MAPPING MUSIC

Author: thomasclarkumich

  • Mapping Music 1. TIME

    “If you want to find the secrets of the universe,

    think in terms of energy, frequency, and vibration.”

    (Nikola Tesla)

    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 vibration, a repetition of compression waves of energy in air (or water). Repetition of an event or series of events establishes a frequency of repetition and the period or cycle length, 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 air-compression 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.

    the periodic time/sound universe

    In this illustration, the Y-axis is speed/frequency (slowest at bottom, fastest on top), the X-axis is regularity of repetition (perfectly regular at left, randomly sporadic time spans at right). The blocks have sharp rectangular edges; if I were a better artist, the boundaries between descriptive categories would actually be curving and very blurred. Though the graph shows firm straight lines separating pitch and noise, there is actually a fuzzy, curving grayscale continuum from pure, simple pitch through complex, colorful pitched timbres to noise.

    Defining time

    What is time and how does it work in our lives and in the rhythms that are the fundamental “substance” of music? I say substance metaphorically, because time does not exist as any physical matter. It is a perceptual construct, a complex quilt stitched out of human experience.

    Discover magazine ran an article in June of 2007 titled, “Time May Not Exist”.

    “Efforts to understand time below the Planck scale have led to an exceedingly strange juncture in physics. The problem, in brief, is that time may not exist at the most fundamental level of physical reality. If so, then what is time? And why is it so obviously and tyrannically omnipresent in our own experience? ‘The meaning of time has become terribly problematic in contemporary physics,’ says Simon Saunders, a philosopher of physics at the University of Oxford. ‘The situation is so uncomfortable that by far the best thing to do is declare oneself an agnostic.’”

    The mysteries of time were explored as early as sixteen hundred years ago by the great Saint Augustine of Hippo, in Book XI of his deeply philosophical work, Confessions.

    “. . . What is time? Who can give that a brief or easy answer? Who can even form a conception of it to be put in words? Yet what do we mention more often or familiarly in our conversation than time? We must therefore know what we are talking about when we refer to it, or when we hear someone else doing so. But what, exactly, is that? [Book XI, Section 17]

    Nicholas Stratas’ thought-provoking article in the July 2007 issue of Wake County Physician, “Time – Continuous Yet Bidimensional” asserts that most of us have a firm concept of Past, Present, and Future. But defining them is challenging, and sorting out how these constructs interact in our consciousness even more so. Michael Spitzer, in The Musical Human (Bloomsbury Publishing, 2021), wrote:

    “Musical time is a window into time consciousness in general. We listen to music in the moment, sitting in the saddle of an ever-shifting Now, as the past whizzes by to become memory, and the present anticipates what is just around the corner. Music’s present tense is really a bundle of memories and anticipations . . .”

    Many years ago, I first read an article translated from Die Reihe, written by a preeminent avant-garde experimental composer, Karlheinz Stockhausen. “Structure and Experiential Time” described Stockhausen’s view that time does not flow uniformly through the experience of a serious musical composition. It ebbs and surges as the composer shapes not just the tempo but the flow of information in the form of repeated or new musical events, simple or complex musical structures.

    “When we hear a piece of music, processes of alteration follow each other at varying speeds; we have now more time to grasp alterations, now less.”

    Even tempo, a supposedly steady clock in most music, ebbs and flows. Computer music composers in synthesizing musical sounds have found that a mechanistically rigid clock tempo sounds artificial. Human musicians are constantly flexing tempo in subtle ways to convey almost subliminally where the music is “going” (another metaphor, that of travel through space).

    Saint Augustine recognizes the slippery challenge of measuring time:

    “ . . . We observe the different ways times lapse, and compare them, and call some longer and some shorter. . . . It is passing time we measure, as we experience it. . . . Time can only be measured as it passes. Once past, it is no longer there to be measured.” [Book XI, Section 21]

    “We measure time as it passes . . . . But how can we measure the present, when it has no extent of its own? . . . Time must be measured in something with extent . . . But in what extended thing do we measure time as it passes?” [Book XI, Section 27]

    “So time is measured, my mind, in you. Raise no clamor against me—I mean against yourself—out of your jostling reactions. I measure time in you . . . because I measure the reactions that things caused in you by their passage, reactions that remain when the things that occasioned them have passed on. . . . Time has to be these reactions for me to be able to measure it.” [Book XI, Section 36]

    Time perception

    Pulling all this together, I’d like to suggest several things about time in classical music.

    • Time is perceptual.
    • Time is multidimensional.
    • Time is elastic.
    • Time is experienced in complex ways as the fundamental basis of music’s richness.

    In LEARNING TO COMPOSE, co-author Larry Austin and I begin the chapter titled “Time Streams” with a quote from a philosopher, and then express in our own words the fundamental nature of time.

    “ ‘Music makes time audible and its form and continuity sensible.’
    —Suzanne Langer

    Music exists in time. Time exists as we sense it, articulated on many levels by changing and cyclically recurring events.

    As beautiful, colorful and essential as sound is in making music, musical sounds are the means to an end, building blocks for events that primarily mark articulations of time.

    We sometimes like to think of music as having two fundamental dimensions, like a graph. The horizontal dimension is the parameter of time. The vertical dimension is the parameter of pitch. But pitch is actually a temporal phenomenon – the frequency (periodic change over time) of sound waves. How amazing are the human ear and human mind to perceive waves of air coming at us a thousand times a second or much faster and distinguish the small differences that make a pitch “in tune” (or not) and the even subtler differences that identify an oboe instead of a violin producing that pitch. All of this from a perception simply of periodic rates in time!

    Stockhausen pointed out that in mentally processing all of these sonic distinctions, we are forced to pay more attention to changes in their qualities, combinations, and “spacing” in time. These are his “alterations”.

    “The greater the temporal density of unexpected alterations . . . the more time we need to grasp events, and the less time we have for reflection, the quicker time passes; the lower the effective density of alteration (not reduced by recollection or the fact that the alterations coincide with our expectation), the less time the senses need to react, so the greater intervals of experiential time lie between the processes, and the slower time passes.”

    The concepts of expectation and information help make some sense of things. “Information” is perceptual data that is similar to what you just heard or logically confirms what you were expecting next. “Entropy” is the opposite perception – surprise, contrast, noticeable change. In musical listening, though we don’t do so consciously, we are constantly “computing,” assessing, retaining, and predicting.

