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Music Theory Course Electives

THYG 555 Psychophysical Analysis Ia:
Tone Color Analysis (Instrumental)

Robert Cogan

Tone color, especially instrumental tone color, is one of the most fundamental yet least examined and least understood aspects of music. This is especially perplexing given the fact that creation of musical instruments has been one of the constants of cultures throughout all of human history. Over the last hundred-fifty years there has been a gradual evolution of scientific, technology-based analysis of sound and sonic coloration. Especially in the past twenty-five years have these developments exploded, with new computer-electronic means of analysis and entirely new conceptual developments based on them. There now exist new ways of observing the physical structures of sound and also of conceiving the neuroscience of hearing and perception. Especially revealing has been the development of spectrographic computer analysis of sound, and the connection of this form of analysis to other, more conventional methods of musical understanding. We have been able to make real progress toward an expanded musical analysis which illuminates the role of both vocal and instrumental tone color in musical structures and expression everywhere and “everywhen.” In introducing sonic analysis in the Seminar, we will make use of the spectrographic analysis facilities of the NEC Music Theory Department. 

Tone-color awareness in music has many parallels with the history of visual color in art (as well as with the analysis of speech sounds in linguistics). Consequently, this semester will include some consideration of vision and of visual color. The Seminar will interfold the following elements:

  1. General technical introduction to acoustical and sonic analysis
  2. Readings and discussion of sonic analysis of musical works (Chinese and Japanese instrumental music; Gregorian chant; Mozart, Beethoven, Debussy, Berg, Stravinsky, Carter, and others); primary text; Robert Cogan, New Images of Musical Sound
  3. Introduction to color vision and visual color analysis (Monet, Turner, Van Gogh, Seurat, Kandinsky, Albers)
  4. Written-oral presentations by Seminar members on selected works by Debussy, Webern, Stravinsky, Varese, Messiaen, and possibly others.

The Seminar’s assistant is available to offer assistance with the readings, to provide material for assignments and projects, and to do spectrographic analyses for special projects that have been approved.

The Seminar aims to cover a considerable range of technical and artistic matter; it is my intention in each seminar meeting to combine technical information with the examination of a variety of musical-artistic sources. To avoid gaps in one’s learning, I do expect regular attendance and active seminar participation.

Please join in with questions when things are obscure, and with thoughts and insights when you have them!


THYG 555 Psychophysical Analysis Ib:
Tone Color Analysis (Vocal)

Robert Cogan

Voices, languages, and music, when combined, form one of the great triads of global human culture. This seminar aims to expand our awareness of the possibilities of that triad. It will do so by:

  1. Analyses of language and music in combination
  2. Including ideas and techniques derived from linguistic
  3. Including ideas and techniques derived from the scientific analysis of sound, especially spectrographic analysis, which has been pioneered by the instructor since 1980
  4. And by integrating linguistic and spectrographic analysis with diverse traditions of musical analysis and understanding

In addition, the triad voice-language-music is a product of another supremely important human triad – the body-brain- mind triad, the ultimate source of all our ideas, emotions, perceptions, actions, memories, and values. Neuroscience is the last fifty years has begun to clarify the fundamental interactions between these two triads. Past distinctions between the “physical” and “mental” have disappeared, as have those between the “intellectual” and “emotional,” the “cultural” and the “personal,” and the “objective and subjective.” One not yet well-recognized aspect of this new understanding is the basic importance of each individual human actor and respondent: human activity and experience are at the core of both triads.

We will begin here what may well be a century-long reconsideration of how all of these features and experiences interact; and how the methods of scientific and artistic analysis, used together, can more deeply illuminate musical art, both as creation and performance. One consequence of this study is that we’ll examine not only linguistic-musical works in the “abstract,” but also and especially their realizations in performance. Indeed, the imaginary gap between “pure music” and “performance” is one we hope to bridge, if not eliminate. Sound spectrographs will give us a new way to image and think about musical performance.

In every seminar meeting we’ll trip to extend our technical understanding of sound, language, and music; and to deepen our insight into their workings in as wide a range of music as possible. This activity will be enhanced by readings: first, in the principal seminar text, my book The Sounds of Song, as well as in other sources. And also by critical listening, critical in both the positive and negative senses. While doing this we’ll assume that every musician, no matter their level and reputation, has the potential for genuine artistry; but that even great professional artists are not always great is every respect.  As just mentioned, for sonic insight we’ll often use the spectrographic technology that has become available in the last twenty-five years. (To the extent possible, this technology will be made available to the vocal students in the seminar who desire to use it for an analysis of their own singing.)

Specific seminars will introduce particular domains of acoustics, linguistics (phonology), neuroscience, and musical analysis. Since each of these interrelated domains is itself vast, seminar participants are expected to: 1) do the requisite preparatory work, and 2) be present and contributive to every seminar meeting. Without this active participation, necessary information and experiences will be missed, or will fly by unnoticed. From the seminar members there will be individual and group analytic presentations, oral or written.  Midway, there’ll also be one exam that covers your acquisition of some basic acoustical, linguistic, neuroscientific and analytical information necessary for doing insightful independent analysis.

I’ve greatly enjoyed and learned much from these seminars; I hope that’ll be true for each of you!


THYG 557 Psychophysical Analysis II
Space-Time Design

Robert Cogan

Concepts of space, time, and their science have immensely changed in recent years. In the almost half-century since 1970, physics and cosmology, biology, genetics, neuroscience and technology, from sub-atomic structure, to the Hubble spacecraft, to genome unraveling, have altered our vision of the universe on every scale. From the hundred-billion star-and-galaxy-universe down to the hundred-billion-neuron human brain (with its hundred-trillion connections) our world has exploded in size, depth, complexity and insight. The practices and understanding of musical space-time and musical science have changed equally. This semester we will explore together the connections and issue of space, time, and science in music and in the larger cosmos as a whole.

