MAPPING MUSIC

Tag: Julia Wolfe

  • Mapping Music 11. TEXTURE

    Imagine a piece of music exploring texture in time, made of single sounds and sonorities occurring one at a time in sustained resonance. Then imagine the points of sound are separated by rests, silence. As the texture drifts in and out of a resonant cloud, the sound events remain unconnected. Suddenly, their pace explodes into a torrent of notes. That describes the following powerful piece by my UNT colleague, Joseph Klein.

    Joseph Klein – Pathways IV: Rhymes & Spirals (2024)

    Sound color

    Our next music map shows a simple color-coding graphic system for classifying most musical timbres, informally the tone quality of sounds. The map intuitively chooses colors of the rainbow. While the color spectrum orders the frequencies of light (another manifestation of periodicity), our sound-color classifying map does not imply any ordered quantification of timbral complexity.

    instrumental color rainbow

    Though we think first of an orchestra for a rainbow of color, chamber music can incorporate a variety of instrumental colors, each produced in vivid isolation by one instrument, standing out or changeably mixed with other colors.

    Augusta Read Thomas wrote Dance Mobile in 2021, scored for 13 instruments: Woodwind quartet (Flute, Oboe, Clarinet, Bassoon); Trombone; String quintet: (2 Violins, Viola, Cello, Contrabass); Piano; 2 Percussion (vibraphone/metal, marimba/wood, drums).

    The piece starts with a single pitch, blending several colors that swell in intensity. Then ensues a kaleidoscopic dance of at least seven distinct color combinations, of two basic types:

    Sustained sounds – strings; high woodwinds; lone brass of the trombone

    Sparks – pizzicato strings; ringing metal sounds; drum strokes; staccato piano

    Augusta Read Thomas – Dance Mobile (2021)

    Though the piece is dedicated “in memoriam Oliver Knussen,” the memory is a joyous dance of color.

    Symmetry

    In the exposition of Webern’s Symphony, Op. 21, we saw that each contrapuntal line duplicates the exact rhythm of the lead line, with each entrance one bar later — a classic canon. But each contrapuntal line presents a different succession of instrumental colors:

    Horn . . . . . . . . . Clar. . . . Cello
          . . . Harp . . . Cello pizz. . . . Cello arco . . . Violin . . . Harp . . . Horn . . . Harp
          . . . . . . Horn . . . . . . . . . Bass Clar. . . . Viola
           . . . . . . . . . Harp . . . Viola pizz . . . Viola arco . . . Violin . . . Harp . . . Horn . . . Harp

    The German term for this is so elegant, we’ll use it here:

    KLANGFARBENMELODIE — melodic or contrapuntal line expressed by a string of changing tone colors

    Webern placed each pitch in every line in a particular fixed octave, except Eb that appears in two different octaves. This makes a striking, symmetrical 13-pitch constellation with a palindromic array, the same array going down as going up.

    Webern 13-pitch constellation

    Not only was he obsessed with symmetry in this piece, but this constellation’s symmetry also proves that he was thinking specifically about the chord voicing in what I have identified in successive interval array form.

    We can use this constellation as a Y-axis for a graph mapping the timbres as they appear in the various parts in canonic lines in pitch space for the first 9 bars. This farben color map looks like one of the later geometric paintings of Piet Mondrian.

    Op. 21 color map

    Pointillism

    Though we often share musical terms and concepts with visual art, we sometimes mean different things by the same term. In painting, a technique developed in the Impressionist style period of the late 19th century that became known as pointillism. The most famous example is Georges Seurat’s “A Sunday Afternoon on the Island of La Grande Jatte” at the Chicago Art Institute. Instead of sweeping brush strokes and palette-blended colors, it used small separate spots of subtly varied colors to make a texture that, when viewed from a distance, seems to merge into a color cloud, giving the impression of animated light.