    Saint Augustine connects Past, Present, and Future with memory, experience, and expectation:

    “What should be clear and obvious by now is that we cannot properly say that the future or the past exist, or that there are three times, past, present, and future. Perhaps we can say that there are three tenses, but that they are the present of the past, the present of the present, and the present of the future. This would correspond, in some sense, with a triad I find in the soul and nowhere else, where the past is present to memory, the present is present to observation, and the future is present to anticipation.” [Confessions, Book XI, Section 26]

    And to make matters more complicated, it is not at all a linear process. Let’s take a metaphor. I can’t resist one that Einstein was very fond of in his thought experiments.

    As listeners, we’d like to imagine ourselves as a train riding on tracks through time, a train that keeps moving forward and doesn’t back up. The clickety-clack of our wheels is a steady tempo measuring time. We only remember back to the tracks the locomotive has passed but still lie under the wheels of our caboose at the end. And we only look ahead a little bit, as the tree-bordered tracks curve, preventing a longer straight view.

    That’s way too simple, a two-dimensional time frame in which we either recall a little of what we just heard or maybe guess a little what might happen next. As Meyers, Stockhausen, Spitzer, and Dr. Stratas all observe, in keen listening to music our minds are filled with memories of not just the previous measure or phrase, but the very beginning of the piece, its theme or launching impetus (Grundgestalt as Schoenberg named it) and, in a more diffuse sense, all that has “happened” up to the present moment. The present moment is not one single phenomenon in time either. Melody, countermelody, bass line, chordal texture, and punctuating sounds are simultaneously tracing distinct paths, each with its own pace through time. At the same time, we are constantly expecting what’s coming, or at least “feeling” where the music might be going. And, as if that weren’t complicated enough, we are busy reevaluating what we just heard in relation to what we had been expecting. Saint Augustine describes it more succinctly:

    “Only in the mind can this [the experience of time] be accomplished, because of three activities there—the acts of anticipating, of observing, and of remembering.” [Book XI, Section 37]

    None of this is conscious, but in describing it in concrete terms, we recognize the dizzying multidimensionality, time arrows pointing in all directions and curling back on themselves. This is what I believe constitutes deep listening, “getting lost in the music”.

    Just one more idea – elasticity. Stockhausen recognizes that in music the sense of time passing changes, stretches or compresses, depending on how much “alteration” is being encountered. This is why music can seem “steady” or “surging ahead” or dissipating and almost “frozen”. It is not at all the tempo that causes this, but rather the rate of change, sharp contrast or subtle evolution, in the harmonies, the melodic character, or the rhythm.

    A rhythmic playfulness in modern music stretches our sense of timing. Tempos change, are interrupted, break down, tumble into avalanches, come to rest. Time itself stretches and becomes the titled thematic element in pieces such as Time Cycles (1960) by Lukas Foss. Here is another example titled about time, written at the starting gun of the new millennium.

    Fred Lerdahl – Time After Time (2000)

    Awe

    In his book When (Riverhead Books, 2018) Daniel H. Pink writes,

    “I used to believe that timing was everything. Now 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.”

    © 2026 – All Rights Reserved

    Thomas S. Clark

    –

    Continue reading Mapping the Music Universe:

    2. RHYTHM

    _____________

    TClarkArtMusic.com

  • Mapping Music — PRELUDE

    “The heavenly motions are nothing

    but a continuous song for several voices,

    perceived not by the ear but by the intellect,

    music that sets landmarks

    in the immeasurable flow of time.”

    Galileo

    When we gaze at stars and planets, they appear as stationary points of light, fixed in place in what seems a random pattern across the entire night sky visible to our hemisphere. Time stands still.

    Throughout human time, humans have imagined that stars make picture patterns we name as constellations: fish, warriors, goddesses, animals. Only the persistent observers, such as astronomers, identify their nightly march across the sky, rising in the east and disappearing below the western horizon.

    Metaphor

    Musical sounds mark points in time, like stars. They form immediately into recognizable patterns we call chords, melodies, rhythms, memorable themes. They convey a sense of motion, time surging forward or slackening in our perception of their well choreographed parade.

    Astronomers observing and mapping (recording) the myriad points discovered that some of the stars are actually whole galaxies, with exotic forms of spirals and clouds. They observed through the color of the light that all these objects are racing away from us and each other in an expanding universe.

    Mapping music means cataloging many possible patterns, distinguishing their contrasts and commonalities. We will explore how to measure and compare the periodic rhythmic streams of musical events and their changing momentum. We will define and employ a simple but powerful math tool for cataloging and then creatively sculpting with all natures of harmony and melodic line in our 88-key chromatic universe. We will explore how master composers weave colorful fabrics and grand structures from skillfully crafted materials.

    Pursuing periodicity

    My music-mapping Periodicity Project began in 2021 as a comprehensive catalog of musical patterns and processes, meant to provide simple tools for understanding the complexities of modern music. It grew into this book, Mapping the Music Universe, written for anyone who is curious about how music works, especially in the 20th-21st-century modern and “post-modern” eras. For me as a composer, it is also an exploration of how some less traveled conceptual paths lead to interesting creative possibilities.

    In 1989 I co-authored a conceptually ground-breaking composition textbook with Larry Austin, Learning to Compose: Modes, Materials, and Models of Musical Invention. My next book, ARRAYS, was an aural skills workbook covering basic modal, tonal, and “post-tonal” music of the Renaissance through the Twentieth Century. Mapping the Music Universe draws in part on the ideas and approaches of both these now out-of-print publications.

    A common assumption within Western culture is that Science is all about observation, measurement, precision, and mathematical rigor . . . and Art is all about the “i” words: imagination, inspiration, intuition, improvisation. Science is Deductive, art is Creative. Our culture has begun to recognize the commonality of all these intellectual strengths, that the best Science can be creatively intuitive and great Art can be rigorous.

    Pioneer map makers

    As an educated musician and professional composer, I also have long been deeply interested in science, especially astronomy. Having read a great deal of general science writing, I am inspired particularly by ground-breaking pioneers who methodically and comprehensively mapped the possibilities of their particular field.

    Johann Joseph Fux — wrote Gradus ad Parnassum in 1725, codifying basic contrapuntal principles of Renaissance music.

    William Smith — a rural surveyor, in 1799 drew a colorful map of the subterranean rock strata of his county in English coal country, launching the modern science of geology.   

