This article was part of a Symposium entitled The Crisis in Theory Teaching. The other authors were A. Tillman Merritt, Andrew Imbrie, and Milton Babbitt. Their articles also appear in SYMPOSIUM Volume 5.

This discussion intends to convey to our readers current ideas on the proper material for undergraduate and graduate theory courses. The contributors were asked to respond to the following questions:

(1) In view of the great advances made in recent years in composition, do you think that "traditional" harmony, counterpoint, etc., are still essential to the training of a music student?

(2) Or do you feel that these courses are outmoded and need to be replaced with new curriculum concepts?

The Editor will welcome comments from readers on this subject.


Most theoretical treatises of the past have had two main objectives: one, to attempt an exposition of the tonal material; and, two, to provide composers with the rules of style and technique common to the period. Many lesser treatises have had only the second objective in mind and are mere handbooks for practical use. But the more serious ones have always begun with a majestic recitation of basic principles—in the earlier works, starting the account with remnants of Greek theory.

In more recent times, a third objective has been added: analysis of composed music (without necessarily a direct relationship to the process of composition) intended to increase the insight of those whose interest is neither in the sweeping universals so dear to neo-Pythagoreans of all ages, nor in the precise methods by which a new piece may be made, which is what most interests the composer.

Allied to the third objective (since it may draw upon it) is a fourth one: the use of theoretical techniques, analytical and practical, to illuminate (from the inside, as it were) the musical literature of the past. Theory, in such a usage, may become an accessory to the teaching of music history.*

In colleges (as opposed to purely professional schools) the trend has been, and is now, to slant theory courses towards the third and fourth objectives described above, since these lead more to general understanding than to technical skill, and they involve procedures congenial to the academic atmosphere—relying, as they do, more on the verbal than on the purely musical.

In discussing the possible obsolescence of present-day theory courses in the light of recent developments in composition, and what can or cannot be done about such obsolescence, I should like to consider theory curricula in the context of each of the four objectives described above.


Those aspects of theory dealing with the tonal material have suffered a steady decline in theoretical writing and teaching since the adoption of equal temperament apparently solved all those problems of intonation and tuning which had been a preoccupation of the theorists from Euclid through Rameau. A glance at Barbour's bibliography will show how and when interest in this aspect of music theory began to decline.

After Rameau's period, the tendency was for theory treatises to become increasingly practical. It was not a music theorist, but a natural scientist, Helmholtz, who once again attempted the broad view—too broad for many of his contemporaries, who had canonized ordinary technical procedures as though they had the blessings of Nature herself. But Helmholtz's unprejudiced scientific sort of viewpoint was an excellent basis for iconoclastic rethinking of "traditional" theory. Among those influenced by Helmholtz was George Ives, who brought up his son, Charles, with attitudes not at all prepared to accept everything out of Jadassohn and Richter. The idea that Nature supported the rules of harmony, questioned by Helmholtz from the scientist's point of view, collapsed completely with the beginnings of twentieth century music. Since Nature did not even support the rules against parallel fifths or explain the minor triad, and since art involves so much artifice anyway, there seemed to be no point in wasting the student's time on "natural facts." Paul Hindemith, in looking to the structure of tone and interval as a basis for his theory, was considered by many to be out of line with the times, and merely indulging his well-known antiquarian tastes. Joseph Yasser, who proposed an expansion of the tonal material from twelve to nineteen tempered tones, all founded on a "natural" basis, was, considering the boldness and originality of his ideas, recognized very little by theorists (historians know his work better).

But whether Nature does or does not support anyone's system of musical composition, the present-day (and future) student will have to take more than an indifferent attitude towards learning about tone, overtone and other related phenomena, because one of the most important developments of his epoch is electronic music, and that metier involves knowing all the usual things that come under the heading of "physics of music" plus much more which is being discovered as the genre develops. In the curriculum of the future, it would appear that a study of the sound material, and the physics relating to it, will probably reassume the important role occupied by its primitive precursors, which dealt merely with simple proportions and their relation to tone and interval.