    Musical pointillism, unlike painting, separates sounds in time and pitch space, not to blend them into a texture so much as to highlight the different qualities of each unique sound event. Webern was a pioneer of musical pointillism in works such as Op. 21. Let’s graph the first 10 bars of this fabric using our timbre color-coding (BLUE = wind, ORANGE = percussion, VIOLET = plucked string) on a broadly distinguished 6-octave pitch range. We get something as colorful as a Mondrian painting!

    Andromeda sound color map

    As a musical fabric, isolation — using the vast available range of pitch and the empty time of rests and silence — is a fitting analog for the vast, mostly empty space of a galaxy. Let’s use it for a demonstration etude.

    Andromeda is the nearest large galaxy, 2.5 million light-years from our own Milky Way galaxy. Our sound color demonstration study uses every sound quality on our sound color spectrum except red. Here is a score of the first 10 bars.

    Notice that the green woodwind notes are doubled with a synthesized vocal-type sound. Yellow brass notes are punctuated by orange metallic percussion attacks. Likewise, blue string notes are articulated by the plucked string sounds of harp.

    Here is the whole colorfully pointillistic 3-minute study:

    Sound Mass

    At a time when electronic music was emerging in the 1950s, new instrumental resources were also developing a new style that was all about animating massive layers of sound.

    German experimentalist Karlheinz Stockhausen composed two early, influential sound mass works, Gruppen (1957) for three orchestras, and Carré (1960) for four orchestras and four choirs. The scores were huge, dense, 12-tone, and monolithic in form.

    A 2002 piece by John Adams, On the Transmigration of Souls, harkens back to a mid-century masterpiece of the Avant Garde. In 1961, Polish composer Krzysztof Penderecki wrote a piece for a massive score of 52 string instruments. Conceived as an abstract, freeform, dense massing of animated and intense musical fabrics, it represents a pioneer in the genre of sound mass music, winning the UNESCO Prize that year. Only after it was heard in performance, he said, “I was struck by the emotional charge of the work … I searched for associations and decided to dedicate it to the Hiroshima victims” — thus the title, Tren Ofiarom Hiroszimy (translated Threnody for the Victims of Hiroshima).

    As a young composer in the ‘70s, I reflected this approach in some pieces titled Animated Landscapes. (The title was inspired by John Cage’s famous Imaginary Landscapes no. 4 for 12 radios.) Beyond referring to the painting genre of landscapes, the title sets the imagination for solid, continuous textures like viewing the shapes of a mountain range, but set into rhythmic motion. (This approach became prevalent in ensemble music, especially of Midwestern composers such as Donald Erb.)

    Considerably predating the music mentioned above, Schoenberg’s Fünf Orchesterstücke, Op. 16 (1909), was originally scored for a large orchestra of 37 parts. It is not thought of as sound mass music, as its five movements each have Expressionist or Impressionist titles: “Vorgefühle” (“Premonitions”); “Vergangenes” (“The Past”); “Farben” (“Summer Morning by a Lake”); ”Peripetie” (“Peripeteia”); “Das obligate Rezitativ”(“The Obligato Recitative”). The third movement, Farben, is of special interest not only for its exquisite mixed-palette painting of orchestral timbres, but also for its thick though delicate fabric of sustained sounds. At the start, nothing moves, the subtle shimmer of instrumental colors fading in and out of a continuous fabric of delicate, faint sounds. (A sound mass can be delicate, not necessarily “massive.”)

    Here is a score of the first page, showing sounding concert pitches for all instruments.

    Schoenberg Farben scoring

    Each measure presents one constellation, recolored with different instruments in the second half of the measure. For the first three bars, the constellation does not change, and then only subtly in the next five bars, maintaining the constant C pedal point in the low strings.

    Farben constellations

    The bass clarinet’s F3 in bar 7 is considered an ornamental non-harmonic pitch. While you can see many recurring smaller constellations imbedded within these changing large constellations, such as 5 5, 3 5 and its inversion 5 3 (which are triads), and some transformations of smaller constituent constellations: 8 3 redistributed to 9 2, 4 7 shrinking to 4 5 (another triad), and 3 4 (also a triad) shrinking to 2 4.