    Meriwether Lewis — kept extensive journals of the 1804-1806 Lewis and Clark Expedition, documenting and illustrating the discovered new world of the Northwest.  

    Dmitri Mendeleev — devised a “periodic table of the chemical elements,” published in 1869, providing a solid basis for modern chemistry through its graphic and organizational genius.

    Amédée Mouchez — launched an ambitious international star-mapping project (Carte du Ciel) in 1887 at the Paris Observatory.

    Henrietta Swan Leavitt — worked at the Harvard College Observatory as a “computer,” examining thousands of photographic plates from telescopes to measure and catalog the brightness of stars, identified 1777 variable stars.

    Lawrence Herbert — invented the Pantone system in 1956 to systematize color for printing ink and fabrics.

    Allen Forte — published an article in 1964 that launched musical set theory, defining, classifying and comparing all possible collections of “pitch classes” drawn from the equal-tempered 12-tone chromatic galaxy.

    The work and insights of the two on the list representing rigorous study of music, Fux and Forte, were part of my formal education in music and later an integral part of my teaching of composition and music theory.

    Maps

    Carte du Ciel was an ambitious second phase of an international star-mapping project initiated in 1887 by Paris Observatory director Amédée Mouchez.  A new photographic process revolutionizing the gathering of telescope images inspired the first phase, the Astrographic Catalogue of a dense, whole-sky array of star positions. Carte du Ciel, never completed after 70 years, used the Catalogue as a reference system for a complex survey of the vast field of even fainter images.

    Celebrating the grand metaphor relating astronomy to art music, here is my 8-minute computer-music sound sculpture. In the music, ghostly wisps of sound are punctuated by brighter bursts, clustered in a natural, not-quite randomly dispersed texture.

    _______________

    Looking ahead

    The blog-post chapters of Mapping the Music Universe will proceed in three broad phases, progressing logically from fundamental — time and periodicity — to pitch space, then to larger structures, texture and form. Within each phase, various topics are presented in a progressive order, but jumping in at any point is fine.

    Terms will sometimes be freshly coined. Graphic figures will include notated musical examples, tables, and graphic illustrations of patterns and their relationships. Big Ideas — Periodicity, Complexity, Symmetry, Relativity — will be explored using precise mathematical arrays as well as broad metaphors. Newly composed sample etudes will illustrate aurally.

    Along the way, “Map Labs” will present step-by-step recipes to compose simple pieces based on models of different compositional genres. Each Lab includes an original sample piece following the Map Lab guidelines, illustrating one possible creative outcome.

    Welcome! Join this creative journey of discovery . . .

    a composer’s expedition.

    © 2026 – All Rights Reserved

    Thomas S. Clark

    –

    Continue reading Mapping the Music Universe:

    1. TIME

    _____________

    TClarkArtMusic.com

  • journal 21. Constellations

    Texas Hill Country, 2021 —

    Retiring as a college music dean in 2020, I turned to writing. Long interested in astronomy, and reading about various sciences, I discovered ground-breaking pioneers who had methodically and comprehensively mapped the possibilities of their particular field — cartography, astronomy, chemistry — and the meticulous journals of Lewis and Clark’s Expedition of Discovery. Inspired by them, my music-mapping Periodicity Project began in 2021 as a comprehensive catalog of musical patterns and processes, meant to provide simple tools for understanding the complexities of modern music. It grew into a book, Mapping the Music Universe, written for anyone curious about how music works, especially in the 20th-21st-century modern and post-modern eras. It is my exploration of how some less traveled conceptual paths lead to musically interesting creative possibilities.

    Mapping the Cosmos

    Along the way, Mapping the Music Universe produced several small etudes to illustrate the compositional potential of musical patterns explained in the book. The inspiration to collect them into a series came from many years of fascination with Bartók’s wonderful Mikrokosmos series of piano pieces in modern styles. Here are two of my favorites to play and to teach:

    Mikrokosmos Vol. 4, No. 101

    Lajos Kertész, piano

    LISTEN on YouTube

    Mikrokosmos Vol. 4, No. 109

    Lajos Kertész, piano

    LISTEN on YouTube

    Book I of my Mapping the Cosmos contained seven etudes originally sketched for piano. The five in Book II were adapted from more complex textures. The seven of Book I are simpler, each etude titled with an astronomical entity named for a mythological character.

    Here are four from Book I that are named for constellations.

    Pisces – The Fish; 12th constellation of the Zodiac

    Cygnus – The Swan; a northern constellation

    Pleiades – Seven Daughters of sea-nymph Pleione; an open star cluster

    Scorpius – The Scorpion; 8th constellation of the Zodiac

    Here are all seven in more colorful sound synthesis:

    Mapping the Cosmos – Book I

    Clark 2023 (TC-114)

    all seven synthesized

    Cassiopeia

    In Journal episode 9, I described a compositional process I began exploring in the 1980s. Inspired by Larry Austin’s groundbreaking Canadian Coastlines, I began tracing natural patterns onto graph paper. Particular points on the graph yielded 2-dimensional coordinate values that could be interpreted as timing and pitch information. The first patterns were shorelines, making the initial sketches for PENINSULA (1984, TC-50).

    Having always been interested in astronomy, I then tried plotting star constellations on two-dimensional matrix graphs. The coordinates of each star in a constellation could be interpreted as time-point and pitch information, resulting in a complex arpeggiated group of notes. More intriguing was the capability to rotate the map, resulting in many possible variants that stretch or compress the rhythm and chord structure.

    The first compositional product of the star map work, LIGHTFORMS 1 – Constellations (TC-65), scored for piano, was published by Borik Press in 1992. Naming these patterns, pitch-time chord arpeggios, as constellations became a breakthrough concept.

    Arvo Pärt: Für Alina (1976)

    The constellation Cassiopeia in the northern sky is named after the vain queen Cassiopeia, mother of Andromeda in Greek mythology. One of 48 constellations listed by the ancient astronomer Ptolemy, its distinctive ‘W‘ shape is formed by five bright stars. Cassiopeia contains some of the most luminous stars known, including three hypergiants. Its brightest star, Cassiopeia A (“Schedar”), is a supernova remnant and bright radio source.

    The music arose from tracing a map of its brightest points of light. The coordinates of these points on a two-dimensional graph were converted into time and pitch patterns articulating a grand sonority. The graph can be rotated, kaleidoscopically transforming the pattern into similar sonorities.

