• American Society of University Composers

Proceedings, 1972-1973

PUBLICATION DATE: SPRING, 1974

American Society of University Composers

Proceedings

'I

The Society gratefully acknowledges the support of THE ALICE M. DITSON FUND in assisting the publication of this volume.·

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Proceedings Editor American Society of University Composers c/o American Music Center 2109 Broadway, Suite 15-79 New York City, N .Y. 10023

Copyright© 1974 The American Society of University Composers, Inc. c/o American Music Center 2109 Broadway, Suite 15-79 New York City, N.Y. 10023 Founding Committee I BENJAMIN BORETZ, DONALD MARTINO, I J.K. RANDALL, CLAUDIO SPIES, HENRY WEINBERG, l PETER WESTERGAARD, CHARLES WUORINEN f

National Council (1972)

JOHN ROGERS, ALLEN BRINGS, ROBERT HALL LEWIS, DONALD MACINNIS, RICHMOND BROWNE, JEFFREY LERNER,

DAVID BURGE (Chairman), RICHARD BUNGER, HOMER KELLER

Executive Committee (1972)

RICHMOND BROWNE, BARNEY CHILDS, JOHN CLOUGH, PAUL LANSKY, JOHN ROTHGEB, NICHOLAS ROUSSAKIS, JOAN TOWER, BARRY VERCOE, GERALD WARFIELD

Proceedings Editor

WARNER HUTCHISON American Society of University Composers

Proceedings of the Seventh Annual Conference, April, 1972

Held at Peabody Conservatory of Music Baltimore, Maryland ROBERT HALL LEWIS, CHAIRMAN

Seventh Annual Conference, 1972, Baltimore, Maryland Robert Hall Lewis was born in Portland, Oregon and has been a resident of Baltimore since 1957. He studied at the University of Rochester, Paris Conservatory, Vienna Academy of Music and the French Institute of the United Kingdom in London. His awards include a Kosciuszko Foundation Chopin Award, a two-year Fulbright Scholar­ ship, the graduation prize in composition of the Vienna Academy of Music, the LADO prize and a Guggenheim Fellowship. He recently received the second annual Walter Hinrichsen Award for Composers for 1972. Mr. Lewis' compositions have been widely performed in the United States and Europe by such organizations as the Baltimore, Boston, Denver, Eastman-Rochester symphony orchestras, the CBC and Lau­ sanne chamber orchestras, the Die Reihe and Juilliard ensembles and many others. Recent performances of his music include the premiere of his Concerto for Chamber Orchestra by the Kol Israel Orchestra in Jerusalem and his Second Symphony at Tanglewood. This season Mr. Lewis' music is scheduled for performance by the Baltimore and New Orleans symphony orchestras and the New York Philharmonic Chamber Soloists. He is Professor of Music at Goucher College and the Johns Hopkins University, and a member of the composition faculty of the Peabody Conservatory. THE PEABODY CONSERVA'TORY

presents

THE AMERICAN SOCIETY OF UNIVERSI'fY COMPOSERS

SEVENTH ANNUAL NATIONAL CONFERENCE

April 7, ~ ~ 1972 6 FRIDAY, APRIL 7

10:30 A.M . Meeting of Executive Committee and National Council - East Hall

12-5 P.M. Registration - Main Lobby

2:00 P.M. Welcoming Remarks - North Hall Richard Franko Goldman, President Peabody Institute A Report on the Index of New Musical Notation Participaats: Kurt Stone, Gerald Warfield, Music Division of New York Public Library at Lincoln Center

4-5 P.M. Visit to the Peabody Electronic Music Studio - Room 317

8:30 P.M. Concert I - Concert Hall Ronald Perera ------Reverberations for Organ and Electronic Sounds (1970) Edith Ho, Organ Ralph Shapey ------Piano Trio ( 1955) Robert Hall Lewis ____ Inflections II for Violin, Cello and Piano (1970) The University of Maryland Trio Joel Berman, Violin William Skidmore, Cello Evelyn Garvey, Piano

- Intermission -

Louis Cheslock ---·------Descant for Unaccompanied Clarinet (1969) Janet Berndt, Clarinet

Allen Bonde ------··----··-·-- ·---·---- ··--··----··-----·--··--- -- Son us I ( 1972)., ., Allen Bonde, Piano

Lawrence Moss ------·-·-·-···-········-·············-·--···------Exchanges ( 1968) Peabody Contemporary Music Ensemble Richard Soule, Sharette Kern, Flutes Dorothy Scott, Oboe Ronald Bange, Linda Bange, Tmmpets Tim Beck, Trombone Robert Spaulding, Percussion Leonard Pearlman, Conductor

*First performance anywhere SATURDAY, APRIL 8 7

8-9:45 A.M. Playing of members' tapes and examination of scores - Rooms 200 and 317

10:00 A.M. "The Role of the Composer as Theorist" - North Hall Participants : Allen Forte, Yale University Carlton Gamer, Colorado College Lawrence Moss, University of Maryland Peter Westergaard, Princeton University Moderator: Richmond Browne, University of Michigan

1 :30-2:45 P.M. Business Meeting- North Hall

3:00 P.M. Concert II - Concert Hall Joel Spiegelman ...... Morsels ("Kousochki") (1967) Raoul Pleskow ...... Three Pieces ( 1968) Leo Kraft ...... Anti phonies ( 1971) - Four Pieces for Piano Duet and Tape Allen Brings, Genevieve Chinn, Pianists Larry Nelson ...... Flute Thing ( 1970) Emily Swartley, Flute Larry Nelson, Tape Operator

- Intermission -

Clifford Taylor ...... Quattre Liriche for Medium Voice, Alto Saxophone and Piano (1970) * Text: Wallace Stevens Infanta Marina Dominio del Nero L'Uomo di Neve / Delusione alle Dieci Diantha Clark, Mezzo-soprano Steve Kennedy, Alto Saxophone Roosevelt Newson, Piano John Melby ...... 91 plus 5 for Brass Quintet and Computer (1971)* Elin Frazier, Daniel A. Orlock, Trumpets Edward Curenton, Horn Robert R. Moore, Trombone Jonathan B. Dornblum, Tuba Roman Pawlowski, Conductor

*First performance anywhere 8

4:30 P.M. Reception - Schapiro House

8:30 P.M. Concert III - Concert Hall Joan Tower ...... Prelude for Five Players (1970) Natalie Parcells, Flute Margo Davis, Oboe Suzanne Grenouillou, Clarinet Wayne Parrish, Bassoon Tamara Trykar, Piano Jean Eichelberger Ivey ...... ,... Three Songs of Night for Soprano, Five Instruments and Tape ( 1971) The Astronomer I dreamed of Sappho Heraclitus Catherine Rowe, Soprano Peabody Contemporary Music Ensemble Paula Hatcher, Alto Flute Suzanne Grenouillou, Clarinet Mary Roggensack, Viola Kevin Plunkett, Cello Pamela layman, Pidno Leonard Pearlman, Conductor

- Intermission -

Peter Westergaard ...... Variations for Six Players (1963) Peabody Contemporary Music Ensemble Sharette Kern, Flute Leon Josowitz, Bass Clarinet Etsuko Doi, Violin Kevin Plunkett, Cello Robert Miller, Percussion Barbara Weintraub, Piano ., Leonard Pearlman, Conductor Ernst Krenek ...... Sonata for Violin Solo (1948) Allegro Deciso Andante Allegretto Grazioso Bruno Bartolozzi ...... Variations for Violin Solo (1964) Robert Gross, Violin

Olly Wilson ...... Piece for Piano and Electronic Sounds (1969) Roosevelt Newson, Piano SUNDAY, APRIL 9 9

10:00 A.M. "Compositional Approaches to Computer Music" - North Hall Participants: David Cohen, Arizona State University Charles Dodge, Columbia University Hubert Howe, Queens College Donald Macinnis, University of Virginia Barry Vercoe, Massachusetts Institute of Technology Moderator : John Melby, West Chester State College

12:00 NOON Adjournment 10 Proceedings, 1972

Contents

11 PANEL DISCUSSION: The Role of the Composer as Music Theorist Moderator: Ridunond Browne (University of Michigan) Participants: Allen Forte (Yale University) Carlton Gamer (Colorado College) Lawrence Moss (University of Maryland) Peter Westergaard (Princeton University)

12 Carlton Gamer The Role of the Composer as Theorist: Some Introductory Remarks 15 PANEL DISCUSSION: A Progress Report on the Index of New Musical Notation Participants: Kurt Stone, Project Director Gerald Warfield (New York Public Library, Music Division)

15 Gerald Warfield Notation: Some Observations on the Engineering Level 22 PANEL DISCUSSION: Compositional Approaches to Computer Music Moderator: John Melby (Princeton University) Participants: David Cohen (Arizona State University) Charles Dodge (Columbia University) Hubert S. Howe, Jr. (Queens College) Donald Macinnis (University of Virginia) Barry Vercoe (Massachussetts Institute of Technology)

22 David Cohen Computer Performance as Model and Challenge

25 Hubert S. Howe, Jr. Compositional Technique in Computer Sound Synthesis 11

PANEL DISCUSSION

The Role of the Composer as Music Theorist

Moderator: Richmond Browne Participants: Allen Forte Carlton Gamer Lawrence Moss Peter Westergaard 12

CARLTON GAMER The Role of the Composer as Theorist: Some Introductory Remarks

What <},oes the theorist do? First, he examines a body of given "facts", data, or phenomena. In the case of music, this examination may be aural or visual, or both, depending upon the significance and availability of the score. The "facts", data, or phenomena include not only existing compositions or compositional materials but also-since composition is a form of behavior-the human sensory and mental apparatus for their generation, reception, and interpretation. From such an examination the theorist derives general or abstract principles to explain the structural relationships which give musical "meaning" to these facts, data, or phenomena. This is the process of analysis. If the objects of examination are existing compositions, the principles derived might be termed "post-dictive" or "post-scriptive"; if the objects are compositional materials or resources-sets or ragas, for example-the principles might be termed "pre-dictive" or "pre-scrip­ tive". The theorist then relates these principles to each other to form a coherent and systematic explication of the music or compositional materials he has examined. The mode of thought employed in so doing-unlike that exemplified by music itself-is verbal and symbolic. (By "symbol" I mean something which denotes or represents a sound-event or a relationship between sound-events; I do not mean sounds themselves.) This systematic explication is the theory. Theory formation requires an understanding of the distinction betweeen musical and non-musical modes of thought. It requires also an understanding of meta-theory, or the theory of theory formation, encompassing (but not limited to) such questions as the nature and principles of rational discourse; definitions and functions of primitives, axioms and postulates, theorems and proofs; propositional algebra; and so forth.

What makes one theory "better" than another? Its power to account for more musical relationships, macro- or micro-structural, gross or subtle, not only within a composition but within classes of compositions, including potential compositions; its internal consistency in meta-theoretical terms; and not least, its "elegance", a concept which includes both its own value as an aesthetic object and its economy of means. 13

How are given theories replaced by "better" ones? By a process of subration. Subration is the mental process whereby one disvalues some previously appraised object or content of consciousness because of its being contradicted by a new experience ... Subration involves: (1) a judgment about some object or content of consciousness [in this case, a theory] .. . (2) the recognition, in the light of another kind of judgment that is incompatible with the initial judgment, that the initial judgment is faulty; and (3) the acceptance of the new judgment as valid ... [The] former judgment is radically denied by a new judgment that is based on fresh insight or experience.1

What is the relationship between theory as an object or content of consciousness and music as an object or content of consciousness? Between "levels" of sense/mental experience a relationship obtains which is analogous to that between good theory and faulty, inadequate, or invalid theory; that is, the "best" music subrates the "best" theoretical formulations about it (or about the class of musical compositions of which it is a member). I am distinguishing here once again between modes of thought. Without elaborating a theory of aesthetics, one can confi­ dently say that inherent in the nature of (and definition of) a successful aesthetic experience is the valuation of it as belonging to the highest order of sense/mental experience. One who experiences a work of art and who feels that his experience is successful, that it provides integration and insight, values that experience in ways which rule out its being contradicted and replaced by another kind of sense/ mental experience2 [for example, by theoretical formula­ tions].

How does the role of the composer differ from that of the theorist? The composer, in his role as composer, functions on a different epistemological level-some might even say on a different ontological level-than in his role (if any) as theorist. As a composer, he fashions a work of art; as a theorist, a verbal/symbolic construct. His actual or potential contribution as a theorist depends upon his understanding of theory formation and his ability to think in verbal and symbolic terms.

1. From Elio Deutsch : Aduaita Vedanta: A philosophical Reconstruction; East­ West Center, Honolulu, 1969, pp. 15-17. Deutsch's "subration" is a variant of the traditional philosophical term "sublation," which is often employed as the English equivalent of Hegel's Aufhebung or of the Sanskrit Badha. See, for example, the passage dealing with the "sublation" of dream states by waking states in the Brahma-Sutra Bhasya of Shankaracharya, trans. by Swami Gambhirananda; Advaita Ashrama, Calcutta, 1965, II.ii.29, p. 423.

2. Deutsch, op. cit., pp. 20-21. 14

Composers vary greatly in this ability; hence their contributions to theory are of greatly uneven quality and value. To be a "compleat theorist'', furthermore, is probably so demanding a task that few composers would be either willing or able to tackle it. Ideally it would involve a knowledge of metatheory and the principles of rational discourse; acoustics and audition (including the perception of music); comparative musical systems (including those of non-Western musics); and the history of "music theory".

What contribution, then, might the composer make as a theorist, and in particular as a teacher of theory? Certainly one important contribution that every composer can make is to share with his students his own compositional concerns and interests. Beyond this, he might make theory himself, if inclined and competent to do so. And even if the composer does not make theory himself, he might seek at the very least to understand what the making of theory involves. From such a vantage point he can effectively assist his students in the analysis of music, which, though it is not synonymous with theory, is nevertheless a very important part of the theoretical process. Hopefully, some may progress from analysis to fullscale theory formation, perhaps even to an eventual "theory of composition" itself. 15

PANEL DISCUSSION

A Progress Report on the Index of New Musical Notation

Project Director: Kurt Stone Gerald Warfield

GERALD WARFIELD

Notation: Some Observations At the Engineering Level

It would perhaps be best to consider this presentation an interim report of my ideas on notation keeping in mind that considerable room still remains for improvements, refinements, and more comprehen­ siveness. In light of this I am particularly interested in the criticisms of composers such as yourselves, especially with respect to the way you think about music and the way the notational ideas here presented may or may not accommodate the requirements of your own compositions. ' Although I am addressing myself to a general overview of notation, I should say that I am not primarily concerned with anything as rigorous as a formal theory of symbols. Such an approach would necessitate dealing with many problems for which we already have at least operative solutions: for example, whether or not two different quarter notes could both be symbols for the same value (due to infinitesimal differences in size, shape, etc.) or whether a hand copy that is note perfect of an original score constitutes a forgery or a legitimate copy of the piece (since in the plastic arts such a copy would certainly be thought of as a fake). A recent treatment of these and similar problems may be found in Nelson Goodman's book Languages of Art. However, the aspects of notation with which I am concerned are distinguished from legitimate theoretical questions in a clear, if heavy-handed, fashion by Mr. Goodman in the following quote: 16

"No requirement of a manageably small number of atomic characters, no requirement of clarity, of legibility, of durability, of maneuver­ ability, of ease of writing or reading, of graphic suggestiveness, or mnemonic efficacy, or of ready duplicability or performability has been imposed. These may be highly desirable properties, and to some degree even necessary for any practicable notation; and the study of such engineering matters could be fascinating and profitable. But none of this has anything to do with the basic theoretical function of notational systems.''1 So it is primarily on this "engineering" level that I will be speaking­ with perhaps occasional references to more fundamental issues. My approach will be to attempt an overview of notation. It is only through such an overview that the details-the individual problems of notation-can be treated consistently, and one can avoid perpetuating the very situation which has engendered a large part of the confusion in which the notation of music finds itself today. That situation is the ad hoc solution to specific notational problems. Don Martino, and pthers, have pointed to this as the origin of many apparently contradictory conventions with the result, in the simplest cases, of one sign designating two or more different events, or two or more signs designating the same event. Such a situation may even come about in circumstances where there is no apparent ambiguity or inconsistency of notation within the context of the piece. For instance, in a piece for solo piano a composer may decide on a certain sign for a specific effect, and he may define this sign in the preface so that it is quite clear to the performer. However, in a more general context that si:t' might have certain disadvantages. For example, the use of the sign to mean pluck the string on the inside of the piano is a particular y unfortunate choice since it means exactly the opposite in harp notation-dampen the string-that, incidently, has probably just been plucked. It is seldom that a composer has the time or inclination to deal with notational problems in a context broader that his own music. It is a luxury, however, that this project must afford. It is essential that such an effort as ours, which hopes to add some degree of order to the present notational situation, adopt consistent attitudes with respect to general notational issues so that recommendations made at the level of specific symbols be an improvement over the already-existing system. And, finally, it should be obv10us that although my presentation is geared towards the notation of contemporary music, most of my points will have application to music of the past as well. I. It seemed to me at first that what I needed was simply a more comprehensive definition of notation that did not obscure either the boundary conditions or the essential components of notation. For example, to say that musical notation is any recorded instruction for,

1 Nelson Goodman, Languages of Art, New York: The Bobbs-Merril Co. Inc., 1968, p.154. 17

or denotation of, music is too broad to be of much practical value, and immediately requires further qualification. Such a definition lumps together the oboe part of a symphony and the Pass Two output of an IBM 360 generated composition. It also fails to differentiate between notations of highly varying degrees of determinacy. The fact that some compositions are non-identifiable without their notation suggests other grounds for very basic differentiations. I wondered also if standardization was appropriate only in cases of music that is precisely notated, and further, at what degree of indeterminacy or at what degree of compositional dependency would it no longer be practical to suggest notational conventions. II. In order to begin an approach to these problems I would like to read a quote. This is by Ben Boretz and is from a paper given in a symposium of the American Philosophical Society devoted to Nelson Goodman's Languages of Art: "Sounds, then, are not part of music, however essential they are to its transmission. And neither are paint, pigment, or canvas parts of paintings, nor masses of bronze parts of sculptures, nor pages and letters parts of poems. Sounds, in fact, are not even what musical notation specifies, a matter which Professor Goodman seemingly overlooks in his discussion of such notation in Languages of Art. What scores do specify is information about music-structural components, such as pitches, relative attack-times, relative durations and whatever other . . . information is functionally relevant."2 I would like to carry this a bit further and suggest another idea the main point of which is that the sounds do not consitute "the piece." "The piece" is, rather, the relationships we form in our head about some sounds: one might savour intervretation of some sounds. The interpretation, or relationships, in our heads are integrally bound up with the reception of the sounds, and although the sounds must be at least theoretically · received, certainly we have sounds on the one hand, and reception-of-sounds-and-interpretation-of-the-sounds on the other. It is in the area of interpretation that we "understand" and thereby form our conception of "the piece." This, however, makes for some very basic problems. There is no real way of knowing whether another persons conception of "the piece" in any way resembles your own. But aside from the possibility of analysis, there is another way, and that way is to listen to a person's performance and compare it to your conception. The transmission of information in this manner is difficult at best, but a great deal can be

2 Delivered at the Sixty-sixth Annual Meeting of the American Philosophical Association, Eastern Division, on December 29, 1969, at a symposium devoted to Nelson Goodman's Languages of Art. Available now under the title "Nelson Goodman's Languages of Art from a Musical Point of View" in Perspectives on Contemporary Music Theory edited by Boretz and Cone; W.W. Norton, 1972 pp. 31-44. 18

learned. It is often in these circumstances that the composer feels it necessary to be more explicit in his notation since he can sense from another's performance how the other person "understands" his piece. Now, if I conjecture that "the piece" is the relationships we have in our heads about some sounds, am I not attempting to separate the reception of a phenomenon from its interpretation? One of the strongest points that Nelson Goodman makes, and one which is not contested by Boretz is that reception and interpretation are inseparable. In the Kantian dictum: "The innocent eye is blind and the virgin mind is empty." I don't think that I should take the time to go into this point, but certainly the Goodman book is worth reading if only for his excellent and extensive elaboration of the non-separability of reception and interpretation.

III. What I am looking for is not so much a definition of musical notation but simply a way of viewing notation which would make clear certain differentiations and enable one to deal with general problems such as those mentioned earlier. As one attempt in this direction let me suggest the following diagrammatical representation of what I would like to call "the process from composer to listener."

COMPOSER ------B------~ MECHANICAL PERFORMANCE

COMPOSER­ PERFORMER­ LISTENER

c ~ PERFORMER-~~~~~~~~~~~__::~ LISTENER LISTENER

The most direct route is for the composer to sit down and play the piece: the middle route (labeled A) 'through the composer-performer­ listener. I add "listener" to the middle stage since it is obvious that the composer is listening, interpreting what he hears, reacting, and so forth (a reception-and-interpretation example). In some cases the composer might change the piece after he played it, in which case a compositional 19 loop could be added to this diagram from the composer-performer­ listener back to the composer. But this (the compositional loop) is not a process with which we are directly concerned here. The entire "A" route could perhaps be best exemplified by jazz, flamenco, and certain types of folk music, though most of the time other performers eventually become involved, making for the more familiar route through a performer-listener: the route marked "C". (Again, a compositional loop could exist since it is a common experience that after a performance, especially a first performance, a composer may feel like changing the piece in some way.) The other route, labeled "B", is through mechanical performance. This route also has a compositional loop typical of work in electronic music where the composer hears his piece and then decides to make some changes. It is at the points marked A, B, and C that notation-type things might tbut not necessarily) appear: A. Through the Composer-Performer-Listener: Whether the composer­ performer-listener uses any mnemonic devices or not is of no concern to us. (Should the listener want to see the notation, however, in order to improve his understanding of the piece, it would then become a different situation.) B. Through a Mechanical Performance Device: Here the notational problems are not severe, at least theoretically, since what is primarily required is precision. The best example of a mechanical performance device is the use of the computer for sound synthesis. The necessity of this precision may produce conceptual problems; one may not know what the precise specifications should be, but that is a different problem from how one should specify them. Another practical consideration is that in mechanical performance it is not usually necessary for the machine to "read" the notation in "real" time, so that many perceptual problems (e.g. sight reading) become unimportant.

