Introduction:  Overview of the semester


Introduction to DMI and to Part I.

To do:
Listening: Pp. 35-51
Discussion in Class #2 of Week 2

Projects 1.1-1.2 (DMI pp. 7-34)
Paper Due: Class #2 of Week 2

I. Melodic Structure: Weeks 1-2

"Constructive analysis": In re-building given tunes (Project 1.1), you are also analyzing in action the structures of these tunes. For example, in re-constructing the tunes, you will discover and actually create:

  • hierarchical structure -- motive, phrase, section
  • sequence
  • repetition and return
  • antecedent-consequent relationships
  • structural functions as responsive to context
  • pitch contour
  • degrees of complexity
  • simple forms: e.g., a b a'

Paper 1

The focus of this paper is your work on Project 1.2, while using Project 1.1 as background and comparison. The tasks:

For each of the block-sets you worked with (two block-sets in Group 1, and one block-set in Group 2), describe and discuss the following:

I.A. The process:

  • the blocks you tried, what worked, what didn't, and why.
  • the strategies you used in making your tune. For instance:
    • cumulating" (going next-next-next);
    • finding a good beginning and a good ending and working on the middle;
    • building modules that worked and putting them together;

  • surprises you encountered -- e.g., hearing a block in a new way as a result of context, finding that pre-built modules didn't always work together, etc.
  • initial attempts at accounting for the decisions you made along the way.

I.B. Completed tunes:

  • the structure of your completed tune, including a diagram showing its structural hierarchy.
  • a comparison of the structures of your tunes with those in Project 1.1.

II. Block-set Group 2:

  • What specific features do you think make these blocks "strange" -- how are they different from those in Group 1?
  • Why do these differences make the blocks more difficult to work with?
  • What does this "strangeness" tell you about the aspects you have come to expect (take for granted) in more familiar music?
  • If you made changes in the pitches and/or durations, be sure to consider the following:
    • what was the problem you were trying to "fix?"
    • what, specifically did you change?
    • how did your changes succeed in solving the problem?
  • Did you eventually discover coherence-making features of the blocks? What were they and did you use them in building your tune?

Note 1: Please save your completed pieces on a floppy disk or a CD and turn the disk in along with your paper.

Note 2: Sample papers for this assignment are in the small bookcase by the door in the Computer Lab and also on the OCW website for this course.

Paper Due: Class #2 of Week 2

Sample Student Project 1: Becky’s French (PDF)
Sample Student Project 1: Becky (MIDI)

(Courtesy of Becky Esquenazi.  Used with permission.)

Week 1:

Class #1:
Introduction to Impromptu
Reconstructing melodies
Log keeping
Picking out tunes on the keyboard
Multiple representations

Class #2:
Introduction to composing your own tunes:
Shared musical structures:
Structural hierarchy

Week 2:


Reading: Basics1

At the end of each Part of the text, there is a section called "Some Basics." These sections are intended to give students just that -- basic information relevant to material covered in the projects.

Class #1:
Analysis of listening examples:
Beethoven, Symphony 9, 4th movement, Variations
Haydn, Symphony #99, Minuet
Vivaldi, Four Seasons, Winter
Bach, Partita #2, Gigue
Liszt, Faust Symphony

For instance, Beethoven's variations (Example 1.2) provide opportunities to listen for "elaborations" on the "simples" in different contexts -- instrumentation, texture, same-different, dynamics, range/register, and character -- what generates the changes in character and what is the continuing "thrust" as the variations develop?

A comparison of the Vivaldi and Bach examples raises the issue of use and function of sequential relations, along with the differences between sectional and continuous organization. Noticed the large sections in the Vivaldi and also the changes in the sequential "template" which marks the boundaries of sections. The Bach is more difficult, the question is, "Why is that?" A possible reason is that contrast and boundary-making are at a more fine-grained level of detail--the rate of change is much faster, and in addition, boundaries are obscured. The motive rather than the phrase is the "unit of perception."

Why does the Liszt example sound so different from the other examples, and what generates its clear and somewhat frightening affect? The "content" of the sequential "template" and the way it "creeps" from one statement to the next clearly make a big difference, along with texture and instrumentation.

