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Library of Congress Cataloging-in-Publication Data
Names: Variego, Jorge, author.
Title: Composing with constraints : 100 practical exercises in music composition / Jorge Variego.
Description: [1.] | New York : Oxford University Press, 2021. | Includes bibliographical references and index.
Identifiers: LCCN 2021009466 (print) | LCCN 2021009467 (ebook) | ISBN 9780190057244 (paperback) | ISBN 9780190057237 (hardback) | ISBN 9780190057268 (epub) | ISBN 9780197599068
Subjects: LCSH: Composition (Music)—Instruction and study.
Starting a New Composition: Challenges and Possible Solutions • 93
Formal Plans • 94
Using Matrices and Vector Graphics • 94
Analysis and Stylistic Imitation • 95
Improvisation • 96
Connecting Worlds • 96
Soundscapes and Nature • 96
Repeat Yourself • 97
Using the Computer as an Assistant • 99
Exercises • 99
Exercise 91: Writing a Compositional Recipe • 99
Exercise 92: Using a Matrix • 100
Exercise 93: Deconstructing and Reconstructing I • 101
Exercise 94: Deconstructing and Reconstructing II • 101
Exercise 95: Creating a Compositional Plan • 102
Exercise 96: Bringing Ideas from Other “Worlds” to Your Music • 103
Exercise 97: Quotations as Triggers • 103
Exercise 98: Articulating Connections • 104
Exercise 99: Oblique Strategies by Brian Eno and Peter Schmidt • 104
Exercise 100: The Computer as Assistant • 104
Appendices • 107
A) Grading Rubric • 107
B) Sample Curricula • 108
C) Select Anthology of Scales and Musical Examples • 110
D) Table of Instrument Ranges and Transpositions • 118
Bibliography • 125
Index • 127
FOREWORD
Constraints are often seen as limitations, but they are omnipresent in the musical context and can unfold considerable creative potential in the compositional process.
To simplify, one could say that in contrast to a rule, which rather formulates a strict if– then relationship, constraints establish a network of conditions in which musical structure can evolve in manifold ways.
In this sense, constraints are the essential basis of every musical analysis and also serve as a conscious or unconscious guideline for the act of musical composition.
As far as analysis is concerned, a work must meet certain criteria in order to be assigned to a certain musical style or the oeuvre of a certain composer. And it is only through constraints that it is possible to transform the analytical approach into a generative one, that is, to write exercises in the style of a particular musical genre or of a particular composer.
Of course, many composers are innovators who break out of the compositional paradigms of their time or introduce radical innovations, but preferably not without being aware of the musical tradition and thus being able to transcend it in a reflected manner.
Apart from these analytical or related style-generating approaches, constraints are also of decisive importance in the compositional process.
The act of composition is framed by a number of constraints, which may be consciously defined or applied unconsciously. Even when relying mostly on their own intuition, the composer is nevertheless confronted with various constraints that determine the compositional structure to a certain degree, such as the dynamic, articulatory or pitch capabilities of the instruments, and more.
Now one could provocatively ask the question, why further “restrictions” beyond the intrinsically given constraints should be actively formulated in the compositional process?
First of all, because for most composers the deliberately chosen constraint is not a restriction but a fundamental means of creating the musical structure—and this does not have to involve sophisticated techniques of algorithmic composition or generative music at all. The process already begins with the choice of instrumentation, the choice of a certain harmonic material, or even the preference for certain rhythmic constellations, just to name a few examples.
Deliberate restrictions, however, not only allow a clear structuring of the material, but additionally give rise to new possibilities of musical expression by opening new paths that would hardly have been possible without applying any constraints—or formulated as a question outside the musical context: what point can lipograms make in literature, apart from the mastered linguistic challenge?
Last but not least, the application of constraints in a musical context abstracts from the individual case and creates a meta- class of possible compositions. On the one hand, this enables experimentation with different musical realizations that nevertheless satisfy a superordinate musical concept through a network of given conditions. On the other
hand, it is precisely this abstraction that allows an analytical view of one’s own work and opens up new ways of reflecting on one’s own creative compositional process.
I wish my esteemed colleague Jorge Variego every success with this book and for the readers I would like to add: May the force of constraints be with you!
Gerhard Nierhaus
ACKNOWLEDGMENTS
Writing a book is a journey, a long and slow one. Throughout the trajectory of writing Composing with Constraints I received the encouragement and priceless help of a number of people without whom this project would have never arrived at its destination. Infinite gratitude to (in no particular order) Ed Klorman, Gerhard Nierhaus, Nathan Curtis, Darius Edwards, Emily Leopin, Caleb Cannon, Karen Wemhoener, Michael Wiley, and Norman Hirschy.