C; Through the Performer-Listener: It would seem that it is at this point that most of the problems of notation with which we are concerned occur. Of course, notation is not imperative here-music can be, as a matter of fact, is most efficiently transmitted aurally, but the present complexity of music certainly makes notation pragmatic. Now, what are the problems at these points. I think certainly that one of the primary difficulties concerns the difference between reception-interpretation and machine translation. Certainly there is a sort-of "interpretation " at B (which I call machine translation), but the important difference is that here it is possible to know what the interpretation is. One might have a very powerful computer macro-language, but one would know how that macro-language was being translated. Or at least one could learn how. At the other points, one could not even be sure the reception was reasonably consistent, much less the interpretation. So, I guess that there is a sense in which one could regard musical notation as an extremely powerful macro- 20

language, the translation processes of which are not entirely under­ stood. There is another important, though amorphous link between the "human" points involved here. Not only is there the shared, characteristic reception-interpretation, but there is also what I would like to call a muscial grammar. I don't like the term music "theory" for this specific notion and the term "syntax" implies certain differentiations which I will not be making. Certainly both the reception and the interpretation are linked to whatever musical grammars the receiver happens to have assimilated. As far as the notation is concerned it must, in a sense, extend at least as far as the grammar of the receiver-interpreter. When this does not happen, notational ambiguity results. Note that in any case information will be omitted, but this only becomes a liability when the omitted cannot be reconstructed, or a reasonable facsimile thereof, in the mind of the receiver-interpreter. There is a view which holds that the primary function of notation is specification of the boundary conditions of each notated event. This seems to me completely inadequate. For example, we might specify

Allegro oboe f and there might be quite a few (theoretically, an infinite) number of events that we would be willing to put in a basket thus labeled. But to think that we could plug any one of those things in whenever such an event is specified would be ludicrous. Such an event is dependent on its context, (where it is in the phrase, how many other people are playing at the same time, when the exact tempo is, etc.). In short, how we might perform this event is determined by the relationships we have formed in our heads about its context. Similarly, some hold that notation is only performance instructions. At best such a statement would have to be modified to read "interpreted performance instructions," and as we have seen earlier, reception cannot be divorced from interpretation; this view has the same inadequacies as does the previous. IV. I would like now to consider the manner in which pieces with a high degree of indeterminancy are viewed within this framework. With respect to aleatoric music and notation I will read the following quote from Ben Boretz, again from his paper on Nelson Goodman: "Precision of notation is, of course, relative to inferred "thresholds" and a piece whose pitch notation specifies only "relative height" may be one where pitch-relational characteristics function only to within "higher-than" determinations. Thus a notation would constrain the appropriate interpretations just to within the "higher-than" boundary criterion without any lack of music-structural "precision." For any interpretation conforming 21

to such a criterion contains precisely "the" correct pitch-structural information for that piece. Now this means that our present pitch notation is not necessarily more precise relative to the piece it notates than, say, that of pre-Gregorian chant, but only that what counts as compliance to it of interpreting sounds may be inferred as being more highly constrained with respect to their pitch components, and thus that our music may be interpreted as invoking discriminable pitch differences more determinately than just in terms of "higher than." However, if it is not known whether one is using a higher-than criterion in the selection of pitches, a great deal of distortion, or perhaps informational static will confuse the listener's notion of "the piece." For a long time common practice aided the listener in knowing what part of the composition varied from performance to performance - that is, how determinant the notation was. And those things that varied from performance to performance were thought of in a particular way - as being in the interpretive domain. If the grammar is such that the listener doesn't know the range of the variables, notational ambiguity results. Is it really necessary that a listener hear an aleatoric piece an infinite number of times to infer what is variable? Is it not enough that a listener know these boundaries intellectually in order for him to reconstruct in his mind a sufficient notion of "the piece." In returning to our framework we might say that with mechanical performance we are conveying something, but with human performers we are attempting to recreate something. I think, certainly, that for the receiver-interpreter to get "the piece" he has to have a fair idea of the level of determinancy of what he is hearing, or perhaps I should say of the structure of what he is hearing. Certainly one would listen to the Klavierstuck XI differently if one thought it were a through-composed piece. The knowledge that its fragments can occur in any order does a great deal to make "more correct" the listener's notion of "the piece." v. Briefly, concerning standardizations, it may be the case that standardization is practical only for the relatively determinate aspects of the notation. Whether one is specifying quarter-tone sharps or only the -relative "shape" of a line, it is those events which will remain the same from performance to performance (within the confines of the grammar), for which we might suggest notational conventions. Of course, the fact that a notation might be relatively determinate does not mean that there will be enough need for a particular symbol to suggest a standard for it. This will be the case for determinate notations that are highly compositionally dependent.

In conclusion, I should say that these suggested conventions should not restrict anyone's thinking either about composition or perform- 22

ance. If such conventions do not precisely suit your purposes, they should not be employed. This holds true especially for symbols and combinations of symbols which reflect a compositional bias such as our common method for specifying durations. Where the notation is an integral part of your conception of the composition, standards may not apply. Certainly we are not interested in standardizing Art; we hope only to perform a service.

PANEL DISCUSSION

Compositional Approaches to Computer Music

Moderator: John Melby Participants: David Cohen Charles Dodge Hubert S. Howe, Jr. Donald Macinnis Barry V ercoe

DAVID COHEN

Computer Performance as Model and Challenge

As someone who has been working longest with computer sound generation and producing the least results, I want to address myself to the subject of some limitations of computer sound generation, and suggest some ways in which working with the computer might interest people whose interest really lies in another direction. When I say limitations of computer sound generation, I am quite aware that, in theory, the computer can do anything that we tell it to do. But one of the major frustrations of someone working in this field, and I speak 23 from bitter experience, is technological. You can count on the fingers of somebody's hand (six fingers, maybe) the number of easily operable converters that we have, and having to deal with this kind of problem keeps many people from working with the computer. It takes a long time to adapt a computer program to the facility available and develop an interface with a converter. The second technological problem is the amount of time that one has to spend learning to use the technique. Even if you have a relatively simple program such as PERFORM, the one I have worked with, the problem of coding is difficult to come to terms with. I believe that coding difficulties will gradually be overcome and fewer people will find this an obstacle. This brings us to another kind of limitation of computer sound generation, one which concerns conception and imagination. If the computer can do anything that we know how to tell it to do, we may wonder why the composer made his particular choice. Why isn't it better, if he wasn't bothered by performers who can't play in tune or can't play the rhythms correctly? I think that some people are bothered by what I have decided to call the "genie syndrome." The challenge is too much; a composer suffering from the genie syndrome doesn't want to face the problem of not having limitations placed on his compositional ideas. If a genie appears before you and says, "I'll give you anything," then suddenly you don't know what it is you want. One is reminded of Stravinsky's statement that "the more limitations I place upon myself, the more freedom I have." The absolute freedom of the computer that removes all performance restrictions has been a source of frustration to me, and I think it is a kind of challenge that many composers don't dare to take. I would like to suggest a way in which the computer would be of use to those who don't really want to work in the medium. I think that the idea of the computer performance as model performance has been neglected. When you give your piece to live performers to play, you have to depend, as Blanche Dubois remarked in "A Streetcar Named Desire" on "the kindness of strangers." But in using the computer, the composer becomes performer and must be very specific about interpretational nuances. You can't simply say "crescendo," and this is a difficulty. Therefore, there are some computer realizations that would never be satisfactory to many composers. However, we know that performers sometimes play a piece better if they've heard a previous performance. Somebody said that the first performance is always the hardest. We know, anecdotally, for example, that the Boston Symphony players would not do Stockhausen's "Zeitmasse"; it was too difficult. But once the Craft performance came out, they decided it was performable, so they did it-probably not knowing that the recording had been pieced together from many takes and that the English horn player reportedly gave up music after the recording was completed. If you have a piece that has ensemble difficulties, and you can get an imperfect computer performance of it for potential performers to hear-imperfect, that is, so far as nuances are concerned, you have a better chance of getting the live musicians to play it. 24

As the technique of coding becomes easier, I think that many composers will want to make use of the computer to provide a first-step model performance of a work. And as computers and conversion facilities become more available, I think that more composers will face the challenge of "what would I do if I weren't worried about performance difficulties?" I don't know how many people are consciously worried about this; certainly if you work with the Contemporary Music Project as a Composer-in-Residence for Podunk High School, you worry about what they can do. But probably more often, it's an unconscious thing, being aware of limitations of range and difficulties of instrumental technique. At some point, every composer should face the challenge of not having to be concerned with performance difficulties, but it's a frightening thing to do.

I want to play a few examples. The first is an example of what not to do with the computer; it is a computer performance of the E Minor Fugue from the first volume of the WTC. (A musical example was played here.) The next example is a piece I wrote for woodwind trio that has been played only once by a trio; it's not really all that difficult, except when you live in Alabama or Arizona and can't find people who can hocket the third and sixth eighth note of a 6/8 measure. If I ever want a woodwind trio to play this piece, I would expect this computer realization of it to make their performance easier. (A musical example was played here.) The performance of very rapid notes is no problem for the computer and is one of the possibilities which I find very interesting. The next example is an acoustic study in which notes are attacked at the frequency of the low A on the piano, 2711z notes per second. I wondered if the rapidity of attack would produce an audible pitch and if the frequency relationships would reinforce a piece written in A. After a number of hearings I still haven't been able to decide. (A musical example was played here.) The final example also employs rapid notes - seventeen notes per second. I intend to combine it with a synthesizer accompaniment. I believe that the combination of computer generated sound with synthesizer as complementary rather than rival media is one of the important directions that electronic music will take as computer sound generation becomes more widely available. (A musical example was played here.) 25

HUBERT S. HOWE, JR. Compositional Technique in Computer Sound Synthesis

Today I would like to discuss some aspects of compositional technique concerning music which is synthesized by means of a digital computer and digital-to-analog converter. I would like to concentrate more upon the "orchestration" of such works, but since it is really impossible to distinguish between "orchestration" and "composition" in this medium, I will discuss both of these aspects together as they apply to my composition Freeze. I hope to give you some idea of the type of compositional reasoning which is made possible by the powerful programming capacities of modern digital computers. In order that we may begin with a clear idea of the type of processes that I will be discussing, I would like to clarify what I mean by the terms "orchestration" and "composition." "Composition" refers to the act of deciding what notes to write in a piece of music and the reasons that we may employ in order to choose them. "Orchestration" refers to the process of deciding what musical or sonic properties we may employ to articulate the notes that we have chosen. These two processes are not necessarily distinct; sometimes we cannot dissociate deciding what notes to write from their articulative properties, in that we always think of such notes as having these specific characteristics. Sometimes we think of having certain articulative properties before we have decided what pitches we want to have these properties. In examining a finished composition there is no way of knowing which of these decisions preceded the other, and sometimes this is true even of our own compositions. After all, this information is not necessarily relevant to the finished product. Computer sound generation provides a composer with perhaps the most versatile orchestrational possibilities of any musical medium, for the properties with which a note can be endowed are virtually limitless. But every characteristic which the sounds are to possess must be specified explicitly by the composer. In a sense, then, this only makes the process of composition more difficult, for there are now many more characteristics to think about. We must also remind ourselves that these characteristics include all the familiar properties of sounds produced on conventional instruments, and so it is not necessarily the case that computer music will sound any different from other music in this respect. This background information must be kept in mind as I now begin to discuss the specific properties of my composition Freeze. The fact that I have chosen to illustrate compositional technique in computer sound synthesis by an extended example means that I will be covering only a very limited area. Nevertheless, I feel that the characteristics I have used in this composition are probably quite different from those which are likely to be used by composers of instrumental music, or even of other kinds of electronic music, and so it is a good example for illustrative purposes. First, I am going to discuss some of the compositional aspects of 26

Freeze, and then the orchestration of the composition. This does not necessarily imply that one of these processes preceded the other, and in fact in this case both of them were conceived together as I composed the piece. Freeze is based upon a multi-dimensional array consisting of eight (3x4) arrays and one (4x4) array which "summarizes" the ways in which the component (3x4) arrays are related. All of the arrays are generated collections, and although a knowledge of the structure and properties of generated collections is indispensable for understanding the internal relations among the component two-dimensional arrays of the multi-dimensional array, I will not cover this subject here because I have written about it extensively in my doctoral dissertation.1 I would like to add, however, that I have used the same arrays in several other compositions, 2 which I possess strikingly different surface character­ istics. Freeze divides into four sections internally, although the surface resemblance of the middle two sections is so similar that they appear to be one large section. The other sections are also similar in this manner, but since they are separated by the inner sections their division is clear. Each section of the composition articulates a succession of pitches which state the same total collection ( excl. 0 1 2 7 o) twice in a different manner. (This collection is stated twice both successively and concurrently, so that, at each moment, several kinds of associations are present simultaneously.) The manner in which this collection is stated, of course, has to do with the structure of the arrays on which the piece is based. The title "Freeze" is in tended to reflect the redundancy in the materials on which the piece is based, but actually, when I began writing the piece I had quite a different idea in mind, for which the term "freeze" is even more appropriate. I envisioned a piece for an ensemble of performers in which each person would play exactly the same thing each time he played something; the structure of the piece would be determined by the way in which these materials combined to form a complete impression. As I worked on Freeze, though, this idea became less and less a part of the piece as it ultimately emerged. The most obvious surface characteristic of the composition which relates to the structure of the arrays is the number of registers in each section and the density of pitch-classes attacked within each measure. The outer sections (1 and 4) employ five registers (5.00-9.00) and a density of five pitch-classes in each measure. (In each measure, however, there are 12 pitches stated, so that there are several octave and unison doublings present.) The pitch content of these sections, measure-for-measure, is identical. Section 2 employs five registers and a density of four PCs per measure, and in section 3, six registers (5.00-10.00) and four PCs per measure, although in section 3 the lower two and upper two registers are coupled, so that certain tones in

1. Multi-Dimensional Arrays, doctoral dissertation, Princeton University, 1972. 2. First Study in Timbre, Interchanges and Macro-Structure. 27 this section are doubled four octaves apart. The duration of each tone is a function of its weight within the statement of the total pitch collection. In sections 1, 2, and 4 some tones receive a duration of half a measure and others a duration of a full measure, while in section 3 the durational values are a full measure, half measure, or a quarter of a measure. Each section except the last overlaps the next section, as each measure overlaps the next measure, to such an extent that, once the piece begins, there is no moment of silence until it is over. Since it lasts over eleven minutes, this fact posed a great problem for the computer, for a full stereophonic recording of the piece at the sampling rate which I wanted to use could not be contained on a single reel of digital tape. I had to employ a sampling rate of 14,000 samples per second, which is rather poor quality. There are several minor distortions of high-frequency sounds on the tape, sounding like rapid "clicks," which would have been eliminated if I had been able to employ a sufficiently high sampling rate. Nevertheless, in spite of these problems, the overall sound quality of the piece is exceptionally good. The tempo of each section is extremely slow: 24 beats per minute in sections 1, 3, and 4, and 20 beats per minute in section 2. This does not mean, however, that tones are attacked only at this rate, because some of the articulative properties used to interpret the pitches at this level consist of several independent components. Each tone always consists of at least two component "sub-tones," and at times the composition appears to have a very fast tempo, even though the super-structure which is controlling the entire mechanism is always moving at the same constant, slow speed. Before I go into the specific articulative properties used in each section, I would like to state the most important "orchestrational" characteristics of the entire composition: each variable characteristic of each tone changes by a factor of one-third over the course of the tone's duration; and over the course of each section, the total variation of all characteristics changes by a factor of one-third. Furthermore, each register employs a different basic speed, the lowest being the slowest and higher registers getting progressively faster. The basic speeds of the registers are, from lowest to highest, 12/48, 13/48, 14/48, 16/48, and 17/48. Finally, the speed of variation of different characteristics is related by a specific ratio. In sections 1 to 3, the characteristics all increase by a factor of one-third over the course of the section, and in section 4 only they decrease. 3Thus, a kind of "climax" occurs at the end of section 3, when the texture returns to that of the opening. The external physical properties of sections 1 and 4 are identical, although the manner of variation of these properties increases in section 1 and decreases in section 4. Each "note" is articulated by two separate

3. The manner of variation is always one-third with respect to the speed at the beginning of the section: section 1 goes from 1 (1.00) to 4/3 (1.333); section 2 from 4/3 (1.333) to 16/9 (1.777); section 3 from 16/9 (1.777) to 64/27 (2.3704), and section 4 from 64/27 (2.3704) back to 16/9 (1.777). 28

tones of identical pitch but different timbre. The basic tone which is used for the entire piece consists of a fundamental frequency and all harmonic partials, at equal amplitudes, up to 4/5ths of 1/2 of the sampling rate SR. Since SR equals 14,000, the highest frequency em­ ployed was 5600 cycles per second, which is higher than the uppermost note on the piano. The timbre of each of the two component tones of each "note" in section 1 is produced by one resonant filter with a different center frequency. All filter bandwidths are 10 per cent of the center frequency, and all tones are first processed by a low pass filter with a bandwidth of 2500 cycles per second before they are fed into their respective filter. The center frequency of each filter is correlated to two properties of each tone. Each property determines a different interval of transposition above a base center frequency, which is dis­ tinct for each register. The base center frequencies start at 8.07 (G above middle C) and proceed upwards by perfect fourths, so that for higher frequencies they start at lower partials. Following the resonant filter the tones are processed by a comb filter with a loop time equiva­ lent to one cycle of a pitch one octave below the minimum base center frequency of the other filters. Each of the two tones which articulate each "note" of the score is attacked several times over the course of its duration. The cycle of each of these envelopes consists of an attack, sustain, and decay time of 1/4th of the cycle, followed by a silence of 1/4th the duration. The two tones are attacked 180 degrees out of phase with respect to each other, producing a kind of "location modulation" and, since one tone decays as the other rises, also a "timbre modulation." This is one of the characteristics whose speed varies by a factor of one-third over the course of the note. The other characteristic which varies in this manner is the overall amplitude of the tone, which produces a crescendo in section 1 and a diminuendo in section 4. The properties used in sections 2 and 3 are considerably more complicated than those in sections 1 and 4. Each tone is given one of two generative properties and one of two articulative properties. One of the generative properties consists of applying amplitude modulation of varying speed and amplitude to the basic tone. The other generative property consists of interpreting a given pitch as the first tone of a sequence of separate pitches in the same register. This type of generative property, by which one "note" is interpreted as specifying multiple pitches in the "foreground" level of a composition, is called a "compositional macrostructure." The speed of attacks of these tones increases by a factor of one-third over the course of each tone, and by a factor of one-third over the course of each section. All sequences consist of the same pitches, which state the entire collection of eight pitch-classes of the arrays on which the piece is based, but the order of pitches within each register is different, and each sequence contains a number of repetitions of the same pitch. The specific order of pitches within each register reflects the rhythm of the entire composition, in a manner that is derived directly from the arrays on which the piece is based. The basic rhythm is also reflected in the number of pitches in 29 the sequence, which consists of 10 pitches in section 2 and 12 in section 3. In sections 2 and 3, both of the generative properties consist of cyclic characteristics whose speed varies over the course of each note. Only one of the articulative properties has this characteristic, however. The two articulative properties are, first, reverberation, and second, a periodic filter modulation. Before considering the specific qualities of the articulative properties, let us cover the basic materials which they operate upon. Each note in sections 2 and 3, as in sections 1 and 4, consists of two tones of identical pitch with a fundamental frequency and all harmonic partials up to 4/5ths of 1/2 of SR which are first fed into a low pass filter and then into a resonant filter. The center frequencies of the resonant filters are determined as in sections 1 and 4, but instead of being overlapped in a process of cyclic reattacking, each tone is performed simultaneously and sent to a different output channel. The generative property of amplitude modulation is then applied to each of these tones 180 degrees out of phase, so that one of the tones increases in amplitude while the other decreases. The generative property of a sequence of separate pitches also produces two tones of identical pitch with different fixed resonant filters. The center frequencies of the vari­ able resonators start at the base center frequencies for each register and vary up to one octave above that center frequency and back over the course of each cycle. Thus, the variable resonator always starts below a given fixed filter's center frequency and sweeps above it before return­ ing to the base level. When these tones are then given reverberation, each output channel is kept distinct, so that different partials of the same pitch are resonated differently in each reverberator. When these tones are processed by variable filters, each channel is also kept distinct, but the characteristics of the variable filters (not the fixed filters) are the same for each channel. Finally, I mentioned earlier that the speed of variation of different characteristics is related by a specific ratio. In sections 1 and 4, there is only one variable characteristic-the cyclic reattacking of the two constituent tones of identical pitch but different timbre-and the primary distinctions between these tones is reflected in the speeds employed for different registers. But in sections 2 and 3 we have three variable characteristics: amplitude modulation, sequences of separate pitches, and variable resonators. The basic speeds of each of these characteristics, in the order presented above, are in the ratio of 5 to 1. This is to say that the speed of amplitude modulation is five times the speed of the sequence of separate pitches (actually, both of these characteristics could never be present on the same tone, because they are both generative properties), which is in tum five times the speed of the variable resonators. Nevertheless, the speeds of each individual register are still kept distinct, and in the same ratio of from 12/48 to 17 /48 as described above. The basic speed of amplitude modulation is 40 cycles per second, but this factor must be multiplied by the 30

appropriate register constant to determine the precise speed for a given register. Thus, the speed at the beginning of section 2 for the lowest register would be 10 cycles per second, increasing to 13.33 cycles per second at the beginning of section 3 and to 17 .77 cycles per second at the end of section 3. The basic speed of the sequences of separate pitches is 8 cycles per second (l/5th of 40), and the basic speed of the variable resonators is 1.6 cycles per second (l/5th of 8 ). The factors for other variable characteristics may be computed from the basic speeds for different characteristics and the registral constants. I hope that this discussion of a detailed example of the sound qualities employed in this computer-synthesized composition provides a glimpse of compositional technique when working in this medium. Depending upon the way you think about it, this may or may not be comparable to "ordinary" compositional technique. Certainly the composer must have a more detailed knowledge of properties of sound and how to specify them in order to use this medium effectively, but he also has a virtually unlimited range available to him. 31

A 33-1/3 rpm recording of computer music compositions and examples referred to in the preceeding articles is available upon request for a minimal handling fee. Fill out the form below. Please allow at least 14 days for delivery.