Discussion of Basics1:
Texture; instrumentation
Expressive markings

Class #2:
Discussion and performance of student tunes
Due Today: Paper 1

II. Rhythmic Structure: Weeks 3-5

Part 2 differs from Part 1 in several respects. We begin with listening rather than immediately jumping into a project. The motivation derives from a sense that the entities that organize time -- in particular the beat and the hierarchy of beats, are of a significantly different kind from the elements at work in Part 1 -- gestural elements of melody such as figures and phrases. Of course these gestural elements are organized by and include both time and pitch, so it is intuitively destructive to consider them separately. However, this process of deconstruction, which seems a pervasive part of teaching -- is necessary to developing and understanding symbol systems which inevitably refer to particular aspects, certain bits and pieces, while ignoring others. But this leaves us with the problem of putting back together that which is, in experience, never in pieces at all.

In Part 2 you will move between your intuitive experience of musical time and motion, and reflections on these experiences as embodied by notations. Multiple views (representations) help you to achieve this passage -- kinds of elements at varying levels of detail as expressed in differing media -- numbers, graphics, sound, action. Towards this goal Impromptu's number notation for temporal relations have been designed on one hand, to help you keep close to your immediate experience of organized movement, and on the other, to help you develop a more general framework for understanding the "norms" of rhythmic structure. In turn you will learn to appreciate how composers perturb these norms to create contrast, affect, and larger design.

Week 3:


Introduction to Part II of DMI
MBME: Pp. 24-44

To do:
Projects 2.1 & 2.2 Pp. 67-98
Discussion in Class #2 of Week 4

Pp. 64-66

Projects 2.1 and 2.2 (Pp. 67-98)

I. This assignment does not require writing a paper. However, it does involve using Impromptu to actively make the principles work that are mostly just discussed in Projects 2.1, 2.2, and the listening examples.

Working in Impromptu's Drummer Playground, use percussion instruments and varied durations to build:

1. Two rhythms that generate duple meter.
2. Two rhythms that generate triple meter.
3. Be prepared to play your rhythms, live, on real drums

You may use 1-3 percussion instruments (in Voices 2-4)

Due in Class #2 of Week 4

Class #1:

Class #2:
Continuing discussion of Project 1.2 tunes.
Introduction to rhythmic structure
Introduction to Drummer

The problem with notations for rhythm is that they are difficult to relate to our experience of the organization of a melody or larger piece which are continuously unfolding in time and sound. What seems essential to this experience is actually a fundamental paradox: a beat is generated by the relations among the varied durations at the surface of a melody or rhythm pattern, while this beat also becomes the unit for measuring the events that generate it.

Week 4:


Discussion in Class#1 of Week 5
Hasty, Meter as Rhythm (Pp. 1-13) handout.
Discussion in Class#2 of Week 5

Class #1:
The metric hierarchy -- triple and duple meter
Figural and metric structures

Bhimpalasi & Hindemith: Beat and non-beat
Lanner & Sousa - triple and duple meter

Class #2:
Performance and discussion of percussion pieces
Due in Class Today: Projects 2.1 and 2.2

Note: Please hand-in your completed percussion pieces on disk.

Week 5:

The process of making mappings across representations of temporal relations serves to reveal the principles that underlie the whole systematic framework of metric relations. Moreover, as one becomes familiar with the notation, it also becomes possible to create rhythms that one would probably not even think of if using CRN. Further, the notation lends itself to asking questions such as, what is it that generates rhythmic coherence in the midst of rhythmic conflict, and how does rhythmic conflict differ from rhythmic chaos?

Class #1:
Performance and discussion of percussion pieces (cont.)
Rhythm notations: similarities and differences.

Class #2:
Discussion of Hasty
Inventing rhythm notations (MBME - pp. 24-44)
Multiple meanings of "fast" and "slow"

Rhythm 2 - Complexity: Weeks 6-7


To do:
Project 2.3 (Pp. 99-108; 118-122)

Pp. 109-118; 123-129

Paper 2: Project 2.3

Make 2 different accompaniments for each of two tunes, Clementine and Tyrol, as described in Tasks 2 & 3 on P. 100. Notice that you will be using just two tunes and that Clementine is substituted for Early and Lanner listed on P. 100.