Our space vision and understanding have expanded out to the edges of the universe, or universes, as well as inward, down to the basis of life-forms in molecular cells, genes, neurons, and DNA spirals. Time how reaches from milliseconds through light-years, back to the very beginnings of cosmic time 13.7 billion years ago. Musical analysis now invokes minute spectral elements and time-instants, as well as large formations of lines, registers, fields, and shaped or self-organized wholes. We now have deep perceptions of the human body- brain-mind system, in which ears and eyes are important points of entrance to the brain’s crucial interactions. Our ideas of science have altered from a single set of unquestioned truths to a constantly changing flux of experimental principles and possibilities. The range of science relevant to musical performance, creations, and insight extends from classical physics to up-to-date psychophysics and neuroscience, and our experience of music extends across almost every previous historical, cultural, and global boundary.

There will not be time, in our relatively few Seminar meetings, to examine in detail every relevant domain and all their implications for music. But we will sample to get the flavors, the gist, the directions of current possibilities, and of the vistas they offer (and have offered in the past) for musical/artistic thought, imagination, and action.   Science relies not only on thought, but also on tools: clocks and pendulums; telescopes, microscopes, x-rays, spectroscopes; cameras, recorders, radio-television, and computers. Books, writing, painting, and recording are tools with a long history that will be indispensable to us: there will be texts,  readings,  and  listening.  A  leading  neuroscientist,  Antonio  Damasio,  has  postulated  that  thinking depends on images. In addition to diverse traditions of musical imaging (notations, graphing) we are lucky now to have recently created spectrographic sound-imaging capabilities (some developed at NEC in collaboration with IBM Research) that reveal previously invisible aspects of musical space, time, and sound. We will use all these resources with the aim of developing a new, deeper, richer illumination of expressive design in musical space and time, as it has emerged at all possible times and places, including the present.


THYG 558 Advanced Sonic Analysis

Robert Cogan

Self-generated, self-executed projects in sonic analysis by the Seminar participants forms the core of the Seminar. I expect that each Seminar participant will plan and execute two projects, a shorter and a longer one. The projects can be of several different types, described below. Each project will go through three phases: planning-formulation, execution, and Seminar presentation-discussion. The planning-formulation will be done in conjunction with me; the execution will be done in conjunction with the Seminar Assistant. For the longer project, the Seminar presentation-discussion may well include a written paper of issues, results, and conclusions. As a consequence of the presentations, everyone in the Seminar will be able to share the results of all the projects. Along the way there will be some relevant general readings, as well as specific readings that may be desirable for particular projects. (Depending upon each person’s specific background, there may also be some necessary reading to fill in particular technical or experiential gaps.) Many of the background issues surrounding sonic analysis are considered, from one perspective, in Part II of my book New Images of Musical Sound; others will be taken up in Seminar meetings.

The nature of the projects:

  1. Projects devoted to the sonic features and designs of specific musical works, composers, performers, musical eras, and cultures
  2. Projects devoted to particular instrumental-vocal sonic practices and possibilities.
  3. Projects devoted to the sonics of electronic and computer music, as well as the larger world of natural, mechanical, and electronic sounds.
  4. Projects devoted to the nature and possibilities of sonic design.
  5. Projected related to compositional and performance work by Seminar participants.
  6. Comparative and pedagogical projects, including examination of various theories of sound and sonic design (of Cogan, Erickson, Lerdahl, Risset, Slawson and others)

These six categories include a virtual infinity of possible specific projects (you might want to suggest some additional categories). I’ll leave it to your initiative to make your own initial project proposals during the Seminar’s first weeks. I may offer some modifications in terms of practicability and realizability, conceptual clarity, etc., but will try to satisfy your interests as much as possible. It should be understood that the nature of such a seminar is experimental; and that experiments proceed by what Karl Popper, the philosopher of science, has called “conjectures and refutations,” the “refutations” being based on emerging evidence. Much will depend on your own initiatives and activity.

One last point I cannot emphasize too strongly: my basic assumption is that we are interested in sounds and sonic understanding in music, and that all such hearing and understanding is ultimately done by humans, is contextual, and is part of human experience. Technology can enlarge and clarify our knowledge of “what is there” (as do microscopes, telescopes, and electronic scans in other domains). It offers us certain images and models of what is there. But in the end, understanding is a human act and experience, a human (indeed personal) way of taking account and making sense of what is there, and of imagining what might be possible.


THYG 580 Analysis of Masterworks
Beethoven’s “Ode to Joy”

Robert Cogan

The “Ode to Joy” is one of music’s great (and controversial) seminal pieces, a summation of what preceded it and a new beginning. The Seminar’s aim is intensive analysis of the Ode’s musical substance and design(s). To realize this, every Seminar member will present to the Seminar an analysis of one of the 9 segments of the Ode. Depending on Seminar size, two students may work on a segment as a pair. Each Seminar member will also be responsible for hearing and introducing, where relevant, the approaches of one of the 15-20 chosen recordings of the Ode. In addition, some suggested readings will supply specific information about the Ode, and about analytical approaches that might be useful. The assumption is that each Seminar member will be an active, contributive participant in moving toward an understanding of this epochal work, not merely listener. (The score, Bärenreiter Urtext of Beethoven’s Symphony No. 9, is the required text.)