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33

American Society of University Composers

Proceedings of the Eighth Annual Conference, April, 1973

Held at Arizona State University in Cooperation with the School of Music, Arizona State University 34

Founding Committee

BENJAMIN BORETZ, DONALD MARTINO, J.K. RANDALL, CLAUDO SPIES, HENRY WEINBERG , PETER WESTERGAARD, CHARLES WUORINEN

National Council (1973)

DAVID BURGE (Chairman), MARSHALL BIALOSKY, GORDON C. CYR, RICHARD HERVIG, MICHAEL HORVIT HOMER KELLER, DONALD MACINNIS, JOHN ROGERS, STEPHEN SCOTT, LUDMILA ULEHLA

Executive Committee (1973)

RICHMOND BROWNE, THOMAS CLEMAN, JOHN SELLECK, BRUCE TAUB, ELIZABETH VERCOE

GERALD WARFIELD (Chairman)

Proceedings Editor

WARNER HUTCHISON 35

DAVID COHEN, CHAIRMAN

Eighth Annual Conference, 1973, Tempe, Arizona A native of Pulaski, Tennessee, David Cohen served briefly as a Criminal Investigator in the Philippine Islands in the post-World-War II period because of an incredible Army foul-up. He studied composition with Vincent Persichetti at the Philadelphia Conservatory and Juilliard School, fugue d 'ecole with Madame Ple-Caussade at the Paris Conserva­ tory on a Fulbright Scholarship and completed his DMA in composition with Ingolf Dahl at the University of Southern California. A participant in both Princeton Seminars in Advanced Musical Studies, he is a founding member of ASUC and is the only member known to have attended all the National Conferences. He has taught at the University of Alabama (1955-67) and Arizona State University (since 1967) and has published notes on Finnegans Wake, music of the "Radical Center" and computer sound generation. Recent electronic scores include incidental music for university productions of Ko pit's Indians, Ionesco's Rhinoceros, Williams' "A Streetcar Named Desire" and Strindberg's Ghost Sonata. 36

DEPARTMENT OF MUSIC ARIZONA STATE UNIVERSITY

presents

THE AMERICAN SOCIETY OF UNIVERSITY COMPOSERS

EIGHTH ANNUAL NATIONAL CONFERENCE

Apriil 6, 7, 8, 1973 37 FRIDAY, APRIL 6

8:00 AM - Registration-East Entrance, Music Building 5:00 PM

10:30 AM "The Society and its Relationship to the Professional Music Theorist-Music Theatre Participants: David Burge, University of Colorado William Penn, Eastman School of Music Gerald Warfield, Music Division of New York Public Library at Lincoln Center Moderator: Richmond Browne, University of Michigan

1:30 PM "Music in China Since the Cultural Revolution"-Music Theatre Chou Wen-Chung, Columbia University ·

3:30 PM Concert I, Music for Clarinet, performed by Phillip Rehfeldt, University of Redlands-Music Theatre James Tenney Monody for Solo Clarinet (1959) Harold Oliver Discourses for a Clarinet Alone ( 1967) Elliot Borishansky Three Pieces for Solo Clarinet ( 1972) Slow Fast Slow Intermission Burton Beerman Sensations for Clarinet and Tape ( 1969) 0 Donald Martino A Set for Clarinet ( 1954) 0 Allegro Adagio Allegro Intermission Barney Childs Barnard I for Clarinet and Piano ( 1968) 0 0 Barney Childs, piano Ronald Pellegrino S & H Explorations for Clarinet and ARP 2600 Synthesizer ( 1972) Ronald Pellegrino, ARP

5:15 PM Reception-Apache Room, Howard Johnson's Motel

8:15 PM Concert II--Music Theatre Carlton Gamer Piano Raga Music ( 1971) Richard Bunger, piano Gerald Warfield Variations and Metamorphosis for Cello Ensemble Variations Metamorphoses Variations 38 1:30 PM Business Meeting-Recital Hall 39

4:00 PM Concert III-Music Theatre

Morton Subotnick Prelude No. 4 for Piano and Tape Virko Baley, piano Roger Harris Silent Things ( 1972) Phillip Rehfeldt, clarinet Ralph Lockwood, horn Sandy Siegel, vibraphone Thomas Hancock, piano Stephen Scott Glacier Music for Woodwind Quintet and Tape Delay ( 1972) Paul Hazlip, flute Paul Dublinski, oboe Jacqueline King, clarinet Ann Vance, horn Andrew Bunch, bassoon William Penn And Among the Leaves We Were Passing ( 1972 ) 4 Channel tape Intermission Victor Saucedo Piano Music No. 11 Harold Kafer, piano Arthur Layzer Morning Elevator (film of computer graphics with computer generated sound) Gregory Levin Black Point Cutoff (film of a performance of the first movement of "The White Goddess") Newton Strandberg ASK!

Paul Hazlip, piccolo Edward Marquez, bass clarinet Tom Hancock, piano Sandy Siegel, vibraphone

Trumpets Trombones Russell Capri Becky Watkins Jason Fisher Brian Miller Ronald Milco Jay Wise Robert Duvo Stephen Gamble Conductor, Ralph Lockwood 8:15 PM Concert IV-Music Theatre Burton Beerman Misogamy for Tape and String Quartet Karel Husa String Quartet No. 3 Allegro Moderato Lento assai Allegro possibile Adagio 40 New Art String Quartet Frank Spinosa, violin Eugene Lombardi, violin William Magers, viola Takayori Atsumi, cello

Intermission

Edwin London Poebells for Narrator, Singers and Percussion Ensemble

L. Vickerman, Narrator P. Parson, soprano H. Crook, tenor T . Siwe, conductor

SUNDAY, APRIL 8

9:30 AM "The State of New Music Performance Ensembles in the Univer­ sity: Past, Present and Future" ( 1972) Participants: Virko Baley, University of Nevada, Las Vegas Sidney Hodkinson, University of Michigan . Pauline Oliveros, University of California, San Diego Richard WP-mick, UnivP-rsity of Pennsylvania Moderator: Edwin London, University of California, San Diego

11:30 Adjournment 41 Proceedings, 1973

Contents

42 PREFACE: A.S. UC: An Overview of the Year's Activity Gerald Warfield (Chairman of the Executive Committee) 44 COLLOQUIUM: New Developments in Synthesizers and Live Synthesizer Performance Paul Earls (Massachusetts Institute of Technology New Music Synthesizer Modules Everett Hafner (Electronic Music Studios of Amherst) The Future of Electronic Musical Instruments Ronald Pellegrino (Moderator) (Oberlin Conservatory) Some Thoughts on Thinking for the Electronic Music Synthesizer Also Appeared: Morton Subotnik (California Institute of the Arts) 61 PROCEEDINGS OF REGIONAL MEETINGS Barney Childs (Johnston College, University of Redlands) Some Notes Toward a Philosophy of Notation David Cohen (Arizona State University) A Reexamination ofAll-Internal Rows Stuart J. Petock (University of Nevada, Reno) Multiple Values in Music Phillip Rehfeldt (University of Redlands) Clarinet Resources and Performance John Selleck (Columbia University) Computer Partitioning 111 EPILOGUE: Letter from Ezra Laderman concerning the proposed bicentennial commissioning by the Chicago Lyric Opera Company ·

112 MEMBERSHIP LIST 42

An Overview of the Year's Activity

GERALD WARFIELD (Chairman of the Executive Committee)

Dear ASUC member:

During the last fiscal year our Society conducted the following activities: 1. There were 16 ASUC concerts all over the U.S. Almost 100 compositions were performed representing the work of over 75 composer members. 2. Publication of the scores of member composers was initiated in the ASUC Journal of Music Scores. 3. The third program in the nationally distributed radio broadcast series was completed. The entire series so far contains works of 16 composers, and over 60 radio stations have either broadcasted or requested the programs. 4. National and local conferences were held throughout the U.S. 5. Two Proceedings were published which contained the writings of 31 American composers. 6. There were three issues of the Newsletter giving reports on the activities of member composers; publication and performance opportunities; awards and grants; festivals; contemporary music programs and positions available. 7. A composition contest was jointly sponsored with the Arizona Cello Society. 8. Support was given toward efforts to revise tax laws that discriminate against composers (CCALM). Between the lines of the above list are two important assumptions. The first is that it is valuable for a composer to know his colleagues. Ordinarily, we know one another to varying degrees through our works, but there is also the benefit of direct personal contact which often provides creative stimulus, greater perspective, new opportunities and (even) encouragement. This is very subjective, of course, and little else need be said here except that from my own personal experience one of the greatest benefits I have received from my work with ASUC has been to come to know many of my fellow composers some of whom I might otherwise have not had the opportunity to work with or to meet. 43

The second assumption is that there are certain things that groups can do more effectively than individuals. Whether the university is our ghetto or our promised land it is surely through a concerted effort that we will improve specific university-related problems and that we can also develop other much needed options for the professional composer. Composers, however, are seldom "joiners." Some feel that their interest in other composers is at the risk of their own artistic integrity. Others, given the financial requisites facing every aspect of the composition and performance of contemporary music, find it easier to insulate them­ selves in a (sometimes) secure academic position. But probably the greatest barrier to social or political unity among composers is their intolerance of one another. It is this which causes us, ridiculously enough, to suffer the most at our own hands. Without undervaluing the individual (composition is still a solitary act) it is my belief that unity may be beneficial, at least, and perhaps necessary if the lot of the composer is to be improved. Those advantages that ASUC has so far been able to offer are possible because we are an organization of composers. Considering the present state of the profession I am sure I do not have to tell you that there is a great deal to be done, but perhaps I do have to remind you that it is we who must do most of it. Gerald Warfield 44

COLLOQUIUM

New Developments in Synthesizers and Live Synthesizer Performance

Moderator: Ronald Pellegrino Participants: Paul Earls Everett Hafner Morton Subotnik

PAUL EARLS

New Music Synthesizer Modules

For the past few years my work has been to use music with the other arts on an environmental scale. As a result of this work I have developed, with the collaboration of Bart Johnson of M.I.T., a series of independent electronic music modules which are suitable for professional studio and instructional purposes as well as for environmental installations. Most of the circuits were modified from those designed for experimental laboratory use at M.I.T. They are characterized by their basic simplicity, flexibility, reliability, stability, and compatibility with other modules as well as with conventional audio and synthesizing equipment. My first environmental installations used existing synthesizers, particularly the portable Synthi and Studio Electro-Comp. Both performed well, but were not as flexible as I needed, and I required additional units to accomplish my goals. One of these installations was at the Wadsworth Atheneum's Tactile Gallery. A multi-timbered sound floor was constructed for collaborative playing by groups of blind or blindfolded people. This combined modified conventional instruments with electronic materials, all of which was organized through chess moves through the matrix, with the knight's moves assigned to the Electro-Comp. Triggering any such unit is easy, but the most successful method we could find for actually altering the system was to assign one space to load a large capacitor patched into the Electro-Comp voltage system. I also altered one of the commercially available intrusion systems (which operates on a Doppler effect) to voltage-control another oscillator. 45

My Sounding Space installation (Hayden Gallery 5/72, and Vancouver Art Gallery 2/73) uses the Eigen frequencies of a large space to generate sound, through controlled microphone feedback, so that movement through the space alters the standing wave-forms, thus the sounded pitches. A Synthi-I was used, on a triggered basis, to spray a variety of pitches into the area to encourage potential unsounded harmonics. However, the real heart of this installation depended upon controlling the high-gain amplifier feedback, which was done with low frequency oscillators and multipliers. At present I have a joint work (with the sculptor Michio Ihara) traveling around to various U.S. Science Museums for which a number of the modules had to be built. It is a large moving sculpture, named PAN, whose movements and sound are inter-active with each other, the outside world, and stored informational patterns. It has the capability of a small synthesizer built into it, along with delay lines, feedback circuits, and some special digital circuity which led to our Extended Pattern Generator. Three modules are now available for others. These are each housed in very tough aluminum boxes with all jacks, knobs, etc., built in, and most have their own power supplies built in so that they can be plugged directly into the wall. It was not my intention to go into the synthesizer business, but circuit boards must be printed in quantity to be economical, and I see no reasons why others should go through the development problems I had to. In my opinion, their performance surpasses or equals any units available on the market, either individually, or as a part of a more complete system. The teaching potential of such a system is enormous, as beginning students need only a few portable units to work with. Yet a dozen such units could be brought together for a very powerful synthesizer. We are now working on a push-button controller for all modules, but they can be controlled by an electric piano keyboard, or any of the controllers available with other synthesizers. All signal and control inputs and outputs are through miniature phone plugs and jacks. Sub-miniature potentiometers and toggle switches are also used, allowing a maximum of controls in a small space. Each module measures 7%"x6"x21h".

Description of the units

MASTER OSCILLATOR Contains three attenuated inputs which mixes with a center-frequency knob to control the pitch, plus an additional input to modulate the duty cycle of a Square wave. Internal pitch control in two ranges; total range is approximately .1 Hz. to 20 KHz. Eight simultaneously available independent outputs, four of which are fixed waveforms (Sine, Triangle, and bi-polar Square (50% duty cycle)), one is a voltage-varible duty cycle Square, plus three mixable outputs: Sine to Triangle, Sine to Square, and Triangle to Square. Has a built-in power supply which can also power other modules. Price, as of 3/73: $165.00. Allow 4-6 weeks for delivery. 46

MULTIPLIER OSCILLATOR A dual unit, with two modules in one housing. Multiplier circuit outputs the product of two inputs, and can be used either to ring modulate or generate envelopes. At sub-audio controlling frequencies it is a voltage controlled amplifier and gating circuit, since zero on either input produces zero at the output. Multiplier has two attenuated inputs, with internal switching directly patching the sine output of its VCO into one of the lines, AC-DC switches on both inputs, and two paralleled outputs.

The Oscillator has two attenuated inputs for voltage control, an internal pitch control, four independent outputs: Sine, Triangle, and bi-polar Square Waves, with a range of approximately .1 Hz. to 10 KHz. Multiplier-Oscillator has its own power supply built in. Price, as of 3/73: $185.00. DUAL OSCILLATOR Contains two identical oscillators, each with two attenuated inputs, range switch, internal pitch control, with fixed and variable waveforms similar to Master Oscillator. Available with power supply ($165) or without ($145). DUAL PATTERN GENERATOR Produces a psuedo-random sequence of voltages, with the pattern length (before repetition) switchable from 16 to 1024 events. BuDt from J/K flip-flops, has potentiometers on every position allowing a mixture of fixed (by voltage width) and random values. Internal clock is variable from .1 Hz. to 10 Hz., or it can be externally clocked by another oscillator. Three outputs, two producing different sequences, and one summing both. Portamento control to interpolate between events. Normal use is to generate voltage values for another module. It generates a DC output. Includes 5VDC power supply, but requires a stable plus/minus 15 VDC external power source, such as is used to power the Master Oscillator. Price, as of 3/73: $165.00. The major portion of the cost of these modules is assumed by the jack, knobs, pots., and power supplies, as well as their mounting. Anyone who has the necessary skills can get these units in kit form for a 15-20% reduction in cost. Also, the trend is for lower prices in integrated circuits, which will result in some reduction in unit costs. All units come with detailed instructions for their use. Also under development are voltage-controlled filters, separate envelope generators, · and environmental processing modules. More specific information, as well as current prices, can be obtained by writing directly to me c/o the Center for Advanced Visual Studies, M.I.T. W-11, 40 Massachusetts Ave., Cambridge, Mass. 02139. 47

EVERETT HAFNER

The Future of Electronic Musical Instruments

If synthesizers for the production of electronic music are to emerge from the studio into the concert hall, several difficult issues will have to be faced squarely and dealt with. The basic ingredients of the problem are, in my view, no different from issues encountered in the evolution of every other musical instrument which, in passing through its experimental stages into final and familiar form, has found its place on the palette of sound that is designed by composers, brought to life by performing artists, and recognized by the listening public. There are, in fact, three classical stages in any such evolution. First, there is standardization of design in the functional sense. Wherever he plays, the pianist knows that he will face 88 keys with fixed register and more or less predictable touch, and an acoustic system (hamm'ers, strings and resonators) with output characteristics that fall within reasonable limits. There are, of course, enormous differences in workmanship and quality between one piano and the next. The maker of a fine instrument takes pride in, and charges us for, such things as its smoothness of action, sonority of tone, stability of intonation and beauty of exterior finish. But since the period of experimental development, which in the case of the pianoforte ended a century ago, he has not permitted himself to stray far from a standard design of the controls most accessible to the pianist's hands and feet. Now at the beginning of its own history, the synthesizer has not yet found a standard form t o any significant degree. Details of electronic design vary widely among the many instruments now available, with the result that it is frequently difficult to interconnect them. For example, the keyboard controller of one system may not be compatible with the oscillators of another. But much more important than problems of this kind is the individuality - indeed, the uniqueness - of each design from the performer's standpoint. In order to master the synthesizer, he must be thoroughly familiar with its panel layout and patching technique, as well as with the characteristics of each of its modules. In the present state of affairs, he tends to be wedded to the system which he encountered, by chance, at the beginning of his training. It is perhaps not too soon to hope for progress toward uniformity in basic aspects of synthesizer design. We are at the end of the first decade of commercialization of these instruments. It has been a time of intense experiementation on the part of manufacturers and composers; we have a right to expect that they can be brought to a consensus on at least a few basic points of engineering and layout. If some agreement could be reached on external features of the instrument, the differences between machines would be confined, as I think they should be, to details of electronic design, quality of components, and overall workmanship of construction. The result would be a generation of synthesizers at different levels of price and sophistication, but all possessing very much the same outward appearance. 48

Every manufacturer of synthesizers has, by now, introduced a small and inexpensive instrument with a basic complement of modules that tend to be more or less common to all: keyboard, three function generators, noise source, filter, envelope shaper, and voltage-controlled amplifier. They differ widely in the technique of interconnecting modules (by patch cord, switch, slider pot or matrix board), in panel layout, in keyboard design, and in the provision of supplementary modules (ring modulator, reverberation, sampling circuit, sequencer, input amplifier, stereo output, XY controller, internal speakers and so on). These differences can be frustrating and bewildering to the composer or performer who is not willing to confine himself to one system. For his benefit, and for the benefit of the industry as a whole, I suggest that manufacturers seek agreement on an optimized basic design, incorporating the best features of all present systems. Following standardization of outward design, the second stage of evolution is the growth of a common repertoire for the instrument. If the musician is not to be entirely on his own, he needs access to a literature of pedagogical studies and performable works, made familiar through recitals and recordings. No significant amount of such a literature can be said to exist for the synthesizer, and the most obvious reason is the lack of a conventional scheme of notation. Another may be the enormous flexibility of the synthesizer which, unless it is controlled by a computer or constrained to play like a clavier, does not lend itself easily to execution of a planned chain of events. But all of the difficulties in the path of a written literature can, I think, be traced to problems in synthesizer design. Too little attention has been given to development of an instrument whose settings can readily be put down on paper. It is also likely that a repertoire will begin to grow more rapidly only after agreement has been reached on design standards. To draw a parallel that is not far-fetched, imagine that the early pianoforte designers had been grouped into proponents of 12-tone, 19-tone, 31-tone and 53-tone divisions of the octave. (The example is not far-fetched because good musical arguments can be made for each of these scales.) Composers would then have had to split four ways, a common musical notation would have been difficult to devise, and a performer's skill on one instrument might not have been easy to transfer to another. If the variety of design had persisted, we would have retained great flexibility in the piano sound, but we might not have had the Beethoven sonatas. Some composers argue that a written notation for electronic sound is impractical and unnecessary. A recording on tape or disk, they say, is the only sensible way of giving permanence and reproducibility to such complex music. Thus the "literature" of the future, to be studied in the same way that the old-timers studied scores, is to be a direct recording. And as for the copyright problem, one can after all produce a written record in the form on an oscillograph output. Or one can make new laws that accept tapes as adequate documents. It is an interesting point of view, and attractive to those who see electronic composition as a complete - and very welcome - break with 49 the past. In a sense, of course, they are bound to be right. The composer need no longer be hemmed in by fixed tonalities and timbres, limited registers, slow-moving fingers and shortage of breath. He can hear, and edit, his most complicated work as soon as he composes it, without having to convene a hundred players. In principle at least, he has the entire spectrum to draw from at the touch of a switch. But another view, which I support, sees electronic production and control of sound as no more than the latest in the long line of technical aids to composition and performance of music. If its promise is fulfilled, it may become the Twentieth-Century contribution to the development whose history includes the Cremona violins of the Seventeenth Century, equal temperament in the Eighteenth, and the symphony orchestra in the Nineteenth. Every such breakthrough produces technical and conceptual changes which, after a period of confusion, are absorbed without necessarily destroying any of the older techn\ques on which music continues to depend. Furthermore, according to this view, the revolution we are witnessing now is not by any means to be the last. There may be limits to the variety of sound that the human ear can sense or the brain conceive, but we are still very far from approaching them. The third and final evolutionary stage is acceptance of new musical techniques by a listening audience whose tastes and expectations have grown beyond their old compass. No matter how they may fascinate composers, experiments in music cannot live and breathe and reproduce until this stage has been reached. And I believe that acceptance of the synthesizer as a musical source will occur only after the instrument has achieved a relatively fixed form, and a literature of studies and concert pieces has grown to the point where a student of the instrument can approach it in the conventional way. Beginning at the level of elementary school, he must be able to find courses of instruction, instruments on loan, practice studios, and opportunities for performance in public. The realization of these goals is not a simple matter; it is the obligation of all of us concerned, whether as composers or performers or teachers or instrument makers, to clear away confusion by moving toward agreement on a number of essential points. For example, we should settle the question of what we are talking about in the most general sense: is it no more than the development of a new musical instrument to be used in music of all forms and periods, or is it a qualitatively new form of musical expression breaking away from almost all past experience? This question, on which I have given my own view already, seems to have been hanging in the air for much too long a time. We speak of the synthesizer (or in common parlance the Moog, one more example of commercial synecdoche) as if the focus were on the instrument and as if a standard configuration had been found. But at the same time we speak of electronic music as if it were an entirely new form with a status comparable with that of, say, opera or the classical sonata. Both of these implications may in fact tum out to be valid, but we are surely not yet at the point where we can say so. 50

We should be wise to begin by giving the instrument a name. Everybody seems to agree that the word "synthesizer" is an unfortunate choice. It suggests that the purpose of the instrument is to fabricate the waveforms and formants of other instruments, in the same way that chemists synthesize nylon and rubber. But most of us insist that this is the least interesting exercise. The word also suggests, from its engineering connotations, that the instrument builds up waveforms by summation of harmonic components. This again is not the case; like any other musical instrument, it generates characteristic waveforms which are filtered, shaped and resonated before they are heard. The word reinforces a common view that the sound of the instrument is cold, unnatural, inhuman and altogether without beauty. And it forces practitioners of the art into the unhappy position of being called "synthesists." Surely, with a world of alternatives to choose from, we can find one that expresses our meaning and is at the same time more graceful. Why not, for instance, look into the past and give permanent recognition to an early pioneer either by using his name or the name he gave his instrument? For example, one of the first inventors in the electronic age of music was Jorg Mager (1880-1939), a Bavarian schoolmaster who constructed a quarter-tone harmonium and then, in 1924, went on to develop a family of electronic instruments using the heterodyne principle that had recently been introduced in radio receivers*. He called his first device the "Spharophon" and it became known in English as the "Electrophone." It happens that the same name had been given, late in the Nineteenth Century, to a telephone service which delivered, in the privacy of the subscriber's home, music from distant concert halls. Mager's instrument, like most of its electronic contemporaries, did not survive; only after the advent of the transistor did it become possible to build versatile, small and economical systems for music, and the response of composers and engineers to the new opportunity was immediate. But the word electrophone, meaning simply "the production of sound by electricity," is as appropriate today as it was fifty years ago. Could we not adopt it once again as the name of a new instrument suited to the needs of musicians of our own time? The major task before us, if we attack the problem along the lines I have suggested, is the adoption of standards of design. There is much to be learned from the experience of composers, performers and engineers over the last dozen years of experiment, but not if we persist in defending one system or another to the detriment of all the rest. Let us instead examine the best features of everything that has been accomplished so far, and combine them in the next generation of

