Preface to a Graduate Course in the History of Music Theory

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As a doctoral degree certifies (among other things) to a breadth of knowledge in the field, one requirement for the Ph.D. in music theory should be a scholarly course surveying the history of theory. To decide on this requirement, however, is easier than to decide what the course should cover.1 It might presumably be limited to theorists who have written in English, German, and the Romance languages, but even so one must cope with the fact—alluded to by Arthur Mendel (1968, p. 149)—that "We call a 'theorist' everyone who ever set words on paper about music."

To select from this literature I would use four criteria. These can be satisfied to a remarkable degree (though by no means entirely) through writings in English or available in English translation. I should like to discuss each of the four criteria in turn, and refer merely by the author's name and a date to the items listed in the bibliography which follows.


People with a theory degree are typically asked to teach counterpoint, harmony, or analysis. I believe that a familiarity with (and due reflection on) the historical mainstream of these pedagogical disciplines will give the teacher-to-be a distinct advantage in sophistication and discrimination.

In addition to someone such as Franco of Cologne (circa 1260) for medieval discant, students in the course should encounter Tinctoris (1477), Zarlino (1558), Bernhard (circa 1660), Fux (1725), Cherubini (1835), Bellerman (1877), and a modern composer-teacher on counterpoint, as well as Marpurg (1753-54) and Gédalge (1900) on fugue. A good secondary source is Crocker (1962) on discant, counterpoint and harmony; also worth consulting if time permits would be Marco (1961) on Zarlino's rules of counterpoint, Palisca (1956) on Vincenzo Galilei's counterpoint treatise in relation to the seconda prattica, Cohen (1971) on supposition and the changing concept of dissonance in Baroque theory, and Sevier (1976) on Ahle's treatment of voice leading and dissonance.

For the history of harmony Lester's brief account (1974) of root position and inverted triads in theory around 1600 may provide an appropriate preface to Heinichen (1728, on the application of thoroughbass principles to composition), Rameau (1722), Kirnberger (1774-79), G. Weber (1817-21, said to have been the first to use Roman numerals), A.B. Marx (1837), Fétis (Traité complet . . . , 1844, especially Book 3), Rimsky-Korsakov (1885), and at least one representative twentieth-century writer such as Schenker (1906) or Schoenberg (1911, or better, Structural Functions . . . , 1954). There is an abundance of useful literature in English. Beach (1974) on the origins of harmonic analysis, Mekeel (1960) on the harmonic theories of Kirnberger and Marpurg, Grant (1977) on the relation between Kirnberger's and Rameau's concept of the fundamental bass, and Mitchell on chord and context in eighteenth-century theory (1963) and modulation in C.P.E. Bach's Versuch (1970) might be looked at by most or all students, leaving to those with a special interest in Rameau the possibility of reading D'Alembert's elegant presentation of his theories (Eléments de musique, 1752), Ferris (1959) on their development, Verba (1973) on his ideas of modulation and chromatics, and for amusement Hayes (1974) on his instructions for playing thoroughbass without knowing how to read music.

Secondary literature connecting, in their historical context, concepts of harmony and of tonal structure would be Jacobi (1967) on harmonic theory in England after the time of Rameau, and Simms (1975) on the contributions of Choron and Fétis to the theory of tonality. Koch (1782), Vogler (1778-81), Galeazzi (1796) and perhaps Kollmann (1799)—or at least some of the secondary literature on their analytical essays—would provide the proper background for Marx (1845) and any one or two of the many late nineteenth-century and early twentieth-century writers—perhaps an Englishman such as Tovey or Prout—on sonata form and related concepts (related in that they all provide something of a descriptive or schematic "program" to guide the listener through the movement). The secondary literature on Koch et al. includes Ratner (1956) on eighteenth-century theories of period structure, William Newman (1963, pp. 19-42) on contemporary descriptions of classical sonata form, Nancy Baker (1976) on Koch's theory of melody, Churgin (1968) on Galeazzi, Weiss (1968) on Reicha, Moyer (1969) on Marx and nineteenth-century concepts of sonata form, Cole (1969) on eighteenth-century and nineteenth-century concepts of sonata-rondo form, and Jane Stevens (1971 and 1974) on those of concerto first-movement form.