    Though there are many triads embedded in the constellations, the overall quality of the sonorities is complex, as the triads are framed within critical dissonances:

    framing dissonances

    Foreground / background

    Most landscape paintings, distant textures of forest, mountains, sky, waves on the sea, or clouds, have some sharp focal point. Often on the horizon (in itself a focusing anchor of the visual display), it may be a barn, a setting sun, a boat, a farmer and dog. If we consider proportion and symmetry in a visual composition, the focal point is best not dead center. A more interesting balance, according to expert photographers, follows the Rule of Thirds, placed one-third from the left or right, one third from the top, or both. Two-thirds is a ratio of 0.667. The Greeks famously defined the Golden Ratio, an ideal ratio dividing a whole length or height into two parts such that the ratio of the smaller part to the larger is the same as the ratio of the larger part to the whole. The ratio is 1.618:1, the solution to the equation: x2 – x – 1 = 0; a 62% and 38% division.

    In a simple traditional musical texture, an accompanying harmonic texture is designed as a background for the focal element of a melody. Sound masses may lack such focus, like the forest or sea waves. When there is to be perceived a standout element of the texture, Schoenberg called this focal element of the musical fabric the Hauptstimme. Though that might translate “highest voice,” the melody or other focal events are not necessary to be higher in the pitch range of the fabric than other elements. But there must be some isolation or distinction setting them off from background in at least one of the parameters mentioned above. The Hauptstimme focal line or textural element can be:

    • in a pitch range isolated from background
    • a color isolated as a single timbre, not a mixed diffusion of background colors
    • slower or faster than background
    • more rhythmically elastic, varied than background
    • not synchronized with background
    • loudest line (the most obvious)

    Schoenberg devised a special symbol for the focal Hauptstimme line of a fabric, a boldface stylized capital H, which you see marking the bass clarinet entrance in bar 7 of the Farben example. Here is how that principal Hauptstimme line continues, a Klangfarbenmelodie of changing color, from bass clarinet to clarinet with trombone to three solo contrabasses.

    Hauptstimme handoffs

    Notice the aggressive rhythmic motive, each time stepping down 2 semitones; and the  7 7 7 quintal-chord constellations in the contrabasses. (The rhythmically aligned clarinet and trombone are separated by 14 semitones, 7 + 7.)

    Beyond color isolation, Learning to Compose makes a distinction for a timbre mixed with itself or other colors spread over some pitch register (“diffuse”) or reinforcing itself in a narrow, confined pitch space (“concentrated”). While Farben’sbackground is diffuse, its Hauptstimme color is isolated in the low pitch register of the bass clarinet and then also concentrated with the three solo contrabasses.

    In the first movement of Anthracite Fields (2015) by Julia Wolfe, the bass clarinet emerges as a focal sound by its loudness and singularity of pitch in a cloud mass of softer sound. Then aggressively loud clusters suddenly interrupt the steady-state background, yielding eventually to repetitive sung chords and floating vocal duets. The sound fabric maintains a three-dimensional depth of contrasting intensities.

    Julia Wolfe – Anthracite Fields I: Foundations (2015)  

    Galaxy groups

    Our sample etude composition for sound mass is a thick score of 10 wind parts and harp, with a fabric the opposite of pointillism: everything sustains and overlaps. There are basically no pauses or holes in the continuous 2-minute sound fabric. Its title, Laniakea, is the name of the supercluster of galaxies that includes the Milky Way.

    Laniakea score excerpt

    Having shown the score with all its notational details, to better illustrate the main point of the example, sound mass, here is a graphic rendering of that actual second system of notes. We can reveal its pointillism by increasing the contrast in a negative image of light on dark. That makes the attack beginning of each sound show up but not the staff lines or sustained resonances . . . a fanciful art image of Laniakea, a vast empty part of the universe dotted with millions of galaxies.

    Laniakea score abstracted

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    © 2026 – All Rights Reserved

    Thomas S. Clark

    –

    Continue reading Mapping the Music Universe:

    12. FORM

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  • Mapping Music 2. RHYTHM

    Rhythm is a stream of event durations. Often repetitive but potentially elastic, rhythm can be steady, as a simple march, or volatile, as a melody that hovers, trots, then suddenly starts running.