    PERSEUS

    CASSIOPEIA

    CEPHEUS

    ROTATED 90 degrees

    The same treatment applied to Cassiopeia’s constellation neighbors Perseus and Cepheus builds a denser field of sounds. All this elaborate graphing and plotting may seem too complex and too abstract. The process, however, resulted in an intentionally abstract musical experience that metaphorically echoes the awe of viewing the brilliant star-studded dark sky through a powerful telescope.

    CASSIOPEIA

    Clark 2025 (TC-157)

  • journal 20. Effulgence

    San Marcos, 2018 —

    “Radiant, resplendent light” . . . a word more poetic than scientific.

    I first wrote a simple canon in 1977 as Sunday morning background music with coffee. A line of glowing tones rises then falls back, then rises higher and back down again. The same line is echoed against itself, a canon building sloping hills and mountain ridges of blending overtones. Almost 40 years later, cellos became the climbers.

    Rainbow Rising

    Clark 2016 (TC-83)

    Texas State cello students
    Boris Chalakov, Joshua Adams,
    Terri Boutte, Simon Reid,
    Anna Trevino, Gabriel Vazquez
    February 6, 2018 at Texas State Univ.

    Back to Czech-American composer Karel Husa. In 1992 I met him in Brno while attending the International Music Festival, for which he was the celebrated guest coming home for the first time since the Czech revolution opened the country after 40 years of Soviet oppression. Later as a professor studying and teaching contemporary music, I discovered his magnificent third string quartet, winner of the 1969 Pulitzer Prize. To me, its rhythmic energy, expressive intensity, and superb craftsmanship make it a work epitomizing the best of modern art music in the third quarter of the 20th century.

    I have used all the possibilities hitherto available. The forms of the four movements are few, based mostly on contrasting colors and inner tension.”

    LISTEN ›

    Smyčcový kvartet č.3

    Fine Arts Quartet

    Streams, shores, trails

    We started this journal with my story of growing up in rural Livingston County Michigan, next to a small river and surrounded by woods and farm fields. Hiking through this nature-scape in all seasons (especially fall), in all weather, in sunshine and in moonlight, became my lifelong habit for 60 years.

    A forest path or a sandy shoreline are physical analogs to a musical line, a melody.

    A line can weave a complex fabric with echoes of itself. My compositional fascination with musical canon began in the early 1970s with study (at the University of Michigan) of Johannes 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 1984 I composed an improvisatory piece for my UNT New Music Performance Lab. EFFULGENCE (the word means “brilliant, shining radiance”) was in the style of Terry Riley’s famous In C, overlapping repetitive patterns that I call “multi-phase ostinato” music. EFFULGENCE employs a canon treatment of differing-length motives to create the constant overlapping of patterns out of phase with other lines. The result is like the rhythmic dance of a fountain.

    EFFULGENCE

    Clark 1994 (TC-49)

    Light and shadow

    In 1985, a wind ensemble piece, OF LIGHT AND SHADOW: Two Canonic Sketches, was a more formal canon construction. Other contrapuntal writing surrounds an extended canon in a 2021 string quartet, Dark Matter.

    Now canon pervades much of my 21st-century writing, a challenging yet stimulating and gratifying approach to texture and continuity of material. Black Canyon (2024, TC-140) is included in both Canyon Sketches (TC-141) and in Book of Canons (2024, TC-148). The title comes from my photographic memories of the Black Canyon of the Gunnison River, named for the ever-present shadows the narrow canyon’s steep, sheer, tall rock walls cast on the river flowing far below. The sheer cliffs of the Black Canyon are metamorphic Precambrian gneiss and schist, streaked with thin, brighter-colored layers of pegmatite. These streaks sketched on the darker rock look like maps of ancient contrapuntal lines, suggesting a simple musical canon in four voices that builds the fabric of Black Canyon.

    Cesty světla

    Book of Canons collects 14 excerpts from these works, showing each canon’s subject, points and pitch levels of answer, and sounding each excerpt scored as a string trio. Forest Paths stitches them together in an ambling journey along a path through a metaphorical sound environment of sunlight, shadows, and leaf-fluttering breezes.

    Forest Paths

    Clark 2022 (TC-123)

    Salem Lake, North Carolina
    San Marcos Texas
    Spilberk Castle, Brno
    Montana
    Blanik massif, Bohemian-Moravian Highlands
    Prague
    Camp Michigania – courtesy of Michigan Alumni Assoc.

    ___________

  • journal 19. Hudba pro Lidice

    Prague, 2017 —

    With cutting-edge contemporary idioms, Czech-American composer Karel Husa’s music expresses superbly the drama and beauty of Czech culture and history. I first became aware of his music when I heard the University of Michigan Symphony Band premiere his powerful piece, Hudba pro Prahu 1968, commemorating the 1968 Soviet military occupation of Czechoslovakia.

    LISTEN ›

    Music for Prague 1968

    Univ. of Texas Wind Ensemble

    Twenty-some years later, I met him in 1992 in Brno while performing again at the International Music Festival. He was the more celebrated guest, coming home for the first time since the Czech revolution opened the country after 40 years of Soviet oppression.

    A Peaceful Place

    Elizabeth and I first visited the Czech village of Lidice on our visit to Prague in the fall of 2017. The phrase, “a peaceful place,” is from the poem, “The Murder of Lidice” by Edna St. Vincent Millay.

    A charming Czech village, Lidice was brutally destroyed by the Gestapo in 1942. On June 10, all the village men were shot, the children taken away to orphanages or gas chambers, the women sent to concentration camps, and the entire village was razed.

    For history, photos, and insights into the Lidice atrocity, go to Elizabeth Cernota Clark’s blog, Lidice Lives.

    My music expresses the dark brutality of the atrocity.

    Lidice Remembered

    Clark 2017 (TC-86)

    Live performance February 6, 2018, at Texas State Univ. Performing Arts Center

    Texas State cello students Boris Chalakov, Joshua Adams, Terri Boutte, Simon Reid, Anna Trevino, Gabriel Vazquez

    Rainbow

    Though horrible tragedy struck this place, now the sloping lawn and babbling creek are a safe haven to peaceful spirits. Looking for the Rainbow, a sequel to Lidice Remembered, continues in complex rhythmic counterpoint of darker sonorities, evoking a restless spirit of searching, anticipating. Written during the COVID pandemic for Karla Hamelin and her Texas State cello students, Looking for the Rainbow expresses both the uncertainty and hopefulness in our collective struggle to survive the storms of disease and violence. A beautiful memorial rose garden in Lidice celebrates the transformative power of hope.