Ian Bent's article on "Analysis" for The New Grove surveys a broad range of approaches that have been exercised in the last one hundred years.

Schenker is perhaps the indispensable twentieth-century figure (for this course) on tonal analysis. Beach's bibliography (1969) should be used, along with Forte (1959) on his concept of musical structure and Grossman's translation (1968) of his essay on organic structure in sonata form. The Fünf Urlinie-Tafeln (1933) and Oster's translation of Der freie Satz should be encountered. A helpful glossary of symbols used in graphing is appended to volume I of The Music Forum (1967). Among critical views of Schenker that of Michael Mann (1949) is well suited to this course. If any followers of Schenker merit a place in a course on the history of theory, I would put Salzer first (1952 and 1967), as he modified and extended Schenker's theories significantly with his concept of modal-contrapuntal tonality.


In general, writings that illuminate the history of compositional techniques should be favored, because theory students are usually more interested in composition than in performance, acoustics, psychology, aesthetics, or sociology.

Ars Nova theory of rhythmic notation (de Vitry circa 1315 and de Muris 1319) should be considered with particular reference to the contemporary development of the isorhythmic motet. Notice should be taken of sixteenth-century advice to compose the voice parts in score rather than in succession (Aaron 1523 and Coclico 1552). A sampling of German Baroque theory of rhetorical figures (Burmeister 1599 and 1606, Nuncius 1613, Thuringus 1625, Bernhard circa 1660, Kircher 1673, Walther 1708 and 1732, and Mattheson 1739) and of the affects (Werckmeister 1702 and Heinichen 1711 as well as Mattheson 1739, Quantz 1752, and Marpurg 1763) should be included because it is so vital to an understanding of the music of the period. The Medieval and Renaissance background has been set out by Gallo (1977) and Warren Kirkendale (1979). Lennenberg (1958) on Mattheson, Buelow (1966) on Heinichen, Palisca (1972) on Burmeister's analysis of Lasso, and Butler (1977) on fugue and rhetoric are other good secondary sources in English. Among writers on temperament, preference should be given to those who discuss its relation to harmony and its effect on "transpositions" (sequences and modulations as well as transpositions in the modern sense) and on the different affective potential of different keys in the eighteenth century (for example, Werckmeister 1697, Rameau 1726 and 1737 and Riccati 1762; see Lindley on "Temperaments" in The New Grove). A number of sources on various aspects or techniques of improvisation—such as organum, discant, melodic embellishment, thoroughbass and fantasia-playing—should be looked at because the improvisational procedures were so often transferred to written composition. One might ignore what C.P.E. Bach's Versuch says about fingering or rubato, and merely glance at what it says about embellishing, but the last chapter—on improvising a fantasia—should be read. Spiess (1948, Vol. 1) on organum theory, F.T. Arnold (1932) on thoroughbass manuals, and Horsley (1963) and Brown (1976) on diminutions and embellishment are good modern surveys. Morley (1597) might serve as an accessible and representative primary source on improvised Renaissance discant, to supplement Ferand (1961).

Theorists who were themselves great composers or who had a particularly close relation to a great composer should be favored. One should read Monteverdi (1605) on seconda versus prima prattica (and therefore Artusi 1600 on Monteverdi; a good modern account is Palisca 1968); some paragraphs from Wagner (1851)2 on text setting; Schoenberg on Klangfarbenmelodie (1911, pp. 506-7) and dodecaphony (1946), and Webern on Schoenberg's early music (in Arnold Schoenberg, Munich, 1912), Hába (1925 and 1927) on microtonal music; Ciconia on semitones (circa 1405; see Clercx 1955, pp. 53-62); and Padre Martini and Albrechtsberger on fugue since they taught Mozart and Beethoven respectively.