* Commercial broadcasting became practical in 1922 with the invention of copper-to-glass seals and water cooling for vacuum tubes at high power. The following decade with a Golden Age of electronic music: after Mager's instrument came the Etherophone (1927), the Ondes Musicales (1928), the Emicon (1930), the Trautonium (1930), the Croix Sonore (1934), the Partiturophone (1935) and the Hellertion (1936). All were outgrowths of the new radio technology. 51

instruments. In the remainder of this paper, I take advantage of our experience at EMSA, where we have had close contact with one of the largest and most advanced manufacturers, as well as with many teachers and studeqts of electronic music across the United States. Most of our work concentrates on equipment manufactured by Electronic Music Studios of London, makers of the Synthi line of instruments and peripherals. They are a talented and aggressive group with a growing reputation for innovative development. They were the first to produce a miniature instrument (VCS-3), which has recently evolved into an even smaller and more sophisticated version (Synthi AKS) .. At the same time their large studio instrument (Synthi 100) is the most completely equipped self-contained system now available. They are also, at present, the only builders of musical instruments that incorporate digital electronics (the Synthi AKS, for example, contains a small digital sequencer using computer techniques), thus introducing the next generation of modern "electrophones." And they have made the industry's best attempts to produce peripherals (filters, random generators, pitch-to-voltage converters, digital sequencers) that are, or can easily be made, compatible with all systems. Acceptance of EMS instruments and concepts is gaining ground among musicians, as well as among scientists who find that a Synthi provides a useful laboratory for teaching and exploring the physics of music. Our experience with this line of equipment, and especially with the Synthi AKS, suggests that it is approaching the criteria that will have to be met in future development of standard instruments. For example, the Synthi uses matrix patching: insertion of pins into a square array of holes makes a set of interconnections among modules of the system. Although the present matrix has drawbacks (crosstalk and impedance mismatch) which may be difficult to overcome in a modest system, it provides an extremely swift and compact way of achieving complex patterns. It also lends itself naturally to automatic external control of the patching configuration. The Synthi AKS has already taken a step in this direction: any given patch can be set by inserting a single prewired plug into a special socket of the instrument. Rapid and flexible patching, and an easily programmed sequencer, make the Synthi a promising instrument for live performance. At the Eighth Annual Conference of the American Society of University Composers, we demonstrated some of the intricate possibilities that open up when two or more instruments of this kind are interconnected. We thus create an ensemble in which sequences can be heard as separate voices, or in interaction with each other. It is in bringing such techniques toward practical realization in the concert hall that these fascinating new instruments may be making their largest contribution. I have emphasized the need for a new notation in the composition of a literature for electronic instruments of music. Here again it appears that progress can be made through concepts now under study at EMS. For example, they have developed a computerized system which stores arbitrarily complex sound as digital information in an impressively efficient way. The principal application of this system is in the 52

construction, storage and transmission of speech. But it also opens up a new approach to the graphic transcription of electronic sound. Given the minimal amount of digital information representing a musical event, we H.eed next to devise a way, such as a computer-controlled graphic display, of translating that information into a written language with a set of conventional symbols. With the appearance on the horizon of developments like this, it seems appropriate to suggest that the community of musicians and manufacturers of electronic instruments get together on some of the problems I have outlined. The effort until now has been scattered. Excellent ideas, carried out in isolation or in a spirit of healthy competition, need to be brought together if a new family of instruments is to enter musical life in a permanent way. Unless we find the incentive to carry out a cooperative program, it may ultimately tum out that the Moog, the Arp, the Buchla and the Synthi - like the Spharophon, the Emicon, the Trautonium and the Hellertion - will be no more than footnotes in some future history of music.

RONALD PELLEGRINO

Some Thoughts on Thinking for the Electronic Music Synthesizer

Electronic music synthesizers have been available to composers since the middle of the 1960's, about eight or nine years now. There are very few music departments in the country without some form of an EM studio, which in some cases is little more than a small synthesizer, a few tape machines, and a monitoring system. There ar·e also a growing number of situations in which extremely elaborate, varied and sophisticated studios are available for the exploration, composition and performance of EM, and, for related activities. Despite the large number of studios and their general accessibility, the bulk of the work in EM is focused on forms and ideas which are more characteristic of the pre-synthesizer era than the present day, that is, compositions for tape alone or for tape and acoustic instruments. However, there are a handful of composers and performing groups who are exploring the conceptual extensions of the synthesizer as a truly new means of dealing with sound, movement and form, that is, as a highly flexible instrument which permits one to explore a hitherto unaccessible conceptual terrain. One of the most fruitful features of the synthesizer is that it offers one the possibility of turning thought experiments into physical phenomena in real time; instant feedback is a concomitant of sustained 53 learning experiences. Since sound is the material with which composers work it should be apparent that the more time one spends with real sound in real time with the provisions to manipulate that sound so as to gain new perspectives, or just as importantly, new combinations of perspectives, the richer the learning experience will be. Discovering a serendipitous event and while it is in the air being able to shape it and pursue its development is undoubtedly one of the most exciting aspects of working with today's complex synthesizing systems. At this point in the evolution of EM it should be evident that the ideas embodied in the design of a particular synthesizer suggest particular ways of thinking for that synthesizer. During the coming year I will be writing a book on "Thinking For The Electronic Music Synthesizer." In addition to an introductory section on basic EM concepts, the book will be concerned with different ways of approaching and employing synthesizers in the music making process. It will be structured according to the logical and intuitive creative processes which I have discovered to be appropriate for the performance and compositional problems which occur when one approaches the synthesizer as a viable musical instrument. Some chapters will be based on principles which surfaced because of particular kinds of compositional questions which were indigenous to a specific work or type of work. Several chapters will be devoted to an exploration of the philosophical bases of the attitudinal shifts which are suggested by the numerous avenues opened to composers by present day technology. The final chapters will be concerned with the various directions pursued by American and European composers of EM in the early 1970's. According to the present plan the table of contents will be:

1. Basic Electronic Music Concepts This will cover the modulation of frequency, amplitude, waveshape, phase, and spatial location, plus the principles of mixing and recording.

2. Principles of "Instrument" Design With emphasis in the area of complex dynamic control voltage systems and their synergistic behavior. An "instrument" is defined as the characteristic sonic products which are the result of the manipulation of the flow of electricity through a series of modules each of which performs one or more operations on the form of electrical waves. Since each instrument design contains a relatively fixed number and order of functions in an analogous way to a traditional acoustic instrument, it is musically sound to approach the design with a similar attitude, that is, to understand all of its variables and their relationships thereby becoming comfortable with it as a means of expression. As one becomes familiar with the multifunctional characteristics of today's synthesizers one realizes that the creation of rich instrument designs is closely related to the complexity and flexibility of the control voltage systems which dne invents. (See Figure 1) Clarinet Microphone Preamp

Reverb Multiple Ring vc Modulator Amplifier

.,, c .c· <: ~ Audio/ "' Envelope Sub-audio Generator rn Sine Mixer "' 2 c." c Trig J: m x c ~ 0 vc ~ Noise Filter/ c;· Generator Resonator Reverb !!'" rn "' c c;~·

0" Sample and Hold

Manual Rate Change c Stable DC Source Sub-audio Pulse Voltage c Processor 55

3. Live Performance Problems. This will cover the following areas: a. The design of elegant instruments, i.e., those which produce a large range of sonic material, yet use the fewest possible number of modules. b. The principles of producing variations of instruments which involve only a few additional modules yet produce sonic material which is quite different from the original. c. Methods of exploring an instrument's potential. d. Adjusting the instruments to the performance space.

4. Principles of Interaction Between Acoustic Instruments and Synthesizers. This chapter will discuss the following: a. The use of the acoustic instrument as a generator of audio signals which can be treated to a wide range of modulation techniques, i.e., amplitude, waveshape and phase modulation, ring modulation, frequency shifting, etc. b. From acoustic instruments the derivation of control voltages which can be used to drive any voltage controllable module. c. The derivation of triggers from an acoustic instrument whenever it exceeds an amplitude or frequency threshold level; the triggers can be used to initiate and terminate events and to shift from event to event. (See Figure 2)

5. Employing the Synthesizer As An Extension Of Acoustic Instruments. This chapter will discuss the problem of designing instruments whose principal variables are under the direct control of an acoustic instrument and are only operative at the command of the acoustic instrument.

6. Principles Of Environmental Design. This will cover the following: a. The use of synthesized signals to control the sequence, combination and intensity of light sources. b. The derivation of control voltages and triggers from the electrical characteristics of light sensors. c. The incorporation of the given space and natural variables into the total environmental syste111 . (See Figure 3)

7. The Generation Of Dynamic Visual Graphics By Means Of An Oscilloscope And Synthesizers. This chapter will cover the use of the outputs of synthesizers to drive the x, y, and z axes of an oscilloscope to produce Lissajous figures which are kinetic light sculptures analogous to organic systems; it will also include a discussion of video synthesis and laser deflection techniques. (See Figure 4) 01 m "11 cE ' Sounder c: ~ Mike Preamp (I) !'l VI .,.... Balanced

(I) Modulator "' Envelope Trigger 0 Detector Control ... 1 Voltage ~ s. c Mixer "11 Ci Env Trig c Det JJ 2 CV m Balanced 0... Modulator ~ Env Trig (;) Stage 1 3 Det Ou ad 3 3 CV Spatial ~ Director 3 in Lopass/ Gate 0 ~ c: 1 i :i c c. Control c !!l Voltage ., Mixer :ic. Lopass/ Gate Cll 2 c: n Continuous c .,=: Random Voltage sc: Discrete "'r; · Change Rate Random Voltage Cll c 0 Sequencer x Pulse Trig ... Generator Envelope (!) Trig -J c Generator ~ On Rate Trig 57

PHOTOCELLS ~KER

LIGHT ' IMAGES \ . \ \ \ I \ 0 1 ROTATING '~,'DISCS

PROJECTION 0 DEVICES

BUCH LA MOOG PUTNEYS ARP

AIR TURNS DISCS LIGHT IMAGES CONTROL PHOTOCELLS CONTROL SYNTHESIZERS

Figure 3. METABIOSIS V: A light, sound and audience environment (19 72) 58

~ 0 g<.> ·u 0 ~ x > N .. • '

~ ~ "'x "'x ~ ~

.... ' ..

.!: c: c. . ~·ca E i5 J: (!) <( c:-O>:;; cr:-o·- " 0 :::;: ·~ <( ..co

0"' ·"'0- -~ <("" ll. I I 0 I '5 I I .t: ,~ " I ..>< .!2 Q) 0 i:J"' ~ c,"' <.> "'O c: __:J- .,_ I c: ·;: ~(ii I~ VJ " 0 I·~ -(.,) ~ 0 I~ '5 I I- .., I I I <("

Figure 4. LISSAJOUS LIVES, Inst. 11-C

8. Performance Rituals For The Presentation Of Electronic Music. a. The inadequacy of the traditional concert hall ritual for tape compositions; this will include some suggestions for possible alternatives. 59

b. The virtues of a free flowing audience into and out of environments. c. The environmental character of real time improvisation presentations.

9. Electronic Music and Ephemeral Forms. Synthesizers permit one to explore the analogies between electrical systems and organisms whose natural forms are transitory, in a constant state of flux, i.e., ephemeral. The microstructure of events produced by instruments I design are normally ephemeral, that is, they have a life of their own in terms of combinations of frequencies, timbres, amplitudes, and sonic configurations; the activity is pseudo-random within the limits of the instrument definition. The macrostructural forms of sound, light , air currents, and audience movement in environments are also ephemeral. The same is true of the forms which emerge from improvisation.

10. Commercially Available Electronic Music Synthesizing Systems. This chapter will give critical appraisals of commercial systems from the viewpoints of programming, performance flexibility, variety of control sources, elegance of design, packaging, provisions for interfacing with other systems, characteristic colors and inherent limitations.

11. The Case For Using Two Or More Synthesizers In The Interactive Mode. Since each particular type of commercial synthesizer is inclined to speak its own peculiar dialect, a composer who is determined to use a personal mode of expression must learn to interface different synthesizers to create colors, gestures and control systems not possible when confined to only one type of synthesizer.

12. Notes On Composers Who Are Designing And Constructing Their Own Special And/Or General Purpose Synthesizers. This chapter will provide an examination of the motivation and ideas behind the current wave of composer-designed and/or constructed systems, ranging from the simple special purpose instrument of Charlemagne Palestine, a composer who is presently doing very subtle sound environments, to the extremely powerful hybrid system of Sal Martirano, a composer who has spent over three years designing, constructing, and, now, finally performing an instrument which is unique in its range of colors, envelopes and densities, its performance logic and flexibility, and its appearance (it's an awesome electronic sculpture which accommodates up to 32 suspended speakers).

13. The European Electronic Music Scene In The Early 1970's. The information in this chapter will be collected while on a six-week tour of European centers of EM during which I will talk to composers, performers and studio directors about the scope and nature of their EM activities.

61

American Society of University Composers

Proceedings of Regional Meetings

(The following papers were given at meetings of Region VIII, November 18-19, 1972 and Region II, January 13, 1973.) 62

BARNEY CHILDS

Some Notes Toward a Philosophy of Notation

Expansion of the range and variety of musical notation in the mid-twentieth century, recently sampled extensively in the Cage and Karkoschka collections,l has been only slowly complemented by a parallel expansion of theoretical investigation of notation until the last few years. Current scholarship, however, reflects a considerable gamut of approaches, from the esthetician to the composer, along with such consistently productive sources as the notation section of Perspectives of New Music. Finally, with the inception of the Index of New Musical Notation and the work already beginning to appear in connection with this several years' project, notational scholarship has become one of the most lively and provocative branches of modern theory. In this paper I wish to discuss some possibilities for thinking about notation, with specific reference to writing by Nelson Goodman and Cornelius Cardew as well as to some ideas explored in a recent paper by Gerald Warfield.2 The concerns we might begin with here are well set out in Carlos Chavez' 1929 article "The Two Persons" (MQ XV:2). Since notation is the device for preserving a musical work, and since we desil-e to transmit it in the second person without error, or the wear and tear of innumerable interpre­ tations, our chief end in this matter becomes a flawless manner of writing. To this end we require a system of marks on paper that can exactly represent all and every one of the properties of sound called for-intonation, duration, inten- ._, sity, and timbre; and besides, a way of indicating the .J' ,_t procedure of performances with which to work out these ( f properties with absolute precision. (p. 155) { K/Here is a three-part division of questions about notation: what is its "\. ,~ "\' function? what is its nature as a symbolic structure? what is the ~ J , relationship of the notation to the performer and to what is to be ~ J . heard?3 Following Cardew, I wish to define a musical notation as a set ~ \ ~ of instructions, usually symbolic, for actions which, if performed, will ~ l produce the sounds wished for by the composer with an accuracy J.:I '. '/~ 1 Notations, ed. John Cage (New York, 1968); Erhard Karkoschka, Das Schriftbild ' ~ der Neuen Musik (Celle, 1966). ~ 2 Nelson Goodman, Languages of Art (New York, 1968); Cornelius Cardew, "Notation-Interpretation, Etc." Tempo (1961 ). Mr. Warfield's paper, "Notation: Some Observations at the Engineering Level," appears elsewhere in this journal.

J 3 "Sounds, in fact, are not even what musical notation specifies, a matter which Professor Goodman seemingly overlooks in his discussion of such notation in Languages of Art." (cited by Warfield from a paper by Benjamin Boretz.) "Sounds," Warfield himself continues, "do not constitute 'the piece_' 'The piece' is, rather, the relationships we form in our head about some sounds: one might say our interpretation of some sounds." I should prefer to delay consideration of the extensive implications of Warfield's treatment to this, especially his focusing on the problem of "attempting to separate the reception of a phenomenon from its interpretation." 63 largely dependent on the precision of a performer.4 Even as each phoneme of a spoken language involves a particular configuration and activity of the vocal apparatus, so also does each symbol in a musical notation concern specific human activity. Just as this definition can be usefully, I believe, considered to clarify the three preceding questions, it may also be used for three a posteriori concerns: "quality" and accuracy of performance, ambiguity and indeterminacy in notation and performance, and the nature of art as ritual or symbolic action. Discussion of these will be deferred until after time spent with the first three questions. The traditional "properties"-or parameters, if you wish-of sound are frequency, amplitude, timbre, and duration. One might think that, since music is time-extended, duration would be of most detailed concern. Curiously enough, until very recently this has not been so. Performers and composers will tolerate variability, even laxity, often of considerable degree, in presenting durations and their relationships: frequency, dealt with as pitch, however, must be maintained with high precision. Pitches even slightly "out of tune" are held far more offensive than durational elasticity or even appartent malinterpretation, this sometimes supposedly justified as "rubato" or even "expressivity."

~ is clearly defined in physical terms, and the discrete intervals and steps represented symbolically on the staff are mathema­ tically established in invariant relation to it. Such a selective ordering of the frequen-cy continuum, thus precisely defined and maintained, provides a finite set of what might be called "nuclear" or "root" notational elements, alterations to which are symbolized by hierarchical systems of notational diacritics. The nature of these diacritics and their ordering must be clarified before we are ready for further investigation. Ben Johnston, in a yet unpublished paper on microtonal resources, clarifies for music the concepts of scalar order set forth by the psychoacoustician S.S. Stevens. A nominal scale distinguishes only same and different. An ordinal scale also distinguishes more than and less than. An interval scale distinguishes equal increments of changes between greater and less. A ratio scale provides relationships between different scale positions. The most important measurable dimensions of music, pitch and duration, are capable of analysis by both interval-and ratio-scale ... Rhythm measured metrically (by equal time increments)

4 He lists "five stages in the production of music," the fourth of which is " the action to produce sound." Most notations deal mainly in (4): ' do what I tell you and the right sounds will come of their own accord' which is not true of course, but there is no-one who is not reluctant to admit just how much he relied on (3) [the player)." (p. 22) Warfield: " ... some hold that notation is only performance instructions. At best such a statement would have to be modified to read 'interpreted performance instructions,' since, as we have seen earlier, reception cannot be divorced from interpretation." (p. 10). ~· u.. 64 ! I ,~ ' I ).rr /lfv"' (Y' ,. ) f , :,....-- uses only an interval scale. 5 17 ( ' Given the five-line staff and the available clef-sign qualifiers, we can stipulate particular frequency by the placement of a locating sign (a notehead) at the proper place on the staff. As Johnston has pointed out, the organization here, definitions which classify what the locating sign represents, is by ratio scale. This includes the diacritics which may preface the locator to indicate "chromatic" alteration ( # b~x bb) and "microtonal" alteration (the signs not completely yet agreed upon).6 Duration organization, usually by linear scale, involves two choices of "color" of locator and two of shape; a set of qualifiers including stem, flags (beams), numbers, and dots; a corresponding set of marks to indicate length of pause, rest, or silence; and such signs as 'and 0 . Amplitude is governed by diacritical markings in ordinal scale (the range from say ppp to fff, crescendo and diminuendo and their synonyms). Timbre depends on stipulation of an instruction naming the instrumental source to be used to produce sound. Each stipulation makes available a set of diacritics inherent in the nature of the instrument (instructions for muting, pizzicato, harmonics, flutter­ tongue, choice of mallets, use of pedal, open string, &c.) Since these are is/isn't decisions, the organization here is by nominal scale. Karkoschka furnishes a tabular sampling of contemporary practice in notation. In addition to the four "properties" already discussed, several other of his categories are useful here. Tempo is conventionally indicated by a second-order set of indicators either in ordinal scale (the group of verbal qualifiers from grave, say, to prestissimo, with various . associated descriptive terms and modifiers) or ratio scale .M. markings). Meter involves instructions for the performer to organize durational units into patterns, establishing a hierarchical ordering of basic pulse and the facility for movement against it (accelerando, ritard, &c.) Articulation symbols are generally in nominal scale but may on occasion present ordinal arrangement (degrees of accent, staccato, &c.) And in contemporary practice there are isolated examples of notating the interpreter by specification (Cardew cites Bussotti's 5 pieces for David Tudor). Any collection of symbols must be accompanied by a corollary collection of definitions establishing what each symbol is to represent. As long as musicians agree upon the semiotic content of each of the symbols of musical notation, a "common practice" is defined: as Goodman might have it, each inscription has an identifiable compliant

5 "Microtonal Resources," pp. 4-5. Note that Henry Cowell (in New Musical Resources) anticipates the mid-twentieth century composers Johnston cites as developing the proportional measurement of rhythm organized by ratio scale, as, to a degree, do the late medieval and early Renaissance theorists with inter-related rhythmic structures. 6 Goodman's paragraphs on indeterminancy's reducing normal pitch criteria to "higher-than" determinations are simply a transfer of this variable to a less precisely structured (here ordinal) scalar order. 65 and a musical grammar exists. 7 New processes of sound production may thus be symbolized with an agreed-upon diacritic, as must use of the "conventional" symbols in an unconventional manner (e.g. the somewhat confusing use of white and black noteheads to indicate "natural" or chromatically altered pitches, as in some work by Henri Pousseur, Larry Austin, and others.) The proliferation of new nota­ tional symbols is a problem only as long as the symbols remain uncodified and unaccepted. A more serious concern is that with ambiguity in the definition of symbols. Goodman finds problems in "the vocabulary of tempo": Apparently almost any words may be used to indicate pace or mood. Even if unambiguity were miraculously preserved, semantic disjointness would not be. And since a tempo may be prescribed as fast, or as slow, as between fast and slow, or as between fast and between-fast-and-slow, and so on without limit, semantic differentiation goes by the board, too . . . The tempo words cannot be integral parts of a score insofar as the score serves the function of identifying a work from performance to performance. No departure from the indica­ ted tempo disqualifies a performance as an instance-however wretched-of the work defined by the score. For these tempo specifications cannot be accounted integral parts of the defining score, but are rather auxiliary directions whose observance or non-observance affects the quality of a performance but not the identity of a work. (p. 185) His objection may be applied in kind to another ordinal-scale set of diacritics, that involving dynamics. Fortissimo will not only vary from flute to violin to trombone to snare drum but will also vary among flute players, violin players, &c., as well as with a given flute player in varying ensemble contexts. Any scale organized to measure ordinally, observing simply "more than" and "less than", will of course fail to meet Goodman's precise requirements for a notational system, that compliance"classes be disjoint and differentiated, i.e. use ratio-scale. Equally unsuitable for Goodman are notational practices which allow performer choice: he cites figured bass and the "free cadenza." And this leads us to consideration of the first of the three questions above, that of the function of a notation. Goodman's concern is "the authoritative identification of a work from performance to perfor­ mance" (p. 189); "Given the notational system and a performance of a score, the score is recoverable." (p. 178) Compare Cardew: "Identity