In addition to the analytic presentations mentioned above, each Seminar member will do a concluding oral or written presentation – this may be a more complete written version of the earlier Seminar presentations, or can focus on another relevant topic (for example, a critical presentation of a particular writer’s view of the Ode; a critical analysis of a particular performance of the Ode; or the exploration of a relevant topic – for example, Beethoven’s variations or fugal procedures, cross-accentuation in the Ode, text-setting, etc.).

The analytical approaches to be used include the textual/musical, formal/structural, linear/registral, harmonic/contrapuntal, tonal/modal, as well as temporal/rhythmic, shape/fractal, sonic/timbral, and whatever others that might be illuminating. Special attention will be given to matters of text-setting, musical motion, montage, opposition/unity, and a variety of performance issues. For continuity of discussion, fullness of understanding, and depth of experience, Seminar members are expected to be present and contributive throughout. The spectrographic resources of the Theory Department are available to the Seminar for the insights into sound, design, and performance which that technology might offer.


THYU 412T & THYG 512T 16th century Counterpoint

Lyle Davidson

Counterpoint is primarily about cooperation and respect. In successful counterpoint, a voice enters and the other voices listen. Then after an appropriate time, the other voices either comment or take up the song. In either case, a dialogue ensues in which the flow of attention moves from one voice to another. After a lull, the process begins again. One voice leads while others support it.

This course is not about exposure to aspects of craft, nor does it involve drill in Fux’s 1725 formulation of Species I through V. Counterpoint is about more than that. Consider Robert Fludd’s depiction of the Divine Monochord (to the left). It represents the role of music and the composer in Renaissance life. The elements (earth, water, air, and fire) and the lowest sounding notes occupy the base of the instrument. The pitches of the gamut lead upward, through the planets, the sun, and the constellations. The proportions necessary for music are aligned with the order of the cosmos. The attentive Divine Hand on the tuning peg at the top maintains all in tune and order. If music reflects the ordered creation, then the maker of new pieces bears the responsibility to contribute to that order. This puts the composer’s role in a new light. The composer’s mission is to craft pieces that reflect the sounding order in a manner that is audible to the listener.

The objective of this course is mastery of contrapuntal thinking and technique. That goal is reached when a student’s motets sound like those that might have been written by Lassus, one of the masters of the 16th century. This requires a great deal of work. The first semester sets the foundation by 32 canons a2 and three motets for the first semester. The second semester focuses on contrapuntal textures. Students complete four versions of five textures (including canons) a3 and two motets plus a movement of a mass (a3, a4 or more) that is based on one of the three techniques commonly used by the masters of the period (cantus firmus, paraphrase, and parody). The role of accents in forming rhythmic textures is studied. Renaissance solmization is learned and practiced. Representative pieces of Lassus and others are analyzed. All work is sung and when possible performed in an appropriate space.


THYG 551 Compositional Practice: Medieval to Bach

Pozzi Escot

We have yet to recognize the large historical framework as the terminology of medieval/renaissance/baroque/classical/romantic/modern was largely formulated between 1850-1950. This terminology by philosophers, historians do not necessarily define the compositions of music. The composers were not known as such and Europe was only Germany, Italy and France. We study the techniques of music produced from very early times to Bach including the vocabulary, writing tendencies, title of the compositions, theoretical background. The early Gregorian chant combines Christianity, Greek music theory, Hebrew, Syrian practices. Boethius discusses the modes as named after the ‘character’ of certain peoples and thus we end with Dorian, Phrygian, Lydian, Mixolydian, Aeolian. Guido D’Arezzo (995-1050) writes Micrologos, devices staff notation and the ut-re- mi-fa-sol-la which became the standard in early medieval music. We will study the compositional techniques of music throughout the ages developed and applied by composers like Schutz, Byrd, Lassus, Palestrina, Corelli, Praetorius, Farnaby, Fux (who writes the first book on counterpoint that we know), de Prez, Couperin, Handel, Rameau (who writes the first book on harmony, and Bach.


THYG 552 Compositional Practice: Bach to Moderns

Pozzi Escot

We use the textbook (now in Japanese, Chinese, Portuguese, French…) “Sonic Design: The Nature of Sound and Music” (1976). We study the development of the Tonal System with the initial approach of Jean Philippe Rameau. The developments of specific areas in the composition as the application of space, language, time and rhythm, color, form; the minor and major conceptions, the harmonic progressions, modulation, tonicization, and the developments which are applied by the 20th century as the new structures with serial techniques. We discuss readings of selected essays by such composers as Milton Babbitt, Pierre Boulez, Robert Cogan, Furtwangler, Marie Jaell, Roman Jacobson, Philipp Jarnach, Heinrich Schenker. Extraordinary developments which change the limited areas of European practices to the global conception of new chordal formations and formal structures.


THYG 563 The Poetics of Simple Mathematics in Music

Pozzi Escot

The course will study the 3 mathematical means of Boethius (475-524) as described in his book The Principles of Music: Arithmetical, Geometrical, and Harmonic means; the Golden Mean; the Fibonacci Series; the Pythagoras-Theano perfect ratios; the Palladio resonating triadic structure; symmetry, statistics, probability; set theory; the non-linear phenomena; field concept; fractality. Music has indeed applied often even very deliberately, all of these at one or another time. Suggested reading from Boethius to Iannis Xenakis give us how all these possibilities for the compositional practice for the climaxes, the phrases, the sections, etc. of a given piece of music. We use the book “The Poetics of Simple Mathematics in Music” (1999).