The production of this work was supported in part by the University of Tennessee, the Swedish Arts Council, and the Visby International Centre for Composers.
Introduction
Composing with Constraints proposes an innovative approach to the instruction of the craft of music composition based on tailored exercises to help students develop their creativity.
The fundamental premise of Composing with Constraints is grounded on my previous book on algorithmic composition, which—in a few words— states that all compositional approaches are algorithmic and can be reduced to a formal process that involves a series of logical steps. When composition gets condensed to a series of logical steps, it can then be taught and learned more efficiently. With this methodology in mind, Composing with Constraints proposes a variety of exercises in the form of algorithms to help the student composer and the instructor create tangible work plans, with high expectations and successful outcomes.
The book is arbitrarily structured around the parameters of melody, rhythm, harmony, texture, and pre- compositional approaches. All chapters start with a brief note on terminology and general recommendations for the instructor and the student. The first five chapters offer a variety of exercises that range from analysis and style imitation, to the use of probabilities. The chapter about pre- compositional approaches offers original techniques that a student composer can implement in order to start a new work. This last section of the book fosters creative connections with other disciplines such as math, visual arts, and architectural acoustics.
Each of the 100 exercises contained in the book proposes a unique set of guidelines and constraints intended to place the student in a specific compositional framework. Through those compositional boundaries the student is encouraged to produce creative work within a given structure. Using the methodologies in this book, students will be able to create their own outlines for their compositions, making intelligent and educated compositional choices that balance reasoning with intuition.
Depending on the class in which it is adopted, Composing with Constraints can be a priceless aid for the instructor. When used to complement a music theory class, the exercises can be used as compositional projects, to provide creative frameworks to the theoretical concepts studied in class and even to trigger group discussions. In a class on analysis, the book can be an invaluable tool for stylistic understanding, appropriation, and imitation. Finally, when used in individual and group composition lessons, the book can provide an enormous palette of concrete assignments that the instructor can use to guide the students’ compositional development and practice.
The grading rubric provided in the book is a tool for both the instructor and the student that intends to quantize intangibles with the sole purpose of making the grading scheme meaningful. Divided in four categories (i.e., followed guidelines, orchestration, idiomatic use of the instruments, and “open spaces”), the grading rubrics clarify in detail the grade awarded to the student, showing the aspects of the work that can be improved with space for comments and recommendations. Through the quantization of “open spaces,” the rubric also helps the instructor ponder the students’ creative use of the aspects of the exercises not constrained or left “free” in the guidelines.
How to Use the Book
The exercises contained in the book can be used in a variety of ways. Far from a manual on how to compose, Composing with Constraints proposes a series of frameworks to stimulate—and sometimes guide— your musical creativity.
All the exercises can (and should!) be changed, adapted, altered, tailored, and even rewritten to fulfill unexpected compositional needs. Remember that they are frameworks to incentivize new ideas and by which to practice writing music.
Additionally, the exercises can be easily integrated in private composition lessons, courses of music theory, orchestration and analysis. They can be used as creative assignments where to apply theoretical knowledge, explore color, and learn more about the different instruments, and use analysis as a source for a creative practice. The latter is embedded in a variety of ways, ranging from deconstruction approaches, to stylistic imitations. Can you write a recipe on how to compose like Chopin? That skill comes with a combination of analysis and its creative application.
Another suggestion can be regarding the way you may want to navigate through the material. First, the exercises are not presented in sequential order. You can freely transit from 92 to 3 to 20. There are some suggested paths in Appendix B that touch a little of every chapter. Second, I recommend that you try the same exercise multiple times exploring the “open spaces” and a different given material. What is not constrained in the guidelines can be explored and exploited creatively.
Composing with Constraints is not a book on music theory. However, all the exercises start with a short theoretical note intended simply to provide context to a specific activity. The goal of the book is to put your skills in action.
Always challenge, be curious, make connections between the worlds that you live in. If you are a performer, bring to your compositions things that resonated with you as a player, if you are a math expert, use your skill to create a function to determine the “next note.” If you are a cook, write compositional recipes. Connect worlds, write lists, make up your own techniques, finish your pieces, and stay creative.
Recommendations for the Instructor
The 100 frameworks contained in the book can be used as “they are” or changed to fulfill the needs of a course, assignment, or individual lesson. All the frameworks’ guidelines are intentionally flexible. Instrumental forces can be modified, meters changed, durations extended, and so on.