The most noticeable dichotomy between present-day theory and practice occurs in regard to the second objective of music theory: the teaching of the principles of style and technique for composition.

Even so recent a composer as Brahms, when he studied harmony with Marxsen, or when he exchanged counterpoint exercises with Joachim, was engaging in theoretical work which bore a direct relationship to the music he was to compose. One generation later, practice had taken such leaps as to make the theoretical methods Brahms used almost entirely obsolete. And yet, two more generations later we are teaching students with essentially the same methods Brahms used. Even some of the most imaginative composer-teachers have fallen back on these methods in order to take no chances when attempting to lead young musicians to a secure technical foundation.

Paul Hindemith was one major composer-teacher who really tried to rethink the whole technical process from the simplest two-part structures (roughly analogous to fifteenth century style) to complex dissonant polyphony. He also tried to develop the necessary pedagogical materials to bring a beginner through from the start to twentieth century composition without having to work inside the cocoon of any previous system developed to support an extinct style. Unfortunately, Hindemith published during his lifetime only the first slim volume of the practical part of The Craft of Musical Composition: Exercises in Two-Part Writing. But he took many students over the road from what they had learned in traditional courses to contemporary writing by a logical route that led from that volume. How it all might have worked with students who had never experienced any other training in harmony or counterpoint was a hypothetical question, because Hindemith's own students were already advanced in traditional theory when they came to him (although he saw a need to put most of them through a condensed review, for which he wrote his Traditional Harmony).

The problem with the acceptance of Hindemith's work, other than the fact that it was never complete, was its strong identification with a single living composer's style. The extent to which Hindemith's style contains the essence of all the non-serial music of the first half of the century still remains to be seen. It would seem that his music, if not his theoretical work, would be one of the most informative sources in which to study what might be called the "tonal chromaticism" of that period. It has the same advantage of rock-like consistency (i.e., beginning with the works from about 1930 onward) which made Bach and Mendelssohn the most quoted composers in terminal nineteenth century harmony books.

As for the possibility of introducing serial methods to beginners, and simply tossing out all the old material, not even Schoenberg himself would have recommended that, if we may take his own teaching procedures as a guide. Serial techniques will have to be taught at the proper stage, and in that regard we are fortunate that there has been a considerable quantity of helpful didactic writing within the last fifteen years. So much so, that it is now easier for an advanced student to get the information about how to analyze a serial work from 1925-35 or 1955-65 than it is for him to get material which will help him to understand a non-serial piece from, say, the period 1935-45. Further, he may have been subjected to an "either-or" approach in which "tonal music" means that which is described in harmony books, while "contemporary music" means that which is serial. On the basis of this sort of training he can have no idea how logically to go about writing non-traditional verticalities or dissonant contrapuntal textures without the justification of serialism, and/or without the covering assumption of atonality. Perhaps he never will need to write in any other manner than serially, aleatorically, or electronically. But if the long cycle should swing musical taste back to the thirties as it did to the twenties, he will be faced with a whole approach to writing for which he has no basic understanding.

Any tendency towards exclusive emphasis on serial techniques in developing a modern theory curriculum involves one point which may be disturbing to those who feel that theoretical methods should derive from and faithfully reflect practice. In sheer statistical terms, the common style of the first half of the twentieth century can scarcely be defined as serial. An analysis of what was actually performed in our concert halls, perhaps made by some historian of the future, would indicate that our contemporary music was, in those terms, that composed by Stravinsky, Prokofieff, Hindemith, Bartok, Britten, Barber, Copland, et al., and not Schoenberg and his school—whether or not, the serialists actually represented the "cutting edge" of twentieth century music. It is true that the blade of the knife is receiving less attention from advanced students nowadays than the cutting edge, and to carry the metaphor further, the average student is still eating with his fingers, having never progressed to the stage of using modern utensils—with or without a cutting edge!