I. For each of these two tunes, Clementine and Tyrol, make two different kinds of percussion accompaniments. To create a base from which to work, begin by building the metric hierarchy for each tune. Then make accompaniments for each tune as follows:

a. Varied durations that reinforce the metric hierarchy.
b. Varied durations that conflict with the metric hierarchy.

II. Be prepared to play your accompaniments and teach them to others to play live on real drums. And this means: make accompaniments that are playable.

III. Write out 1.a and 1.b in CRN. If you use a repeated pattern, write them just once and indicate the number of repeats.

IV. Develop "mini-theories" based on your work as follows:

a. What are the features of temporal relations that generate a beat?
b. What are the distinctions between figural and metric structures? Give examples from your own work and/or from the listening examples (see, for example MBME, pp. 24-30).
c. What are the differences between "rhythmic conflict" and "rhythmic chaos" -- e.g., see DMI pp. 118-119.

Paper 2 Due: Class #2 of Week 7

Week 6:

Class #1:

Class #2:
Making and playing percussion accompaniments for tunes:
Some Impromptu examples.
Introduction to rhythmic conflict.

Listening (Pp. 109-118):
Stravinsky: Petruchka
Mozart, Piano Concerto
C. Porter, Night and Day

Week 7:

Class #1:
Rhythmic complexity (Pp. 123-128)

Ziporyn, "What she saw there."
Haydn, Quartet
African drumming
Stravinsky, Rite of Spring

Class #2:
Discussion and performance of Project 2.3 student pieces.
Due Today: Paper 2

Note: Be sure to hand in your completed pieces on a disk along with your paper.

III. Pitch Relations: Weeks 8-10


Introduction to Part III of DMI (pp. 136-143)

To do:
Project 3.1

No Paper, Discussion in Class #2 of Week 8

The focus throughout Part 3 is on tonality as a framework for generating coherence. As in the earlier chapters, the importance of context is emphasized, particularly in light of the central investigation which began already in Part 1: what generates a tonal center, its sense of centrality, and its sense of stability?

The purpose of Project 3.1 is to give you a functional, practical orientation to notational systems and to the theoretical structures upon which they depend. You will be helped to make a smooth transition (perhaps transformation) from Impromptu tune blocks and pitch contour notation to conventional staff notation (CSN), while drawing out the differences along with the advantages and disadvantages of each.

Carrying further the investigation into your intuitive knowledge, the major scale is derived and its structure made explicit; intervals, tetrachords, the model of a major scale are discussed. And giving names for things will help you account for what, in some intuitive sense, you know already.

Week 8:

Class #1:
Introduction to intervals and structure of scales

Class #2:
Tonic function and 1->5->1
Project 3.1 in Class Today

Week 9:


Some Basics3 Pp. 200-211

To Read and Do:
Project 3.2

No Paper, Discussion in Class #2 of Week 10

The focus in Project 3.2 is again on tonality, now enhanced by the experience of disrupting it through modulation -- i.e., what we call making a melody "migrate" from one key to another. In doing so, we focus on the changing function of the same pitch when embedded in new pitch environments. It is argued that tonality is "an internal affair," -- the result of internal relations among pitches as they occur through time. The perception of tonality results from the habits of mind we have acquired by listening to the music of our own culture, these perceptual habits guiding the specific organizing of internal pitch relations we seem just to fin there.

In all of this, the fifth relationship in its many manifestations comes forth as the critical pillar upon which the generating of the tonal framework rests.  That idea, along with the concept of the framework as a large, interconnected network of relations, emerges as central to the work of the course up to this point.

Class #1:
Analysis of Listening Examples 3.1-3.5 and the pervasiveness of 1->5->1 pp. 187-199.

Class #2:
Discussion of final projects.

Week 10:

Class #1:

Class #2:
Review of Basics 3 and Projects 3.1 and 3.2:
Scales, keys, key signatures, circle of fifths, etc.

IV. Making Music out of Theory: Weeks 11-13


Introduction to Part 4, p. 213.

To read and do:
Project 4.1 pp. 214-219.
No Paper, Discussion of compositions in Class #2 of Week 11

To do:
Project 4.2
Paper 3: Due in Class #1 of Week 12

Project 4.1 recalls the tune building projects in Part 1 but now you are bolstered by new concepts, abilities to focus on more aspects, and with these, increased possibilities for accounting for your intuitions. The list of questions on p. 215 quite explicitly reviews issues covered previously while going beyond them. For instance, in addition to motive and phrase boundaries, we add boundaries of key areas, where/when do they occur, what generates them, and how are the key areas on either side related to one another? Structural functions of blocks is now embedded in the additional context of functions within different keys. Further, the role of modulation enters as another means of enhancing larger structural relations.

Exploration 1 turns back on the tune, Dutch, to an analysis in greater detail of the importance of 1-5-1. The intertwining of these fifth relations at different levels of structure (scale degrees within phrases and key relations across sections), should help to give the fifth the credit it is due as a fundamental structural pillar. The analysis of Dutch also brings back the importance of context in generating pitch functions, in particular, the tonic (as "an intimate affair") and the changing functions of the same pitch when embedded in new contexts.

No paper is required for this project, but please do compose tunes that migrate using the British and Salem blocks, and study Explorations 1 (Pp. 216-219). Be prepared to discuss your work in class.

Due in Class: Class #2 of Week 11

Paper 3: Project 4.2
Pp. 214-247
Due: Class #1 of Week 12

Read carefully the introduction to Project 4.2 (pp. 228-229). This project brings together all the issues and concepts we have discussed in previous weeks. As it says in these pages:
"Through the experiments in this project, your intuitions will again be both the source and the target of your work.  And in the course of it, you will need to practice much of what you have learned in the previous projects and explorations to make new melodic coherence." Take your time with it; let the possibilities roll around in your thinking and hearing.


  Throughout Project 4.2 (Tasks 1 and 2), the main point is to pay attention to and try to account for the kinds of features and relations that generate the grouping boundaries you hear and make.  


Task 1. Given only a set of varied durations all playing the same pitch (MAKETUNE.D), listen for figural groupings. Then give pitches to the durations so as to bring out these groupings and to make a coherent melody. Do only DUR2 and DUR3. Instructions are quite complete on pp. 230-231. Listen especially to boundary conditions: how tonal functions (stablity-instablity; pitch movement) intersect with rhythmic functions(accent/meter/short-long) to generate musical objects and on a larger level, arrivals and departures of motion.

To help account for the grouping boundaries you hear and make, look carefully (in the Edit Window, by number or by letter) at the given pitches while listening to your new block. Notating it (in CMN) and playing it on the keyboard, will help you to consider possible aspects that are generating boundaries and relations among boundaries. For instance:

  1. Tonal center -- its arrivals and departures.
  2. Goals of motion at boundaries (e.g., 1 and 5).
  3. Pitch contour (direction of motion; leaps or steps).
  4. Repeated notes, repeated figures, varied repetitions such as sequences.

Task 2 is in two parts: For Task 2A, the pitches are pre-composed; in Task 2B the pitches have been randomly generated, but the work is the same for both parts:

Given a set of varied pitches all with the same duration, listen for figural groupings, then give varied durations to the pitches to bring out these groupings and to make a coherent melody. More complete instructions and related materials are given on pp. 235-247 which you should read carefully.    

For Task 2B do only RAND2 and RAND3. RAND1 is discussed in excruciating detail in Explorations 3 which should be read carefully as an example of what to look for. You may not be able to depend on coherence-making features generated by clear tonal functions, but this can liberate you to listen for other means of boundary-making. At the same time, pay attention to tonal functions that may be lurking behind the apparent non-tonality!!  Explorations 3 will be helpful particularly with regard to noticing subtle tonal relations.

For Task 2B only, you may change one or two pitches in the pitch list if you want to. But if you do, you must say why you made these changes and comment on the effectiveness of the results.


  Notice that there is a new, Final Task within Task 2.B. You must design a second set of durations to make the pitches in each of the rand blocks regrouped in new ways.  

Your work on this project and our discussion in class is an opportunity to reflect on many of the issues that we have covered throughout the semester: the tonal network, rhythmic structure, melodic analysis, movement towards arrivals and departures, moving up and down the structural ladder, simplicity and complexity.

Week 11:

Class #1:
Listening and analysis of Large scale compositions:
Beethoven Op. 59#2
Discussion of final projects

Class #2:
Discussion of Project 4.1 pieces
Discussion of final projects

Week 12:

Class #1:
Discussion and performance of Project 4.2 pieces

Class #2:

Weeks 13-14:

Final project presentations