7 I am put off by some 'vagueness in Warfield's definition of musical grammar and his wish not to discuss the term syntax: it seems to me that in his own terms-"an event is dependent on its context," for example- he is presuming syntax as a part of his thesis. A recent paper on these problems (John Grey, "Musical Structure") defines syntax as "the organization of the input or output so as to be compatible with the human processor .. . we will consider music as a culturally shaped stylistic syntactic system used for the processing of acoustic data with respect to some abstract aesthetic content," completely in keeping with Warfield's position. Unfortunately lack of space precludes further discus­ sion here of Grey's important material. 66

(of a piece of music). A senseless but useful concept. What is essential to a piece of music constitutes its identity ... A musical notation is a language which determines what you can say; what you want to say determines your language." (p. 21) And Chavez: " ... notation is the device for preserving a musical work ... " There is common ground here, of course: the performance and the notation are separate but inter-related, and the notation itself is not the piece of music. There is also a difference: in each case the inter-relation is viewed apart from the others. For Chavez, the notation would seem to be almost a posteriori to the performance, the music-as-sound, a convenience to facilitate making the particular music as often as one may wish. For Cardew the notation is a sort of visible envelope containing and embodying the audible as potential. And Goodman would appear to regard the:: notation as a criterion against which the audible be measured. I do not find any difficulty here in concern for the notation itself; the problem arises in the notation/performance relationship. Notations admitting performer choice will be discussed, as one phase of this problem already mentioned, later. Much of Warfield's paper deals with the composer-performer-listener relationship, and this is connected with his concern, mentioned above, with the "non-separability of reception and interpretation." •. The interpretation, or relationships, in our heads are inte­ grally bound up with the reception of the sounds, and although the sounds must be at least theoretically received, certainly we have sounds on the one hand, and reception-of­ sounds-and-interpretation-of-sounds on the other. It is in the area of interpretation that we "understand" and thereby form our "conception" of the "piece." (p. 5) If I may perform some impromptu additive surgery, perhaps we can say there is the third hand as well, the score (with, abstracted, its prescribed activities). We have seen that this is neither the sound nor the piece, yet [_ if properly realized in its own terms it is formal cause of the sounds and becomes part of the totality of the piece. Further, the score may furnish information for "reception" and even for judgment without being realized into sound (e.g. augenmusik; or a performer's statement, "I can't play this; it looks too difficult.") A danger here is, I believe, the assumption that a communication system must include, to be operative, prediction or stipulatior:i of the behavior of the receiver above and beyond the qualifying function of reception. Even accepting the inevitability of the reception-interpretation connection, as I am not quite prepared to do, and although some music may have been designed to produce a predictable response in the listener within a "common practice" acculturation (as program music, say, or as Deryck Cooke suggests in The Language of Music), must we accept that this response is going to be inevitable and predictable for music in general? must we reaffirm the doctrine of the affections? Again, are some of Satie's verbal qualifiers on scores intended to have an effect on what the listener is hearing or on how the performer feels about what he's doing? what about metanotational material? say the presence in a concert 67

program of commentary or "explanatory" material that purportedly shapes interpretations of information received?8 Jerome Rothenberg cites C. G. Jung: The matter of interest seems to be the configuration formed by chance events at the moment of observation, & not all the hypothetical reasons that seemingly account for the coinci­ dence. (pp. 489-90)9 and continues himself: "whatever falls within the same space deter­ mines the meaning of that space." (p. 490) Time-succession itself provides ordering, coherence, and continuity, and is the backdrop for "the relationships we form in our head." These relationships may have been intended, within the particular musical grammar used by the composer, and we as well may impose relationships depending on how we are concerned with the events we observe. Warfield's work on what he calls "the process from composer to listener" is an important majority of his paper, and can, I believe, serve as the base for fruitful further investigation. Goodman is concerned further with bad performance: Since complete compliance with the score is the only requirement for a genuine instance of the work, the most miserable performance without actual mistakes does count as such an instance, while the most brilliant performance with a single wrong note does not. Could we not bring our theoretical vocabulary into better agreement with common practice and common sense by allowing some limited degree of deviation in performances admitted as instances of a work?lO The phrase here that bothers is "actual mistakes." How are we to define a "mistake" given varied scalar organization of the components of a notation? How loud is too loud, or how slow too slow? It would seem

8 Cf. my comments on the titles of musical compositions in the paper on musical continuity (Proc. ASUC. 6 [1973], p. 62) Even more convoluted are the problems involved in intent, be it of composer, performer, or listerner. The dilemma is nicely contained herein: "When an act is taken as an expression of an attitude, the justification consists in the nature of expression." Stuart Jay Petock, "Expression in Art: The Feelingful Side of Aesthetic Experience," JAAC XXX:3 (Spring 1972), p . 305, agam a valuable source of which space precludes further investigation. Cf. also Morse Peckham on playing the role of artistic perceiver (Man 's Rage for Chaos, p. 59 ff.) 9 Technicians of the Sacred (New York City, 1969 ). Cf. John Cage's anecdote about the Japanese rock garden. My position is clarified by this: "When we view art as an object we view it in opposition to the process of signification . .. Meaning follows from the presence of the work of art, not from its capacity to signify absent events or values .. . formal complexity is not an index of richness of content." Lawrence Alloway, "Systemic Painting," Minimal Art, ed. Gregory Battcock (New York, 1966) pp. 55·56. 10 My ex-student Joel Coble notes here, "But how do you distinguish wrong notes from notes merely badly off-pitch?" Cardew: "I have heard people criticizing interpretations of music in a variety of ways: 'he played some wrong notes, but was faithful to the composer's intention', or, 'he played correctly but seemed to miss the point.' Such criticism disturbs me (though I have often found it valid) because it implies that there is something behind the notation, something the composer meant but did no t write." (p. 27) 68

that only stipulated ratio scale or linear scale organizations, as frequency and metronomic rhythm, can be subject to "actual mis­ takes." Beyond this we are involved with Goodman's "limited degree of deviation" and immediately thereby precipitated into judgments against our interpretive model. Challenging recent work on this matter is furnished by Edward T. Cone's article, "Beyond Analysis" (PNM 6:1). If ... we still insist on seeking some basis for making distinctions that we still feel to be somehow essential, let us tum to the third alternative: that there is, and can be no analytical ground for concrete musical choices, i.e. no ground within the internal structure of the music itself; yet that these choices are crucial in determining musical values, i.e. salient characteristics that afford a basis for distinction, comparison, and judgment. (Critical listeners, as well as composers, must also make such choices, although in a slightly different sense; for all judgments are based upon implicit comparisons between actual and possible composi­ tions, and hence on a choice among concrete values ... ) (p. 44) We may set up any scale ,of "limited degree of deviation," but this must of necessity be an absolute judgment; it is, in Cone's phrase, beyond analysis. A score is the basis of the set of all performances which are made from it. Expertise in performing the prescribed actions, and fidelity to the prescriptions, variable depending upon the particular scalar order of varieties of diacritical information and, finally, upon absolute "critical" and "esthetic" judgments, will determine the "good"-ness of any specific performance.11 The problem of score/performance relationship is compounded when indeterminate music is considered. "I [ Cardew] would say that a piece is indeterminate when the player (or players) has an active hand in giving the piece a form."12 A work is indeterminate when the notation allows fields of possibilities, limited or otherwise, for performer choice and "realization." Information is not here omitted, it is simply placed in less precise scalar orders than customary. A notation as such cannot .. 11 "The traditional role of notation was to fix certain elements of performance while leaving the others to the 'musicianship' passed on by a player by his teachers and absorbed from his environment. Many of the things done by the musician, and absolutely essential to good performance, were not to be found in the score: deviation from the metric values, differentiation in timbre and intonation, types of pedalling and tonguing and sliding, as well as aspects of the sort described by a vague word or two-'con fuoco,' 'lebhaft'-words so vague they had meaning only to a player culturally conditioned to them. "It was taken for granted that any player could obey the notation's literal demands. Whether he was talented or not depended upon whether his 'musicianship' could 'breathe life' into the music." David Behrman "What Indeterminate Notation Determines," PNM 3 :2, p . 58. ' 12 P. 21 Indeterminacy is not to be confused with composition by chance means: the result of the latter may or may not be indeterminate in admitting player choice. The pedantic coinage "aleatoric" is loosely applied to both sorts of music; I would hope Mr. Warfield might abandon it in his future writings. 69 be indeterminate, since the definition and, if used, limiting and bounding conditions, of these fields is fixed in the score. A notation is invariant in itself. An extreme spirit of laissez fa ire has led some composers to use systems that restrict only slightly the performer's freedom to play what and as he pleases. Such latitude is not incompatible with notationality; even a system with only two characters, one having as compliants all piano performances beginning with a middle c, and the other having as compliants all other performances, would be notational-though for this system there could be only two different works. (Goodman, p. 190) Assume as a criterion Goodman's "Given the notational system and a performance of the score, the score is recoverable" (p. 178); an indeterminate work will provide a different score with each perfor­ mance thus "recovered." David Behrman has dealt with this by "recovering" into score parts of works by Feldman and Wolff, using "common practice" notation; neither work's original score is in this notation.13 These works could be re-cast into score using any manner of notation we wished to invent, just as a specific notation allowing indeterminate choices can produce a variety of audible realizations.14 A notation could be developed which would produce as one of its possible realizations at the keyboard a Beethoven piano sonata; given a recorded performance of the sonata, one could transcribe it into a "different" notation as one of the notation's results. Several composers' work illuminates the development of concept and execution in notations allowing performer choice, and suggest that Goodman's "laissez faire" is a trivial judgment. Earle Brown, for example, began his search for a "mobile situation" in music through concern with the spontaneity and creativity of visual artists, notably

13 In the article cited above. 14 Behrman: "One of the criteria with which to judge a notation is the question of what, if any, the consequences are of playing well or badly (what incentives there are for realizing the notation in the way intended and expressed by the composer). In Wolff's notation, the players must listen with such care to one another that an inaccuracy is liable to alter the signal received by one's partner and so to disturb the continuity . . . Elsewhere, Feldman's scores present the player with an 'honor system' notation. With no one to check up on what he does, the player's incentive for doing his best is (presumably) the pleasure of contributing to a sound world whose transparency is such that the smallest detail remains perfectly audible in it." (p. 7 3 ). Morton Feldman, in an unpublished interview with Robert Ashley (1963): "I know that in performance I have occasions within my work where I would designate a certain amount of notes to play in the graph things, and I would hear 'Yankee Doodle' coming out of the horn section. The players decide together before the concert, actually to sabotage it-and they decided in this particular section they were going to play 'Yankee Doodle,' with the amount of notes called for and in the register in the score- there was nothing I could say if that wasn't inherent in the instructions of the piece. But of course I said 'Manslaughter is one thing, but not homicide; I have not given you license to murder the piece.' So for the younger generation the implication is a moral question that has to be decided ultimately." A performance available with similar (but not as immediately perceptible) 'sabotage' is the recording of Cage's Concert for Piano and Orchestra in the 25-year retrospective album. 70

Jackson Pollock ("action painting" as suggestive of a musical "action notation") and Alexander Calder (the idea of a musical mobile). The works included in Brown's collection Folio are each steps toward what the composer calls "open form,"15 involving, as in his work Hodograph I, "explicit notation "-conventional or nearly conventional notation allowing little if any performer choice-and "implicit notation"­ graphics allowing a quasi-improvisatory response by the performer. The phrase of Brown's which seems apposite to his work is "the poetics of transformation. "16 Similar development in notation allowing indeterminacy can be followed in the work of John Cage, Christian Wolff, Morton Feldman, Udo Kasemets, and others. Cardew's work, however, seems to me to merit particular attention here: each composition is a different and illuminating development of symbolic ambiguity in a notation.17 Autumn '60 provides pitches and rhythms, but each pitch has above it a number of diacritics, some mutually exclusive or impossible on certain instruments. Each performer realizes his own part, eliminating various diacritics by necessity and by choice and filling out his part through his selection of action to be performed in response to certain ambiguities in some of the diacritics themselves, following Cardew's instructions. The accompanist's part in Solo with Accompaniment is realized from matrixes inv0lving diacritics and numbers: "the numbers in 'Solo with Accompaniment' refer to quantities that can change with the changeable climate of musical thinking. "18 Each symbol in the notation is assigned a referent, through Cardew's instructions or by performer choice. Again, contradiction and exclusion of alternatives is a shaping process in realization of a version in "conventional" notation to be performed. With Octet '61 for Jasper Johns Cardew moves away from the limitation of discrete notational diacritics. Each musical event of the sixty-one provided is a notation so combining diacritics and numbers that not only is the conventional identity of each blurred and interwoven, using allusion, echo, suggestion, and contradiction, but the

15 Proc. ASUC 5 <1972) PP. 8-14. Brown discusses " open form" extensively in "Form in New Music," Source 1. Cf. my concern with "form" and "structure": "Indeterminacy and Theory," The Composer 1:1, pp. 27-8.

l6 Ben Johnston has been also concerned with "transformation" as a directly animating musical procedure, especially in such works as Quintet for Groups. 17 The composer's notes to Four Works and Octet '61 for Jasper Johns should be read in this context. Warfield: "it may be the case that standardization is pragmatic only for the relatively determinate [variables of higher scalar order] aspects of the notation .. . it is those events which will remain the same from performance to performance (within the confines of the grammar), for which we might suggest notational conventions." (p. 12) The section in parentheses is important here: as long as there is a grammar, which will of course be defined, minimally, by the complete continuum of material in the notation, notational conventions may be provided whether the piece admits indeterminacy or not. I find it curious that Warfield's composer examples for indeterminate music are Stockhausen, Bussotti, and Logothetis: why all European and derivative?

18 Notes to Four Works, p. 4. 71 symbolic nature of the material as visual is developed, paralleling Jasper Johns' use of numbers as allusive beyond their merely functional appearance. The performer may realize directly from the score in performance, although, as Cardew states in the instructions for the work, this will be unlikely until a performer is thoroughly familiar with the notation. Performer action is here conditioned not only by the content of the notation in diacritical terms but also by the graphic nature of the notation, as pop art asks the perceiver to consider the nature of images which have been placed in new contexts. Finally, in Treatise, we come face to face with the problems of visual image.19 The performer is provided with many pages, each with a graphic construct and with two empty staves across the bottom of the page providing space for realization. Performer action is here, as in certain other contemporary scores (a strong example is Philip Krumm's Concerto for Anything), a response to what one sees as evocative visual material (including of course the evocative nature of two empty staves on each page); in some scores this may be shaped by instructions qualifying responses for the performer. Treatise material is suggestive through use of signs which resemble those of musical notation and through a sense of time-movement not present in field-notated works bounded by the edges of the page (even despite directionality of symbols in the field, as in work by Ichiyanagi, Mizelle, and Edward Miller.) Treatise includes the entire world of performable sound as potential; the performer serves as screenout, as filter, through his particular responses.20 There is a clear distinction between Treatise and theatre pieces; in the former the sound is the end product, and the means of producing it are, outside this, unimportant, and in the latter performer action as such becomes part of the piece. We can thus fix endpoints for a gamut of possibility. One of these endpoints is the totally "notated" work which is in the "perfect performance" invariant (compositions for tape would be examples of "perfect" performance); the gamut passes through works in which performer action and sound are of equal importance; and the other endpoint compo~itions in which sound, if it occurs, is completely incidental to the performer's action. The score here may simply be instructions for an action to be performed, written out in prose; the action may even be humanly unperformable, provided only for consideration. 21

19 I have tried to get a start on the extensive and pesky problem of the musical image elsewhere (cf. n. 1 5 supra): aural images include not only the citation of previously familiar musical material as well as, in electronic music, of familiar sounds from "real life." Further work has to be done of the function of and response to direct visual images in a notation (as for example the baseball drawn on one page o f Alvin Curran's Piano Piece.)

20 A similar but less extensive "filtering" is provided by the nature of the performer's instrument as concerning what pitches he will play in Cardew's later Volo Solo.

21 Cf. Henry Flynt on " concept art" in An Anthology (New York, 1963). A special case is that in which the physical presence of say a specific musical instrument, with its richness of conventional implicit connotation, is in some fashion 72

There has been much recent concern with the composer-performer­ audience relationship, particularly expressing itself in distaste for the "performance ritual" and its apparent formalizing and stratifying effect.22 Involvement with the nature of ritual has been almost universal, since it has been a part of our lives since our primitive beginnings. It often involves the performance of a set of instructions without error-certain extended Navajo ceremonial chants, for example, are rendered completely invalid if a single mistake is made in their recitation. This concern for accuracy results in turn in two further complementary tendencies. One tendency is toward elabora­ tion and intricacy of ritual form. Such elaboration has occurred even in the rituals that we term " primitive" ... The other tendency is toward conservatism, especially after a substantial vital structure has been achieved and given literary and institutional form.23 Certainly this suggests a background for the formal complexity /richness of content equation mentioned previously. And these comments may throw some light on the dismay felt by such critics as Leonard Meyer with the premises of indeterminacy. One must keep in mind, however, that there is rarely any laxity in the rigor of the instructions themselves in indeterminate music, particularly in works admitting theatre in some form. The aural or visual results of the acts may be variable from performance to performance, but the execution of the actions is as rigidly governed as that for any work which is compositionally wholly determinate. With levels of acculturation, the vocabulary of music has become mannered and perfected to symbolize certain states of feeling. In today's general musical taste, certain musical complexes have been given extra identity: medieval contrafactum and polytextuality, as might be paralleled by use of a blues tune and its lyrics in a "religious" musical setting, might often be thought improper. The nature and the content of a ritual may become equivalent to the nature of its occasion. In these terms a notation is a guide not merely to action, but to symbolic action; as such it may have the symbolic property of the activity transferred to it by the perceiver and be held even in its unrealized form to partake of the particular ritual and symbolic nature connected with its realization. As the title of this paper suggests, its material is only notes, working sketches, from which much more investigation should be developed. I hope your acquaintance with this material will suggest to you further avenues along which to carry your own speculation and concern.

re-defined by performer activity ignoring or denying this connotation, as in La Monte Young's Piano Piece for Terry Riley.

22 Cf. Source 2. David Burge has written a parable in which extraterrestrials, after' having visited several concerts, conclude that audience applause is the activity for which the people have gathered and toward which all else is directed. 2 3 Winston L. King, Introduction to R eligion (New York, 1968 ), p. 4 7. 73

DAVID COHEN

A Reexamination of All-Interval Rows

The article on eleven-interval twelve tone rows by Stefan Bauer-Mengleberg and Melvin F~rentz which appeared in Vol. 3 No. 2 of Perspectives of New Music together with the supplementary listing of 1928 interval-row generators would appear to be the definitive presentation of the subject. Bauer-Mengleberg and Ferentz deal, however, only with twelve tone rows and do not mention other divisions of the octave. Furthermore, their list contains redundancies - interval-row generators which can be easily derived from others on the list. It would increase our knowledge of the frequency of all-interval rows relative to the total possible tone rows if we obtained an irreducible list of independent row generators. There are three sources of redundancy in the list given: inclusion of retrograde forms, prime number transforms and tritone-partition forms. To obtain a prime number transform, one multiplies each pitch (or interval) number of an n-tone row by a number prime to n and substitutes for the original number the remainder of division of that product by n. (Two numbers are prime if they share no common factor other than 1. 1, 5, 7 and 11 are the only numbers less than 12 which are prime to it. The procedure described above is sometimes referred to as multiplication and reduction modulo (n).) Tritone-partition forms result from the fact that the final pitch class of an all-interval row must be a tritone away from the initial pitch class. This condition exists for all-interval rows for any even division of the octave. There are no all-interval rows for odd divisions of the octave. An example of tritone-partition is shown in the following diagram: ~ ~ ~ 1 2 4 7 8 T 3 6 E 5 9 (6) // 1 2 4 7 8 T 3

Given the method of deriving the list, explained in detail in the article cited, it would have been difficult to exclude retrograde forms and would have made the list must less useful. One type of prime 1 number transform, namely inversion, was excluded, but the authors chose to include what has since been discussed as the "circle of fourths transform." (See Composition with Arrays by Godfrey Winham, PNM, Vol. 9, No. 1, for a detailed discussion of the circle of fourths transform.) Obtaining a list of non-redundant interval-row generators is achieved by crossing off all generators on the list of 1928 generators given by Bauer-Mengleberg and Ferentz which can be derived from a generator higher on the list employing one of the three methods given above. Upon completing this process and tallying the results, we discover that there exist 266 independent eleven-interval row generators. All-interval structures are even rarer than the relatively small list given by Bauer-Mengleberg and Ferentz would have led us to believe. Whether the frequency obtains for other divisions of the octave has not yet been 74

determined, but preliminary research which I have made on 23-interval 24 tone rows indicates that the percentage of all-interval rows becomes smaller for smaller intervallic divisions of the octave. As an application of the investigation of all-interval rows, I would like to present some experimental results of the coordination of fifteen interval sixteen-tone rows (employing equal tempered 3/8 tones) with duration rows. In the example to be played, the duration of each tone is determined by the size of the interval which follows it. This approach to rhythmic organization is related to Milton Babbitt's point of attack correlation of durations and pitch class numbers, although less rigorous than his. The work to be heard combines eight prime number transform related rows beginning simultaneously. Starting pitches are arbitrarily placed nine 3/8 tones apart. Since there are eight numbers less than 16 which are prime to it, there are more prime number transforms for sixteen tone rows than for twelve tone rows. It may be relevant to mention that the set of all numbers which are smaller than a given number n and are prime to it form a mathematical group under the group operation of multiplication and reduction modulo (n). The set of prime number transforms of an n-tone row derived from these form a permutation group. The group structures for different values of n are not necessarily isomorphic. The original row on which the work to be performed is based is perhaps the most obvious all-interval row, the " wedge." Such a row can be obtained by moving up one "step," down two "steps," up three "steps" and so on. In this case the "steps" are 3/8 tones. In the following table it is assumed that a descending interval is represented as the complement of an ascending interval of the same size. 1 14 3 12 5 10 7 8 9 6 11 4 13 2 15 3 10 9 4 15 14 5 8 11 2 1 12 7 6 13 5 6 15 12 9 2 3 8 13 14 7 4 1 10 11 7 2 5 4 3 6 1 8 15 10 13 12 11 14 9 9 14 11 12 13 10 15 8 1 6 3 4 5 2 7 11 10 1 4 7 14 13 8 3 2 9 12 15 6 5 13 6 7 12 1 2 11 8 5 14 15 4 9 10 3 15 2 13 4 11 6 9 8 7 10 5 12 3 14 1

Interval-row generators for a 16 tone " wedge" and its prime number transforms. Although the "Network of Wedges and Transforms" is rigidly prestructured, it does assert the importance of a contrapuntal approach to microtonal music, the variety inherent in all-interval rows and the need for further investigation of the relationships between prime number transform related rows. (The musical example was played.)

