Undergraduate Training in Music Theory

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This article was part of a Symposium entitled The Crisis in Theory Teaching. The other authors were Andrew Imbrie, Howard Boatwright, 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.


The primary purpose of this paper is to discuss that basic study of music that is normally called theory at the level which occupies the undergraduate years in the modern American university. It will not be to consider original composition, or theory of an advanced or speculative nature such as one can find expounded in any number of renaissance treatises or hammered out again to-day in books and articles in journals that devote themselves to this subject.

College music as a whole cannot be considered in a vacuum, of course, so that a brief look at the necessary preparation for it, as well as what it leads to, will have to be taken. The problems involved are complex: conditions differ in different universities and communities, each individual student presents a new and different challenge, teachers differ and musicians differ.

It should be said at the beginning that to-day's music undergraduate is in many respects superior to his counterpart of a generation ago. He usually is far more eager, aware and sophisticated and shows that his experience with music is generally much greater. Yet, in other respects he is often not as adroit as his predecessor, particularly in his ability to put easily into practice many of the things he is supposed to know. This is not always true; once in a while an unusual youth will turn up even as a freshman with training worthy of a college senior. But these persons are so rare that they will not be considered per se in this paper.

A disinterested musician need only look at the results of examinations in theory that are given to graduating college seniors to determine whether they should be admitted to graduate study to see that far too often their undergraduate training has been faulty and inadequate. These examination results do not necessarily show a lack of musical sensitivity, although this too seems at times to be true. They rather show a lack of training in basic musical horse sense, in listening to music as sound and in the ease of writing notes to make an artful and satisfactory essay in music, short as that may be for purposes of illustration of technique acquired. All too many show elementary ineptitude and strain—strain far beyond that caused by the fact that they are taking an examination, which is natural to most people. They do not seem to know how to go about handling a perfectly simple phrase or series of phrases in terms of sound, hearing the tonal direction, writing a sensible and fitting cadence to a phrase or dealing with a short series of imitations. When tested they often cannot identify immediately even simple intervals or chords. In short, they reveal the fact that they have had little experience in such things, particularly in a practical way. They seem to approach most of the problems posed almost entirely from an intellectual point of view rather than from a properly and fully educated musical one.

The regret most often expressed by intelligent graduate students is that as undergraduates they had so little harmony, so little counterpoint, so little experience in practice of writing and analysis. As a result they feel greatly handicapped in their graduate work.

In order to put undergraduate music study into perspective let us first examine briefly the kind of preparation every pre-college student should have if he has any idea that he may go into music in college. These preparations are simple, but they require much practice and time. It goes without saying that habitual singing from earliest childhood, alone and with others, is something most young people do, and this is most desirable. But there are two types of positive preparation that are highly important:

1. The ability to play reasonably well a musical instrument. Facility on any orchestral instrument is all to the good, but the ability to play the piano well is particularly important since it will be necessary not only during college music studies but also throughout life.

2. The ability to sight-read music easily. The slow and painful performance of music at sight is a very serious handicap to the student of music of the type he should encounter in college.

Instrumental facility, particularly on the piano, and ease of sight-reading have no peers as preparatory studies and techniques, regardless of what branch of music the student wishes to pursue or, contrary to expectations, finds himself pursuing. If he can do both these things well and if he is eager to learn, no freshman should fear plunging into what the university has to offer him as an undergraduate.

During undergraduate years the foundations must be laid, laid as securely as possible, for the student's future musical studies, no matter what field of specialization he finds himself attracted to or believes himself particularly talented in. This is not only desirable in itself but it also provides for the changes in direction which not a few students undergo during their college careers: some find that they are not as talented along certain lines as they had thought; others discover talents they never suspected before; interest as such often broadens and changes from one aspect of music to another. To prepare irrevocably during college for life only as a composer, only as a performer on some instrument, only as a singer or as a conductor, to mention those musical professions to which the majority of young people are so powerfully attracted to begin with, and to neglect basic studies that are necessary to all musicians is very risky and can lead to bitter disappointment. It is all the more unfortunate when this neglect has left the student unprepared for work in a field which could eventually have been more congenial and in which he finds he possessed extraordinary gifts.