Students with a particular interest in Bach have a rich vein of theoretical writings to take an interest in; notes after Bach himself on thoroughbass (1725); the books of his son Carl Philipp Emanuel and his pupil Kirnberger; perhaps also the writings of Mizler as a former pupil; Heinichen, whose Generalbass Bach admired and became a selling agent for; Marpurg on Bach's fugues; Sorge for citing him on temperament; and Scheibe for his criticism of the "artificial" quality of his music. For many of these, excerpts in The Bach Reader would suffice for this course.


A number of treatises and topics which might not find a place in the course by the first two criteria are nevertheless so likely to be regarded by a musicologist as belonging to the history of music theory that they should be encountered, however superficially, by every advanced theory student.

Boethius is a prime example of a writer in this category, and perhaps the only non-musician who is so important to the history of theory that his entire treatise (circa 500) should be looked at. Other influential non-musicians are Augustine (circa 400, see Knight 1948), Cassiodorus (circa 550), Isidore of Seville (circa 625) and Alcuin (circa 800); Jean de Muris (1319); Mersenne (1636); and Helmholtz (1863) and Ellis.

There have also been some accomplished musicians who wrote historically important treatises about some aspect of their art which might, however, be of only slight interest to many present-day theory students: Odo of Cluny (circa 935) and Guido of Arezzo (circa 1025); Johannes de Grocheo (circa 1300); Marchetto of Padua (1310s; see Pirrotta 1955); Ramis (1482) and his opponents (see Jeppeson 1941); Caccini (1602); Leopold Mozart (1756) and Quantz (1753); Berlioz (1843) and Rimsky-Korsakov (1896). The encyclopaedic writings of Jacques de Liège (circa 1330; see Smith 1968); Ugolino of Orvieto (circa 1440; see Seay 1955); Tinctoris and Gafurio (Clement Miller 1968 summarizes Gafurio's Practicae Musicae); Zacconi, Cerone (see Gallo 1968) and Praetorius; Kircher, Tevo (see Gallo 1967), Nassarre, and Walther; and Riemann and D'Indy should be surveyed. Certain relatively minor treatises might be included because they represent so nicely some aspect or moment of the history of theory. I am thinking of Aurelian of Réôme (circa 850, exemplifying the Carolingian renaissance), Arnaut (circa 1440, applying fifteenth-century science to the devising of instruments), and Descartes (1618, at the threshold of the Enlightenment). The total of all these is obviously unwieldy, and can only be dealt with by a combination of guided browsing, thematic summaries, and bibliography.

Many treatises can be represented well enough in this course by a brief description and excerpt (especially those which are significant for only one or two things); and for many others it would suffice to do little more than examine the chapter headings and grasp the meaning and spelling of the title. The ability to tell something about a treatise from such an examination is valuable in its own right. A person well informed about what kinds of books have been written on music can usually "place" an unfamiliar work in a few moments and then proceed efficiently to find out whether the first impression was correct.