THYG 579 The Music of Hildegard van Bingen

Pozzi Escot

It is the first course given anywhere exclusively devoted to the composer and her music based on its historical, notational, analytical, and performance studies. Hildegard van Bingen (1098-1179) composed the largest and most significant collection of chants by a single composer that we have for the 12th century. Her music vividly reveals the compositional practice of early medieval Europe. Required reading will include the English translation of her first book, Scivias, which contains one chapter (III/13) describing a theoretical basis for the composition of her music; her most recent biography by Sabina Flanagan (Oxford Press); selected letters translated by Joseph Baird and Radd Ehrman (Oxford Press), which specifically refer to the theory and composition of her music; and selected published essays by diverse authors discussing her music. Course materials will be on reserve including the facsimile of the Dendermonde and Wiesbaden codexes and the Barth Gothic Notation (1969) of the over 70 chants.


THYG 583 20th Century American Composition
and Theory

Pozzi Escot

Explorations through readings, analysis, listening, and performance of innovative 20th century American music and of important theoretical developments which revolutionized and influence the compositional practice throughout. These developments will be exposed, researched, studies and discussed. As introduction will let us see the past and what previous American composers like Charles Griffes, Edward MacDowell, Sousa, Chadwick plus how North American Indian, African and other cultures might have influenced the compositional practice of the American composers of today. These 13 American composers were selected by a five-member board headed by Prof. David Lewin of Harvard University in the summer of 1990.

It opens with Ives, Hanson, Sessions, Anthiel, Crawford, Partch, Carter, Cage, Nancarrow, Babbitt, Shapey, Cogan. Most of these composers wrote theoretical treatises which have and continue to deeply influence the understanding of the compositional practice today. Hanson’s Harmonic Materials of Modern Music was the first book to be devoted to unordered pitch-class sets of all sizes. Sessions’ books The Musical Experience and Harmonic Practice show extraordinary musical inter-disciplinarity.

Babbitt is today recognized as the father of serial development and Cogan for his pioneering writing on the development of spectrographic analysis of music and the co-author of the extraordinary book “Sonic Design: The Nature of Sound and Music.” The great American composer Elliott Carte writes re. the “Sonic Design” book that “These two composers are the pioneers to view the large field of music we live in today as a whole and to derive general concepts and principles that describe and explain methods of each style, age, and people.”


THYG 572 Beethoven’s String Quartets

Roger Graybill

Beethoven’s string quartets reveal the full sweep of his stylistic development as a composer, starting with his six op. 18 quartets, which emerge directly from the quartet-writing tradition of Haydn and Mozart, and culminating with his profound and forward-looking utterances in his late quartets. On a purely compositional level, virtually all of these seventeen works merit close analytical attention; just as remarkable is their astonishingly rich and wide-ranging expressive language. Considered together, this entire collection works represents one of the major artistic achievements in Western music.

This course begins by focusing on selected sections or passages from the quartets, which will allow us to explore particular issues in depth by means of multiple examples (for instance, phrasing, form and harmony, and instrumental interactions.) However, by the fourth week, we will begin working entirely with complete movements. In his middle and late periods, Beethoven paid increasing attention to the ways in which movements relate within the larger context of the quartet as a whole, so we will also explore two complete quartets in depth by the end of the semester. The goal here is for class members to gain the conceptual and analytical tools for approaching any of Beethoven quartets, even those we do not have time for in class.


THYU 361 The String Quartets of Beethoven

Roger Graybill

Beethoven’s string quartets reveal the full sweep of his stylistic development as a composer, starting with his six op. 18 quartets, which emerge directly from the quartet-writing tradition of Haydn and Mozart, and culminating with his profound and forward-looking utterances in his late quartets. On a purely compositional level, virtually all of these seventeen works merit close analytical attention; just as remarkable is their astonishingly rich and wide-ranging expressive language. Considered together, this entire collection works represents one of the major artistic achievements in Western music.

This course begins by focusing on selected sections or passages from the quartets, which will allow us to explore particular issues in depth by means of multiple examples (for instance, phrasing, form and harmony, and instrumental interactions.) However, by the fourth week, we will begin working entirely with complete movements. In his middle and late periods, Beethoven paid increasing attention to the ways in which movements relate within the larger context of the quartet as a whole, so we will also explore two complete quartets in depth by the end of the semester. The goal here is for class members to gain the conceptual and analytical tools for approaching any of Beethoven quartets, even those we do not have time for in class.


THYG 577 The Chamber Music of Johannes Brahms

Roger Graybill

Brahms wrote an impressive array of chamber works for various combinations, ranging in size from the duo sonatas to the string sextets. Most of these works include piano, though he did write a substantial amount of music for only strings as well, including three quartets, two quintets, and two sextets. This course will focus primarily on entire movements from selected works, and we will also look in depth at one or two complete works. At the beginning of the semester we will spend some time on duo sonatas, which will allow us to introduce some basic concepts and principles within a reasonably uncomplicated textural context.

The student will come away from the course with the following knowledge and skills:

  1. An understanding of how Brahms blends traditional and progressive tendencies in his chamber music.
  2. The ability to find your way through the formal and tonal plan of a movement.
  3. An understanding of Brahms’s use of developing variation, and how this compositional technique affects (1) form and (2) rhythm and meter.
  4. The ability to interpret instrumental interactions as a type of musical narrative.


THYG 589 Musical Narrative and Analysis

Roger Graybill

Very often we speak of a piece of music as though it conveys the sense of a story or narrative.  While we see this most clearly in opera, instrumental works also lend themselves to such narrative interpretations. Even our every-day language about music reflects this idea: we say that a phrase of music pushes towards a climax, or that a phrase takes a detour on the way towards an important arrival point, and so on. This course explores various ways for developing such narrative-driven analyses, not only within shorter contexts, but over the span of entire sections and movements.