The basic musical studies come under what is traditionally called the theory of music. The term is not completely apt, as it implies only half of what it should; the other half is practice. This broad subject concerns the anatomy itself of music, the understanding and mastery of which involves not only the intellectual comprehension of the principles upon which music is founded, but also the actual practice in writing notes—many notes—for the sake of acquiring a personal grasp of the workings of these principles, both past and present. As related earlier, the graduate entrance examinations too often suggest a certain awareness of theoretical principles at the same time that they show a deplorable, even pitiful, inability to demonstrate these principles by example.

The so-called training that has such results is for practical purposes and to a large extent of no value to a person who is preparing to spend his life as a serious musician. It is practically the same result that can be obtained easily and in the course of a few good lectures on the principles of melody, rhythm, harmony or counterpoint to an audience of intelligent and musical but totally untrained persons. These persons too can grasp such concepts. If this kind of instruction then is almost as effective in such a short time for non-musicians why should two or three or more years be expended instructing music undergraduates to accomplish little more? But, unfortunately one sometimes hears further that hardly any time at all has been spent by individual students on these studies.

It is sometimes said that some students are just not gifted in theory, and that they have no talent for composition. The latter may very well be true, but to equate the two is as far from the point as to say that a student does not show any gifts as a poet and should therefore not be expected to be able to write a letter that makes any sense or understand and appreciate the works of Milton or Joyce. If a student with excellent instruction of a practical nature proves to have no ability whatever to deal with notes as musical sound he should be advised to turn quickly to some non-musical profession, even though he does "love" music. If he demonstrates on the other hand that he can think and act musically he can be trained, at least up to a certain point. It should be superfluous to have to say that not everybody is equally gifted, even in writing letters.

No satisfactory substitute has ever been found for the traditional courses which deal with the anatomy of music. At the undergraduate level the basically essential ones are harmony and counterpoint. These course titles sound time-worn. But so do many of the titles of undergraduate courses in other fields, and so do the names of the majority of activities people inevitably pass through at various stages of their development. New names may be given to these courses to make them seem more attractive, but their intent must remain essentially the same. They offer to the student the concentrated opportunity to learn the basic principles of music as an art at the time when he should master them to the best of his ability.

Harmony and counterpoint have long been considered two sides of the same coin; all music that consists of more than one voice, even though performed on a solo instrument, has both its vertical and its horizontal aspects. The only essential difference between these two studies is the emphasis; it lies mainly on the vertical aspect in harmony and on the horizontal aspect in counterpoint. Both must deal with many of the same elements: melody, rhythm, phrase construction, cadences, color and other ingredients of successful and artistic accomplishment in terms of music. Many times they have been taught as one course. Whether or not they are offered as separate courses or as one is not of vital importance except insofar as a decision must be reached within any one college or university by those in charge in order to avoid confusion and needless duplication. The end result should be the same.

The methods of presenting materials in harmony and counterpoint have changed appreciably over the years, and in general for the good. There was a time when one instructor or author had his "method," another his. It often happened, however, that each, in perfectly good faith and as a good musician, had devised "rules," composed examples (usually very short) and advised certain procedures which not only differed considerably one from the other but were not always very applicable when considered in terms of "real music." The most gratifying improvements in recent years consist of the facts that the best instructors and authors of harmony and counterpoint manuals deduce their "rules" from actual musical compositions, that they choose for purposes of harmonization basses and sopranos, long and short, from actual compositions of the masters, that they select from actual compositions the beginnings of contrapuntal exercises to be elaborated, that they furnish many excellent examples and that they propose at the right time realistic musical tasks for the student to perform on his own. These changes in the manner of presenting materials in progressive and realistic fashion from the simplest to the more advanced are splendid, for they involve the student in "real music" from the beginning.