ED. NOTE: The musical example mentioned above can be obtained from the author, David Cohen, Department of Music, Arizona State University, Tempe, Arizona 85281. 75

STUART J. PETOCK

Multiple Values in New Music (A portion of this paper appears in MUNDUS ARTIUM, June, 1973)

What are the foundations of evaluative judgments about new music? How do they relate to value in musical experience? I raise these questions because having no regard for aesthetic principles, a great deal of music criticism amounts only to irrelevance or to autobiography. I believe that aesthetics can help us to elevate our critical judgments, much as criticism has helped elevate the quality of art. One reason for poor criticism is that critics are often unclear about the relationship between their verdicts and what those verdicts apply to. The result is that critics tend to be ignorant of how to test their criteria for relevance. Moreover, when a piece of music has satisfied their criteria, little generalizable significance results. Needless to say, what holds for professional critics also holds for us amateur critics. I shall propose that musical meaning be taken as the foundation of aesthetic value in musical experience. And I shall describe three ways musical value can arise from that foundation, each way applicable to a different kind of music. To establish the worth of my recommendations I shall refer to some works that I believe illustrate both the validity of my distinctions and the applicability of my concepts. Ordinarily, the judgment that something is good implies a recommendation. As a matter of courtesy we distinguish what we like from what we think other people might like, or ought to like, and we reserve our favorable verdicts for what we believe will suit other tastes, perhaps with the stipulation that the other tastes be as good as our own. If I prefer Spanada to Chateauneuf du Pape, as a reasonably educated man I have to see that my taste is aberrant and that my preference should not be generalized; a wine as sugary as Spanada would complement nothing except the onions on a hotdog. Still, if I like it I'll drink it; I simply won't recommend it. Because we evaluate wines in part according to how well they go with certain kinds of food, we can infer from an authoritative judgment that a wine judged good will become a part of a good meal. To take a somewhat coarser example, since I am the sort of person who enjoys any excuse not to work, I like to have a car that breaks down a lot. This way I can fix the car instead of working. But if you were to buy my favorite car on the basis of my favorable verdict, you surely could claim I lied when I said the car was a good one. We know what wines and cars are supposed to do. And so where wines and cars are concerned we can extract criteria with which to determine the propriety of a favorable evaluation. But what about music? Is there something music is supposed to do from which we can extract similar criteria? Some cases are obvious. A farmer who serenades cows to get them to make more milk can measure the validity of his verdicts in quarts. And a psychiatrist who soothes savage breasts can measure the validity of his 76

verdicts in nervous breakdowns. But our interests are neither bovine nor medical; we want to know about aesthetic value. Our questions about musical value are not put forth in a context in which we can allude to some special purpose in order to work out a quantifiable criterion. We are not asking if music is good for something; we want to know if it is good for nothing. Perhaps this is not the best way to phrase the question. Let's consider instead if we can find for music some aesthetic reason for being, a reason for being that rests in an immediate satisfaction rather than in a good that serves a more remote need. If we can find such a reason for being, we can try to incorporate a concomitant purpose into our description and then extract criteria with which to decide what circumstances justify our favorable verdicts. The question is, why do we value musical experience? Why do we listen to music? I, for one, listen to music because it is fun. I find good music engrossing and challenging; it is genuinely rewarding in a variety of ways. In what I hope will be not a completely trivial sense, I like good music because I find value when it is the object of involved listening. What follows supposes that others listen for similar reasons. If the judgment that a piece of music has value could be proved by describing the grounds for the judgment, as, for example, a dairy farmer could, criticism would be fully objective. If a critic's taste were aberrant, say, mutatis mutandis, because of an early experience with a cow, we could doubtless discover if his aberration corrupted his judgment by comparing selected cows' outputs. Now I do not believe that anyone can develop aesthetic criteria that relate as neatly to facts as do the ones that deal with the contentment of cows. But I do believe that I can show some ways of thinking about musical value that have a significantly higher degree of objectivity than do individual likes and aversions. Despite some eminent aesthetician's pronouncements to the contrary, music exists as fact in the world, just as much as cars, wine, and cows. I shall try to show how music's objective reality can be reflected in value judgments about it. I suggest that musical value be thought to consist in meaning. In my view, the conditions for musical meaning demand that one sound refer to another sound in a way that is intelligible to a qualified listener. Heteronomous meaning, where sounds refer to extramusical events or objects, e.g., magical fire or merry pranks, presupposes the autonomous meaning I think important. But the two are by no means identical. Today· I am concerned with autonomous meaning, because it provides a more general · base for creative, informed listening than does heteronomous meaning. My recommendations rest upon the conviction that when a creative listener interprets good music he engages in an activity that is at once challenging and stimulating. In my view, music is good, or has value, to the extent to which felt satisfactions are the rewards of careful, creative listening. Later, I shall have to discuss the qualifications for arriving at well founded verdicts. Not just anyone can determine if music is good, just as not just anyone can tell if a stereo system is good - or even if it is a 77 stereo system. As Descartes has said, our will to pass judgment far outpaces our ability to pass judgment. To derive meaning from good music a listener must engage in two kinds of activities, each of which may itself be worth doing. He must absorb sounds through his senses, and he must interpret his sensations in his imagination. Interpreting music is a matter of recognizing the relatedness of the events that make it up. Uninterpreted sounds are meaningless to a listener, and they can therefore contribute little value to his experience. Even if we agree with Cage that the coughs in the audience are more interesting than the chords from the orchestra, to be interesting the coughs must be experienced in a larger musical context, of which they are felt to be a part. If value is grounded in meaning, then the quality of a piece of music will depend upon its susceptibility of being understood. As Bergson and Dewey have pointed out, there are two ways in which we can connect the various moments of experience. We can organize our sensations and imaginings conceptually, as when we use sonata form to interpret the sounds we hear according to key relationships and themes. Or, we can organize our sensations and imaginings feelingfully and intuitively, without the mediation of general concepts. In this latter case our experience coheres just because it feels right. This intuitive, feelingful kind of organization is the more important one for the arts. And the meaning that binds the sounds together is more directly significant for musical value than the meaning that the intellect finds with the help of general rules. My view is that the labor of listening to sounds and then relating them to each other has an affective side, as all activity that challenges our abilities has an affective side. The great value of music is that we can get the excitement of interesting work without the distractions of practical goals and the fear of the consequences of failure. The labor of creative listening is the labor of sensation and active imagination. Up to a point, the harder the work, the more intense the excitement and therefore the more value the experience. Past that point we are over our heads and the coherence that a more talented listener would find in the music is lost. Fine music may be too rich for an untutuored ear. As Spinoza has said, "All things excellent are as difficult as they are rare." To be rich in meaning a musical event must demand and be demanded by other musical events. This is no quantitative affair. There is no question of involving a mere maximum of events; the way the events are involved is what matters. One gets a sense of propriety in meaningful music; the events that occur are the events that the musical context has led up t o. A melodic phrase or a sequence of textures may feel as if they need the event. Or the event may be other than what was led up to; it may be a timely surprise. When a piece of music is meaningful one senses that what one hears belongs, even if he did not anticipate the event in question. For a musical event to be rich in meaning it must fully belong to a process of sound. And that process must have enough going on in it that for a listener to hear it as a process he must bring most of his perceptual and synthesizing powers to bear 78

on the sounds that comprise it. In musical experience as in other kinds of experience, the intensity of feeling varies with the extent that one's powers to act are taxed. Driving in traffic can be exciting. If the traffic is moderately heavy we have much to watch out for and much to react to. If the traffic is so heavy that it does not move very much, or if it is so light that it can be dealt with easily, then either we fill out the experience by turning on the radio or by thinking about something else, or our powers to receive data and act upon them tum back on themselves, and ennui is the result. Driving fast and driving in moderate traffic can be interesting, and often it is the kind of experience we value. Driving faster than we feel secure driving, or driving in traffic in which too much happens, is frightening. We sense that our powers to act have diminished below what the exigencies of the situation might demand; we feel the material of the experience crowd in on us, and the experience becomes a disvalue. An engrossed listener is free to pursue the values of musical experience, while other kinds of experience make practical demands that call his attention away from what is immediately worthwhile. Finding a comfortable seat where we can hear music without the intrusions of the consumptive's cough, the ticking watch, or the clanging of an exhibitionist's charm bracelet, is about all we have to do to hear. But driving in traffic our lives are at stake, and this is sometimes a distraction from the thrill of coping with the material of the experience. In musical experience we can involve ourselves fully in hearing sounds and understanding them as a musical process. Music challenges without threatening. And music challenges in a variety of ways. Some varieties of musical challenge are relative newcomers. As a result new music often calls for listener activities that are very different from what music used to require. Traditional music is almost always organic. Theme, key, rhythm, and tone, all hopefully combine to make a movement a single, coherent unit. But with the elimination of key and with the introduction of electronically produced sound, different kinds of organization arose. When John Cage said that a sound should simply be, that its valu.e need not depend upon an organic context, he was more prophetic perhaps than even he thought. At first blush he had to be wrong. Cage celebrates novelty and surprise in his thinking about musical value. But without a context there can be no expectation. And without expectation there can be neither novelty nor surprise. Nevertheless, Cage insightfully recognized that aural qualities need not be subordinate to structure. In fact, many young composers have shown that even the reverse is possible, that where novelty and surprise or musical texture are the values to be cultivated, then it can be for their sake that the sounds are chosen and arranged. In music of this kind surprises and textures do not exist to highlight a movement. Rather, they exist as immediate values. 79

When a listener thinks that all music is like Beethoven's his imagination is misinformed. He may hear contemporary sounds. But to what purpose? The best part of musical experience involves understanding them, but a misinformed imagination is useless for feeling the significance of sounds. A listener with inappropriate beliefs about musical value will fail to divine meaning. What he hears will appear meaningless, and therefore valueless. And the listener will be much the poorer for it. In my view there are at least three kinds of objective bases of musical meaning, namely, organic structure, musical texture, and novelty and surprise. Hence my view presents three kinds of musical value and three kinds of creative operations a listener can engage in. I believe there are three fundamentally different ways to enjoy sound. Often more than one way to listen will do for a given work. No matter whether a listener uses one technique or all three, his choice should be founded upon the felt needs of the music. The test of a listening technique consists in its payoff in musical experience. A listener who attends chiefly to the tones of the instruments in a Haydn quartet, while ignoring thematic development, will find the piece used up in a moment. In fact, if the textures are really what a listener cares about, then he will do much better to listen to sustained tones or arpeggios. Haydn's themes and rhythms are almost sure to be a distraction from texture rather than a value added. Stringed instruments can indeed produce nice sounds. But not nice enough to absorb very much attention. The value of their sound depends chiefly upon its service to something else, in this case coherent organization. But a listener who tries to relate the sounds that make up Ligeti 's "Lux Aetema" the way he properly relates the sounds of the Haydn quartet will feel very much at sea. For the layers of sound, blending and contrasting, have little to do with what makes Haydn's music good. The sounds that envelop any one sound in the Ligeti have nothing to do with thematic development. Rather, they function to contrast and complement the sound enveloped. Listening to Legeti's music one determines meaning according to the service each sound provides for the others, quite irrespective of its place in the whole. Stockhausen's "Momente" illustrates the need for still another listening technique. Here, the sounds are surprising and novel; they are not especially interesting as textures, although they might have been so without hurting the work. The meaning in Stockhausen's sounds does not consist either in enhancing textures or in developing themes. We take in Stockhausen's sounds and enjoy them precisely because they contrast abruptly with the traces of experiences that make up our musical memories. If the sequences of singing, clapping, and laughing that Stockhausen uses so effectively were ever to become as commonplace as sequences that follow according to the rules of harmony, "Momente" would be banal beyond toleration. But since the sounds are not that commonplace, we can still listen carefully and enjoy the strange combinations; the work of understanding is not excessively easy. 80

My view holds that different works embody different kinds of values, and consequently different kinds of operations are called for from listeners. For some works what matters most is structure, for others it is texture, and for still others it is surprise and novelty. This has implications for the way composers think about their colleagues' work. For composers who subscribe to one set of values may not recognize the application of another set. A composer who values textures and organization, for example, Xenakis, fr, likely to think that the work of a composer who values novelty and surprise, e.g., Stockhausen, is slick and tawdry. Similarly,Xenakis and Stockhausen might both think that the music of a formalist, such as Lutoslawski, is academic and dull. Composers are often narrow-minded critics because many of them apply to other composers' work criteria that are relevant for the values they cherish themselves, but not for the values the others cherish. Happily, in dealing with parochial criticism we find that bringing out the irrelevance of a set of standards will nullify an improper verdict and raise questions that will suggest ways to correct it. There are other important differences between the various kinds of musical value. Music that is organically structured usually requires multiple hearings to disclose its worth. Music that affects novelty and surprise may have a strong immediate appeal, but unless there are other values accompanying the surprises its appeal is likely to be short-lived. Composers such as John Cage know that the appeal of their work will not last. And so they design their compositions so that successive performances will be very different from one another. Texturalists seem to enjoy the best of both worlds. But in fact after a few hearings their work too is often exhausted by an astute listener. This is no more a disadvantage for them than for the novelists, however, since texturalist's styles of composition assure a large output of fresh material. Not surprisingly, there are dangers in mixing values. A work that is highly organized will demand multiple hearings. But if the work contains important elements that are novel, then when the novelty wears off the work may be marred by banality. Even worse, the organic values may never surface because listeners will either be distracted by the novelty, or believing the work to be exhausted, they will be discouraged from learning it sufficiently. I suspect that much that is good in Ives' music is lost to most listeners because of the musical quotations. Still, dangers can be met. Berio's well known "Sinfonia" interestingly combines novelty with texture. But his use of surprise seems clearly subordinate to the textures so that one keeps finding new things in it even after he learns to expect the quotations. Although presently less well known than Berio's "Sinfonia," Larry Austin's "Quadrants" equally effectively combines textural values with structural values. Austin exploits qualities of space and sound only recently opened up to composers by developments in electronic instruments and multiple-track recording tapes. "Quadrant's" spatial and aural textures derive some of their impact from the contextual 81 modifications of what precedes and follows each sound. But much of the value of the textures grows out of their relationship with the whole; "Quadrants" is a coherent process in which the first moments are important for the last precisely because the work develops around the growth of one sound. By using fairly obvious modulations, Austin deftly surmounts the very real hazard that a listener will be distracted from the music's coherence by the qualities of its textures, thereby missing some of the worth of the piece. "Quadrants' " organic merits emerge with its textural ones. The significance of the feeling of the sounds' locations in "Quad­ rants" and in some other new music differs from the significance of ordinary stereo spatiality. Stereo, and even quadraphonic equip­ !Ilent a

record or go to a performance. Occasionally, too, we want insights into something to which we are already committed, in order to get as much out of our musical experience as we can, for example, as when we already own the record or have already bought tickets for a repeat performance. The reliability of criticism depends upon the critic's ability to respond creatively to music in ways that are either like ours or are different in ways we can take constructively into account. For example, the critic's responses may be different in ways we would like to develop ourselves. If a critic believes that some recent recording of Tchaikovsky's Fifth Symphony is the greatest thing ever to hit Schwann, I know that I can safely ignore his judgment about a piece by a composer whose work I do not know. On the other hand, if a critic with the credentials of an Eric Salzman or a Robert Marsh thinks differently from me about a piece of music, then I take note. It is not that I feel obliged to acquire his opinion. But if there is any sense in which taste can be improved - and I am convinced that there is -then I can learn from someone whose qualifications I take to be respectable, thereby sharpening my own ability to discriminate worth and enjoy music. This is not to deny the propriety of idiosyncratic factors that determine what set of values a composer will find meaningful for him or what preferences a listener will ultimately exercise. But a rational verdict itself refers to the music as a ground of meaning and value, and it reflects the qualifications of the critic. Ideally it contains nothing idiosyncratic but rests solely upon objective grounds in a way that can be confirmed by any other qualified listener who can think beyond his own special preferences.

PHILLIP REHFELDT Clarinet Resources and Performancel

A prominent part of what has become commonplace in much of America's music since Ives has been the development and exploitation of non-traditional sound resources for traditional instruments. In the literature for the clarinet, such devices have included wide vibratos, pitch bends, glissandi, flutter tongues, resonance (or color) fingerings, quarter-tones, hum and play indications, high reed squeaks (with teeth), key and finger pops and rattles, reed snaps with finger, sub-tones, air alone, muting, "nasty" saliva sucks, and multiple sonorities.

1. Originally presented in the form of a lecture-demonstration at the First Annual Regional Conference, Region VIII, of the American Society of University Composers, Arizona State University, Tempe, Arizona, November 18, 1972. Revised July, 1973. 83

The matter of whether the presence of these devices continues to be in the spirit of experimentation, or not - if indeed it ever was - is, in 1973, no longer of much concern to anyone. In the works, especially of such competent clarinetist-composers as Donald Martino, Burton Beer­ man, William 0. Smith, Sydney Hodkinson, Paul Zonn, and Dorrance Stalvey, as well as many other non-clarinetist composers, a place in the literature has already been established, the potential satisfactorily dem­ onstrated. My purpose is not, therefore, to add to this list of possibilities. The need, as I see it, is rather for an attempt toward the establishment of more standardized practices. From this standpoint, the majority of the devices mentioned are completely self-evident, needing little or no fur­ ther comment. Others, however, owing in large measure to technical matters of performance problems, are less easily understood. This is particularly true in the case of multiphonics, for which there is a great need for further dialogue. It is toward the items glissando, vibrato, pitch bends, and especially multiphonics, therefore, that I would like to di­ rect the major portion of my comment. Before proceeding, however, because they pose a special type of problem, let us briefly consider the items resonance fingerings and quarter-tones. As yet, universally acceptable fingering charts have not been developed. In the case of resonance fingerings, the number of possibilities is overwhelming, the notation difficult. Until such a work appears, those who understand the topography of the clarinet can fol­ low the general rule that tones can be colored by venting a hole directly beneath the pitch desired and by adding fingers or keys beneath the vented hole. This, of course, will not apply to fingerings which extend farthest on the instrument (e', f', g', b", c", d") or to the notes c', e", g"', orb"'. 2 These last pitches, however, can be colored by use of the low e' key, usually a safe coloring device for most pitches. The register key is a useful color device for b", c", and d". It is important to note that, generally, the further away the resonance fingering is from the vented hole, the less apparent the effect. The situation with quarter-tones is much the same. There is one significant difference, however, in that all pitches on the clarinet can be bent at least a quarter tone with the jaw alone. It is usually sufficient to simply indicate which tones are to be altered, allowing the player to establish his own best method, whether with finger or with jaw. Since vibrato, glissando, and pitch bends all involve, to varying de­ grees, a non-normal alteration of pitch, an understanding of the tech­ nique of production is prequisite to an understanding of the device. On single reed instruments, pitch can be controlled in two ways: the player can blow harder or softer, causing the reed to vibrate more and less, resulting in appropriate fluctuations in pitch, or he can press more and less on the reed with the jaw, changing the free vibrating length of the reed, and, therefore, the pitch. Because dynamics are usually rigidly

2. The apostrophe(s) indicate register, i.e., e ' is the lowest "e" on the instrument. Pitch is as sounds. 84 specified, the pitch of a given note must be controlled, finally, with the jaw, according to the dynamic. Jaw movement is highly important, therefore, even for the Mozart Concerto! The amount that a given pitch can bend with respect to these devices is restricted according to the acoustical make-up of the clarinet. In general, the amount of potential flexibility increases as the pitches get higher. The range from low e' to c-sharp" allows only microtonal ad­ justment; the range d" to e"', approximately a minor second; f"' and f-sharp"', a major second; g"' to a"', a minor third; a-sharp'" to f-sharp"", a major third; g"" to a'"', a major second; a-sharp"" to c"", again microtonal; and high c-sharp"" and d'"', practically nothing. A smooth glissando to about c-sharp" is next to impossible, as is the range from high a"" and beyond. Multiphonics warrant much more extensive investigation. Owing to the relatively few years since their appearance in the literature, a stan­ dard method of performance has yet to be adopted. This has resulted in a preponderant attitude that they are unstable and difficult to control, therefore a dangerous and unpredictable device when used in serious music. The major problem remains that they are produced with varying degree ofreliability from player to player. It is imperative, therefore, that any such presentation or suggested multiphonic possibilities be further qualified according to equipment employed as well as manner of per­ formance. The main consideration, in the development of the accompanying set of fingerings, is that the reed or mouthpiece need not be altered in any way to accommodate the production of multiphonics. It is con­ sidered important that the reed and mouthpiece be equally suitable for all types of literature, even on the same program. The mouthpiece is one made by Bob Mario in North Hollywood (S .45), the reed of mod­ erate strength, flat on the back, well balanced for maximum resonance, and able to produce at least a high b"". The instrument is a standard Buffet R-13. The technique for production is a sensitive adjustment in jaw pressure on the reed, fundamentally identical to that used for glis­ sando, vibrato and pitch bends (as well as regular pitch adjustment).3 The throat muscles remain relaxed at all times. It is well to note, in addition, that the clarinet reed is far from being a stable entity, and that many of the characteristics described below (precise dynamic in­ dications, relative stability, amount of flexibility, or even pitch itself) can vary slightly from reed to reed and even with the same reed as it absorbs more and more water in performance. It is remotely comfort­ ing, however, to realize that this problem is apt to affect a performance of the Mozart Concerto with equal severity - it is the irreconcilable