We will establish a foundation for the course as a whole by addressing the following questions:

  1. In what ways can music be heard as an unfolding narrative, and what is the purpose of such an interpretation?
  2. What problems and limitations arise in attempting narrative accounts of music? How can we work through these problems and limitations?
  3. How does performance bear on the narrative interpretation of a work, and vice versa?
  4. Does a narrative interpretation make objective claims about the music? How do we avoid the danger of rampant subjectivity?
  5. How does a narrative interpretation of a musical work relate to other ways of conceiving musical structure?


THYU 382 Music as Narrative

Roger Graybill

This course explores narrative-driven approaches to musical analysis, and provides students with the concepts and tools that will facilitate such analysis. We will first consider how a non-texted work can (or cannot) be regarded as a narrative, and then proceed to investigate topics such as the role of metaphor in musical discourse, musical agency, gesture and music, and musical plot. The work for the course includes occasional readings, but the primary emphasis will be on the analysis of music from the repertoire.

Questions will consider will include the following:

  1. In what ways can music be heard as an unfolding narrative? What is the purpose of a narrative interpretation?
  2. How does performance bear on the narrative interpretation of a work, and vice versa?
  3. What kinds of claims does a narrative interpretation make about a musical work, or about our experience of that work? What is the ideal balance between “objectivity” and “subjectivity” in carrying out a narrative-driven analysis?
  4. How does a narrative interpretation of a musical work relate to other ways of thinking about musical structure?


THYG 537 Teaching Music Theory:
Foundational Principles

Lyle Davidson and Roger Graybill

Teaching music theory is a very special calling. It requires not only strong musicianship skills, but also a clear understanding of the relationship between verbal knowledge and skills, and between sensory-motor knowing and more abstract conceptual knowing. It involves having an informed view of the nature of learning, as well as an appreciation of and sensitivity for the role and balance of academic knowledge, perception, and reflective thinking.

This course contains three basic components:

  1. Pedagogical philosophy: We will consider questions such as: What is the purpose of theory training? What is the proper role of skills training in a theory curriculum? What philosophical assumptions underlie current pedagogical materials and teaching methods?
  2. Pedagogical materials: The course will include a survey of texts focusing on current approaches to teaching music theory in various subareas, specifically: fundamentals, sight singing, ear training, harmony, counterpoint, and analysis.
  3. Teaching skills: We will devote time to helping students develop hands- on pedagogical skills.

The coursework includes readings, assignments, an annotated bibliography of selected texts and journal articles, and a small research project that explores issues covered in the course. Students will also be asked to do at least one teaching demonstration during the semester.


THYG 581/582 Interpretive Analysis

John Heiss

Analysis for performers; concepts of rhythm, line, harmony, and form; performance implications of analytic conclusions; performance and analysis of works from students’ areas of specialization.


THYG 584 Introduction to Transformation Theory

Justin Lundberg

This course is an introduction to various topics in musical transformation theory including group theory, Neo-Riemannian theory, voice leading, networks, and graphical models of musical features. Originally developed by David Lewin in the 1980s, transformation theory focuses on the connections between musical objects, such as notes, triads, chords, or keys, rather than the objects themselves.

These connections are then often represented by motion within some abstract musical space. The course will include analytical studies of a wide variety of musical styles including 19th-century music, music of the 2nd Viennese school, post-tonal triadic music, process music, and popular music. In addition to analysis and visualization, the course will examine transformational artifacts as compositional resources.


THYG 575 Music Since 1945

Katarina Miljkovic

The course Music since 45 presents an extremely rich creative period, driven by close interdisciplinary connections between arts, sciences, literature, architecture and music.

Students will learn about reactions of artists to cataclysmic consequences of World War II resulting in challenging the conventional norms: linear thinking, notion of order, space, time, language and meaning. The course focuses on works that pushed the boundaries of Western music by borrowing concepts from other fields.

During the course, students will experience the process of dissolution of dogmas and emergency of new ways of thinking and music organization that had liberating power for future generations. Through listening, reading, analysis, writing of short original pieces and performances in class, students will learn about paradigm shifts in the later 20th century that had led to current musical developments.


THYG 586 Musical Minimalism:
Beginnings to Living Practice

Katarina Miljkovic

The course traces beginnings of minimalism, rooted in reduction, constant pulse, insistent repetition, extended time and form as process. Students follow the transformation through which minimalism gradually turns to new tonality, more elaborate forms and cross pollination of classical, electronic, rock, pop and film music.

Special attention is dedicated to perception of musical time, including rhythmic domain, phase shifting, additive and subtractive processes. The class is not approaching minimalism as a compositional technique, but as an aesthetic orientation that will be examined through scholarly writing and analysis of works, including opera, art film and multimedia.

Material for the class includes an abundance of web links, live recordings, videos, interviews with composers and art films. Phillip Glass, Steve Reich, La Monte Young, Terry Riley, James Tenney, Alvin Lucier, Michael Gordon, Julia Wolf and David Lang are among composers presented and discussed in class.


THYU 371 American Experimental Music since 1960

Katarina Miljkovic

The course is centered around works of John Cage and the consequences of his innovative ways of musical organization. Beginning with the seminal Lecture on Nothing and 4’33, students will follow the development of American experimental school of music trough study of the scores, analysis and performance in class. Emphasis of the course is on getting familiar with the practices, writings and musical thinking of the selected composers in order to better understand the concepts behind their music and multiple possibilities of interpretation.