Granted this kind of improvement, a question frequently arises nowadays to plague instruction in the basic musical techniques at the undergraduate level, though it need not. That is the question of what to base the studies on, what style or period or composer(s) can best serve as models on which to lay the foundations of instruction. This is an important question, the answers to which we may examine.

The cardinal point is that whatever is chosen must be capable of serving as the basis for discipline of a practical nature. So-called training that does not result in a reasonable degree of mastery of a discipline or which is not practical is not worthy to be called training. It leads either to dilettantism or to the eventual necessity for real training of a remedial nature at a time when the student rightfully should be at another stage of his education, unhampered by the obligation of making up deficiencies.

It is a fact difficult to dispute that all human beings have to begin to learn anything by imitating and that the learning process not only entails imitation in theory but also in practice. To imitate without understanding soon becomes pointless; to understand without the ability to act is not productive.

One answer to our question of what to use as early models to imitate is to conduct a survey of harmony or counterpoint through the ages. This may sound far-fetched, but it has actually been done. If students were to remain perpetual students in the formal sense it might be accomplished over a period of a considerable number of years, but given the facts of our life span as well as the desirability of progressing efficiently, solidly and reasonably rapidly to prepare ourselves for independent activities it is hopelessly impractical, and shows lack of judgment.

A second answer is to use the music of to-day, that of the mid-twentieth century, as the models for instruction, imitation and practice. This is infinitely more reasonable. On the face of it instruction with this music as a basis would be up-to-date; it is the music in the midst of which we now find ourselves; every forward-looking musician should be aware of it and anxious to know more about it.

Nevertheless this paper will have to decide against it as the basis for undergraduate studies in theory and to advise that it be postponed until the student is in graduate school or goes as a budding composer to pursue his post-college studies with a private master. The first almost insoluble problem is what composer or school of composers can serve our purpose at the level we are considering; there are not a few directions in which music is moving in our time. Eventually these different schools may, and probably will, be considered as branches of the same musical tree. But at present their differences seem at times almost bewildering, not only to the cultivated musical public but to many excellent musicians. A second difficulty arises from the practical point of view, and that is the complexity and sheer difficulty of performing most of it; it is difficult to get at until after one has acquired a reasonably large fund of musical experience and ability. A further consideration should not be forgotten, but in fact should be stressed: training in undergraduate theory is not solely for the sake of the undergraduate who may or may not become a composer. At this stage it is equally necessary for all other serious musicians, whether they intend to become performers, critics, musicologists, teachers or anything else. They will all inevitably be concerned with past music as well as contemporary, and they all need a solid practical training to cope with it in their various capacities. Our contemporary music has not yet been sifted sufficiently to determine what is basic and what is peripheral. As much of it as possible should be heard and studied assiduously by students and musicians of all kinds, but it cannot serve practically the purposes of normal undergraduate theory students, at least at the basic level.

A third answer to our question is the only generally practical one. It is the answer given by such masters, no longer living but still influential to-day, as Hindemith and Schoenberg, not to mention the great majority of the living masters. It is the music of the tonal period for both harmony and counterpoint and, if one wishes, music of the modal period for counterpoint especially. Practical studies at an early stage in any field can rarely identify themselves completely with the latest developments in that field. Preliminary studies must be made for them, and music is no exception.

If it be argued that our contemporary music is "tonality-less" and that to study tonal music is to master a technique no longer valid it can only be replied, yes, music does change; neither was music always tonal. Tonal music developed from non-tonal (modal) music; now non-tonal (atonal if you will) music has in turn developed from tonal. Each one had inevitably served as a kind of "prima prattica" for its successor. The fundamental aspects of music, such as melodic construction, simultaneous sounding of notes, rhythm, and the very fact that music is above all an art of ordered sound, continue throughout the ages. The external features may seem to change considerably. An element that for so long seemed normal and basic, tonality, has certainly changed. But there is no reason to throw the musical baby itself out with the tonal bath. The student who is well and practically trained in the tonal style who cannot move on as he gains experience to a more difficult style either for the purposes of writing or of analysis can only be said to lack musical imagination, or industry, or interest.

