MAPPING MUSIC

Author: thomasclarkumich

  • 1. Forest Paths

    Howell, 1967 —

    In 1967 I was already earnestly composing for piano, trombone (my own instrument), even for orchestra. Living beside the Shiawassee River’s glacial-moraine beginnings in rural Livingston County Michigan, my best pastime was hiking along the creek’s forested banks. I was already going to Ann Arbor for trombone lessons and Youth Symphony rehearsals.

    In fall 1967, after my 18th birthday, I moved to Ann Arbor and enrolled at the University of Michigan. Though not yet a music major, I began playing bass trombone in the university orchestras. For 8 years, Ann Arbor with beautiful Huron River running through it was my forested Michigan home.

    The year before I was born, John Cage wrote a gentle, beautiful piece for piano, one simple enough that my 1967 piano skill could have handled. It also expressed my own urge to amble along freely improvised paths of musical exploration.

    John Cage – Dream (1948)– Damian Alejandro, piano

    At age 17, I never dreamed that I would meet John 24 years later (in Denton Texas of all places), a gentle soul who loved mushrooms. And I had yet to discover this piece or any John Cage music. But I was also writing simple and (I thought) beautiful piano music.

    Two pieces for piano that expressed my attitude of wonder while wandering in the woods were updated fifty years later with my 2023 editing skills. “Mystic Breeze” and “Light” were my 12th and 18th completed TC compositions. “Riverbank” is from a 1967 sketch of an “interlude” for trombone and piano.

    They make a nice set of three, revealing that before formal study my compositional explorations were already discovering more exotic harmonies and rhapsodic forms resembling Debussy’s Impressionism and even the post-tonal possibilities of 12-tone rows.

    ARBOR SKETCHES

    Clark 1967 (TC-12/18)

    • 1. Breeze
    • 2. Riverbank
    • 3. Light

    Brno

    Twenty-four years later in 1991, I was invited to perform at the 26th Brno International Music Festival. It would lead me on a path of musical and cultural exploration that has filled my life since with beauty. (I had also married a beautiful Czech-American woman in 1976.)

    Brno is the capital of the Moravian province of what was then Czechoslovakia. Brno was the home city of the great 20th-century Moravian composer, Leoš Janáček. After visiting his home and school in Brno and his summer home in Hukvaldy, I began to study his music.

    Two things captured my interest. Like Bartok, he embraced and collected the folk music of his homeland. He also exalted in nature, walking around the wooded hills of Hukvaldy’s castle ruins, and collected his own transcriptions of bird calls.

    While there on the first visit, I was commissioned to compose a ballet for the local dance theatre company. Inspired by Janáček’s birds, I began to write my own music for what would become the ballet, PTACí (“Birds”).

    Lesní cesty

    In a music store in Brno, I also discovered his marvelous 1911 set of piano pieces, the title of which translates “On the Overgrown Path.” On a return trip, I was able to visit the Moravian Music Archives in Brno to examine his original hand-written manuscript of the pieces.

    Excerpted from Series I:

    • No. 5, They Chattered Like Swallows
    • No. 6, Words Fail!
    • No. 7, Good Night!
    • No. 8, Unutterable Anguish
    • No. 9, In Tears
    • No. 10, The Barn Owl Has Not Flown Away!

    Po zarostlém chodníčku – – – Josef Páleníček, piano

  • Paths of Light

    a composer’s journal –

    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

    LINK TO CHAPTER

    CONTENTS

    LINK TO CHAPTER

    Read it all:

    a composer’s journal

  • Book of Canons

    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.

  • Timing of Awe

    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 – preview

    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.

    Purpose

    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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  • GALAXIES: Musical Structure and Relativity

    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.

    Texture

    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.

    Other topics

    • Counterpoint
    • Rhythmic alignment
    • Canon
    • Farben
    • Symmetry
    • Pointillism
    • Repetition
    • Multi-phase ostinato
    • Sound mass
    • Hauptstimme
    • Density
    • Relativity

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    Mapping the Music Universe by Thomas S. Clark . . . CONTENTS

  • CONSTELLATIONS: Pitch Space, Arrays, Tonality

    Introduction

    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.

    Topics

    • Tuning
    • Constellations
    • Interval Arrays
    • Scales
    • Scale prototypes
    • Scale patterns and set classes
    • Harmonic complexity
    • Constellation streams
    • Constreams and 12-tone sets
    • Progressive alterations of arrays
    • Clusters
    • Cells – melodic molecules
    • Cell class

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    Mapping the Music Universe by Thomas S. Clark . . . CONTENTS

  • STARS: Time points, periodicity, perception

    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.

    Topics

    • Defining time
    • Time perception
    • Periodicity
    • Meter
    • Definitions
    • Stress and accent
    • Rhythmic molecules
    • Harmonic rhythm
    • Beyond meter
    • Prime numbers

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    Mapping the Music Universe by Thomas S. Clark . . . CONTENTS