Through performance of mobile, verbal and graphic scores, students will learn about indeterminacy, open form, music as a gradual process, contextual process, game elements and other forms of experimental music that emerged after 1960. At the core of the course is a concept of “deep listening” as a basis for making creative decisions while studying the scores as well as in real time, during the performance. The goal of the course is an understanding of the necessity for close connections between musical creation and an infinitely rich, ever changing sound world around us. Listening to the entire field of sounds and accepting it as an integral part of a musical creation make each performance unpredictable and unique, the same as each moment in our daily life.


THYU 329 Order and Chaos in Music since 1945

Katarina Miljkovic

This course is dedicated to the research of various compositional systems in music of the later 20th and 21st century. Students will look into different designs of musical time, pitch, rhythm, timbre and form, in selected works from repertoire.

The beginning point of the course is an analysis and discussion of examples from various fields: architecture, visual art, literature and nature. Students observe and discuss systems of organization that are encountered in everyday life and commonly perceived as beautiful and harmonious. This thread of thought extends throughout the course by applying similar observations to music.

The class will trace chaotic consequences of WWII and disintegration of established musical norms, rooted in the tradition of Western music, hyper-organization leading to an increase of indeterminacy, total reduction of minimalism and its consequences, new nature of complexity emerging from science and mathematics. Selected works by Boulez, Stockhausen, Cage, Feldman, Glass, Reich, Sciarrino, Lachenmann and Grisey are the core repertoire of the course. Students are invited to bring works of their own choosing, and discuss them in class.

The goal of the course is to introduce a student to dialectical opposition between hyper- order and randomness, driving forces of music development since 1945.


THYU 372 Music Modernism and Thereafter

Stratis Minakakis

The course examines music modernism during the first half of the 20th century as a multi-faceted phenomenon, consisting of several distinct yet interrelated tendencies. Starting with the turn-of- the century precursors of modernism, it covers the first post-tonal period of the Second Viennese School; iconoclastic works by Stravinsky and Bartok; the twelve-tone system; and modernist and experimental movements in America and the European periphery.

The course concludes with assessing the impact of various modernist tendencies in the radical developments in music after 1945. Designed to approach the subject from analytical, performance, compositional, and historical perspectives, the course appeals to a wide variety of audiences, including composers, performers, theorists, historians, and music lovers with an adequate theoretical background.


THYU/THYG 419 & 519T Music of Xenakis and Ligeti

Stratis Minakakis

The work of Xenakis and Ligeti is of seminal importance to contemporary music. Both outsiders to the Franco-German post-1945 avant-garde, their unique vision established them as two of the most formidable explorers of music in Europe and throughout the world. While their personal idioms are highly distinct, both Xenakis and Ligeti frequently addressed common compositional issues. From their 1950s critique of serialism, to their later interest in complex patterns, their development was often triggered by identical impulses. This course examines aspects of Xenakis’ and Ligeti’s work through the prism of the solutions both composers provided to the same problem.

In addition to score analysis and reading assignments, students have the opportunity to creatively engage the issues addressed in class through compositional exercises, frequently with the aid of software programs such as IRCAM’s OpenMusic.


THYG 576 Ragas and Talas

Peter Row

A close examination of the concepts of raga (melodic mode) and tala (rhythm systems) as a generative grammar for composition and improvisation in North Indian (Hindustani) music. Many types of ragas and talas are analyzed in the context of various performance traditions drawing, in part, from descriptive models developed by Bharatamuni (Natyasastra, c. 200 AD), Vishnu Narayan Bhatkhande (Kramik Pustak Malika, 1954-9), Walter Kaufmann (The Ragas of North India, 1968), and Nazir Jairazbhoy (The Ragas of North Indian Music, 1971).


THYU 305 Twentieth-Century Compositional Practices

Felicia Sandler

At the turn of the 19th century into the 20th century, there were profound shifts in the music world from a Romantic aesthetic to that of early Modernism. A few schools of composition flourished at this time, defining the period as well as setting the stage for new developments that would take hold and shape the century. We explore the work of three pivotal composers – Claude Debussy, Igor Stravinsky, and Bela Bartok. Students will compose new works modeled on the music of these three composers. The aim is not so much to develop a unique voice of our own, but to create music that, ideally, would be mistaken for theirs. In this way, we come to understand, to the extent that we are able, the inner workings of the composer’s style and craft.


THYU 368 American Art Song & 20th c. Tonality

Felicia Sandler

The music of composers such as Samuel Barber, Ned Rorem, Dominick Argento, Aaron Copland, Libby Larsen – though very popular among performers and audiences alike – is often neglected in academia and from canonic study. Lack of attention to these works is due, at least in part, to the lack of a well- established, systemic analytic approach to the repertoire. Because much of this music has tonal impulses, many consider the analytical methods necessary for its study to simply be extensions of those employed in the study of tonal repertoire. Such approaches are woefully incomplete.

Performers who engage the works of these composers, and others like them, are often at a loss for support in their analyses. This course seeks to address this problem.


THYU 442 Music in Ghana, West Africa:
a theoretical look

Felicia Sandler

This course involves an engagement of select traditional and contemporary musics created in Ghana, West Africa. The course addresses reading, writing, performing, singing, and analyzing music from different perspectives. In particular, students will learn various ways that theorists have sought to describe the music of Africa and the controversies that surround that work. In addition to learning some traditional forms, we will explore the music of a select number of contemporary Ghanaian composers who integrate their Western art music training with their indigenous culture.