    Looking for the Rainbow

    Clark 20121 (TC-111)

    Where My Home Is

    “Kde domov můj“

    national anthem of the Czech Republic

    After the war, concerned British citizens led by Sir Barnett Stross convinced the world that the village should be rebuilt. The women of Lidice were able to return and were given beautiful new Czech-style homes in a planned village next to the Memorial Gardens.

    Another piece celebrates this hopeful outcome of the story. A New Lidice is scored for SSAA treble choir and string trio. Lyrics are taken in part from a stirring Stross speech, but the voices are those of the women who bravely rebuilt their community.

    A New Lidice

    Clark 2019 (TC-97)

    Texas State Aurora Voce, Lynn Brinckmeyer cond.
    with string students Kailey Johnson, Kelsey Sexton, Tina Moritz

    “We build a new village, while a just world watches.

    “Stavíme novou vesnici. Spravedlivý svêt bude sledovat.

    “Lidice belongs to the world of all who suffered.

    “Mankind has one common enemy – War.

    “Only a realization of our common humanity can save mankind.

    “The just world will watch.”

    ___________

  • journal 18. Autumn Rain

    San Marcos, 2016 —

    The style that we now hear as the sound of America in the 20th century — where did it come from? Before Henry Cowell or Aaron Copland, before Lou Harrison or John Cage, it came from the bold, eccentric music of Charles Ives.

    Ives not only created the musical sound of 20th-century America, he wrote about American life, literature, and places. His Piano Sonata No. 2, Concord, Mass., 1840–60 (1915)explores the ethos of New England writers in its four movements:

    1. “Emerson” (after Ralph Waldo Emerson)
    2. “Hawthorne” (after Nathaniel Hawthorne)
    3. “The Alcotts” (after Bronson Alcott and Louisa May Alcott)
    4. “Thoreau” (after Henry David Thoreau)
    LISTEN ›

    Ives – Concord Sonata

    Stephen Drury on YouTube

    One of Ives’ most performed and well-known works is Three Places in New England (1914) for orchestra. Each “place” is a musical sketch of a place’s unique atmosphere, painting a picture of life at the dawn of 20th-century America. It epitomizes the unique style that established Ives as an icon of American music in the 20th century.

    That style, which built what became the defining sound of American music, featured:

    • sound masses of dissonant tone clusters
    • chaotic layering of multiple simultaneous tunes
    • huge, sudden contrasts of loudness and texture

    The movement sketches are subtitled:

    1. The “St. Gaudens” in Boston Common (Col. Shaw and his Colored Regiment)
    2. Putnam’s Camp, Redding, Connecticut
    3. The Housatonic at Stockbridge
    LISTEN ›

    Three Places in New England

    Cleveland Orchestra on YouTube

    Frost

    If Charles Ives is the iconic composer of 20th-century America, Robert Frost is the iconic poet. I became an ardent admirer of Frost’s writing as early as 1966, reading his complete works by the time I was in grad school. Two poems had a profound early impact on my spirit and sense of artistic possibility. “Mending Wall” (1914) and “The Road not Taken” (1916). To me, the latter is wondering about looking into the uncertain future, expressed in a woodland metaphor typical of Frost that resonated with my rural Michigan youth. (That is probably why I quoted it in my very first public speech, my valedictory address at the 1967 Howell High School commencement ceremony.)

    “THE ROAD NOT TAKEN” excerpt

    Two roads diverged in a wood,
    And sorry I could not travel both
    And be one traveler, long I stood
    And looked down one as far as I could
    To where it bent in the undergrowth;

    Fast forward to 2016, when my colleagues Ian Davidson, Ames Asbell, and Vanguel Tangarov at Texas State asked me to write an unaccompanied solo for each of their instruments, oboe, viola, and clarinet. As the Pleasant Street Players, they recorded what was to be a whole album of my music, including a duo, two quartets, and a quintet for their trio plus guest colleagues. The recording project was exciting and bore excellent musical results. But it slammed into the COVID epidemic and could never be finished and published.

    Here is what its roster of 7 tracks would have been:

    Snow and rain

    Two memories of walking in the snow stand out in long-term memory. In about 1965, one recreation of a restless Michigan teenager on winter nights was to put on boots and parka and hike through snow-covered fields and forest in the moonlight. In 1992, my composer friend Arnošt Parsch led me on a walk into the logging forest above his Moravian village, Bílovice nad Svitavou. Through late-fall snowflakes, we retraced the steps of Janácek, passed the natural-spring well and the Sokol tavern up to a beautiful promontory view of the snow-covered village below.

    Sur la Neige is a snow fantasy on three quoted musical ideas. The work begins with an obscure quote from Stravinsky’s L’Histoire du Soldat, elaborated and then transitioning into a quote from Debussy’s Prelude No. 6 in his Préludes, Book I, subtitled “de pas sur la neige.” Eventually, a small decorative figure from Janácek’s Sinfonietta appears and quickly disappears like a scurrying bystroušky (fox).

    In each poem below, I will boldface some of the imagery that particularly inspired ideas for sounds, rhythms, and mood.

    Frost’s first poem that I set to instrumental music in 1973 was his 1913 “My Noember Guest,” an exquisite expression of loss and sadness.

    “MY NOVEMBER GUEST” excerpt

    My sorrow, when she’s here with me,
         Thinks these dark days of autumn rain
    Are beautiful as days can be;
    She loves the bare, the withered tree;
         She walks the sodden pasture lane.

    She’s glad the birds are gone away,
    She’s glad her simple worsted grey
         Is silver now with clinging mist.

    The desolate, deserted trees,
         The faded earth, the heavy sky,

    In 1971 in Ann Arbor, I wrote Autumn Rain for oboe and piano. Much of its melodic material was incorporated into the solo English horn piece for Ian in 2016. Its four movements:

    • “these dark days of autumn rain”
    • “my sorrow” (remembering Lidice)
    • “the bare, the withered tree”
    • “the sodden pasture lane”

    The second movement’s memorial to the atrocity of Lidice quotes the Czech national anthem Kde domov můj (“Where My Home Is”). Other musical material expressing darkness, death, and perseverence is a quote from the Lux aeterna of Mozart’s Requiem.