To complement or review the fruits of this "browsing" technique the course should include in some form a summary account of certain recurring themes of music theory which have little or no direct bearing on harmony, counterpoint, analysis, or composition. Among these are: musica mundana, musica humana, and musica instrumentalis and similar classifications (Pietsch 1929) and related social distinctions such as musicus vs. cantor; natural vs. artificial music (Bower 1971); harmony of the spheres (Spitzer 1963, Bragard 1929, and Walker 1978); monochord ratios and Latin terminology for proportions; myths about the origin of music and its power; musica rhythmica and musica metrica in medieval theory (Crocker 1958 is a particularly calm guide); solmization (Lange 1900) and the Guidonian hand (Waesberghe 1969); species of fourth and fifth, and the diatonic, chromatic and enharmonic genera; the thirteenth-century rhythmic modes (Knapp 1952 is one good source); musica ficta (Lowinsky 1964 seasoned by Apel 1972 and Jacobs 1968); the church modes and early concepts of key (Andrews 1935 on medieval theory; Chailley 1960; Atcherson 1973 on key and mode in seventeenth-century theory; and Tolkoff 1973 on French modal theory before Rameau); humanistic ideals from Greek music theory (Walker 1941-42 and perhaps Herman's work in progress on V. Galilei); microtonal divisions of the octave (Mandelbaum 1961); tactus and the bar line (Apel 1940, end of Part II, vs. Mendel 1968 on tactus, and perhaps Carpenter 1968; Houle 1960 on the musical measure as discussed by theorists from 1650 to 1800) and modern theories of rhythm (Alette 1952 and Smither 1960); and—insofar as they were deemed by their practitioners to be a branch of music theory—acoustics (Dostrovsky 1975 on seventeenth-century vibration theory, and Truesdell on later writers in The New Grove s.v. "Physics of Music") and psychoacoustics (for example, Pilker 1966 on the history of experiments in the musical interval sense). To set out these themes need not be as time-consuming as the list suggests, since most of it would be a matter of refining and organizing what students will already have learned, and many of the readings listed here can be summarized in class rather than assigned. This course is the place, however, to cultivate an appreciation for the philological approach to terminology, as exemplified by the Handwörterbuch der musikalischen Terminologie (Eggebrecht et al., 1972 as well as by special studies like those of Grant (1977) on "fundamental bass" and Haar (1971) on Zarlino's definitions of fugue and imitation. Students cannot be equipped for valid philological work in one year, but at least they ought to know what it is.

If a proper balance of approaches is embodied in the course—a blend of contact with primary sources in facsimile, excerpts in translation, and secondary readings—bibliographical surveys can then readily extend a student's grasp just as intelligent browsing and philological overviews can do. I think the psychological "context," in this sense, of a bibliography is as vital pedagogically as the qualities of thoroughness or discrimination in the bibliography itself. At first glance a list of writings usually informs us of our ignorance, and yet one hallmark of a learned person is that this information can be endured through a certain confidence due to the shapeliness and weight of what he does know. I would therefore delay the bibliographical aspect of the course, and then preface it with a reading and discussion of Reaney (1964) on the question of authorship in medieval treatises, Seay (1971) on French Renaissance theory and Jean Yssandon, Hoffman (1953) on nineteenth-century German treatises; and perhaps Chenette (1973) or Jamie Kassler (1971) on British Enlightenment theory. Cohen et al. (1972) on national predilections in seventeenth-century theory, and Palisca's article on "Theory" in The New Grove and its appended bibliography are also valuable surveys. Sixteenth-century theory books are listed in Davidsson (1962), and Lesure (1971) offers a comprehensive list of theory books to 1800. Also comprehensive, though by no means complete, are the bibliographies of manuscript treatises from the Carolingian era to 1400 by Waesberghe (1961) and Fischer (1968). Coover on translations (1959 and 1969) would be invaluable to this course, and students should be familiar with the listings headed 29tr, 39tr, 49tr, etc., in Adkins and Dickinson (1977 or any later edition).

The multivolume Geschichte der Musiktheorie forthcoming under the auspices of the West German Staatliches lnstitut für Musikforschung (but with several chapters by Americans) should also be mentioned here. It will complete the undoubtedly worthy task of making Riemann (1920) obsolete beyond repair.


Apart from exchanging ideas with musicological colleagues, pursuing a theoretical interest in composition, and teaching counterpoint, harmony and analysis, a music-theory expert may occasionally encounter colleagues in a nonmusical discipline who, having read some of the psychology, aesthetics, sociology, or modern physics of music, will expect him likewise to know some of these writings.

Here especially, lack of time for a solid platform of readings must be compensated by a judicious bibliographical and terminological scaffolding with two or three well-chosen planks across it. Yet this part of the course, if well organized, could give students an invaluable perspective on the whole enterprise of music theory, a habit of asking by and for whom it has been written and even a sense of which aspects of current theory they should seek to develop.