3. I can't resist the temptation to add that because the ability to glissando, vibrato, and bend pitches is necessary simply to play in tune, it is advisable to include it among those items which go together to determine a "correct" tone quality. The other considerations are rapid tonguing without change in color to sustained tones, dynamic degrees from ppp to fff without change in pitch, and the ability to play smoothly and rapidly from one note to any other. It follows that the clarinetist who has difficulty with the glissando (i.e., the opening of G. Gershwin's Rhapsody in Blue, or the closing of A.Copland's Concerto etc.) will also have problems with multiphonics- as well as control of pitch. ' ' 85 incubus of the reed-instrument performer. The sonorities have been divided into two large categories according to means of production. Those in category I are produced with general­ ly less jaw pressure and with jaw often further forward than required for normal playing. The result is a more homogeneous sound complex, generally more restricted in range, and produced with superior control owing to a greater wind resistance factor. These multiphonics are fur­ ther grouped into categories a, b, c, and d, according to maximum dynamic limitations. On a scale of 1-8 (ppp to fff, or a point just after "subtone" to a point just prior to "overblow"), those in category a will sustain a dynamic to fff; those in b tend to crack above ff, and some­ times f; those in category c reach a limit at about mf and note a more resistant quality; those in d can only be used at soft levels, p to pp (ppp being generally unreliable for multiphonics), and increased resistance is even more noticeable. Unless further limited by nos. 1-4 (see below), all multiphonics in category I can be used in series and at soft dynamic levels, irrespective of the assigned loud limitations. The pitches are fairly stable (note no. 2, below) and are producible with rather good consistency. The sonorities listed in category II are produced with increased jaw pressure and are characteristically of wider range, higher tessitura, more shrill in quality, and produced with a reliability factor which often borders on indeterminate. They generally require free amounts of preparation time and ought not be used in rapid succession. These are further divided into categories !!_ and Q according to relative ease of production, those in category ~being more readily produced than those in Q. Individual dynamic limitations are provided. Each sonority has been further qualified by a number or numbers, ranging from 1-4 (if applicable) which appear next to the fingering. They indicate the following: 1. Pitches are more difficult to find and/or sustain than normal, depending upon the individual characteristics of the reed. 2. A pitch adjustment, primarily with respect to the upper pitches, of at least a quarter-tone is possible without destroying the multi­ ple characteristic. 3. The sonority can be sustained to (or initiated from) the most prominent upper pitch, as well as the lower. 4. Soft tones, i.e., below mf, are immensely difficult. Keys are identified by the pitches they produce in the lowest octave and are in the approximately correct position. Pitches are notated as they sound on the instrument. The sonorities work equally well for A and B-flat clarinets. Notation O most prominent pitch ~ beats between pitches • less prominent pitch -[:, or J/ microtone higher ( •) barely audible or microtone lower [ J variable pitches q 11 86

Q)__ J; ® ~ ~: Q) b ~ L 0 _b ~ @_s __~~_: © i=--- -::=t:=_-::t---=1- 1=?1. = _·~~~ :Fe_====__; i::::-·- ,, ±.-:I---+- ·===:=-R==.....L--=::=--;==EE ~- = .I=: ---. -:t~o - ---~ -v- ~ # @iii 80 60 ee e• f f'IO 9o oo 0 0 0 • *0 0 0 • • 0 • ; 2,4 -;- -;;- 2,4 • 2,4 0 2,4 • 2,3 .. 2,...3 g G~ ~ g r. g cl : : a'· ~

Figure la. fff dynamic possible, the most reliable and versatile of the six categories. 87

@ 4 @ *_Q_ 0 #-e- ® ~~ 0 0 -.: I i! [ ~ ,_ ·II b%4f=1 -0- •• 1T •• ~: •• •• 11 E;•• ••• .!c# le' ..!_ rr: r' .!. E E... • • 2 • 2,.J • 2 • 4 • ;.~: • ~= GI: G' 0• • •' '

..,_ _._ (:J'_l (f) .. #-e- @ l-o- @ #~ I •l 0 ® ~'-D- @ l I I I I g ;: i ~ · II ' ••0 : •o ••0 ••0 ••0 rr .! '-e- ~ • • ·~• .!..• 2. 2 ~ 4 .2.,.J 0 4 • • • 2 •0 t: •0 G'~ • • •' • •

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Figure lb. Dynamic limitation at ff and sometimes f, tendency to break at louder levels. 88

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;: I lit f o• .. o ~6 •o eo £~_£ e~l • .!..• .!..• lei 3 0 4 • 2,.J g -3 0 .J • 0 0• 0 • 0 • 0 0 0 • " I

Figure 1c. Dynamic limitation at approximately mf, more resistant quality. 89

lFA -e- 0 -e- 0 0 0 t-0- ® I • I (t:) I I I I D I 1~ eo eo eo ,: •o •• • Et_; ..!.• • ..!.• .!• • • • .J • d • F': FJ: c: ;#: •

Figure ld. Soft dynamics only possible (p to ppl, extreme resistant quality.

,Vo :c: l: _g_ [!) (J) - #t:._ 0 @ [l:J [~J 0 ® @ ().) --=-r== ~f b2 f ± _ _ ===::---_ I P-=-i1=1 -e- -e q mp-j • mp F: mp t.P_ 0 c~> @ ;q ~- i~b E~ _£ •' I • mp Figure 2a. Produced with relative accuracy .

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(~) ® ~~l ® [;~] ® (l'g_ I I I ;o eo 1v ~o A ••0 • • • ..!. ~ Ii':0 I e:0 I e:• I mp; m; mp Figure 2b. Produced with increased difficulty. 90

The entire matter of esthetics is one that the author would prefer to avoid altogether. The matter of whether the multiphonics sound "good" or "bad" is, of course, highly personal or even irrelevant. Such pronouncements usually change with time. If one experiences the "dis­ sonances," for example, occasioned by the ninth and thirteenth chords at the end of the divergent area in the opening movement of the Bach Fifth Brandenberg Concerto, or the Neapolitan six-five "dissonance," followed by a dominant ninth, before the new theme in Beethoven's Eroica Symphony simply as either pleasing or displeasing sonorities, he misses the primary point, which is one of function, to surprise, to contrast, to attract attention, in these cases, to important aspects of formal structure. Within the context of the present century, the situ­ ation is, at least potentially, perhaps similar. I would like to add, in conclusion, that the set of multiphonic pos­ sibilities presented has been developed in consideration of the works about and containing multiphonics of Bruno Bartolozzi, Peter Griffith, William 0. Smith, Gerald Plain, Burton Beerman, Dorrance Stalvey, Barney Childs, Pavl Zonn, John Heiss, Bill Sydeman, and Hans Leh­ mann. It is an expanded compilation of sonorities many of which already exist in the recent literature for the instrument. The major intention has been to produce a list which is selective as opposed to exhaustive, and an attempt has been made to eliminate fingerings which produce identical or closely identical results. It is provided here not as the ultimate word on clarinet multiphonics, but simply with the hope that, for the present, it will be useful.

JOHN SELLECK

Computer Partitioning (This article was given to a meeting of Region II, ASUC, New York City, January 13, 1973.)

This paper serves to introduce the preliminary results of an investigation of partitioning via computer assistance. Those familiar with the compositions of Milton Babbitt and Peter Westergaard will have some idea of the problems involved in uncovering the possible partitionings of a 12-tone set which are pertinent in a given compositional situation. There are some general rules in certain instances as related in Westergaard's article: Toward A Twelve-Tone Polyphony (Cf. Perspectives on Contemporary Music Theory edited by Benjamin Boretz and Edward T. Cone, pp. 238ff.). Practical techniques are wanting development, and general knowledge in this area is 91 unavailable to most composers not well-versed in the mathematics required. An admittedly interim solution to the problem is the generation, by computer, of partitions of 12-tone or other sets, which, of course, is not a general solution, but a tool which will aid in gathering information either for specific compositional use, or for perusal in the search for more intuitive rules for partitioning less dependent on mechanical generation. Before plunging into the actual results of the various computer runs it might be helpful to define in some manner just what kind of thinking was used to devise the computer programs involved. Concept of lmbedding: Given an ordered set of pitch-classes, some order positions will constitute subsets, all 12-tone transformations of some specified type. Figure la shows an instance where all imbeddings are forms of one 3-element subset. Here the imbeddings exhaust the 12-element set, but the imbedded subset forms are not mutually exclusive, i.e., any element of the set is part of more than one imbedded subset form. On the other hand, imbeddings of a specific subset might not be exhaustive. In figure lb the hexachord 0 1 3 6 8 11 is the only one of its type imbedded in the set 0 1 2 3 4 5 6 7 8 9 10 11. P-forme

imbeddings all of type 0 1 J

Figure 1 a

Figure 1b

Concept of Partitioning: Partitioning will be defined here as the extraction of imbedded subset forms such that the imbedded subset forms are exhaustive of the total set and mutually exclusive in content. Figure le shows a couple of possibilities. The imbedding concept may or may not be useful compositionally, but it was involved in the design of the first program which finds all possible imbeddings and then procedes to examine groups of these to 92

Figure le imbeddings are mutually exclusive and are all transpositions of each other subsets of type 0 1 2

partitioning involves adjacent order numbers

imbeddings are of different forms of the same subset type RI

p

subsets of type 0 2 6

partitioning involves non-adjacent order numbers

Figure le

see if any particular collections are exhaustive as well as composed of subset forms that do not share any elements of the set being partitioned. Figure 2 shows the results of an algorithm which finds all possible imbeddings of a specified type in two concatenated forms of the same 12-element set. Later versions of the program deleted the printing of these results as they are not usually very useful. Figure 3 gives one non-exhaustive solution which was useful in a particular compositional scheme. It was thought that the partitioning of a pair of sets related by being transformations of each other by the usual 12-tone operations of I, R, or RI (at some transposition), would be of more interest than just that of a single set. The latter would also be taken into account in the operations on the former. The program generates all possible distinct pairings of two sets of the type indicated to the program as the set to be partitioned. Of the 16 possible pairings of a set with some transformation of itself, not all need be examined since they are not all unique forms. The possible concatenations of one set with another are: p I R RI p PP IP RP RIP I Pl II RI Rll R PR IR RR RIR RI PRI IRI RRI RIRI 93

PRIME PRIME 0 1 6 3 4 9 2 7 8 5 10 11 1 2 7 4 5 10 3 8 9 6 11 0

IMBEDDINGS OF SUBSET 0 1 5

0 5 PRIME 0 5 PRIME 0 4 5 RETR-INV 0 4 5 RETR-INV 0 8 7 RETROGRADE 0 11 7 INVERSION 0 5 PRIME 0 4 5 RETR-INV 1 9 8 RETROGRADE 1 9 8 RETROGRADE 1 2 6 PRIME 1 5 6 RETR-INV l 2 6 PRIME 1 5 6 RETR-INV 6 2 RETROGRADE 6 7 11 PRIME 6 7 11 PRIME 6 5 INVERSION 6 10 11 RETR-INV 6 10 11 RETR-INV 6 7 11 PRIME 6 10 11 RETR-INV 3 4 8 PRIME 3 4 8 PRIME 3 2 10 INVERSION 3 2 10 INVERSION 3 7 8 RETR-INV 3 7 8 RETR-INV 3 11 10 RETROGRADE 3 2 10 INVERSION 3 7 8 RETR-INV 3 4 8 PRIME 4 8 9 RETR-INV Jf 5 9 PRIME etc.

Figure 2 There are, however, only 6 unique concatenations. All the others can be derived by applying the operations of I, R, or RI to those six as shown below:

ri pp II RR RIRI Pl IP RIR RRI PR IRI PR IRI PRI IR IR PRI RP Rll RP Rll RI RIP RIP RI (lower case letters signify operations) 94

RETROGRADE INVERSIO N 11 10 7 9 8 5 6 3 2 4 1 0 9 8 5 7 6 3 4 i 0 2 11 10

I MBEDDINGS OF SUBSET 0 1 5 4 8 9 2 3 7 6 l b 11

RETROGRAuE 10 9 5 6 2 8 7 3 4 0 11

Figure 3

If either retrograde or retrograde-inversion degeneracy (P=R or P=RI) is the case, the P with P and P with I are the only unique forms; all others can be derived from these two. Figure 4 is an example of the first form of the program EXIMBED which has partitioned out subset forms of one specified type from a 24-element string composed in the manner just described. Each subset form extracted is labelled as to what form of the subset it is. Already we have a way of examining the properties of partitioning which far exceeds any practical extractions "by hand." The possibilities are usually too great to allow finding all of them, or so few that the possibility escapes one. The computer program can in a very short time find all the possibilities, if there are any. The usefulness of this information is fairly obvious. The goal of a compositional activity employing partitioned sets allows for an integrated contrapuntal display of pitch material, or some other method of relating pitches in an hierarchical structuring. 95

'1l z z Q > 0 > O > >>> > z H ZH z ~~~~ zzz z H Ul H Ul H H HCJH HH H H '1l 1 '110::'11 I 0::'11 WW I '1l I I 0 I :O';O:::Efil:EO::W:E :;;::;;: o:: :;;:o::o::o::o:: ~ ~ d: d: d: ~~d: H 8H > H E-4 >H H H8 H E-fE-f~ l 8 H HE-48 8 H H E-4 g; ~g;;:; g;~ ;:;g; g;g;~g;~ ~ ~~ g;g;[i!~~g;g;~

0 0 1 01 I I .-t .-

0 0 0 .-t ...... °' °' °' '° '° '°

(XJ (XJ (XJ

.=t .=t .=t "" "" "" '1l :;;: H "' "' .... 0:: N N N .-t A. ....0 ...... -t .-t I .... .-t .... I .... . I 0 '° 0 0 I 0 +' .-t I .... CV t I °' I '° (XJ '° '° t I I t I I t I I I °' I °' I °' I "' (XJ I (XJ I (XJ I .,__ Ul I I I I I z I I "'H I I Q "' I "' I "' "" Q .,__ I .,__ I .,__ N '° w I I ~ I I :;;: I I .=t .-t H I "" I "" "" I I "" '1l N I N I N N .-t 0 > I I I H I I I u E-< .=t I .=t I .=t I .=t 0 E-< Ul I I I w ::i w I I I Ul «: :;;,; .... I ,...; I .-t I .-< JI. ~ :i:: H I I I w :::> >< 0:: I I I I Ul Ul '1l A. 0 1 0 I 1 0 10

Figure 4

By combining the results of several examples generated by this program one can construct such an hierarchical arrangement. Figure 5 shows string S, composed of four related 12-element sets generated by an 0 1 6 trichord. The forms of the trichord in the Prime form of the set are P+P+RI+RI. A hexachord composed of two prime forms of an 0 1 4 trichord was given as data to the program indicating the type of partitionings desired. It was found to partition P 0 +P 2 as well as R11 +R1 such that the partitions could be arranged so as to form the 12-element extractions labelled A, B, C and D in figure 5. One of these, D, has the form P+P+Rl+RI. This particular set was then partitioned by 96

. n A ...... n ; n ·~ -• . A ' ~I \ I I\ \ ~ ~ I I 7 J .I ' .. B ·- . . . -' (\ . \. I I I " - T ". .... c ~- .J p p\ RI \ RI \ I/ (\ 1/ \I .u v ;~ ·~ '- n D "' . J

Figure 5

the program using an 0 1 5 trichord. The subset forms extracted are shown in Figure 5 as 1, 2, 3, and 4. Complete 0 1 5 sets of the form P+P+Rl+RI can be obtained by successively transforming the entire structure to P 8 , R110 and Rl0 . Note that the trichords 1, 2, 3 and 4 already exist as subset forms P8 , Rl10 and R1 0 (and P6 ). This process could be continued indefinitely producing an infinite number of levels. Any structure involving partitioning can be subjected to manipula­ tions similar to those performed on any set; one can form "syntactical" modals which in tum can be used to generate larger structures for actual compositional usage. Consider Figure 6a, for instance. The extraction of the hexachord 9 10 2 5 1 0 and others of its type from a 97

c D ..'. .... u• " 5 Ulll. ... - :1 ·1 } \ \ .. \ I ....A . • 6 \_U \_ .IP'z . •1

II \ ' \ JI ...\_ - " 7 ,..,. • •u " -f''o II I \ \ ...\ • • • I 8 ..._., .... - ': -· . - R1_ . 5 - F igure Ga set whose R 9 is 9 8 7 6 5 1 10 2 3 4 11 0 plus its concatenated form 18 (A + B in Figure 6a) can be transposed t6 resulting in the situation labelled C + D. The hexachordal extractions of A + B are labelled 1, 2, 3 and 4; those of C + D are labelled 5, 6, 7 and 8. 1 + 5, 2 + 6, 3 + 7 and 4 + 8 are four complete 12-element sets which are all forms of each other. Since the hexachordal extractions are related by t6, 5 + 1 is also a form of the derived set, etc. The original sets A, B, C and D have RI com binatorial properties such that A combined with D will produce hexachordal aggregates; similarly B with C. If the entire structure A+B+C+D (or C+D+A+B) is inverted we obtain the results given in Figure 6b. The inversion of A produces an RI form 98 / ,, RI 5 o' P6 c 6 ,; 5 , 8 ,, 7 ' J

, A

Figure 6b

of the original set which is trivially combinatorial with set D (i.e. its retrograde), so it is labelled D'. Similarly B inverts to C', C to B' and D to A'. We can see that the 48-element string D'+C'+B'+A' actually a retrograde of A+B+C+D. However, the disposition of elements in the partitions is still the "prime" form. A permutation of the derived sets which are also in retrograde has occurred; 6'+2' (retrograde of 2+6) is in the position occupied by 1 +5 in Figure 6a, etc. Therefore the structure in Figure 6b is not simply a retrograde of the structure in 6a. Various vertical aggregate forming possibilities exist between the two structures. A with A', B with B', C with c· and D with D' are possible as well as the internal possibilities cited above. One can form aggregate f;; SETe 2 3 7 1 5 6 4 8 0 9 11 10 a.c :::;"~ ...... C'D CD SUBSETe 2 3 7 8 9 0 .... . 'O ,; )> :J :::!. EXHAUSTIVE IMBEDDINGS c+ :J :::;" c+ CD C'D C'D PRIME RETROGRADE 0.. ("') (') >'1 0 C'D rn 2 3 7 8 9 0 PRIME s E. 0 0 4 5 6 10 11 RETR-INV 'O c+ ("') 4 0 11 1 0 rn 5 7 INVERSION rn ...... , CD 6 3 2 1 9 8 RETROGRADE tt ~ 0 0 ,; )> :J s CD EXHAUSTIVE IMBEDDINGS e:.."' PRil'l'.E 'O RETROGRADE-INVERSION >'1 2 ,, 0 :J .c· (') c: C'D ... 2 J 7 8 9 O PRIME rn ....,0 C1> 1 4 5 6 10 11 RETR-INV ;n "-l )> 5 4 0 11 10 7 INVERSION "zj trj 6 3 2 1 9 8 RETROGRADE ~ .... . CD CD ~'""" >'1 $: ,; EXHAUSTIVE IMBEDDINGS C'D t:O trj ("') -J tj RETROGRADE PRIME ...... :::..: 0...., 0 0 c c+ 10 1 2 rn C'D n 3 7 8 RETR- INV ~ :J 11 0 4 5 6 9 PRIME »> rn )> 9 6 5 4 0 11 RETROGRADE c+ :::;" 8 7 3 2 1 10 INVERSION ~ 0 CD CD 0 ::;J )> :J 'O . 10 1 2 3 7 8 RETR- INV 11 0 4 C'D "'c+ 5 6 9 PRIME rn c+ 9 6 5 4 0 11 RETROGRADE c C'D (') >'1 8 7 3 2 1 10 INVERSION :::;" ~ 100 partitions all f orms of 3 1 2 O ------"whole-tone" hexachords P1 Po

n l•lo ""•·.. " . .... ,, \'',, ' ' ,_, ' to. ... - ft "--, - ff I II \ \\ I \\.. ' I \>·'- \ ~- "= -~~ \ \ \,_ \ \ I I '\ ' .... ·. ' ·,I '"", I ~ I -~ ·~ v~ . \\ \ \ y II I I I IT \ ... .. \ " '•".. . - ... .. -J .... -~ I\ I \I/ I I - ..... , ·- - ti. II -i;.. I

Figure 8

patterning. Particular subset pairs which are R or RI related have order-position patterns which are all "RI" related. Figure 8 shows a 3 1 2 0 extraction from two forms of the set 0 10 3 8 1 11 6 4 9 2 7 5. The set itself contains several interval-class 2 sequences which are also found in the subset forms partitioned out. In the passage for cello and bassoon this dyad is projected by dynamics and articulation. Each 101 I .-1NNNf'"'lf'"'I .-1 .-< NN N N .- > 0<1;00 0 H H o:::z z HO:::HH H {/) {/) OH H UJoUJC/l UJ o:::wwo:::w~ WWOIW I o:::oo:::o:::w0::: i:.i;;;;;:;;;;;:w;;;;;: :;;; :;;; 0:::0::: :;;: 0::: >HH>HH HHE-tE-tHE-t ~~~~~~ zo:::o:::zo:::o::: zr.izzo::: z HP.,P-.HP.dl., g;g; ~~ ~ ~ HO:::HHP-.H

!:'- !:'- aJ ...... 0

0 0 ...

f'"'I f'"'I -=:t

N N f'"'I 0 0 ...... I I I ..... I I .-1 N I I I I I WI I "' "' w '° QI i i Q !:'- .- w II UJ UJ UJ < :;;;: I ..:t i 1 ..j" E-< 11'.lll'.l ll'.l :i::: H w :::>:::>:::> >< 0::: UJ UJ UJ UJ w p., 10 I I 0 figure 9

subset form is given a registral placement. The dotted lines indicate 4 "whole-tone" hexachords which result when the partitions are placed in two aggregate groupings as in the example. This feature is realized by the instrumentation. To prevent overlapping of the hexachords in each instrument the Eb from one subset form was exchanged for that from another. 102

SET= 0 1 2 J (~RI) MODULUS = 4 SUB SET 1= 0 1 (~ R I) SUBSET 2= 0 2 (~R ) (P=RI)

EXK.~USTIVE I MBEDDINGS PRIME PRIME ------O 1 ------T 1 2 J T 1 0 1 T 1 2 J T 1 ------6t~:------0 1 ------T 1 2 J T 1 0 2 T 2 1 J T 2 ------etc:------0 2 ------T 2 0 I 1 2 I l T 2 ------~~~~------