    AUTUMN RAIN

    Clark 1971 / 2024 (TC-85)

    The solo clarinet piece was based on this Frost poem:

    “BIRCHES” excerpt

    I’d like to go by climbing a birch tree,
    And climb black branches up a snow-white trunk
    Toward heaven, till the tree could bear no more,
    But dipped its top and set me down again.
    That would be good both going and coming back.

    Musical material quotes the beginning of Bartok’s powerful fugue in Music for Strings, Percussion and Celeste. The fugue theme is scored for the orchestra’s viola section, but in Bending Birches I’ve placed in the beautifully dark chalumeau register of the clarinet.

    BENDING BIRCHES

    Clark 2018 (TC-89)

    The viola piece, Before I Sleep, began as a solo based on this 1922 poem:

    “Stopping by Woods on a Snowy Evening”

    Whose woods these are I think I know.
    His house is in the village though;
    He will not see me stopping here
    To watch his woods fill up with snow.

    My little horse must think it queer
    To stop without a farmhouse near
    Between the woods and frozen lake
    The darkest evening of the year.

    He gives his harness bells a shake
    To ask if there is some mistake.
    The only other sound’s the sweep
    Of easy wind and downy flake.

    The woods are lovely, dark and deep,
    But I have promises to keep,
    And miles to go before I sleep,
    And miles to go before I sleep.

    Some of the imagery (again boldfaced above) lends itself to ideas for sounds, rhythms, and mood. The solo viola piece is titled Before I Sleep.

    BEFORE I SLEEP

    Clark 2018 (TC-90)

    Concord

    If Charles Ives was unapologetically brash, his music could also be lyric and transcendent, a gentleness akin to the contemplative voice of Robert Frost. Back to Concord . . .

    Concord Sonata – 3. “The Alcotts“

    Jeremy Denk on YouTube

    After the demise of the Pleasant Street album project, the three solo pieces began to come together, merging into a single piece for viola and strings. The result embodies the expressive and sonorous essence of the whole Frost stream of work from 1973 to now.

    FROST SERENADE

    Clark 2024 (TC-145)

    ___________

  • journal 17. First Light

    McDonald Observatory, 2010 —

    When a new telescope is commissioned and opens its optics for the first time, it captures its “first light.” I got up close below the 10-meter Hobby-Eberly Telescope on Mt. Fowlkes at the McDonald Observatory in the Davis Mountains just a few years after it was commissioned.

    When Texas State University opened its new Performing Arts Center, the 2015 inaugural concert in the acoustically splendid Recital Hall was a program metaphorically titled “First Light.”

    Magic song

    An older “First Light” reference is to native American mythology, which tells origin stories of the First People who emerge from the Dark World into the light of the rising sun (the Blackfoot sun god is called Natosi). In Navajo mythology, “Early on the morning of the fourth day, Little Dawn Boy began to sing his magic song. As he finished the song, an arch of shimmering light, all rose, violet, blue, and every color, and delicate as a veil, began to stretch from the summit of the purple mountain to the top of the white cliff. He then saw a bright rainbow bridge grow before his eyes. Singing with delight, he hastened over the Rainbow Bridge. As he ran a wind sprang up and blew a many-colored mist to the top of the cliff.” [First People: American Indian Legends]

    First Light

    Clark 2018 (TC-93)

    Gas giants

    Gustav Holst’s The Planets (1917) is revered for its masterful orchestration evoking the majesty of the solar system. The final movement portrays the dim, distant last light we can see in it — the planet Neptune’s pure, mystical light.

    LISTEN ›

    The Planets – NEPTUNE

    Royal Liverpool Philharmonic

    We all enjoy the mysterious splendor of moon rise, large and deeply-hued in the eastern evening sky. My sonic metaphor for that visual phenomenon portrays instead the rising of Jupiter, the largest object in the solar system other than the sun itself. It only looks much, much smaller to us than the moon because it is so much farther away.

    One of my favorite Mozart symphonies is Symphony No. 41 in C Major, K.551. His longest and last symphony, it is nicknamed “Jupiter” — fitting that his lengthiest and greatest symphony is named for the largest planet, a great gas giant. A vivid musical motive begins and generates the majestic final movement.

    I relentlessly deploy that motive as the canonic subject for Jupiter Rising. My rhythmic setting of the motive is designed irregularly, so that the two lines seldom move at the same time in what I would call a contrapuntal accent. This creates a floating quality of the contrapuntal rhythm. At some moments, as many as eight contrapuntal soundings overlap each other in a cloud-like texture.

    One refreshing feature of a sound sculpture is this freedom from the metric march of time. The music does not progress, but instead creates a sonic cloud to be experienced by relaxed absorption and contemplation.

    Jupiter Rising

    Clark 2020 (TC-103)

    The largest of Saturn’s moons is also the second largest moon in the Solar System. Its dense atmosphere obscures a unique feature: it is the only place beyond Earth on which clear evidence has been found of stable bodies of surface liquid.

    That may be partly why an experimental extreme-depth earth-ocean submersible vehicle was named for it. The Titan submersible famously imploded in 2023 while headed down to view the shipwreck of the Titanic in the cold North Atlantic.

    Our imaginary musical exploration of the moon Titan, its atmosphere and ocean depths, is completely tranquil, experiencing only gentle waves and currents of dark and brighter sonorities.

    Titan Sea

    Clark 2023 (TC-135)

    Nebula

    Far beyond our solar system, nebulae are where other stars and planetary systems are formed from collapsing clouds of gas and dust. One of the most familiar and well studied objects in space, the Orion Nebula is enormous, 24 light-years across with a mass of about 2,000 times that of the Sun.

    Debussy’s “Nuages” (Trois Nocturnes, 1892-99) depicts earthly clouds as gently undulating, colorful orchestral lines and chords. For a soundscape of cosmic nebulae, my generating concept is similar: a slow, almost timeless metamorphosis of complex 4-pitch constellations, some bright, some darker “celestial” harmonies.

    NEBULA

    Clark 2024 (TC-139)

    ______________

  • journal 16. Thermal Energy

    San Marcos, 2012 —

    Pondering the physics of molecular heat energy applied metaphorically to music . . .