Spender on "Psychology of Music" in The New Grove traces a wide range of writings (not all of them very rewarding) by behaviorists, Gestalt psychologists, psychoanalysts, and other varieties of psychological researchers; and Portnoy (1954) on historical relations between philosophy and music contains a certain amount of useful information. Some specialized studies of more consistent quality are those of Kristeller (1947) on music and learning in the early Italian Renaissance, and D.P. Walker (1953) on Ficino's "spiritus" and music; Lessem (1974) on French and English eighteenth-century concepts of musical expression and imitation (in the nontechnical sense), and Kivy (1973) on these concepts in Mattheson. For more recent aesthetics, some key figures are Rousseau (on the origins of language), Hanslick, the last half-dozen authors in Strunk (1950), and perhaps Suzanne Langer (1953). Finkelstein (1952) on ideas in music presents a vein of midcentury Communist thought that is rather more accessible than the intricate philosophical and sociological essays of Adorno, which in this course might better be read about (in Rose Sobotnik 1976) than actually read. But Max Weber (1921) on the rational and sociological foundations of music could well be deemed indispensable to the course, as he represents a watershed in the development of musical sociology. A good bibliography is appended to Boehmer's article on "Sociology of Music" in The New Grove. Finally some studies of particular fascination for students interested in historical links between music and the exact sciences are those of Werner (1956) on the mathematical foundation of de Vitry's Ars Nova; Gingerich (1973) on Kepler's theories of planetary motion; Palisca (1961) on scientific empiricism in musical thought in the seventeenth century; Dostrovsky (1975) on early vibration theory; and D.P. Walker (1978) on musical science in the writings of Zarlino, Tartini, and various seventeenth-century figures.

All this is more than a one-year course can cover, even a tightly organized one resembling—as might be appropriate in this instance—an undergraduate course in chemistry rather than a seminar in gastronomy. But the criteria outlined here do provide a basis for shaping the materials reasonably and in accordance with the interests of the students and the professor.

The a priori limitation to the history of theoretical writings in English, German and the Romance languages (mentioned at the beginning of this article) is one which should at least be discussed critically in the concluding sessions of the course, even if it does not seem feasible to transcend it to any great extent. (Strictly speaking, however, Rimsky-Korsakov, Stravinsky's teacher, would by this rule be a marginal figure!)

A sense of wider horizons should naturally arise from the sociological readings; and in many respects some well chosen history of non-Western theory, for instance the appropriate sections in Powers on "India" and Owen Wright on "Arabia" in The New Grove (see also Wright 1978) would be extremely worthwhile even for students with little interest in non-Western music. But at the same time the course should offer enough rewarding contact with primary source facsimiles and texts to show what would be lost by limiting oneself, in the name of broader horizons, to secondary sources.




AIM American Institute of Musicology
JAMS Journal of the American Musicological Society
JMT Journal of Music Theory
MD Musica Disciplina
MR The Music Review
RISM Répertoire Internationale des Sources Musicales
UM University Microfilms

Aaron, Pietro. See Berquist 1970.

Adams, R.D.W., trans. 1948, Arnold Schoenberg, Theory of Harmony, abridged (New York).

Adkins, Cecil, and Alis Dickinson 1977, International Index of Dissertations and Musicological Works in Progress (Philadelphia).

Agate, Edward, trans. 1923, Nikolai Rimsky-Korsakov, Principles of Orchestration (Berlin; abridged edition New York, 1950).

Albrechtsberger, Johann Georg. See Merrick 1834 and A. Mann 1958.

Alette, Carl, 1951, Theories of Rhythm (University of Rochester dissertation and microcard 93).

Apel, Willi, 1940, The Notation of Polyphonic Music (Cambridge, Mass.).

Aristoxenus. See Macran 1902.

Arlin, Mary Irene, trans. 1971, François-Joseph Fétis, Esquisse de l'histoire de l'harmonie (Indiana University dissertation, UM 72-30,396).

Arnaut de Zwolle, Henri. See Le Cerf 1932.

Arnold, Frank Thomas, 1931, The Art of Accompaniment from a Thoroughbass as Practised in the 17th and 18th Centuries (London).

Artusi, Giovanni Maria. See Strunk 1950.

Atcherson, Walter Thomas, 1960, Modal Theory of Sixteenth-Century German Theorists (Indiana University dissertation, Library of Congress microcard 60-6280).