Once the instructor has determined the exact contents of the exercise, it should then be followed as strictly as possible by the student. This is quite important, as it is one of the pillar premises of the book: the more strict constraints we impose to ourselves, the freer we become as creative artists. Again, the flexibility of the 100 exercises should let you (the instructor) adjust them to a specific need (e.g., use only woodwind instruments to match a specific module in an orchestration course). On the other hand, the student should have a clear set of non-modifiable guidelines to complete their work when assigned. In sum, the instructor has flexibility to adjust the guidelines, but once set, those enabling constraints should be followed with the utmost rigor.
The repetitive spirit of the book is intentional because none of the 100 exercises are identical! In most of the chapters, an exercise introduces a new topic and is followed by two or three that build up on it with small variations. This approach complements with the fact that the material can be navigated in any direction, following the exercises in any order. The curricula proposed in Appendix B can be modified. An interesting experiment is to assign students the same exercise several times throughout the course of a semester!
The problematic of orchestration is embedded in every exercise and not in a dedicated chapter. The challenges of working with different instrumental forces are included in the book from the very beginning and conceived as an integral part of the compositional craft. In this book, orchestrational color is engrained in the study of composition. The chapter on texture contains a few exercises that focus on changes of color (74) and orchestrational volume (76).
Guidelines and “open spaces.” All the exercises contain both a set of clearly denoted guidelines and “open spaces.” The purpose behind those free spaces is to stimulate students to explore different outcomes within the same set of constraints. These intentionally open doors are presented literally (i.e., “all other parameters are free”), and some can be discovered (i.e., finding a “non- constrained” parameter in the guidelines). These spaces should be stretched to the limit, taking the same exercise to different endpoints without compromising the given constraints. The rubric proposed in Appendix A considers the “open spaces” as one of the pillars for the evaluation of the projects.
Appendices C and D offer extra resources that augment the scope of the book. They can be a source for consultation and enhancement of the material contained in the exercises.
• Supplemental melodic excerpts for analysis and application.
• Piano excerpts for the study of texture, harmonic progressions and others.
• A transposition table. Though not exhaustive, this tool can become handy when dealing with transposing scores.
• A suggested grading rubric that can help quantify aspects of the students’ creative work. The percentiles are intentionally left open to facilitate grading adjustments to a course requirement or individual lesson planning.
• Twelve- week suggested curriculums are included to help navigate the book in a variety of ways.
The book can be navigated in a variety of ways because the exercises are not structured in ascending difficulty (i.e., 23 is not harder than 5 and 1 is not easier than 45). Many paths can be followed; some suggestions are included in Appendix B. The proposed curricula in
Appendix B are structured upon two typical one- semester courses: 1) weekly individual sessions, 2) group sessions with two meetings per week. The 12- week plan is designed around a balance between chapters and musical parameters tackled; it should also give enough room for change when needed. Additionally, the exercises can be repeated, assigned multiple times with different results.
Most of the exercises provide an example of the suggested process in order to complete it. Even though this is not a requirement per se of the exercises, it could be a fruitful addition to help students articulate about their creative processes.
1 Melody (Exercises 1–20)
Preliminary Notes
When present in a composition, a melodic line can have a prominent role. Ravel, Palestrina, Piazzolla, Clarke, and Ginastera are some of the many composers who have written memorable melodies.
In preparation to composing your own lines, it is a good practice to analyze the melodies of others and attempt to extract their structural components. Pitch collections, intervals, durations, ranges, contours, and implied harmonies could be things to look for. Let your findings influence your own writing, use your analysis as a creative tool! The composition of a melody is much more than deciding on a succession of pitches. It can be informed by a number of other factors. Before starting with the exercises, this non-exhaustive list proposes several points for reflection:
1) Rhythm: the rhythmic structure of a melody can influence its forward motion and pace. It can also affect the relative importance of its notes (i.e., the notes with longer durations can be perceived as more important, the opposite can happen to the shorter values).
2) Contour: the arc and the focal point in a melody can suggest the existence of a tensionrelease dichotomy. On the other hand, if the contour is mainly flat (without a focal point), the areas of ambiguity increase.
3) Pitch collections: if the collection of pitches used in a melody is a pentatonic scale (with no semitones), then the color will be characteristic and all five pitches could be equal points of repose. On the other hand, if the collection of pitches is a major scale, then some tendencies and the primacy of scale degrees 1 and 5 can emerge. A 12- tone row can influence the outcome substantially in a completely different way!