There are ways, I believe, in which instruction in undergraduate theory can and must be improved if we are to train every one of our young musicians to be as solid and practical as possible. Again let it be said: this fundamental musical education is the cornerstone for future studies in all areas of serious musical endeavor. Before we discuss these ways it may be helpful to recognize some of the reasons why this undergraduate study, the foundation, the heart and center, of musical training, has become an unusually underprivileged area, so to speak. Like the hearts of many large cities undergraduate studies generally have sometimes been allowed to run down and have not kept pace with the luxuriant growths of the surrounding suburbs. Where this has happened the time has come when rehabilitation must take place. There is no getting around it permanently.

We all know that the last quarter of a century or so has witnessed an unprecedented and overwhelming flood of students into the colleges and universities. The universities particularly have made a valiant effort to accommodate themselves to the emergency, but the phenomenal flood has set off a series of chain reactions, some of which have not only been necessary but also beneficial, others of very questionable value.

To begin with the size of the undergraduate enrolment in colleges and universities has had in nearly all places to be drastically increased. Many state universities have tried to ease the situation by establishing numerous branches in different localities about the state. This in turn has created an unprecedented demand for teachers to man the new faculties as well as the enlarged faculties at the home bases. More and more emphasis has been put upon higher, and yet higher, academic degrees for the candidates for the new posts. This has caused not only an urgent demand for greatly enlarged graduate schools in those universities already having them but also the establishment of new ones at what had formerly been liberal arts colleges, normal schools, agricultural colleges and of course at the newly established branches. These graduate schools then have often become the flourishing "suburbs" of the undergraduate "city."

At the same time, psychological reactions have often set in. The university has for one reason or other become increasingly aware of its "image." It has placed increased emphasis not only on the number of faculty members possessing higher degrees, but it has also tried increasingly to attract men (and women) with well-known names to its various faculties, often agreeing not only to reward them with unusually attractive stipends but also to allow them to do a minimal amount of teaching so that they may continue to pursue their own writing and research. And, further, pressures have in certain instances been put upon instructors without tenure to do more independent writing and research as a prerequisite for promotion. The decision as to whether they are to be promoted or not is sometimes reputed, at least, to be based on their publications, regardless of their teaching abilities. All these tendencies naturally seem to undercut all teaching as such, although doubtless they are not intended to, but rather are intended mostly to insure alertness and productivity of faculty members so that they may be the more effective teachers. And it must be acknowledged that sometimes there are not sufficient posts open and available at the right moment to permit the promotion of all the younger men eligible for them, no matter how productive or how good teachers they are.

The very attitude towards teaching has at times imperceptibly altered in another way. The increased emphasis upon the graduate school and the training of graduate students has led to a subtle and often possibly unconscious shift in attitude on the part of faculty members to the effect that it is more desirable, more interesting and actually reflects higher status to teach graduate students than to teach elementary or middle group undergraduates. When this has happened foundation courses have tended consequently to come into the hands of younger impermanent faculty members. This in itself is not a bad thing; younger and impermanent men (or women) may actually be, and certainly can be, superb teachers. But in any event they inevitably are less experienced than the older permanent ones; and, if these younger faculty members are not promoted to permanency their departure means that they have to be replaced. If such replacements are frequent, and if they consistently involve instruction in certain undergraduate courses, the continuity in these courses becomes uncertain and the lack of it seems to rob the courses themselves of true importance.