What we very much need at this time is a synthesized method giving the student (within the two or three years now devoted to harmony and counterpoint) a knowledge and some command of the full range of tonally organized music, up to, let us say, 1950. In addition, he should receive a proportionate introduction to serial methods. The student in the year 1965 may well regard the cut-off point at which "modern" music begins as 1950 rather than 1900. He can perhaps be expected to understand that what has occurred since about 1950 may be too new for evaluation and inclusion in basic training, although it must be a matter of concern for the advanced student and the specialist. But what has been done before 1950 (the date will sound ancient to him!) he should have a right to expect to find woven into the main fabric of his theory courses.


The third objective of music theory, analysis, is gaining more and more favor, in college curricula especially. It goes without saying that whereas one student may be capable of constructing a workable example in a given style, ten may be capable of analyzing one which already exists. While acknowledging the obvious value analytical techniques may have in deepening the student's insight into composed music, analysis cannot be a substitute for technical training which involves actual construction. The ability to analyze a Bach chorale does not in itself supply the technical skill needed to harmonize a chorale melody. Now does the analysis of the serial devices in a contemporary work assure the student of success in building a new form with such devices.

Analysis ought not to overbalance synthesis in the college curriculum. The danger exists that it might do so, in that the latter is openly directed towards developing "skill" while the former purports to be directed towards developing "understanding." The liberal arts atmosphere is naturally more sympathetic to procedures which involve broadening understanding than it is to those which "merely develop skills." What needs to be kept in mind is that while analysis may develop no skill at all, skill may very well develop understanding.


The fourth objective of music theory, to serve as an accessory to the teaching of music history, is one still insufficiently exploited in college teaching. How frequently does a liberal arts student elect a basic theory or history course, only to find the former narrowly focused on the practice of one given period, while the latter ranges over the whole of Western music. Theory courses, from this point of view, are where the music literature course of thirty years ago were: concentrated almost entirely on the period of common practice. Even worse is that attempts are seldom made to adapt material developed for the conservatory (leaving entirely aside the question of whether or not that material itself is au courant) to the quite different needs of the liberal arts student, whose main objective is intelligent listening to music.

The teaching of music history has moved steadily towards discussing music on and in its own terms, as opposed to the "music appreciation" approach of some years ago. As a result, many of the newer texts include material really in the domain of music theory. (For other reasons, the reverse is also true: some theory books now incorporate material from the domain of music history.) While the presence of theoretical material in history texts has demonstrated the need, there is at this time no book designed from the outset to use the methods of music theory to support a study of music history, providing not only the bare rudiments of music for the non-musician, but some controlled experiments in actually constructing examples of styles from all periods. Such a theory course would give the liberal arts student a broader and more integrated view than he now gets from the awkward combination of a broadly presented history course and a narrowly specialized theory course.

Even this brief discussion, I believe, brings forth the fact that much new and really creative textbook writing is needed in the field of music theory. If one compares the music history texts of thirty years ago with recent publications, one sees the remarkable progress made by the historians in raising standards within their area. Unfortunately, the same cannot be said for theory texts which have been published during the same period. Most of them have neither kept up with the present nor incorporated much of our improved understanding of the past. Perhaps the excuse of music theorists may be that many of them are composers first of all, and their real creative outlet is musical composition, not the writing of textbook prose. But the historians could counter that their true business is historical research and professional reporting of the same, not rehashing known material for teaching purposes.

However it may be, those concerned primarily or secondarily with music theory in college teaching (and elsewhere) need to do more to eliminate anachronistic practices in their field, to make it serve more meaningfully in developing general understanding of our musical heritage from the distant and recent past, and to connect it more realistically with the events of the present.

*I have intentionally omitted from this discussion a fifth objective of music theory: the support of performing skills (ear training, keyboard harmony, etc.).

3084 Last modified on November 14, 2018