THYU 452 Solfege Through Vocal Music

Larry Scripp

Solfege through Vocal Music is about advancing solfege skills through its application to vocal music performed a cappella and with small or large instrumental ensembles. It is a theory elective course designed for ALL graduate and undergraduate majors interested in learning, reinforcing or expanding sight singing and score reading skills through their application to a cappella and accompanied vocal music of various genres*.

For undergraduates this course counts for 3 Theory Elective Credits for students who have already passed their solfege requirements. This credit structure is especially useful for those students who passed out of earlier solfege courses and need credit for extra theory elective courses. The prerequisite for the course is Solfege IV, but students at any level of theory requirement may petition the instructor for permission to take the class.

For graduate students: this course counts for zero (0) Theory Credits for students who wish to review, reinforce and expand their sight singing and ear training skills without using up course credits. This course is designed to provide support for graduate students who did not pass sight singing or melodic ear training components of the graduate competency exam (MMTCE).

For both undergraduate and graduate instrumental, vocal, and composition majors, this course is project based and therefore will not use departmental exams for evaluation. Instruction, repertoire and assessment will be differentiated according to the background of the student and prior level of solfege skills. A significant proportion of vocal music explored in this course is selected according to the particular interests of students in the class.


THYU 307 Extended Tonality

Deborah Stein

The 19th century produced some of the most expressive, dramatic and audacious music in the tonal language.  Much of the music was prompted by a poetic text or dramatic narrative, but purely instrumental music also extended the range of expressivity and musical innovation. In this course we explore many of the techniques of tonal expansion, including new chords and harmonic relationships, tonal designs that explore new tonal relations and intensification of rhythmic, phrase, and metric complexity. Performers learn to think about and play this rich and nuanced music with a deeper understanding of chromaticism, musical tension, ambiguity, and multiple ways to manipulate musical structure. The composers range from Schubert to Debussy. I explore much of the course material in two books: Hugo Wolf’s Lieder and Extensions of Tonality (Ann Arbor, Michigan: University of Rochester Press, 1985)and Poetry into Song: Performance and Analysis of Lieder, co-authored with pianist Robert Spillman (Oxford and New York: Oxford University Press, 1996)


THYU 315 Analysis and Performance of
19th-century Lieder

Deborah Stein

Die Lotosblume ängstigt              The lotus-flower fears
Sich vor der Sonne Pracht,           before the sun’s glory,
Und mit gesenktem Haupte          and with bowed head,
Erwartet sie träumend die Nacht.  awaits, dreaming, the night.

The first verse of Heine’s “Die Lotosblume” expresses the dichotomy of lively day and dreamy night. This poem was set by Schumann in 1840 as op. 25/7.

The German Lied flourished in the 19th century, as poetic nuances and complexities inspired Lied composers (Schubert, Schumann, Brahms, Wolf, among others) to create new languages that conveyed ambiguity and confusion (tonal, metric, formal), dichotomies and dualities (double tonality, metric duality), transformation (beginning and ending in different keys), and emotional expressivity (musical tensions, irresolution, fragmented melody, harmonic progression and form). In this course we explore how every aspect of the music reflects the poetic text. This includes study of melodic expressivity and many of the instrumentalists in class have transcribed Lieder to perform in their recitals! The text for the course is by me and pianist Robert Spillman, Poetry into Song: Performance and Analysis of Lieder (Oxford and New York: Oxford University Press, 1996).


THYU 327 Performer’s Introduction to
Schenkerian Analysis

Deborah Stein

Schenkerian theory and analysis is a powerful and wonderful way to understand tonal music at different levels of structure, and students normally need several semesters at the least to truly understand and gain technical ability in Schenker’s analytical system. I offer this one-semester class to introduce many analytical techniques that are particularly important to performers, including the notions of prolongation, interdependence of structural levels, the melodic anchor called the Primary Tone, and various linear techniques. Where possible, students perform in class, seeing how this analytical approach differs from other ways of understanding the music. I have explored the application of Schenkerian analysis to the German Lied in Hugo Wolf’s Lieder and Extensions of Tonality (Ann Arbor, Michigan: UMI Research Press, 1985)


THYG 564 Ambiguity in 18th and 
19th century Music

Deborah Stein

Like the poem, music also is full of ambiguity. As it evolved from around 1750 through the 19th century, the tonal language is rich in complexity and nuance, and composers explored and developed every aspect of the language from harmony and tonality to rhythm and meter and various formal designs. The challenge of understanding and performing this music is being able to recognize when the music is really ambiguous, where you cannot know where you are harmonically or tonally or the meter is unclear, or where you don’t know where you are in the form. In this course we explore how to recognize ambiguity and how to determine between two or more interpretations of both small-scale and larger aspects of the work.

For performers of this wonderful music, this course can help transform a hesitant or an uncertain performance into one that is powerful and full of conviction. I have studied ambiguity throughout my career. My book Hugo Wolf’s Lieder and Extensions of Tonality, (Ann Arbor, Michigan: University of Rochester Press, 1985) proposes an Ambiguity Principle that is developed in Wolf’s songs to an extraordinary degree, and I offer an “Introduction to Musical Ambiguity” in a book I edited, Engaging Music: Essays in Musical Analysis (New York and Oxford: Oxford University Press, 2005). I also explored the poetic and musical ambiguity in ”Schubert’s ‘Die Liebe hat gelogen:’ The Deception of Mode and Mixture,” Journal of Musicological Research 9 (1989).


