary. The Theoretical Writings of Jean-Philippe Rameau. Washington: Catholic University of America Press, 1961.
Keiler, Allan. “Music as Metalanguage: Rameau’s Fundamental Bass.” Music Theory: Special Topics (1981): 83-100.
95 Keller, Hermann. Thoroughbass Method. New York: W.W. Norton & Company, Inc., 1965.
Kiernan, Colm. “The Enlightenment and Science in Eighteenth Century France.” Studies on Voltaire and the Eighteenth Century 59 (1973).
Krehbiel, James. “Harmonic Principles of Jean-Philippe Rameau and His Contemporaries.” Ph.D. diss., Indiana University, 1964.
Lester, Joel. Compositional Theory in the Eighteenth Century. Cambridge: Harvard University Press, 1992.
______. “An Analysis of Lully from circa 1700.” Music Theory Spectrum 16 (1994): 41-61.
Lewin, David. “Two Interesting Passages in Rameau's Traité de l'harmonie.” In Theory Only 4 (1978): 3-11.
Marshall, Robert L. Studies in Renaissance and Baroque Music in Honor of Arthur Mendel. Hackensack, NJ: Joseph Boonin, Inc., 1974.
Neumann, Frederick. Essays in Performance Practice. Ann Arbor, MI: UMI Research Press, 1982.
Newman, Joyce. Jean-Baptiste de Lully and his Tragedies Lyriques. Ann Arbor, MI: UMI Research Press, 1979.
Ohl, John F., and Carl Parrish. Masterpieces of Music Before 1750. New York: W.W. Norton & Company, 1951.
Paul, Charles. “Rameau's Musical Theories and the Age of Reason.” Ph.D. diss., University of California, Berkeley, 1966.
______. “Jean-Philippe Rameau (1683-1764), The Musician as Philosophe.” Proceedings of the American Philosophical Society 114 (1976): 140-54.
Parrish, Carl. A Treasury of Early Music. New York: W.W. Norton & Company, 1958.
Rameau, Jean-Philippe. Treatise on Harmony. Translated by Philip Gossett. New York: Dover Publications, Inc., 1971.
96 Sadler, Graham and Albert Cohen. “Jean Philippe Rameau.” The New Grove French Baroque Masters. New York: W.W. Norton & Company, 1986.
Shirlaw, Matthew. The Theory of Harmony. London: Novello & Company, Limited, 1955.
Sloan, Lucinda Heck. The Influence of Rhetoric on Jean-Philippe Rameau's Solo Vocal Cantatas and Treatise of 1722. New York: Peter Lang, 1990.
Scott, R.H.F. Jean-Baptiste Lully. London: Peter Owen Limited, 1973.
Verba, Cynthia. “The Development of Rameau’s Thoughts on Modulation and Chromaticism.” Journal of the American Musicological Society 26 (1973): 69-97.
______. “Rameau’s Views on Modulation and Their Background in French Theory.” Journal of the American Musicological Society 31 (1978): 467-79.
SCORES
Lully, Jean-Baptiste. Lully-Opera. Edited by Henry Prunieres. New York: Broude Brothers Limited, 1966.
Rameau, Jean Philippe. J.P. Rameau-Complete Works. Edited by C. Saint- Saens. New York: Broude Brothers Limited, 1968.
Telemann, Georg Philipp. Orchestral Suite in F Minor. Wolfenbuttel: Karl Heinrich Moseler Verlag, 1977.
______. Ouverture D dur. Wiesbaden: Breitkopf & Hartel, 1981.
______. Suite in D. London: Musica Rara, 1935.
97
APPENDIX
The appendix is divided into four sections; grouped according to category. Examples listed have not been mentioned in the text and have been renumbered.
MECHANISTIC MOTION
Rameau, Castor et Pollux
Example 1, Rameau, Castor, mm. 52-57.
98 99
Example 2, Rameau, Castor, mm. 58-60.
Example 3: Rameau, Castor, mm. 108-13.
100
Example 4: Rameau, Castor, mm. 114-19.
101
Example 5: Rameau, Castor, mm. 120-25.
Rameau, Hippolyte et Aricie.
Example 6: Rameau, Hippolyte, mm. 5-7.
102
Example 7: Rameau, Hippolyte, mm. 13-14.
Example 8: Rameau, Hippolyte, mm. 15-16.
103
Example 9: Rameau, Hippolyte, mm. 26-30.
Example 10: Rameau, Hippolyte, mm. 48-52.
104
Example 11: Rameau, Hippolyte, mm. 58-63.