_________ 1973, "Key and Mode in Seventeenth-century Music Theory Books," JMT XVII, 204.

Augustine. See Strunk 1950.

Aurelian of Réôme. See Ponte 1968.

Bach, Carl Philipp Emanuel. See Mitchell 1948.

Baker, Nancy Kovaleff, 1976, "Heinrich Koch and the Theory of Melody," JMT XX, 1.

_________ 1977, "The Aesthetic Theories of Heinrich Christoph Koch," International Review of the Aesthetics and Sociology of Music, VIII, 183.

Banchieri, Adriano. See Marcase 1970 and Garrett 1972.

Beach, David, 1969, "A Schenker Bibliography," JMT XIII, 2.

_________ 1974, "The Origins of Harmonic Analysis," JMT XVIII, 224.

Bellamy, Laurette, 1974, The Sonido Trece Theoretical Works of Julián Carrillo: A Transcription with Commentary (Indiana University dissertation, UM 73-19,731).

Berquist, Ed Peter, Jr., 1964, The Theoretical Writings of Pietro Aaron (Columbia University dissertation, UM 65-7496).

_________ trans. 1974, Pietro Aaron, Toscanello in Music (Colorado Springs).

Berlioz, Hector. See Clarke 1856 and Strunk 1950.

Bermudo, Juan. See Stevenson 1960.

Bernhard, Christoph. See Hilse 1973.

Blum, Fred, 1958, "Santayana's Music Aesthetics," JAMS XI, 20.

Blumenfeld, Harold, trans. 1970, Michael Praetorius, Syntagma Musicum, Vol. 2 (Kassel).

Boethius, Anicius Manlius Severinus. See Bower 1967.

Borgese, Elizabeth M., trans. 1954, Heinrich Schenker, Harmony (Chicago).

Bower, Calvin M., trans. 1967, Boethius, The Principles of Music (George Peabody College dissertation, UM 67-15,005).

_________ 1971, "Natural and Artificial Music: The Origins and Development of an Aesthetic Concept," MD XXV, 17.

Bragard, Roger, 1929, "L'harmonie des spheres selon Boece," Speculum, IV, 206.

Briscoe, Roger Lee, trans. 1975, Demonstration du principe de l'harmonie and Nouvelles reftexions de M. Rameau sur sa Démonstration du principe de l'harmonie (Indiana University dissertation, UM 76-2791).

Brouncker, William, trans. 1653, Renatus Descartes Excellent Compendium of Musick (London).

Brown, Howard Mayer, 1976, Embellishing Sixteenth-Century Music (London).

Buelow, George J., 1966, Thorough-bass Accompaniment According to Johann David Heinichen (Berkeley).

_________ 1966, "The loci topici and Affect in Late Baroque Music: Heinichen's Practical Demonstration," MR XXVII, 161.

Butler, Gregory G., 1977, "Fugue and Rhetoric," JMT XXI, 49.

Carrillo, Julián. See Bellamy 1974.

Carter, Henry H., 1971, A Dictionary of Middle English Musical Terms (Bloomington).

Cassiodorus, Magnus Aurelianus. See Strunk 1950.

Chandler, B. Glen, trans. 1974, Jean-Philippe Rameau, Nouveau systeme de musique théorique (Indiana University dissertation, UM 75-23,465).

Chapman, Roger E., trans. 1957, Marin Mersenne, Harmonie universelle, the Books on Instruments (The Hague).

Chartier, Yves, trans. 1972, Hucbald, La Musica d'Hucbald de Saint-Amand. Introduction, établissement du texte, traduction et commentaire (University of Paris dissertation).

Chenette, Louis Fred, 1967, Music Theory in the British Isles During the Enlightenment (Ohio State University dissertation UM 68-2965).

Cherubini, Luigi. See Hamilton 1837 or Clarke 1854.

Churgin, Bathia D., 1968, "Francesco Galleazzi's Description (1796) of Sonata Form," JAMS XXI, 181.

Clarke, Mrs. Cowden, trans. 1854, Luigi Cherubini, A Treatise on Counterpoint and Fugue (London).