The various shifts, psychological and otherwise, that have worked often to the disadvantage of undergraduate instruction have affected the undergraduate too. Young men and women at the undergraduate age, being endowed with the invaluable virtue of impatience at the same time that they feel themselves to be, and are, at the keenest and most educable period of life, often react, as they can be expected to, by concluding that the undergraduate years are a time to be hustled through as quickly as possible and to be used as much as possible for specialization, even at the expense of thoroughness in fundamental training. Nobody thrills to the excitement of research and creative writing more than wide-awake undergraduates. They too like to have a sense of participation in what they recognize to be important, to be taught by professors of deserved reputation, to feel that what they are being asked to do is of permanent educational value; they unfold in an atmosphere of approbation and security in the belief that they are on the right track. To a lover of teaching there is nothing more gratifying than to aid in the development of bright and happy undergraduates. They are many times very keen, they are fresh, they are having the experience of growing into adults and of acquiring the abilities of adults, they learn for the love of learning and they are not yet subject to the later pressures of job hunting, making a living and rearing a family. It is no service to allow them to be unduly short-changed; it is most likely that a certain number of them too, if they can prove themselves capable, will roost a bit later on the graduate perch, for all graduate students have had first to be undergraduates. This then brings us back full circle to the grave inadequacies of training in theory that are all too often demonstrated by candidates seeking admission to graduate school.

There are three areas in which we can seek to achieve improvement in instruction at the undergraduate level, especially in music theory. There are undoubtedly others, but these are fundamental. They sound simple, but they will not be accomplished over night, for they will often require changes in attitude, and they will cost money.

1. Undergraduate theory instruction must become more personal as far as the student is concerned. It is quite impossible to instruct beginning or even middle group students with genuine effectiveness by means of large lecture courses in harmony and counterpoint.

To obtain satisfactory results the daily work done by students must be examined and appraised in their presence. And, it must be done in small enough groups for each member of the group to see as well as hear what is good as well as what is faulty, and why, and to participate as an individual in suggested improvements. Music of any kind cannot satisfactorily be examined on paper only at this stage; it must be played or sung. As a regular practice it is of little or no value to assign tasks to be handed in, corrected by the instructor, graded and turned back to the student, above all if the student is never asked to make revisions and improvements. These are the methods of Beckmesser and are entirely out of place in respectable theory training in the university.

Regular and extensive practice and experience in playing and singing both of work done by the student and of models being examined and analyzed must be an essential part of the instruction. There must be first-hand experience on the part of the student; the normal student wilts with inaction on his own part and loses interest when he cannot participate. It is at the very moment when students become habitually inactive and non-participating that their training can first begin to be theoretical only rather than practical, superficial rather than vital.

If there are provisions made in the curriculum for general keyboard training and sight-singing, well and good; they too must be vital and lively. But even so, general training in these aspects of music, be it ever so excellent, is not immediately applicable and cannot substitute for the personal participation of each student in the theory groups themselves.

This breaking up into small groups of undergraduates in music theory is costly, for it requires an excellent staff of teachers in numbers commensurate with the number of students to be taught. But we may rest assured that until this has been accomplished to the greatest extent possible there will be an ever increasing number of students ill prepared for further work, and even disinclined toward it. Our more advanced courses will be increasingly filled with students stumbling along, unable to take full advantage of the opportunities they are offered.

2. Students must earn promotion from one stage of study to the next, regardless of the innate gifts they show or seem to show. It is one of the commonest phenomena in the musical world to see young people composing music, even long before they become undergraduates. These youthful efforts are most commendable; they even frequently show great talent. But by no stretch of the imagination do they ordinarily show mastery, even though their composers may in their innocence be extremely pleased with them and may have been greatly encouraged by their families or former teachers. To use these exhibits of talent as a basis for allowing such young people to bypass, skimp or shirk elementary training in music is a great disservice to them, no matter how disappointed they may be at the time. To admit such students, or comparable ones who have done research in musicology, to advanced composition or musicology seminars, even though they are still required to take the basic courses, and do, is automatically to debase psychologically the less advanced courses in their own minds. They may be told that such courses are necessary, but the normal ambitious student in this era almost inevitably reacts by concluding that this more elementary work is irksome, time-consuming and not necessary.

It would be a gross mistake to advise such a student to stop his independent writing altogether. His efforts can and must be regarded sympathetically. In many instances he knows already, to some extent, that he does not yet have mastery in his art, otherwise he would not wish to do further study as an undergraduate. Therefore he will usually accept the suggestions of the new teacher with whom he wishes to study. If he is not aware of all of his deficiencies they can easily and kindly be pointed out to him, and he can be persuaded that while he is at liberty to continue writing on his own he must master the various techniques in whatever courses he needs before he can be admitted as a fully prepared member of any of the seminars.

One would certainly not go so far as to say that no undergraduate should ever be permitted to bypass any of the elementary of even middle group theory courses. If a student can demonstrate easily that he has had a truly adequate practical training up to a certain point it would be pedantic to insist that he go through the motions again. But the greatest possible care should be taken to determine what this point is. Past school grades or recommendations of sponsors, no matter how high or how flattering, cannot be accepted automatically without proof by the student himself that is prepared to enter studies at any advanced level.

Persons with experience in such matters know that a successful meal cannot consistently begin with the desserts, no matter how tempting, delicious or rewarding they may be. Younger persons without this experience sometimes have to be persuaded that to indulge in such a gastronomic order leads to indigestion, loss of appetite and headache, if not permanent injury to their health.

3. Not only must continuity in terms of staff be reasonably assured but also there must be increased participation in the teaching of undergraduate theory by senior faculty members, where this is not already practiced. It should, when possible, extend even to the teaching of elementary courses.

Far from being less important and desirable than teaching graduate students the teaching of undergraduates can be just as interesting and just as rewarding to the professor who is willing to divide his teaching duties between the two, or alternate between one and the other from time to time. In fact undergraduate teaching is often even more stimulating from certain points of view. In any event it is vital for the sake of future musicians. In large institutions where there are large numbers of students it is impractical to suppose that any one professor should teach personally all the small groups in any large course. But at least he should be responsible for the work that goes on in these small groups, and in order to indicate that he too considers the work important he should be willing to teach at least a group or so. These groups must be coordinated, each group being as nearly as possible equally well taught as the others.

The subsidizing by the modern university of both artists and scholars of repute is commendable. But it can be carried only so far before it becomes too costly, not only in terms of money required but also in terms of the practical benefit it confers upon the students for whom, after all, the university exists. The use of money for "image" value to the detriment of the best possible educational opportunities for the students would appear to be less than wise. Mere "visibility" is not necessarily educationally productive, and a permanent faculty that does not shoulder its responsibility of teaching, both of undergraduates and graduates, can gradually become removed to an ivory tower far from the academic world where it has its base. Whereas a teacher who not only teaches but does creative work in composition or research brings something special to the classroom, it has yet to be proved that the ivory tower musician serves the true aims of the university. These true aims must be to offer an education that is "liberal," for in the end, paradoxically enough, it has been shown time and again that this kind of education is the most "practical."

The undergraduate of to-day entering the gigantic educational supermarket that the large American university seems to have become is bound to be a seemingly small customer, confronted with unending temptations of an educational nature. Many of the decisions as to what he will avail himself of will have to remain his own. He will have to learn gradually, perhaps by trial and error to a certain extent, what he can pay for and what not. In the aisle of music theory he must have a reasonably individual guidance; it is here that his choices are crucial. He must not be allowed or encouraged to select a product beyond his means; the product must be serviceable in terms of his later purchases since a return for refills will be irritating, time-wasting and inordinately expensive. He can later rightly lay the blame where it belongs, but this will not undo the original error in making the purchase.

Music theory has become the gateway through which any serious college undergraduate intending to make music his career must pass. It is at this gateway that he must prepare his basic equipment for the musical journey he expects to make. The shoddier and more undependable this equipment is the surer it is that he will have to take time off later to repair it if it is not to become tormenting and retarding to his progress. The more durable it is, and the more enlightened it is, the farther and the more easily he can expect to advance.

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