Rameau: La Princesse de Navarre
Example 12: Rameau, La Princesse, mm. 1-4.
105
Example 13: Rameau, La Princesse, mm. 7-9.
Example 14: Rameau, La Princesse, mm. 15-20.
106
Example 15: Rameau, La Princesse, mm. 21-27.
Example 16: Rameau, La Princesse, mm. 28-30.
107
Example 17: Rameau, La Princesse, mm. 61-68.
Example 18: Rameau, La Princesse, mm. 84-88.
108
Example 19: Rameau, La Princesse, mm. 104-09.
Lully: Alceste.
Example 20: Lully, Alceste, mm. 10-12.
109
Example 21: Lully, Alceste, mm. 18-20.
Example 22: Lully, Alceste, mm. 34-36.
110
Lully: Cadmus et Hermione.
Example 23: Lully, Cadmus, mm. 19-22.
Example 24: Lully, Cadmus, mm. 63-65.
111
Lully: Adamis.
Example 25: Lully, Adamis, mm. 9-11.
Example 26: Lully, Adamis, mm. 19-20.
112
Example 27: Lully, Adamis, mm. 28-29.
Example 28: Lully, Adamis, mm. 31-34.
113
Telemann: Suite 1 for Trumpet, Strings, and Basso Continuo.
Example 29: Telemann, Suite, mm. 1-4.
114
Example 30: Telemann, Suite, mm. 26-33.
115
Example 31: Telemann, Suite, mm. 51-53.
Example 32: Telemann, Suite, mm. 61-65.
116
Example 33: Telemann, Suite, mm. 66-69.
117
Telemann: Ouvertüre D-Dur für 2 Trompeten, Pauken, Streichorchester und Basso
Continuo (Cembalo).
Example 34: Telemann, Ouvertüre, mm. 23-31.
118
Example 35: Telemann, Ouvertüre, mm. 34-39.
119
Example 36: Telemann, Ouvertüre, mm. 43-44.
Example 37: Telemann, Ouvertüre, mm. 52-54.
120
Example 38: Telemann, Ouvertüre, mm. 60-65.
121
Example 39: Telemann, Ouvertüre, mm. 66-71.
122
Example 40: Telemann, Ouvertüre, mm. 72-77.
123
Example 41: Telemann, Ouvertüre, mm. 78-80.
Example 42: Telemann, Ouvertüre, mm. 98-101.
124
DOUBLE EMPLOYMENT
Rameau: Castor et Pollux.
Example 43: Rameau, Castor, mm. 70-75.
Example 44: Rameau, Castor, mm. 120-23.
125
Rameau: Hippolyte et Aricie.
Example 45: Rameau, Hippolyte, mm. 20-25.
126
Example 46: Rameau, Hippolyte, mm. 29-33
127
Rameau: La Princesse de Navarre.
Example 47: Rameau, La Princesse, mm. 53-62.
128
Lully: Alceste.
Example 48: Lully, Alceste, mm. 5-7.
Lully: Cadmus et Hermione.
Example 49: Lully, Cadmus, mm. 9-11.
129
Example 50: Lully, Cadmus, mm. 35-36.
130
Telemann: Suite 1 for Trumpet, Strings and Basso Continuo.
Example 51: Telemann, Suite, mm. 9-10.
Example 52: Telemann, Suite, mm. 70-71.
131
Telemann: Ouvertüre D-Dur für 2 Trompeten, Pauken, Streichorchester und Basso
Continuo (Cembalo).
Example 53: Telemann, Ouvertüre, mm. 40-41.
Example 54: Telemann, Ouvertüre, mm. 56-57.
132
Telemann: Ouvertüre-Corona Werkreihe Für Kammerorchester.
Example 55: Telemann, Corona Werkreihe, mm. 41-42.
133
SUPPOSITION Rameau, Castor.
Example 56: Rameau, Castor, mm. 40-45. Measures 40-41: the ninth scale degree, F, is the new seventh with G as the new fundamental bass, and E-flat as the supposed bass. Measures 41-42: the B-flat from the G-minor triad is now the seventh with C as the fundamental bass. Measures 42-43: the ninth scale degree, E-flat, is the new seventh with F as the fundamental bass and D as the supposed bass. Measures 43-44: the A from the F-major triad is now the seventh with B-flat as the fundamental bass. Measures 44- 45: the ninth scale degree, D, is the new seventh with E-natural as the fundamental bass and C as the supposed bass.