    Defining some basic terms:

    TIME POINT — a precise moment in time marking the beginning of a span of time extending until a comparable event marks the next time point

     TIME SPAN — the duration of time from one point to the next point marking a comparable event

     STREAM — a series of events formed by the elements of consecutive groups

     PERIODIC — a stream of events whose elements exhibit equivalent time spans

     PULSE — ungrouped periodic time marking in a speed of about 48 to 1,000 per minute (above 1000 per minute becomes pitch)

     METER — a nested hierarchy of periodic streams of of time points

    Nested means that two or more time-spans at a quicker level are synchronized with the next longer durational level. Two eighth-notes “fit” within the metric time-span of one quarter-note, for example. Meter creates the perception/expectation of events happening at periodic time points on more than one level of speed/duration.

    BEAT — pulse that constitutes the primary level of a meter’s hierarchy, the connector between both quicker subdivided and slower grouped levels

    PACE — general quickness / slowness of rhythmic activity in a line or whole fabric

    HYPERMEASURE — extension of metric hierarchy grouping measures, typically in two- or three-measure units

    PHRASE — grouping of molecules, shapes, motives, chord changes, etc. in a coherent stream, typically the length of the human breath

     PERIOD — grouping of phrases, typically concluded with a significant harmonic cadence and/or melodic sense of arrival

    Pulse and Beat

    Underneath the sense of a beat, pulse is primordial periodicity – clapping hands, stomping feet, banging rocks, running strides – features we inherit from our primitive musical ancestry and still use to organize our musical actions.

    Susie Ibarra – Sky Islands (2025)

    A rapid pulse can drive music with frenetic motion. Much of jazz relies on this power source. The tension between a fast, steady pulse vs. unpredictable accents (syncopations) and other turbulence generates energy and excitement.

    SYNCOPATION — an accent not synchronized with the beats, or a note length shifted from its regular metric starting point

    Listen to how a relentless, fast pulse drives this music.

    Julia Wolfe – Believing (2012)

    Rhythm makes meter, Meter drives rhythm

    Rhythm first generates meter by marking periodic time points at different levels of speed. The marking is just the moment of initiation of each note but also accents, chord changes, etc. at broader time levels. As a great example, let’s use a famous theme from a piece nicknamed for a planet:

    Jupiter Symphony theme

    This melody first establishes periodicity of half-notes but nothing shorter for a while. This could be any duple meter. Once we hear these first four equal notes, we tend to perceive them as two pairs, establishing the whole-note measure-level meter. We feel the time point that begins the third measure on two levels of periodicity even though no note happens to mark it. In this third measure, eighth-notes then divide those half-note time spans into four parts. In the middle of measure 3, a quarter-note fills in the missing level of meter. Finally, in the last beat of the measure, a burst of sixteenth-notes establishes the fourth, quickest periodicity of the nested hierarchy. This example extends the hierarchy to show 2-bar hypermeasures in a 4-bar phrase.

    Once the tune repeats, our sense of that nested hierarchy of speeds is in full cognitive play. While jumping from metric level to level, half-notes to eighth-notes to quarter-notes then 16th-notes, the melodic rhythm undergoes a compression of pace, moving from longer rhythmic values to quicker and quickest, while the Allegro tempo does not change.

    More definitions

     

    CYCLE — the duration of equivalent time spans in a periodic stream of events

     ELEMENT — a point and following time span of an event or group of events, relating to other consecutive elements to form a group at a broader (slower) level of time

    COMPRESSION — an element of a group or stream is a shorter span than the previous element

    Example: rhythm changing from half-notes to quarter-notes to eighth-notes, compression of pace.

     EXPANSION — opposite of compression, elements of a group or stream are longer spans than previous elements

     ACCELERATION — consistent successive small compressions of beat or pulse

    PROPORTION — relationship of time spans expressed as a ratio, reduced to smallest-possible integers (whole numbers)

     RHYTHMIC GROUP — consecutive related elements, with a point of initiation and accumulated durational span

     RHYTHMIC RANGE — ratio of longest duration to the shortest

    In the Mozart Jupiter example above, the rhythmic range is 1:1 conformity for the first two bars, then 4:1 with three different note values in the third and fourth bars.)