Figure 10

EXIMBED was quite adequate for preliminary experimentation, but soon it was felt that certain limitations should be overcome by modification or extension. First, the program was made to accept more than one subset type as shown in Figure 9. One other change whose significance has yet to be demonstrated involved allowing the modulus (normally 12) to be variable. Figure 10 gives the results of partitioning a modulus 4 set. This example may appear to be merely a restriction, but Figure 11 shows the partitioning of a modulus 8 set where it can be seen more clearly that if the results are interpreted in a 12-tone system the normal operations of T, I, R and RI do not produce congruent results; in fact, interpreting the subset forms modulus 12, the transpositions of the modulus 8 extractions have interval sequences which are all different; but combinatorial properties are maintained and what is gained are permutations not normally possible. The parentheti­ cal notes in Figure 11 show what pitch-classes would have been generated had the modulus been 12. The notes in brackets show what ~ the pitch-classes of the imbeddings would have to be if the modulus were 12.) Given all the possible techniques that one might devise to use the information obtainable from EXIMBED, it was felt that more interesting results could be obtained if the scope of the material to be partitioned were greater. Unfortunately the more elements in the string to be partitioned, the greater, by geometric, if not factorial progression becomes the number of possible imbeddings. Even computer operations calculated in l/lOOOths of a second were not fast enough to practically partition a string of more than 24 elements. Since the program up to this point stores all possible imbeddings, the storage requirements also would be impractical. A new algorhytm was devised which did not need to extract all possible imbeddings first. It simply extracted those, in a 103

' ,. ·..•• ··~· , *• . set subset

.,,, Io RI r • I ·~'"" , ·-~ U&• .) I - \ ' \ I RI ,.'" . .... ·~ \ '"'J ' \ .. ~I ... - -,...... ,. " ,l

r'I \ I ~ I 7 • ... - -.-v--

~u .) l secondary set

p

RI

p

RI

secondary s et

Figure 11 particular order, that it needed to complete a partitioning. By maintaining systemetic procedures, the algorhythm can weave its way back and forth through the string to be partitioned, finally arriving at all possible combinations that work. The procedure was found to be much faster, although the reason for this is not at all obvious. For instance, many imbeddings would have to be relocated several times in different stages of the scanning process. However, the number of imbeddings which for the average case are not used in any partitioning is evidently great enough that not having to search for them saves time in the long run. 104

+> +> +> +> +> +> +> +> +> +> +> +> +>+>+>+>+>+>+>+>+>+>+>+> Q) Q) Q) Q) Q) Q) Q) Q) Q) Q) Q) Q) Q) Q) Q) Q) Q) Q) Q) Q) Q) Q) Q) Q) wm wmrnrnrnrnmrnm m rn m rn m rn m rn m m m m m .0 .0 .0.0 .0 .0.0 .0 p .OP .0 .o.o.o.o.o.o.o.o.o.o.o.o ;:s ;:s ;:s ;:s ;:I ;:I ;:I ;:I ;:I ;:I ;:s ;:s ;:s ;:I ;:s ;:I ;:s ;:I ;:s ;:s ;:s ;:I ;:I ;:s rn m m m m m m m m rn rn m mmmmmwmwmmwm 'H 'H 'H 'H 'H 'H 'H 'H 'H 'H 'H 'H 000000000000 '8 '8 '8 'cl '(; '8 '8 '8 '8 '8 '8 '8 E-

Figure 12

The next form of the program was one which considered four concatenated sets whose maximum length is 12 elements each. No transformations of these sets are effected; it was felt that by this time \.. particular sets would be of interest and that an exhaustive examination of all the possible combinations of up to four 12-tone transformations of a set was not practical, nor particularly interesting. Also, with this program, called SPECIBED, sets which differ widely from each other can be subjected to partitioning together. Figure 12 shows the results of this program given four sets which, as it happens, are related.* Figure 13 shows the possible greater complexity that can result. Structures for compositional use can be constructed which are not simply the combination of smaller structures, but are integrally unique in their own right.

*Since one character is needed to represent a pitch-class, 10 and 11 were replaced by the letters T and E , respectively. 105

,-c MM ...trlN ..... NMC\IMN ..-tMMM..-4N,-cNC\INC\IN : +' +'+' +' +' +' +' +' +' +' +' +' +' +' +' +' +' +' +' +' +' +' +' +' IQ) Q)Q) Q)Q)Q)Q)Q)Q)Q)Q)Q) Q) Q)Q)Cl)Cl)Q)Q)Q)CI) Cl) Cl) CI) I Ul UlUl UlUl!llUlUlUlUlUlUl !llUllll!lllllllllllrllUlrll!llUl Ip pp p p p pppppp PPPPPPPPPPPP I ;:I ;:I ;:I ;:I ;:I ;:I ;:I ;:s ;:I ;:s ;:I ;:I ;:I ;:I ;:I ;:I ;:I ;:I ;:I ;:I ;:I ;:I ;:I ;:I I Ul WW !lllllUl!llUlUlUl!llUl Ul lllUll/lrllrll Ulrlllll lllUlrll •,... 'H'H 'H't-.'H'H'H'H'H'H'H 'H 'H 'H 'H 'H 'H 'H 'H 'H 'H 'H 'H 00000 0 000000 000000000000 88E-18E-

'°\/"\ '°\/"\ 8 8 .....N N ....

('... °' ('... °' °'co c--'° 'I co co .:t I 0 0 0 8 1 Pr.l Pr.l .... c--co \/"\ Pr.l I .:t I .:t I 0 "" ... +---·------· --~- · \/"\O"".-t I co I co H I I ..... 0:: I Pr.l "" I Pr.l "" .-t .:t .-t N II I 0 I 0 p.. I .:t I .:t I I NC""'\0,..-f I \/"\ '° I \/"\ '° "" I .... I ...... 8 1 N I N '° ...... :t °' (!:I I °' I °' Ul I 8 ~ ('... ('... co °''° ('... 0 0 0 .:t Ul .:t .:t C-- .-t \/"\CO '° Cl z (!:I "" (!:I \/"\N H "" C""\N..-40 0 8 °' 8 °' ON N N .... 0 .:t (!:18 ...... :::t ..-t Nr-t i:Q[!:I :;;: Ul '° ~--'' ...... ('... H "' '° °'¥) I .-<'-0 °'.:t 8 8 I Pr.l \/"\ \/"\ I II u > ...... I 0\1"\0"" .- '°('... '°('... I .-< N "".:t Ul Ul I 8E-1E-1E-1 i:Qi:Q ;'.j E:: I .:t"" .:t"" I r.:tr.:tr.:tr.:t ::>::> ><(!:I I (!:I Pr.l I U)U)U)U) Ul Ul Pr.l Ul 10 0 I

Figure 13

At this point it was not possible to extend the program SPECIBED without running into the rather mundane limitation of its graphic depiction, i.e. it would not be easy to print out the results, say, of the partitioning of a 144 element string without devising some complicated format. This was side-stepped in favor of the satisfaction of the very great desire to have a program which could perform extractions upon a two-dimensional set structure. Needless to say the partitioning of two or more sets simultaneously was hard even to conceive of, and a great deal of trial and error was required to actually devise a systematic procedure for doing so. Nevertheless, with considerable effort such a program, SIMBED, was finally constructed whose operation was strangely enough almost identical to that for one dimensional strings. The printing out of the results of SIMBED proved problematic since what was before a two-dimensional display of a one-dimensional string, the added dimension showing the partitioning, was now a situation 106

SET la 5 4 3 2 1 9 6 10 11 0 7 8 SET 2= 5 6 7 8 9 1 4 0 11 10 3 2 SUBSET 1= 0 1 2 3 ( P=RI) EXHAUSTIVE IMBEDDINGS ------5 4 J 2 1 2 6 T E 0 z 8 AlT AlT AlT AlT

Cll Cll Cl I Cll ElT ElT ElT ElT 5 6 z 8 2 1 4 0 E T J 2 Bll Bll Bll Bll DlT DlT DlT DlT

Fll Fll Fll Fll ------eic:------5 4 3 2 1 9 6 T E 0 7 8 AU" \ \ j. ,_,., J' -.....__ \ X.. Bl-T BlT BlT Cll'CU c1v··; "' / ~ ';; D:NI" / "' .~v / " _,- / / V "- FlT FlT FlT .r I / . '-• '\., 5/ 6 Z 8 2 "-1 ~ 4 ~O E T 3 2 All All All BlT Cll DlT DlT DlT Ell Ell Ell FlT ------

Figu re 14 requiring three dimensions, the added dimension needed to show which set was part of an element of an extracted subset form. What was finally settled upon is shown in Figure 14. The sets given as data to be partitioned are printed underscored and each element is identified underneath by a three character field indicating imbedding, subset type, and subset form, respectively. All the elements of a particular imbedding are listed in the same row and all have the same first character. This representation is sufficient, but not completely adequate because it is not possible without actual comparison to know the order of the vertical elements of the extractions. 107

Figure 14 depicts the situation of two simultaneous sets. One feature of partitionings in general is clearly exhibited: that many, and in this example all, are formed from one basic pattern, the first here; all subsequent partitionings are formed by an exchange of order numbers which contain identical pitch-classes. Here six such interchanges are possible, so any or all of them in combination with each other will produce 41 combinations which in this case is the total number of partitionings. The first and the last with all the six interchanges are given here. The program operates such that the most vertical imbeddings are located first. The scanning proceeds down each column so that imbeddings that have elements of the same order number proceeding downward will be found before those with such elements proceeding upward in a column. The original form of SIMBED would examine up to four simultaneous 12-element sets. This was soon to be expanded to allow for 12 sets. This would allow the possibility of partitioning all the forms of a 12-tone row together as demonstrated by the results of such a program run in Figure 15. The sets are arranged in the familiar "magic square" so that the columns are the inversions of the rows. The subset forms of the partitioning have been collapsed here to save space. Three of the imbeddings are circled to illustrate the kind of arrangements that are found in the first partitioning. Most of the partitions are vertical proceeding downward in a column when more than one element appears with the same order number. The subset-type in this example is formed from a symmetrical partitioning of the set where it occurs in prime and retrograde forms in prime forms of the set. In the foregoing examples the two-dimensional formations that were to be partitioned were arranged such that the order numbers of the sets that are the same are aligned vertically. This is not necessarily desirable in all cases. Other arrangements are possible; in fact a set, in terms of data fed into the program, need not actually be a set in compositional terms, but only a specific horizontal component in two-dimensional space. Also elements which are to be simultaneous need not have the same order numbers; nor do the sets all have to be the same length. All this implies the concept of a null element which could be put into the actual order positions of the computer arrays in which the sets are stored. Figure 16a shows four 12-tone sets and one hexachord which were arranged for introduction into the program in the form seen in Figure 16b. This assures that the partitions that are extracted will allow the sets t o be arranged in such a manner in the actual composition and no partitioning will conflict with such an arrangement. If hexachords of the type indicated as set number 7 in Figure 16b are extracted, the results shown in Figure 16c are one possibility. Again two of the partitions are emphasized with circled connections. To accommodate input with null elements, the total length of a set was expanded to 24 elements. The program first identifies all null elements and considers them as the first imbedding. This removes them from further consideration in the rest of the partitioning operations. Later the first 108

SET l= 0 11 4 3 2 10 1 5 6 7 8 9 Sb."'T 2 = 1 0 5 Li- 3 11 2 6 7 8 9 1 0 SEI' 3 = 8 7 0 11 10 6 9 l 2 SEI' Li-= 9 8 \ l Q ll 7 l 1 0 2 3 ~ d::h SET 5 = 10 9 2 l 0 8 11 3 4 5 6 7 SET 6 = 2 1 6 5 Li- 0 3 7 8 9 1 0 11 SE'l' 7 = 11 1 0 J 2 1 9 0 4 5 6 7 8 SET 8= 1 0 9 5 8 0 1 2 3 4 S li:T 9 = # 1110 9 8 li- I :z 11 0 11 2 3 SGT 1 0 = 9 8 7 3 6 1 0 11 0 1 2 SET 1 1= 4 3 8 7 6 2 5 9 1 0 11 0 l S i-'~T 12= 3 2 7 6 5 l 4 8 9 10 11 0 SUBSET l= l 0 11 7 5 6

EX1-IA UST IVE IM BEDDIHGS

0 E 4 3 2 T l 5 6 7 8 9 ITT Gl T H T LlT LlT MI T Ll T ulK Pl T SlR SlR SlR

5 4 3 E 2 6 7 8 9 T A T E T D T NlT SlH K VlI Ol T WlK UlK

8 0 E T 6 9 1\ 2 3 Li- 5 c T I T I T Q. T L rr S R 0 rr M T Ul K XlI ' 9 l 0 E 7 T 4 5 6 D T C T l" T M 'r F T N T H M T R R XlI

T 2 l 0 8 E 6 7 ElT El. JlT J l T NlT J l T H T RlR x I I 2 1 6 LJ- 0 3 I 7 8 9 T E FlT F T H T 0 T H R p T V I Ol T Wl K X I I E T l 9 ~ r l 5 6 7 8 I\ T A T D T K T Hl T N T Ml T U K R R W K I 7 6 9 5 s/ l 2 3 lJ: c T A T T -J l T q,lT Kl T lR Pl T Vlr Wl K

6 5 8 4 1/ E 1 2 3 C T IlT KT I T p T Q T K VlI VlI W K J T 5 4 i I k 7 3 6 T E\ l 2 GI T AIT GI T F I T JIT EI T NIT C' l T QI T Pl'r WI K I Li- 3 ~ { 7 6 2 9 T 0 1 Gl T J l T El 'r Dl T F l T Dl'l1 ~ K MI T T 1\ lJ K X I

_3_ 2 5 l L 8 9 T E 0 GlT Cl T Hl T K T L T VlI K UlK X I

Figure 15 109

Sets to be partitioneds T 2 9 6 E 7 4 8 J 0 5 1 4 8 J 6 E 7 T 2 9 0 5 1 6 1 5 8 4 9 0 7 E 2 T J 6 1 5 2 T J 0 7 E 8 4 9 9 4 8 E 7 0

Figure 16 a Sets arranged for introduction into SIMBED

Set 1= E 8 1/ J 7 )) ~ I . ' 1 fl / l Set 2= /rf~I /IIA/ I 6l / tl / l/o 1 1 1 Set J= 6 · 0/ / 8 E 2 5 . Set 4= A A ·"', 7I tfI / 51;! I Et Set 5= 6 f f/ f/; .!' f, o" /t/"9 Set 6= 0 2 /6f T 7 4 Set 7= 9-4-8--E-7 0

Figure 16b imbedding, so called, is ignored in the printed output procedures. Patterns are harder to see in the output from SIMBED. It is difficult to notice any kind of general symmetries etc. except with the most limited examples. Not all the partitionings are the result of order number interchanges as pointed out in Figure 14. It is not difficult to see whether this is the case or not in the one-dimensional program outputs, but here it is almost impossible to see without some effort. The implications of computer partitioning would seem to be very great, but until some sort of systematic experimentation is done, no general principals can be stated which would make the results predictable for particular compositional situations. So far the output obtained has been a matter of guessing what might work and by trial and error coming up with interesting data that can often supply a compositional demand. Even so, the information obtained is certainly more than one could ever hope for given a trial and error m ethod without computer assistance. 110

SUBSET 1= J 10 2 5 6 EXHAUSTIVE IMBEDDINGS

2 E 8 1 1 AlT 2 J ClT 4 DlT 5 6 7 GlT 8 9 T 0 1 Al T Al T 2 J 4 5 6 Fl R 7 Gl T 8 9 6 1 2 J 4 5 ElR 6 7 GlT 8 9 IlK IlK 4 7 T 1 2 J Cl T 4 5 El R 6 fljl, Fl R 7 8 Hl K 9 E 0 1 2 BlT J ClT 4 El R ElR g FlR Fl R 7 Gl T 8 Hl K 9 IlK

8 0 2 6 T 7 4 1 AI T 2 J ClT 4 Dll 5 El R 6 7 Gl T 8 Hl K Hl K 9 2 4 8 E 0 1 Al T z 2 J ClT ClT 4 g Fl R 7 Gl T 8 Hl K 9

Figure 16c 111

EPILOGUE

A Letter From Ezra Laderman to the Society

Received by the Proceedings editor:

"Dear Sir: According to a recent news item, the Chicago Lyric Opera has commissioned an opera to honor the bicentennial of the United States. In the apparent belief that two hundred years of independence are insufficient for America to have produced a native composer equal to the occasion, the powers that be in Chicago have awarded their commission to the Polish composer, Krzysztof Penderecki. We certainly intend no reflection on Mr. Penderecki's undoubted abilities, but the American Music Center, on behalf of its large membership of composers, deplores this regrettably all-too-typical example of reverse chauvinism. In any other country with a musical culture as highly developed and creative as ours, the idea that.such a significant national anniversary should be commemorated with a foreign work, would be greeted with shocked incredulity. We don't suppose the Lyric Opera intended to make a deliberate gesture of contempt for the community of American composers, but such a gesture, made inadvertently, remains equally offensive. Perhaps other musical organizations making similar plans will wish to ponder the implications of this commission."

Sincerely yours, Ezra Laderman President American Music Center

Our Society, of which Mr. Laderman is also a member, shares his concern and feels that despite trends away from nationalism in the Arts, hopefully, the United States has not arrived at a point where its citizens ignore the heritage of its own gifted native composers. 112

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RODNEY ASH RONALD R. ELLISTON MR. STEPHEN SCOTT ·western State College 200 13th Street Dept. of Music Gunnison, Colo. 8 1230 Alamosa, Colo. 81101 Colorado College Colorado Springs, Colo. PROF. DAVID BURGE 80903 Dept. of Music Univ. of Colorado Boulder, Colo. 80302 PROF. CARLTON GAMER RUTH SHAW WYLIE 1439 N. Tejon St. 1251 Country Club Dr. SARALU DILLER Estes Park, Colorado 900 Lincoln Place Colorado Springs, Colo. Boutder, Colo. 80302 80907 117

Region VIII (Arizona, Southern California, Nevada, New Mexico)

MARSHALL BIALOSKY TED HANSEN JEROME N. MARGOLIS 2043 Via Visalia 5102 N. 32nd Place Harvard School Palos Verdes Estates, Ca. Phoenix, Ariz. 85018 3700 Goldwater Canyo n Rd. 90274 N. Hollywood, CA 91604 ROGER W. HARRIS MR. RICHARD BUNGER 557 N. MacDonald STUART J. PETOCK 303 South Avenue 57 Mesa, Ariz. 85201 Dept. of Philosophy Los Angeles, CA 90042 Univ. of Nevada HARV ARD SCHOOL Reno, Nevada 89507 RODNEY H. BUTLER 3700 Goldwater Canyon Rd. 14427 S. Vermont No. 15 N. Hollywood, CA 91604 PHILIP R EHFELDT Gardena, CA 9024 7 School of Music THOMAS N. HAYES Univ. of Redlands MR. BARNEY CHILDS Redlands, CA 92373 Johnston College lf ~i ~~fiC~rfut;nia University of Redlands Santa Barbara, CA JOHN D. ROBB Redlands, CA 92373 2819 Ridgecrest Dr., SE KEITH HUMBLE Albuquerque, N. Mex . 87108 THOMAS J. CLEMAN Music Dept. 409 W. Havasupi Rd. Univ. of Cal- San Diego VICTOR SAUCEDO Flagstaff, Ariz. 86001 Box 109 1866 Loyola Court La Jolla, CA 92037 Chula Vista, CA 92010 DAVID COHEN Music Department LINDLEY SMITH HUNTER PROF. ROBERT J. STEWAF Arizona State University Verde Valley School Dept. of Music Tempe, Ariz. 85281 Sedona, Ariz. Calif. State College Fullerton, CA 92634 MR. WILSON COKER FLORENCE WERNER JOLLEY 1619 W. Robinwood Lane 1134 Tenth Street Fresno, CA 93705 Santa Monica, CA 90403 GUNTHER TAUTENHAm 1321 S. Irena Avenue EMMA LOU DIEMER JOSEPH JULIAN Redondo Beach, CA 90277 77-A N. San Marcos Rd. Univ. of Cal.-San Diego Santa Barbara, CA 93111 Music Dept. U.C.S.D. DAVID WARD-STEINMAN Box 109 Music Department PROF. La Jolla, CA 92037 San Diego State College PETER RACINE FRICKER San Diego, CA 92115 Dept. of Music GEORGE HEUSSENSTAMM Univ. of California 5013 Lowell Ave. DR. RONALD WILLIAMS Santa Barbara, CA 93106 La Crescenta, CA 91214 Dept. of Music University of Nevada Reno, Nevada 89507 RONALD GEORGE STANLEY HOFFMAN 624 Santa Fe Drive 7657 Orion Avenue RONALD L. YATES Encinitas, CA 92024 Van Nuys, CA 91406 3e8!iif. ARTHUR GITTLEMAN tJ~~c WARNER HUTCHISON Santa Barbara, CA 93106 2500 Grant Avenue P. 0. Box 3174 Redondo Beach, CA 90278 Univ. Park Branch Las Cruces, N.M. 88001

Region IX (Alaska, Northern Calif., Oregon, Washington, British Columbia)

RAYMOND BARKER CHARLES L. MOON PROF. ROBERT H. STOLTZE 1828 Palm Ave. Dept. of Music Dept. of Music Chico, CA 95926 Rumbolt State College Lewis & Clark College PROF. JACK BEHRENS Arcata, CA 95521 0615 SW Palatine Hill Rd. P. 0. Box 1695 Portland, Ore. Bakersfield, CA 93302 PROF. FREDERICK A. FOX VERA N. PREOBRAJENSKA SERIALS DIVISION Dept. of Music 5423 Ygnacio Ave. Main Library Calif. St. Col. at Hayward Oakland, CA 94601 Univ. of British Columbia 25800 Hillary St. Vancouver 8, B.C. Canada Hayward, CA 94542 GARY SMART 1218 F St. ~~~~I 1!r'Wu~~ KELLER Anchorage, Alaska 99501 Univ. of Oregon Eugene, Oregon 97403

CJ/'u inCE.p.tion of a uniqLL£ muiic i£7.l.£i ASUC Journal of

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Vol . Vol. II (in preparation) ( Jonathan Kramer , Jan Pfischner McNeil Elaine Barkin Elliott Schwartz Will Gay Bottje Joan Tower John Heiss Robert Stern Otto Luening

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v Designed and published for the American Society of University Composers by Stanley F. Bennett, Portland, Oregon. Printed in U.S.A. by Lake Grove Printing, Box 1516, Lake Grove, Oregon 97034. al I

• American Society of University Composers Proceedings, 1972-1973

PUBL/CA TJON DA TE: SPRING, 1974