retrospectively logging places, events, ideas, and sounds of a life of composing.
Each chapter remembers a time and place in my career, and explores a particular compositional design approach derived from my study of 20th-century masterworks. Audio clips offer listening to all pieces cited, both the masterworks and my later compositions inspired by them. Take some time to listen as well as read! – TC
CONTENTS
My compositional fascination with musical canons began in the early 1970s with study (at the University of Michigan) of Ockeghem’s 15th-century polyphony, the 10 canons in Bach’s 18th-century The Musical Offering, and Webern’s 20th-century Symphonie Op.21. As a young professor in the 1980s teaching 16th-century counterpoint at what was then North Texas State University (now UNT), I used canon as a challenging contrapuntal writing assignment. In 1985, a wind ensemble piece, Parallel Horizons (Homage to Schoenberg), was my first formal composition constructed by canon. In Dark Matter, other contrapuntal writing surrounds an extended canon. Now canon pervades much of my 21st-century writing, a challenging yet stimulating and gratifying approach to texture and continuity of material.
The definition of this ancient form of Rumpelstiltskin magic, spinning complex counterpoint out of a single melodic line:
CANON
A leading line is echoed after some delay by one or more answering lines of identical rhythmic values and melodic shape (possibly transposed)
For a collection of 21st-century examples – 14 studies in 3-voice canon – go to my BOOK OF CANONS in the appendices. For pedagogical demonstration purposes, the subject of each is shown, with indications for when and at what pitch level each answer will occur.
Read more at Mapping the Music Universe: COUNTERPOINT.
In his book When (Riverhead Books, 2018) Daniel H. Pink writes, “I believe that timing is everything. . . . The experience of awe changes our perception of time. When we experience awe, time slows down. It expands. We feel like we have more of it. And that sensation lifts our well-being.” He quotes researchers Rudd, Vohs, and Aaker in Psychological Science 23 No. 10 (2012): “Experiences of awe bring people into the present moment, and being in the present moment underlies awe’s capacity to adjust time perception.”
Read more about time at Time perception
Mapping the Music Universe is written for the literate musician, including college music students through music scholars, and anyone who is intellectually curious about how music works, especially in the 20th-21st-century modern and “post-modern” eras.
The mapping project is a comprehensive catalog of patterns and processes, meant to provide simple tools for understanding modern music. This is not a theoretical treatise but a practical guide for all educated or educating musicians and the intellectually curious, requiring only basic music literacy. For me as a composer, it is also an exploration of how some of the less travelled conceptual paths lead to interesting creative possibilities. Sample composed etudes will give examples to connect the abstractions back to our musical imaginations.
In 1989 I co-authored a composition textbook with Larry Austin, Learning to Compose: Modes, Materials, and Models of Musical Invention. We felt it was conceptually ground-breaking. My next book, ARRAYS, was an aural skills workbook covering basic modal, tonal, and “post-tonal” music of the Renaissance through the Twentieth Century. They were intended as college-level textbooks, ARRAYS basic and Learning to Compose quite advanced — maybe too advanced to succeed as a textbook, turning out to be more of a technical monograph than a basic guide. Mapping the Music Universe draws in part on the ideas and approaches of both these now out-of-print publications.
The three parts progress logically from fundamental — time and periodicity — to pitch space, then to larger structures — texture and form. They can be read in this sequence or separately in any order. Likewise, within each part, the various topics are presented in a progressive order, but jumping in at any point is not to be discouraged. As terms are defined, they are set off to the right. Figures include musical examples, sample etude compositions, tables, and graphic illustrations of patterns and their relationships.
Read full Introduction . . .
Mapping the Music Universe by Thomas S. Clark . . . CONTENTS
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Pursuing a grand cosmic metaphor, think about the levels of structure scientists study in our physical universe. They have dived deep below the atom’s structure of electrons spinning around a nucleus of protons and electrons to discover subatomic particles like the meson and boson. On the other extreme of scale, they have gathered observations to speculate about the shape of the entire expanding universe. We understand the structure of our planet, of our solar system, and our Milky Way galaxy.
Painting engages techniques to create texture, rising to broad descriptions of style that actually describe structure: impressionism, cubism, pointillism. Musically, macro-structure is thought of as texture and form. Texture has been treated in broad descriptive categories: monody, homophony, polyphony, counterpoint, and more recently, sound mass, each focusing on the number of distinct parts, voices, or layers and how they interrelate. At the risk of invoking too many different metaphors, I like to think of the musical texture as a fabric.
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Mapping the Music Universe by Thomas S. Clark . . . CONTENTS
Galileo revolutionized astronomy, in part by using a new tool: the telescope. Schoenberg revolutionized harmony by evolving an existing concept, the chromatic scale, into a new tool: the 12-tone scale. (He also devised the compositional tool of the 12-tone row — but that’s another story.) Allen Forte took Schoenberg’s ideas to another level of abstraction: defining Pitch Class and applying basic math to the 12-tone universe. Christman focused on intervallic essence of pitch patterns: defining the “successive interval array.” I am merely another explorer using their maps but choosing my own creative path. In doing so, I will define some of my own terms, while adapting and clarifying some established terms that fit what I’m thinking and expressing.
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Mapping the Music Universe by Thomas S. Clark . . . CONTENTS
We start with time. Everything in music involves time, is of time, sound events occurring in our perceived flow of time. Sound itself is periodic, a repetition of compression waves in air (or water).
Repetition of an event or series of events, establishing a frequency of repetition and the period or cycle length of the elapsed time duration from each event’s starting time point (moment) to the starting point (moment) of its repetition.
We perceive the frequency of the waves as pitch if they are faster than 20 per second and slower than about 4,000. Frequency is typically measured in cycles per second, called Hertz.
Non-periodic waves faster than about 20 Hz are perceived as noise. Events or time cycles slower than 20 Hz are perceived as pulses, tempo, rhythm, phrase structure, etc. At these slower sub-sonic event speeds, it is more convenient to identify the duration of the cycle, its period, than the frequency.
Periodicity, this repetitive aspect of sound events in time, gives us a dimension to map all the possibilities, from extremely fast to almost frozen slowness, and from simple, highly regular repetitions to a very complex succession of variants.
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Mapping the Music Universe by Thomas S. Clark . . . CONTENTS
MAPPING MUSIC 