THYG 573 German Lied:
Analysis & Performance

Deborah Stein

Und meine Seele spannte            And my soul spread
Weit ihre Flügel aus,                   wide its wings,
Flog durch die stillen Lande,        flew through the silent land,
Als flöge sie nach Haus.              as if it were flying home.

Stanza 3 from Eichendorff’s “Mondnacht,” set by Schumann in 1840 as part of his song cycle Liederkreis, op. 39.

The German Lied flourished in the 19th century as the genre combined German Romantic poetry (both dramatic and lyrical) with music that strove to depict the rich and elegant verse. The composers (Schubert, Schumann, Brahms, Wolf, Straus and Mahler) created innovative musical structures to depict such poetic emotions as anger and fear, despair and melancholy, love and devotion, awe and wonder, along with a deep abiding love of nature. Every aspect of the music is related to the text, including the use of harmony and tonality, rhythm and meter, and form. The nuances of notation are also explored, how texture, tempo, register, dynamics and articulations are combined to convey the poetic progression, the tensions and ironies and the myriad other elements in the poetry. Singers and pianists provide in-class performances wherever possible, and the text for the course is by me and pianist Robert Spillman, Poetry into Song: Performance and Analysis of Lieder (Oxford and New York: Oxford University Press, 1996).


THYU 362 Bach’s Music for
Solo String Instruments

Matthias Truniger

Johann Sebastian Bach’s unaccompanied Cello Suites and Violin Sonatas and Partitas have been called the Himalaya Mountains of the string repertory. Whether we agree with this judgment or not, one thing can hardly be doubted: Bach’s solos “senza basso” offer an unusually wide panorama of musical forms. As a group, they encompass virtually all movement types and characters found in Baroque instrumental music, from improvisatory preludes to majestic fugues, lively dances, sublime adagios, and ingenious variations.

Their richness, moreover, is achieved through a remarkable economy of means, by relying on the resources of a single melodic instrument. How is this possible? How can one violin or cello realize such a variety of textures and designs? What are the harmonic, rhythmic, and structural processes that underlie and shape these works? To be able to answer these questions, we will analyze Bach’s music and explore its compositional aspects through a number of creative projects based on his preludes and dance movements. Additional insight will come from texts by eighteenth-century theorists such as Mattheson, Kirnberger, and C. P. E. Bach. Students who are playing Bach’s solo Sonatas, Partitas, or Suites are welcome to perform selected movements in class.


THYU 414T / THYG 514T
Fugue in the Style of Bach

Matthias Truniger

Fugues occupy a prominent position in the work of Johann Sebastian Bach. Whether written for solo instruments, chamber ensemble, or chorus, Bach’s fugues epitomize a kind of musical thinking that was central to the Baroque period, and that continued to exert its influence throughout the eighteenth and nineteenth centuries. Focusing on examples from the Well-Tempered Clavier and the Art of Fugue, this course introduces students to the principles and techniques of fugal composition. Aspects of structure and style will be explored through analysis, listening, and performance, as well as through constant writing of contrapuntal exercises modeled on Bach’s music. As a final project, each student will compose a four-voice fugue for keyboard or four melodic instruments. All projects will be performed and discussed in class.


THYG 548 Contrapuntal Principles and Practice:
Bach to Present

Matthias Truniger

Counterpoint is the technique of combining independent melodic lines simultaneously. It is perhaps one of the most distinctive features of Western art music. This course traces the evolution of contrapuntal practice and its underlying theoretical principles from the Baroque period up to the twentieth century. Music to be examined includes works by Bach, Beethoven, Brahms, Schoenberg, Stravinsky, Webern, and Carter. Students will deepen their understanding of tonal and atonal counterpoint through constant writing of compositional exercises as well as through analysis, listening, and performance. Further insight will be gained from theoretical texts by Mattheson, Kirnberger, Seeger, and Krenek. There will be weekly assignments (analysis, counterpoint exercises), a midterm project (composition in tonal counterpoint), and a final project (composition in atonal counterpoint). All projects will be performed and discussed in class.


THYU 334: An Introduction to Pitch-Class Set Theory

Bert van Herck

The modernist music that emerged in the early 20th century is the result of a long evolution that can be traced back to the tonal practice period of the 18th century (and beyond). Yet the analytical concepts from the tonal tradition are inadequate for post-tonal music. This course offers a creative approach for exploring and understanding this repertoire and the underlying theoretical concepts. For this purpose, the basics of the pitch-class set theory will be discussed in detail. This theory has established fundamental concepts for 12-tone music that have been acknowledged as the standard for discussing this repertoire in academia and scholarly publications.

The focus of this class is dual: a theoretical understanding of post-tonal music and its concepts; and developing a musical sensitivity of these concepts through creative work. Musical examples are drawn from a broad range of repertoire including composers such as Schönberg, Webern, Stravinsky, Varèse, Bartok, Lutoslawski, Berio, Knussen, and Boulez among others.


THYU 417T/418T & THYG 517T/518T
Microtonal Compositions & Performance

Julia Werntz

Students learn to hear, sing and play intervals as small as a twelfth tone, and discover a thrilling new world of melody and harmony through compositional and improvisational exercises. Students are performing their own short works by semester’s end. To put these pursuits in context, we also take a look at early explorations with microtonality from the turn of the twentieth century through the 1950s (Carrillo, Ives, Wyschnegradsky, Partch and others).

Listening to recordings, studying scores and reading essays, we try to answer the question “Why microtones?” As writing and improvisational exercises become more extensive, our exploration of style, esthetics and practical matters becomes more involved. A recital at semester’s end concludes the year. Our study of recordings and scores also continues, focusing on the period from the 1950s to the present.

Course Electives

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