    Lower to higher energy of musical masses comes from four factors: Tempo — standing stillness to frenetic pace; Rhythm — regular pulse to unpredictably varied; Textural rhythmic alignment — synchronous to random; Loudness — hushed to explosive.

    Starting with low-energy, low-temperature continuous cool sound, listen to a favorite piece by my late colleague, co-author and friend, Larry Austin. His 1982 score for double bass quartet is“dedicated to my friend and mentor, John Cage, in his seventieth year”. I describe it in my book:

    “The harmonies sounded by ambient counterpoint will all consist of only the pitch classes C, A, G, and E, created by scordatura open strings and harmonics. And the open-ended improvisational nature of the work, expressed by an artistically drawn matrix score, is an obvious and elegant homage to Cage’s deep interest in chance and open form.”

    Thomas Clark —

    Larry Austin: Life and Works of an Experimental Composer

    (Borik Press, 2012)

    In gentle sustained tones, the texture moves continuously through a matrix of sound projecting a subtly changing but almost steady-state sonority. Very low temperature music . . .

    LISTEN ›

    art is self alteration is cage is …

    Robert Black, bass

    Water sounds

    The many bodies of water figuring prominantly in my life include:

    • Shiawassee (rural Michigan)
    • Huron (Ann Arbor)
    • Lake Michigan (Leelanau)
    • Puget Sound (Seattle)
    • Lake Spanaway (Tacoma)
    • Lake Texoma (Texas)
    • Vltava (the Moldau, Prague)
    • Green Lake and Duck Lake (Interlochen)
    • Lake Ray Roberts (Texas)
    • Albamarle Sound (Outer Banks)
    • Salem Lake (Winston-Salem)
    • Gulf of Mexico (Port Aransas)
    • San Marcos River (San Marcos)

    Inspired by the great serenades for strings of Dvořák and Tchaikovsky, my string serenade explores musical metaphors for the physics of water in interesting atmospheric and geographic settings.

    Three States of Water

    Clark 2021, TC-107

    I. Cold front (VAPOR becomes SOLID)

    In low clouds on mountain tops, water vapor can become super-cooled and become freezing fog, filling the air with small ice crystals and freezing to surfaces, similar to very light snow. In the western United States, the common name for freezing fog is “pogonip.”

    II. Ice Dunes (SOLID)

    In the Leelanau Peninsula of Michigan, the Lake Michigan surf sometimes whips up and freezes in mid-air, forming weird ice caverns and ice dunes.

    III. Nuages (VAPOR)

    French for clouds, Nuages is one of Debussy’s three beautiful Nocturnes for orchestra, quoted here as a theme for variations. Water vapor is technically invisible. The clouds we see are actually masses of minute liquid droplets and frozen crystals. Thus this movement embodies all three states of water.

    IV. Vltava (LIQUID)

    The great river Vltava flows majestically through Prague. Smetana’s depiction of it in his monumental Ma Vlast is usually translated as The Moldau.

    Quarks

    The aggressive rhythmic character of the opening part of Joseph Schwantner’s 1980 piece is an opposite to the serenity of Austin’s art is self alteration is cage is . . . Boiling heat:

    LISTEN ›

    Schwantner Percussion Concerto

    U.Mich. Symphony Band

    Modern physics understands that all matter is built up from just five fundamental “particles”: electrons, up quarks and down quarks with electrical charge; and gluons and photons with no electrical charge. They are not exactly particles, though, but infinitesimal points of spin in space/time.

    That’s where the next sound composition experiment began. Two 4-pitch segments of the octatonic scale appear (“quarks”), then spin at their own speeds, while smaller 3-pitch sets (“electrons”) spin above and below them. At times, the sound mass explodes with a shower of electron sparks, then reforms.

    More clouds! We had Nebula, clouds of gas and dust in space, then Nuages, puffy white clouds in a blue sky. Now storm clouds . . .

    Meteorology

    Clark 2022 (TC-121)

    Nimbus

    While quarks are hard to imagine and impossible to visualize, we love to watch puffy white cumulus clouds. Their kinetic energy becomes more visible when they grow into dark, precipitation-bearing cumulonimbus storm clouds, bringing rain and crackling electricity.

    Squall

    A tree limb branching out from a trunk, then smaller limbs branching from it, again and again to smaller and smaller branches — a classic example of a recursive process. Sometimes lightning shows this same recursive branching process. While the tree branches take years to fill out, lightning is a sudden explosion of electricity over a split second. Thunder, as sound travels much slower than light, is heard later than the lightning flash is seen — unless, of course, it is very close by!

    ______________

  • journal 15. Seven angels

    Raleigh, NC 2007 —

    In Zuni origin mythology, according to Wikipedia, thunder sounded, and all The People climbed from darkness, emerging into the daylight world. Seeing the Sun (Awonawilona) and not used to such intense light, they cried. Where their tears fell, sunflowers sprang from the earth.

    Angels of Bright Splendor was the second in a series of pieces about angels that began seven years earlier with The Fourth Angel, computer music with optional instruments.

    Angels of Bright Splendor

    Clark 2013 (TC-78)

    The Fourth Angel portrays an image from the Biblical book, Revelation. The seven angels in chapter 16 inflict suffering upon humanity. It was commissioned and premiered in 2007 by the Arts Now Series at North Carolina State University in Raleigh, directed by Dr. Rodney Waschka II. The commission was for an artistic contribution to The Ericka Fairchild Symposium on Climate Change.

    The title refers to one of the “seven last plagues” as they were called in the King James Version of the Bible. In the NRSV translation, Revelation16:8 reads:

    “The fourth angel poured his bowl on the sun,

    and it was allowed to scorch people with fire;

    they were scorched by the fierce heat.”

    The Fourth Angel

    Clark 2006 (TC-77)

    The other six angels and their bowls wrought plagues of painful sores, bloody seas, bloody rivers, darkness, a dried up Euphrates, and finally the seventh angel’s loud voice pronouncing, “It is done!” Standing in the middle of the sequence, the prophecy of the fourth angel is a dramatic metaphor for global warming.

    Animus

    Though there are some literal sound references, the fourth angel is portrayed more broadly as a metaphor for the forces of nature. Rather than capturing actual samples of nature sounds, however, the computer-generated sounds are all synthesized, musical objects constructed employing a now-common computing technique called grain-table synthesis.