_________ trans. 1856, Hector Berlioz, A Treatise on Modern Instrumentation and Orchestration (London).

Clercx-Lejeune, Suzanne, 1955, "Johannes Ciconia théoricien," Annales musicologiques III, 39.

Coclico, Adrianus Petit. See Seay 1973.

Cohen, Albert, 1971, "La Supposition and the Changing Concept of Dissonance in Baroque Theory," JAMS XXIV, 63.

_________ et al., 1972, "National Predilections in Seventeenth-Century Music Theory," JMT XVI, 4.

Cohen, Gustave, trans. 1891, Eduard Hanslick, The Beautiful in Music (London).

Coover, James B., 1959, "Music Theory in Translation: a Bibliography," JMT III, 70; supplemented in JMT XIII, 230.

Crocker, Richard L., 1958, "Musica rhythmica and musica metrica in Antique and Medieval Theory," JMT II, 2.

_________ 1962, "Discant, Counterpoint, and Harmony," JAMS XV, 1.

Daniels, Arthur Michael, 1962, The De Musica Libri VII of Francesco de Salinas (University of Southern California dissertation, UM 62-6046).

Davidsson, Åke, 1962, Bibliographie der musiktheoretischen Drucke des 16. Jahrhunderts (Baden-Baden).

Davis, Ferdinand, trans. 1965, André Gédalge, Treatise on the Fugue, revised after Louis Vierne (Norman, Oklahoma).

Day, Thomas C., 1976, "The Downfall of Western Music as Described by Nordau, Spengler and Toynbee," MR XXXVII, 52.

Descartes, René. See Brouncker 1653 and Robert 1961.

Dostrovsky, Sigalia, 1975, "Early Vibration Theory: Physics and Music in the 17th Century," Archive for the History of the Exact Sciences, XIV, 169.

Dowland, John, trans. 1609, Andreas Ornithoparcus, Compendium of Musical Practice (London).

Egan, John Barnard, trans. 1962, Marin Mersenne, Traité de l'harmonie universelle, Book II (1634) (Indiana University dissertation, UM 62-5029).

Eggebrecht, Hans Heinrich, et al., 1972, Handwörterbuch der musikalischen Terminologie (Wiesbaden).

_________ and Fritz Reckow, "Das Handwörterbuch der musikalischen Terminologie," Archiv für Musikwissenschaft, XXV, 241.

_________ 1970, "Bericht II uber das Handwörterbuch der musikalischen Terminologie," Archiv für Musikwissenschaft, XXVII, 214.

Ellinwood, Leonard, 1945, "Ars musica," Speculum, XX.

Ellis, Alexander, trans. 1895, Hermann von Helmholtz, On the Sensations of Tone as a Psychological Basis for the Theory of Music (London, New York).

Euler, Leonhard. See C. S. Smith 1960.

Evans, Edwin, Sr., trans. 1913, Richard Wagner, Opera and Drama (London).

Federhofer, Hellmut, 1964, "Ein Salzburger Theoretikerkreis, Acta Musicologica, XXXV, 50.

Ferand, Ernest T., 1958, "Guillaume Guerson's Rules of Improvised Counterpoint (c. 1500)," Miscelánea en homenaje a Monseñor Higinio Anglés (Barcelona), p. 253.

_________ 1961, Improvisation in Nine Centuries of Western Music (Cologne).

Ferris, Joan, 1959, "The Evolution of Rameau's Harmonic Theories," JMT III, 231.

Fétis, François Joseph. See Arlin 1971.

Finkelstein, Sidney W., 1952, How Music Expresses Ideas (New York).

Fischer, Pieter, 1968, The Theory of Music from the Carolingian Era up to 1400, Vol. II (RISM B III2).

Forte, Allen, 1959, "Schenker's Conception of Musical Structure." JMT III, 1, reprinted in Yeston 1977.

Franco of Cologne. See Strunk 1950.

Fux, Johann Joseph. See A. Mann 1958 and 1965.