4) Repeated notes: the note that is repeated in a melody can be perceived as more important in context.
5) Beat and meter: the pitches of a melody occurring on the strong part of the beat can be perceived as structural, while the ones placed on off beats can seem to have a less important role. Similarly, the melody notes that happen on the downbeats (i.e., the beginning of the measure) can also be perceived as more significant.
6) Intervals and implied harmonies: the intervallic content of a melody can be a resource to imply an underlying harmony or to negate it. A melody mainly built on thirds can suggest a tertian harmonic progression (i.e., with chords built upon thirds). A line that moves by step does not distinctly imply any harmonic progression.
7) First and last pitches of a melody: the notes where a melody starts and ends can be perceived as being more significant.
8) Register: a drastic register change can alter the relative importance of the pitches around it and also the perception of the pulse and note groupings.
9) Pulse: a melody where the pulse is not perceivable can favor a focus on other of its aspects.
10) Articulations and dynamics: these can influence the character, playability, perception of the meter, and the relative importance of the pitches.
11) Pitch collection and “dissonance”: the idea of dissonance in a melody can be associated with the context (e.g., in a melody composed only with the pitches of the G major scale, the occurrence of a C♯ can create dissonance because of the context in which it appears—even though it does not clash vertically with another sound).
12) Complex or compound melodies: a single melodic line can embed several lines in one, creating the illusion of a polyphony.
13) Commonalities: scales and arpeggios are compositional commonalities because they are used very often. A melody built mostly on commonalities will hardly become memorable.
This non-exhaustive list shows a number of points for reflection when writing or analyzing a melody, also intended as anchors to guide the listening.
In this chapter, the exercises focus on the single melodic line. Exercises 1 to 6 are based on the idea of writing melodies with given pitch collections (ordered and unordered), using focal points and pitch collections that have elements in common. The goal of frameworks 7 and 8 is to compose melodies using concatenated triads; 9 and 10 focus on the use of segments (of equal and unequal duration); 11 proposes the “translation” of a given image into sound; 12 through 14 incorporate the concept of integer notation. Simple use of probabilities is the basis of exercise 15. Numbers 16 and 17 use 12- tone rows and simple transformations. In 18 the objective is to use analysis (specifically the inventory of interval types from a given melody) in a creative way. Exercises 19 and 20 use the concept of simple melodic motifs and processes of elimination to compose melodies. The outcome of the 20 work frames of this section can be taken further, solved multiple times, combined with other processes or simply used in part to trigger new ideas. Additionally, the melodies composed in this chapter can be reused for any of the exercises contained in other chapters.
Exercises
Exercise 1: Focal Point
In this exercise you will compose a melody for solo flute using the given constraints.
Guidelines:
1) Create a scale that uses between five and seven different pitches.
2) Using exclusively the notes of your scale in any order or register, compose a melody that fulfills the following requirements: a. Duration: between 10 and 12 measures.
b. Meter: 4/4.
c. Instrument: flute.
i. The score should include all markings for articulations, breath marks, dynamics, phrasing, and tempo.
ii. You must consider the instrument’s range (see Appendix D).
d. The melody must have a focal point (i.e., the highest note of the melody).
e. The rhythmic component must be constructed exclusively using material extracted from the excerpts contained in Figure 1.1.
3) You must show the scale that you created clearly in your score.
4) All other parameters are free.
Exercise 2: Using a Scale
In this exercise you will compose a melody for solo oboe using a given scale.
Guidelines:
1) Use the scale given in Figure 1.2.
2) Using exclusively the notes of the given scale in any order and register, compose a melody that fulfills the following requirements:
a. Duration: between 10 and 12 measures.
b. Meter: 3/4.
c. Tempo: quarter note = 80.
d. Instrument: oboe.
i. The score should include all markings for articulations, breath marks, dynamics, phrasing, and tempo.
ii. You must consider the instrument’s range (see Appendix D).
e. The melody can have a focal point (i.e., the highest note of the melody) but it is not mandatory.
f. The melody must start and end on different pitches (i.e., if you start on a C, you must end on any note but C).
g. The rhythmic component and articulations must be constructed exclusively using material extracted from the excerpts contained in Figure 1.3.
Figure 1.1. Rhythmic excerpts.
Figure 1.2. Given scale for exercise 2.
h. All other parameters are free.
Exercise 3: Using a Scale and a Subset
In this exercise you will compose a melody for solo clarinet using a given scale and applying transformations to it.
Guidelines:
1) Use the scale given in Figure 1.4.