    The choice of machine synthesis over nature sampling suggests a particular belief about the causes of global warming. These synthetic sound images form a broad range of simple and complex musical rhythms and textures evocative of the natural world: sunlight reflected off water and ice, glaciers calving and cascading into the ocean, solar radiation, and night sounds. Extending the metaphor, sounds echo and swirl in sound space, just as do the dynamic, powerful weather systems that shape our global climate.

    In the 1970s as part of Contemporary Directions at U. Mich., I specialized in performing new and experimental works for solo trombone, with and without electronic tape sounds. Animus I (1967) by Jacob Druckman was a fascinating challenge, combining advanced trombone-playing techniques with a complex, pre-recorded and graphically-notated electronic tape part. The music portrayed an increasingly antagonistic interaction between humans and machine technology.

    Druckman – Animus I

    Thomas Clark, trombone

    The last angel

    Global warming is already devastating the earth and all life on it. Going back to Revelation and its seven frightening angels, we read that the last one pours out the voice of doom.

    Revelation 16: 17-20 — Then the seventh angel poured out his bowl into the air, and a loud voice came out of the temple of heaven, saying, “It is done!” And there were noises and thunderings and lightnings; and there was a great earthquake, such a mighty and great earthquake as had not occurred since men were on the earth. Then every island fled away, and the mountains were not found.

    A musical statement about all this required “pulling out all the stops.” The electronic sounds of The Fourth Angel and Angels of Bright Splendor make layered counterpoint for a dark, unearthly montage. String Theory, originally imagining spinning subatomic energy, provides an ironically human voice, both frantic, engulfed in the threatening sound environment, and soaring hopefully above it.

    The final Angel

    Clark 2025 (TC-156)

    _______

  • journal 14. Pi, Primes, Palindromes

    Blue Ridge Mountains, 2005 —

    In 2005 through 2008, I lived in North Carolina only an hour away from the Parkway. October Saturdays always involved a scenic drive up to the Parkway to absorb the glorious fall colors and trickling of secret waterfalls. So many wonderful waterfalls, I recorded many videos, mostly for the sound.

    Falling Water

    Clark 2016 (TC-82)

    Concrète

    Some of the earliest electronic music compositions in the 1950s were called “Musique concrète” because they used recorded “real” sounds instead of electronically produced ones.

    LISTEN ›

    Etude aux objets

    Pierre Schaeffer (1959)

    Back to planets, spheres . . .

    Ever since it was viewed and photographed from space by Apollo 17 in 1972, Planet Earth has become known as the Blue Planet.

    The Blue Marble photograph of Earth, taken by the Apollo 17 mission. The Arabian peninsula, Africa and Madagascar lie in the upper half of the disc, whereas Antarctica is at the bottom.
    The Blue Marble

    Such a distant perspective reveals the pervasive blue water of oceans, brilliant white of cloud layers, and some brown/green shapes of land masses beneath.

    Magic of Pi

    It also reveals the spherical shape of our globe. (Euclid said a sphere is a hollow 3-dimensional rotation of a circle, and scientists have measured that Earth is not a perfectly round ball but a solid ellipsoid.) Nonetheless, the eternal, perfect rotating sphere is our iconic notion of Earth’s shape.

    Spheres and the Euclidean circle that generates them in three dimensions are governed by the mathematical constant π, defined in Euclidean geometry as the ratio of a circle’s circumference to its diameter.

    Pi is magic, an irrational number that cannot be expressed as a common fraction. Its decimal calculation never ends, never settling into a repeating pattern of digits, which appear to be random . . . and infinite. It starts 3.1415926535897932384626433 . . .

    The beginning of its decimal expression — 3 1 4 1 5 9 — was used in composing Blue Sphere as both a rhythmic timing pattern and a corresponding dance of the lowest 9 pitches of a Pythagorean overtone series.

    This is one way to literally hear π, expressing musically the eternal restlessness of our rotating blue sphere, its tides, weather, techtonic plates, etc.

    Blue Sphere

    Clark 2022 (TC-119)

    Prime numbers

    Back to the “real” sounds of musical instruments . . .

    Included in my “Animated Landscapes” Sketchbook for small orchestra, Appalachian Autumn (2024, TC-142) by its title pays homage to Copland’s 1944 masterpiece, Appalachian Spring. My currently developed harmonic sensibilities resemble Copland’s open, bold sonorities. In my composition studies in the 1970s, I was fascinated by Appalachian Spring the ballet as originally scored for only 12 orchestral instruments. This original scoring was a masterpiece of orchestral painting blended with the clear contrapuntal lines of chamber music, highlighting each instrument’s colorful voice.

    LISTEN ›

    Appalachian Spring

    Perspectives Ensemble

    The number 12 is interesting in that it is readily divisible in four different ways with just whole numbers (integers). A set of 12 items can be divided neatly into two groups of 6 items each, three groups of 4 each, four groups of 3, or six pairs. That relates to common musical meter signatures of 2, 3, 4, or 6 beats per measure that break down into equal subdivisions.


    A prime number is interesting in that it cannot be divided without fraction by any whole number. There are theoretically an infinite number of prime numbers, but the smallest that are useful for our pattern purposes are 1, 2, 3, 5, 7, 11, 13, 17, 19, etc. The only even prime number is 2; taken out, it leaves an interesting set of odd primes, 1 3 5 7 11, that as time chunks make rhythms that do not break down into subgroups, seeming to float rather than march.

    example from Appalachian Autumn

    In this illustration, the durational note values are measured below in number of eighth-notes of time. Melodic intervals are measured above in number of semitones (“half steps”). Both the intervals and the duration values measure in only prime numbers. That means though the passage is written in 4 4 time, no measure breaks down into half-measure subunits; and no duration note value is immediately repeated. The rhythm cannot be felt as marching quarter notes in half-note pairs, and even some of the downbeats avoid being moments marked by a new note. The rhythm floats, like the curving Blue Ridge Mountains skyline.

    Palindromes

    The basis for pitch organization in Appalachian Autumn is the following 12-tone row:

    Identified above the line, the serial intervals from one pitch to the next measured in semitones, form a symmetrical pattern. The sequence is identical backwards as forwards — a palindrome!

    By this calculated means, melodic lines and sonorities float through different pitch-set collections suggestive of different scales and tonalities. This continually morphing tonal feel is an Impressionistic reflection of the many shapes and hues of that famous blue skyline on the Blue Ridge Parkway.

    Appalachian Autumn

    Clark 2024 (TC-142)

    ______________