    RHYTHMIC VARIETY — number of different note values in a stream of notes

    In the Mozart Jupiter example above, the rhythmic variety is 4 (halfs, quarters, eighths, sixteenths).

    Stress and accent

    Classic poetry classifies each syllable grouping (a “foot”) in a line of poetry according to which syllable in the grouping is stressed or longer length (agogic stress). (The last, a “reversibrach,” is my addition to complete the set of possibilities for musical purposes.)

    Metric “feet” in poetry

    Rhythmic molecules, groupings of two or more notes, can be similarly characterized, though with more stress possibilities:

    • Strength (accent) stress
    • Length (agogic) stress
    • Metric stress (strong beat vs. weak beat; on the beat vs. off-beat)

    A molecule can have one stress pattern in accent contradicting a different stress pattern in length or metric placement. Another familiar Mozart example: the opening themes of the first movement of Mozart’s Symphony No. 40 in G Minor. The first theme is fast (allegro) but steady (low elasticity).

    Symphony No.40 1st theme

    Analyzed as three rhythmic molecules:

    Three quick, predictable anapests, in which the longer, metrically-accented note is precisely the same length as the pair of shorter notes that lead to it. It also shows a narrow rhythmic range, 2:1, and little rhythmic variety, with only two rhythmic values, the eighth-note and quarter-note.

    Now the contrasting second theme, a soaring oboe line, highly elastic in rhythm.

    Symphony No.40 2nd theme

    This phrase launches with a long trochee, beginning-stressed in both length and metric placement. This rhythm uses four different note values, the longest of which is 12 times the length of the shortest. The first note sounds stretched, like an elastic band that is then released after the third note, unleashing the quick notes that scamper to the last.

    This is just a glimpse on the micro-level of rhythmic contrasts and a temporal elasticity that propels the exciting roller-coaster allegro opening of this great symphony. All our perceptual and gestalt faculties are engaged in a grand game of play with time.

    Molecules

    Here are the opening notes of three famous 20th-century unaccompanied flute pieces, by Debussy, Varese, and Berio, respectively.

    Each uses a three-pitch motive that, when analyzed as a pitch-class set, is a segment of the chromatic scale.

    • Syrinx: A Bb B = +1 +1 semitones chromatic scale pattern
    • Density 21.5: E F F# = +1 +1 semitones, same scale pattern
    • Sequenza: G G# A = same +1 +1 chromatic scale pattern (G displaced by an octave)

    Shown above in their chronological order of writing, it is likely that one influenced the next, and it the next in a chain of evolving variation. While this shared pitch-class-set characteristic is the usual basis for comparison, it is also interesting to compare the rhythmic molecules of their generating motives.

    Syrinx starts with a clear front-stressed dactyl, repeated then echoed in bar 2.

    The Density 21.5 motive is more complicated. Its opening three notes, from a short/long durational standpoint, is an end-stressed anapest. But the first note, though short, has the metric accent, being the only note of the three written on a beat. That first note is also emphasized by the tenuto mark. Those accent factors point toward a front-stressed dactyl like Syrinx. The next three notes starting with the C# are a more ambiguous stress shape.

    The opening three notes of Sequenza have no clear metric or dynamic accent difference; they are all strong. But by duration, the third note is “longer” in effect in the time stream (agogic stress), as the silent time after it, before the next note comes along,is longer. Also the third pitch, G, is much higher, giving it a registral or contour accent. This 3-note molecule is an end-stressed anapest.

    In all three pieces, however, the sense of simple repetition of matching poetic feet is not established or maintained. It is more productive to understand throughout each piece how rhythmic range and variety expand and contract and pace intensifies or subsides.

    © 2026 – All Rights Reserved

    Thomas S. Clark

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    Continue reading Mapping the Music Universe:

    3. CHANGE

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