134
Example 57: Rameau, Castor, mm. 46-51. Measures 45-46: the G from the E-flat major triad is now the seventh with A as the fundamental bass. Measures 47-48: the ninth scale degree, F, is the new seventh with G as the fundamental bass and E-flat as the new supposed bass. Measures 49-50: the F from the D-minor triad is now the seventh with G as the fundamental bass.
135
Example 58: Rameau, Castor, mm. 52-57. Measures 51-52: the D from the B-flat major triad is now the seventh with E-flat as the fundamental bass. Measures 54-55: the fourth scale degree, B-flat, is now the new seventh with C as the fundamental bass and F as the supposed bass.
136
Example 59: Lully, Alceste, mm. 30-33. Measure 30: the D from the D-minor triad is the seventh with E as the fundamental bass. Measure 31: the C from the C-major triad in m. 30 is now the seventh with D as the fundamental bass. On beats 3 and 4, the B from the B-minor triad is now the seventh with C as the fundamental bass. Measure 32: the A from the A- minor triad found in m. 31 is now the seventh with B as the fundamental bass. On beats 3 and 4, the G from the G-major triad is now the seventh with A as the fundamental bass. Measure 33: the F from the F-major triad found in m. 32 is now the seventh with G as the fundamental bass. On beats 3 and 4, the E from the E-minor triad is now the seventh with F as the fundamental bass.
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Lully, Cadmus. Example 60: Lully, Cadmus, mm. 14-18. Measures 16-17: the fourth scale degree, C, is now the new seventh with D as the new fundamental bass and G as the supposed bass.
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Example 61: Lully, Cadmus, mm. 31-36. Measures 32-33: the A from the A-major triad is now the seventh with B as the fundamental bass.
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Example 62: Lully, Cadmus, mm. 37-42. Measures 36-37: the ninth scale degree, B, is now the new seventh with C as the fundamental bass and A as the supposed bass. (See example 52 for m. 36.) Measures 38-39: the E from the A-minor triad is now the seventh with F as the fundamental bass. Measures 40-41: the G from the G-major triad is now the seventh with A as the fundamental bass.
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Example 63: Lully, Cadmus, mm. 43-48. Measures 43-44: the C from the C-major triad is now the seventh with D as the fundamental bass.
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Example 64: Lully, Cadmus, mm. 49-54. Measures 48-49: the ninth scale degree E is the new seventh with F as the fundamental bass and D as the supposed bass. (See example 54 for m. 48.) Measures 50-51: the fourth scale degree A is the new seventh with B as the new fundamental bass and E as the supposed bass. Measures 51-52: the E from the A-minor triad in m. 51 is the new seventh with F as the fundamental bass.
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Example 65: Lully, Cadmus, m. 55-60. Measures 55-56: the D from the D- minor triad is the new seventh with E as the fundamental bass. Measures 57-58: the G from the G- major triad is the new seventh with A as the fundamental bass. Measures 59-60: the G from the G-major triad is the new seventh with A as the fundamental bass.
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TRANSFORMATION Rameau, Castor.
Example 66: Rameau, Castor, mm. 90-95. Measure 91: the D-major triad transforms into a D dominant seventh then moving to the G-minor triad in m. 92. Measure 93: D- major triad transforms into a D dominant seventh then moving to a G-minor triad in m. 94.
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Example 67: Rameau, Castor, mm. 108-13. Measure 110: the D-major triad transforms into a D dominant seventh then moving to G-minor triad in m. 111. Measure 112: D- major triad transforms into a D dominant seventh then moving to a G-minor triad in m. 113.
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Rameau, Hippolyte.
Example 68: Rameau, Hippolyte, mm. 26-30. Measure 26: the D-major triad transforms into D dominant seventh and then resolves to a G-major triad. Measure 27: the G-major triad transforms into a G dominant seventh that resolves to a C-major triad in m. 28. Measure 28: the C-major triad transforms into a C dominant seventh that resolves to a F- major triad in m. 29. Measure 29: the F-major triad transforms into F dominant seventh which resolves to a B-flat major triad in m. 30.
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Example 69: Rameau, Hippolyte, mm. 48-52. Measure 49: the A-major triad transforms into an A dominant seventh that resolves to a D-major triad in m. 50. Measure 51: the D-major triad transforms into a D dominant seventh that then resolves to a G-major triad in m. 52.
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Lully, Alsceste.
Example 70: Lully, Alceste, mm. 34-37. Measure 34: the E-major triad transforms into an E dominant seventh that resolves to an A-major chord in m. 35. Measure 35: the D- major triad transforms into a D dominant seventh that then resolves to a G-major triad in m. 36.