Gaffurius, Franchinus. See C.A. Miller 1968.

Galilei, Vincenzo. See Herman 1973.

Gallo, Franco Alberto, 1963, "Pronuntiatio: ricerche sulla storia di un termine retorico-musicale,"Acta Musicologica, XXXV, 38.

_________ 1967, "Citazioni 'da un trattato di Dufay," Collectanea Historiae Musicae, IV.

_________ 1967, "Il Musico testore di Zaccaria Tevo," Quadrivium, VIII, 101.

_________ 1968, "Il Melopeo di Pietro Cerone," Quadrivium, IX, 111.

_________ 1972, "Philological Works on Musical Treatises of the Middle Ages," Acta Musicologica, XLIV, 78.

_________ 1973, "Astronomy and Music in the Middle Ages: the Liber Introductoris by Michael Scott," MD XXVII, 5.

_________ 1977, Il medioevo II (Vol. 2 in a multivolume Storia della musica by various members of the Societa italiana di musicologia; Turin).

Garrett, Lee Raymond, trans. 1972, Adriano Banchieri, Adriano Banchieri's Conclusioni nel suono dell'organo of 1609: A Translation and Commentary (University of Oregon dissertation, UM 73-7895).

Gasparini, Francesco. See F. Stillings 1963.

Gédalge, André. See Levin 1964 and Davis 1965.

Gingerich, Owen, 1973, "Kepler, Johannes," in G.C. Gillespie, ed., Dictionary of Scientific Biography (New York), VII, 300.

Glareanus, Heinrich. See C.A. Miller 1965.

Gossett, Philip, trans. 1971, Jean-Philippe Rameau, Treatise on Harmony (New York).

Grant, Cecil Powell, 1977, "The Real Relationship Between Kirnberger's and Rameau's Concept of the Fundamental Bass," JMT XXI, 324.

Grocheo, Johannes de. See Rohloff 1972.

Grossman, Orin, trans. 1968, Heinrich Schenker, "Organic Structure in Sonata Form," JMT XII, 164; reprinted in Yeston 1977.

Gruber, Albion, 1969, Evolving Tonal Theory in Seventeenth-Century France (University of Rochester dissertation, UM 69-19,779).

Guido of Arezzo. See Strunk 1950.

Haar, James, 1971, "Zarlino's Definition of Fugue and Imitation," JAMS XXIV, 226.

Haagh, Raymond H., trans. 1962, Hugo Riemann, History of Music Theory. Books I and II: Polyphonic Theory to the Sixteenth Century (Lincoln, Neb.).

Hamilton, J.A., trans. 1837, Luigi Cherubini, A Course of Counterpoint and Fugue (London).

Hanslick, Eduard. See G. Cohen 1890.

Harman, Richard Alec, ed. 1952, Thomas Morley, A Plain and Easy Introduction to Practical Music (London).

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Herman, Robert, trans. 1973, Vincenzo Galilei, Dialogo della musica antica e della moderna of Vincenzo Galilei: Translation and Commentary (North Texas State University dissertation, UM 74-4032).

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Hoffmann, Mark, 1953, A Study of German Theoretical Treatises of the Nineteenth Century (University of Rochester dissertation).

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Kivy, Peter, 1973, "What Mattheson Said," MR XXXIV, 132.

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_________ 1978, "The Recognition of Major and Minor Keys in German Theory: 1680-1730," JMT XXII, 65.

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_________ 1965, The Study of Counterpoint [translation of section of J.J. Fux, Gradus ad Parnassum] (New York).

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_________ and Claude Palisca, trans. 1968, Giuseppe Zarlino, The Art of Counterpoint (New Haven).

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_________ trans. 1968, Franchinus Gaffurius, Practica musicae (AIM).

_________ 1968, "Gaffurius's Practica musicae: Origin and Contents," MD XXII, 105.

_________ 1970, "Sebald Hayden's De arte canendi: Background and Contents," MD XXIV, 79.

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1The first decision does require a modicum of academic integrity.

2I have in mind Part III: the epitomes and paragraphs 442 and 473.

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