2) Using the notes of the given scale in any order and register, compose a melody that fulfills the following requirements:
a. Duration: between 10 and 12 measures.
b. Meter: 4/4.
c. Tempo: quarter note = 60.
d. Instrument: clarinet in B♭
i. The score should include all markings for articulations, breath marks, dynamics, phrasing, and tempo.
ii. You must consider the instrument’s range (see Appendix D) and transposition (write your solution in transposed score).
e. The melody should employ all the available pitches in any order and register in the first five measures of the exercise. From measure six until the end, use only a subset of four pitches of the original scale (e.g., C E F♯ G or E F♯ G B♭).
f. All other components are free.
Exercise 4: Using a Scale with a Substitute Pitch
In this exercise you will compose a melody for solo bassoon using a given scale and applying the given transformations to it (using a substitute pitch).
Figure 1.3. Rhythmic component for exercise 2.
Figure 1.4. Given scale for exercise 3.
Guidelines:
1) Use the scale given in Figure 1.5.
2) Using the notes of the given scale in any order and register, compose a melody that fulfills the following requirements:
a. Duration: between 10 and 12 measures.
b. Meter: 5/4.
c. Tempo: quarter note = 120.
d. Instrument: bassoon.
i. The score should include all markings for articulations, breath marks, dynamics, phrasing, and tempo.
ii. You must consider the instrument’s range (see Appendix D).
e. In the first five measures, the melody should employ all the available pitches from the given scale in the given order and register. Pitches can be repeated freely. From measure six until the end, you should substitute one pitch from the original scale with one of your choice not present in the original collection (i.e., in the scale in Figure 1.5 the B♭ becomes B natural).
f. Use only eighth notes and eighth note rests.
g. All other components are free.
Exercise 5: A Scale in a Given Order
In this exercise you will compose a melody for solo trumpet using a given scale and applying simple transformations to it.
Guidelines:
1) Use the scale given in Figure 1.6.
2) Using the notes of the given scale in the given order and register, compose a melody that fulfills the following requirements:
a. Duration: between eight and ten measures.
b. Meter: 4/4.
c. Tempo: quarter note = 108.
d. Instrument: B♭ trumpet.
i. The score should include all markings for articulations, breath marks, dynamics, mutes, phrasing, and tempo.
Figure 1.5. Given scale for exercise 4.
Figure 1.6. Given scale for exercise 5.
ii. You must consider the instrument’s range and transposition (see Appendix D). Write your solution in transposed score.
e. All other components are free.
Exercise 6: A Scale in a Given Order with Ordered Rhythm
In this exercise you will compose a melody for solo vibraphone using a given ordered scale and rhythmic structure.
Guidelines:
1) Use the scale given in Figure 1.7.
2) Using the notes of the given scale in the given order and register, compose a melody that fulfills the following requirements:
a. Duration: between eight and ten measures.
b. Meter: free.
c. Tempo: quarter note = 108.
d. Instrument: vibraphone.
i. The score should include all markings for articulations, type of mallets, dynamics, phrasing, and tempo.
ii. You must consider the instrument’s range (see Appendix D).
e. The rhythm must be one of the structures from Figure 1.8. It can be repeated multiple times.
f. The ordered scale can also be repeated (restarted) multiple times.
g. All other components are free.
Figure 1.7. Given scale for exercise 6.
Figure 1.8. Rhythmic structures for exercise 6.
Exercise 7: Concatenating Triads
In this exercise you will compose a melody for solo French horn following the given guidelines.
Guidelines:
1) Using exclusively pitches from concatenated major and minor triads (i.e., the next triad has one or two pitches in common with the previous one) compose a melody that fulfills the following requirements:
a. Duration: between eight and ten measures.
b. Meter: 6/8.
c. Tempo: dotted quarter note = 60.
d. You can start and finish on any note.
e. Instrument: French horn.
i. The score should include all markings for articulations, breath marks, dynamics, phrasing, and tempo.
ii. You must consider the instrument’s range and transposition (see Appendix D). Write your solution in transposed score.
iii. All other parameters are free.
Process:
1) Start with a triad (major or minor) of your choice.
2) Use the last pitch of that triad to build the next triad (see Figure 1.9). 8
Figure 1.9. Example of concatenated triads with one note in common. Major and minor triads only.
Exercise 8: Concatenating Triads of Any Type
In this exercise you will compose a melody for solo bass clarinet following the given guidelines.
Guidelines:
1) Using exclusively concatenated triads (i.e., major, minor, diminished, and augmented triad that have one or two pitches in common) compose a melody that fulfills the following requirements:
