MAPPING MUSIC

Tag: Impressionism

  • MapLab 8. A Small Sonata

    Sonata is typically a multi-movement piece for solo piano or an instrument with piano. A shorter form with just three connected sections, the middle slower and quieter, can be called a sonatina.

    An inside look at how one was composed gives a guided tour in the form of a recipe to write your own sonata.

    1. Choose a model

    I started formal composition study in 1968, first with composer Eugene Kurtz, based in Paris but filling in that semester at the University of Michigan. A proponent of modern French music, his compositional models included Debussy and Ravel. He assigned me to immerse myself in deep study of their music, in particular Ravel’s 1905 work, SONATINE.

    I met Beth, a flower lover, in Interlochen in 1975. She had been a promising flute student at Aspen, but was then embarking on a journalism career specializing in horticultural writing.

    The Ravel study came back to me later in my career, as I began to adopt its lush, bright harmonic language and a gentle French Impressionist quality. My SONATINE for Beth (2025) brings together the Ravel study, the flute sound, and (in my video version on YouTube) even the flower motif.

    2. Start with a generating idea

    The impelling theme can be a melody, a rhythmic pattern, a special kind of chord, or a non-musical image such as a painting or poem.

    Sonatine for Beth is spun entirely from a single harmonic progression, seven chords, each stacking one Perfect 5th interval above another.

    The Perfect 5ths in the two hands are separated by one or more octaves, highlighting this strong interval as a characteristic sound for the piece.

    Now some basic tools to develop and vary a generating theme.

    3. Transposition

    The whole five-chord progression can be transposed. The harmony is heard plainly in a middle section as ten block chords. The last five chords are a transposition of the first five, up three semitones, starting on the bass pitch Eb instead of C.

    Sequence is successive statements of a pattern transposed by a consistent interval.

    Here is another transposition of the whole ten-chord sequence:

    This harmonic material generates melodic lines and many arpeggio patterns, in successive variations of changing register, intensity, and rhythmic pace. Let’s go through the compositional unfolding of this thematic idea.

    4. Extract a melody and bass

    Since the starting idea is simply a chord progression, we can select individual tones from each chord for a melody. The most obvious selection is the highest pitch of each chord, even if it is not in a soprano singing range.

    At letter A the melody is given a slightly independent rhythm to help set it off from the chords, in addition to the different sound color of the flute. Also, the lower chord tones are articulated one at a time, making a bass line also rhythmically distinct, faster than the half-note chords. (The Bb in the bass line’s first bar is a passing tone, not a chord tone.)

    5. Add arpeggios

    An arpeggio is any pattern articulating chord tones one at a time. Usually in order lowest to highest or back down, the individual chord tones can be articulated in any order. At letter A shown above, we already saw the left hand articulate its chord tones one at a time. In the introduction, the right hand is partially broken up into arpeggios.

    In the next variation below, right-hand treble chord tones and still some bass chord tones are arpeggiated. Now all three lines (flute, right hand, left hand) have distinct rhythmic patterns, though congruent with each other in the established 4 4 meter.

    Next, the flute arpeggiates chord tones in eighth-notes, with the left hand simplified to quarter-notes of two pitches from each chord.

    6. Rhythmic variations

    Variation D simplifies the flute melody to just two half-note chord tones per bar.

    The two hands reunite rhythmically to place some chords after the downbeat and between flute notes.

    7. Counterpoint

    The original term, contrapunctus, translates “point against point” — two or more independent lines interacting in time.

    A more active rhythm for the flute line leaves time gaps that can be filled in by another line. The right hand selects chord tones to make a similarly playful rhythmic line that mostly alternates and sometimes lines up with the flute rhythm.

    The harmonic progression is still there but just hinted at by the chord tones selected for these interacting lines.

    Variation F continues this back-and-forth rhythmic interaction of the flute and piano right hand, now adding back in the left-hand chord-tone pairs with a simple rhythm for a supporting third contrapuntal line.

    8. Texture

    Having reached a complex level of three rhythmically interacting, independent contrapuntal lines, a nice contrast will be to simplify. Variation G reduces to a lower-register flute line and only a much simplified skeletal supporting line above it in the right hand.

    Then the texture begins to revert rhythmically to a simpler alignment of all chord tones.

    This paves the way back to a simple piano texture revealing the fundamental thematic chord progression.

    9. Shape a time form

    What is the plan for the whole? How will the various versions of the generating idea unfold in the larger time span of the whole piece?

    The quiet letter I variation is the apex of an arch form . . .

    • starting with simple
    • building up more rhythmic and textural complexity
    • reaching a stable plateau
    • subsiding back to what started it all.

    That sets up a recapitulation of the whole process, building up textural complexity again, first with the high two-part counterpoint:

    Then with three voices:

    Flute line “calming down”:

    10. Coda

    A good essay ends with a conclusion or a summary restatement of the thesis.

    Our musical coda summarizes with a last return to the beginning. The chords are back to their very low and very high registers. The flute makes a small melodic arch, ascending to the pitch B, then climbing down gently to its lowest possible pitch, C.

    11. Fine

    A final edit and audit are mandatory. In the case of our example, listening revealed that the beginning needed a piano introduction with some rhythmic vitality. Some sections were also reordered to improve the flow. Thus, the piece will not begin with a plain statement of the progression, and there will be a somewhat different order of other events.

    Now listen to the whole 6-minute parade of variations on a single chord progression.

    Sonatine

    –

    © 2026 – All Rights Reserved

    Thomas S. Clark

    Back to the beginning of . . .

    Mapping the Music Universe

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  • Mapping Music 9. LINE

    Think about levels of structure scientists study in our universe.

    They dive deep into atomic structure, below electrons spinning around a nucleus of protons and neutrons, discovering subatomic particles like the meson and boson. At the other extreme, they gather 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.

    “We are slowed down sound and light waves,

    a walking bundle of frequencies tuned into the cosmos.”

    — Albert Einstein

    Think about how artists build structures that establish a style  . . .

    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.

    Structure and Relativity

    Shrinking our metaphor from the vastness of the universe down to the physical immediacy of cloth . . .

    A woven fabric has a longitudinal warp and a perpendicular crossing weft. Part II explored the vertical-pitch “weft” of harmonic design. Now we return to the “warp” in music, longitudinal time streams of events. In keeping with our standard conception of time as horizontal and pitch as vertical, let’s name each longitudinal “warp” element:

    LINE — an element of a musical fabric consisting of a conforming stream in time of similar events (notes, pitches, colors, drum sounds, etc.)

    Now we can go back to “monody, homophony, polyphony” and at least identify how many lines are in a musical fabric, from one (monody) to many (polyphony). But to distinguish between homophony with its matching, rhythmically aligned lines from polyphony with its more diverse set of lines of different nature, we must distinguish different types of lines to determine the extent to which the lines of a polyphonic fabric “match.”

    There are limitless number of combinations of characters for a line and thus an infinite number of fabrics possible. We will stick to six parameters and simple observational characterizations for each parameter. Since we are swimming in the painting and weaving metaphors, we will color-code these six parameters. Each parameter will be distinguished with just two binary descriptors, a simpler or purer character or a more intense or complex character in that parameter.

    distinguishing parameters

    Since there are 7 parameters and two possible descriptors for each parameter, the total number of permutations is 2 to the 7th power = 128 possible combinations. That means, however, if there are two lines in the fabric, the number of possible combinations rises to 16,384 — plenty of choice for creative composing. And with 4 lines, the number of possible combinations explodes to more than 268 billion!

    More simply, with these defined characteristics we can redefine “homophony” to mean more than one line that match characteristics, and typically are in rhythmic alignment (synchronized). Indeed, most musical fabrics involve quite a bit of similarity between multiple lines. In a typical traditional “melody-and-accompaniment” fabric, there are only three distinct lines, melody, bass line, and chords, even if the chords are actually in two or more matching instrumental or vocal parts.

    The following example is taken from the Allegretto movement of Beethoven’s String Quartet Op. 135.

    String Quartet Op. 135 Allegretto, mm. 25-48

    In the first two bars of this example from Op. 135, there are actually only two lines in the fabric, the melody (1st violin) and repeated chord tones (the other three instruments aligned in 16th-notes) — common homophony.

     Op. 135 violin vs. other lines

    Though there is no dynamic marking for the 1st violin, it will be played as a prominent line, what Schoenberg would have called the Hauptstimme. By the third bar of the second system (11th bar of the example), there are three lines, violins / viola / cello, and by the next bar, briefly, all four instruments have distinct fabric threads. By the end of the excerpt, all parts have joined in homophonic unity.

    Melodic shape

    Melodic connotes a singable tune of primary focus; here it is meant simply as any line of successive single pitches. In the general descriptors of texture, we referred to smooth and angular shape. Let’s be more precise. First, there is the general size of melodic intervals. As music practice moved from Medieval/Renaissance through 18th-Century styles, smaller intervals, steps and small skips predominated. 19th-Century styles introduced a greater proportion of larger “leaping” intervals, 6ths, 7ths, 9ths. And those large, disjunct intervals became the norm for much 20th-Cenury music.

    Another important melodic shape factor is directional.

    TURN — a melodic note is approached in one direction (up or down) and left in the opposite direction

    Some turns are trivial and do not complicate melodic shape, such as trills and back-and-forth oscillations.

    turns in Elegy line

    The first phrase, starting on Eb, goes up to E then down to D — turning on the middle note, E. The next two phrases are increasingly complex in shape.

    Elegy 2nd and 3rd phrases

    The phrase starting on the lower B rises to G# then turns down on that G# to A, then back up from A, and finally back down, turning on Bb. There are three turning points, G#, A, and Bb, in a phrase of only six pitches and five melodic intervals. Combined with the fact that each melodic interval is a different size (9 s.t., 3, 8, 1, 3) except the last (reusing the downward 3 semitone interval), this is a rather complex, angular shape.

    The third phrase, starting on the higher B, is even more complex in angular shape: turns on every pitch except the C# — that is five turns in just 7 melodic intervals between 8 pitches.

    A side note of analytic math:

    • Number of pitches (#P) minus 1 = number of melodic intervals
    • Number of melodic intervals minus 1 = number of “opportunities” for the line to turn (#P – 2)
    • Shape complexity = #T / (#P – 2) ranging from zero to 1

    Pitch recurrence

    RETRACING — melodic line returning within a phrase to the same pitch (in the same octave) as previously sounded in the phrase

    Distinguished from a pitch being repeated (immediately), a retracing is a recurrence after other intervening pitches. It contributes to structural stability in the phase, a sense of staying in one place. Conversely, when retracings are avoided in the shape of the line, the sense is more of progressing, even of wandering, as in the Elegy example above. (Use of a 12-tone row to construct a line is a way to methodically avoid retracing any pitch until all 12 pitch classes have been introduced.)

    Back to Bartók — two orchestral lines studied in the Pitch chapter. The first example (from the opening fugue of Music for Strings, Percussion and Celeste) is scored for viola, but here I show it in bass clef for those a bit challenged by alto clef.

    fugue subject

    Mapping the line on a time/pitch graph for analysis, the first phrase avoids any retracing. The next three phrases make only one retracing each: back to Bb in the second phrase (highlighted in blue); back to C# in the third (in red); retracing back to C in the fourth (in green). (There are fainter retracings back to the previous phrase in each not shown.)

    The second is a low string line from the opening of Concerto for Orchestra.

    Concerto for Orchestra retracings

    In this example, both phrases are built with two retracings, C# and F# in the first phrase, F# and B in the second phrase.

    In this manner, retracing of pitches builds the support structure for the architecture of many lines.

    –

    © 2026 – All Rights Reserved

    Thomas S. Clark

    – 

    Continue reading Mapping the Music Universe:

    10. COUNTERPOINT

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    TClarkArtMusic.com 

  • journal 2. Musique Française

    Ann Arbor, 1968 —

    Having begun composing in 1963, I started formal composition study in 1968 at the University of Michigan in Ann Arbor. American composer Eugene Kurtz, based in Paris but filling in that semester at Michigan, was assigned to teach the new freshman. A proponent of modern French music, his compositional models included Debussy and Ravel.

    Sonatine

    Kurtz assigned me to immerse myself in deep study of their music, in particular Ravel’s Sonatine (1905).

    Ravel: Sonatine

    Judith Valerie Engel on YouTube

    Fifty years later in my career as a more experimental composer, my compositional style began to mellow toward a gentler Impressionistic approach and a lush, bright harmonic language reminiscent of Debussy and Ravel.

    Homage to Ravel, my new Sonatine is spun from a single harmonic progression, seven chords each stacking a Perfect Fifth interval high above another.

    This material (what Schoenberg would call a Grundgestalt) generates melodic lines and many arpeggiation patterns, in successive variations of changing register, intensity, and rhythmic pace.

    Sonatine

    Clark 2025 (TC-155)

    Nocturnes

    In 1907, French composer Claude Debussy wrote, “I am more and more convinced that music, by its very nature, is something that cannot be cast into a traditional and fixed form. It is made up of colors and rhythms”. Color, light, and texture were also the hallmarks of a new style of painting developed by French artists — Impressionism.

    At the threshold of the 20th century on 15 December 1899, Debussy completed the first of his Impressionist masterpieces for orchestra, Trois Nocturnes. He avoided labeling it “symphony” or “tone poem” by calling the movements “three symphonic sketches”. The first sketch of Nocturnes is subtitled “Nuages,” premiered on 9 December 1900 in Paris.

    Debussy’s biography describes the genesis of the piece while crossing the Pont de la Concorde in Paris in stormy weather. The composer’s notes say, “‘Nuages’ renders the immutable aspect of the sky and the slow, solemn motion of the clouds, fading away in grey tones lightly tinged with white.”

    Debussy: Trois Nocturnes

    Vienna Philharmonic on Youtube

    Adopting the French language and musical style recognizes the early French explorers of the Great Lakes region of North America. The first decades of my life began there in Michigan’s Lower Peninsula (the “mitten”). It has its own smaller Leelanau Peninsula in the northwest corner (the mitten’s “little finger”) near Interlochen’s National Music Camp, where I spent many summers. Nearby Grand Traverse Bay has its own even smaller Old Mission peninsula, where I loved to visit its lighthouse. The Leelanau has a grand lighthouse at its northern tip and a scenic drive, state highway M21, winding for 64 miles all the way around the peninsula’s shoreline, through forests and past the Great Sleeping Bear Sand Dunes.

    In 1984 my piece titled PENINSULA for piano and sound synthesis was a more experimental work that traced a map of the Leelanau and its landmarks to determine by their spatial coordinates the timing and pitches of sound constellations.

    Moving forward from that mapping phase of my compositions, my Impressionistic phase produced the sound sculpture Leelanau Sketches in 2022. Some of its musical material reappears now in five symphonic sketches, Belle Péninsule. Here is the fourth movement, which quotes Debussy’s “Nuages.”

    Belle Péninsule

    IV. “Nuages blanc“

    Clark 2024 (TC-147)

    La Mer

    Debussy’s completed his second composition of three symphonic sketches for orchestra, La Mer, in 1905. It is a monumental work of Impressionist sound-painted textures and a textbook model of lush, beautiful orchestration. The three sketches are titled:

    “De l’aube à midi sur la mer”

    “From dawn to midday on the sea”

    Jeux de vagues”

    “Play of the Waves”

    “Dialogue du vent et de la mer”

    “Dialogue of the wind and the sea”

    Debussy: La Mer

    Orchestre national de France

    My homage to La Mer, Sea Sketches, sound-paints waves, deep currents, wind, and sun-sparkling surfaces, employing swelling sound colors and post-modern cyclic techniques in a pan-diatonic tonal setting. The end briefly quotes the opening arpeggio of Debussy’s “La fille aux cheveux de lin” (“The Girl with the Flaxen Hair”) from Book I of his Préludes for piano (1909-1910).

    Sea Sketches

    Clark 2023 (TC-132)

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