MAPPING MUSIC

Tag: Hauptstimme

  • 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 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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  • GALAXIES: Musical Structure and Relativity

    Pursuing a grand cosmic metaphor, think about the levels of structure scientists study in our physical universe. They have dived deep below the atom’s structure of electrons spinning around a nucleus of protons and electrons to discover subatomic particles like the meson and boson. On the other extreme of scale, they have gathered observations to speculate about the shape of the entire expanding universe. We understand the structure of our planet, of our solar system, and our Milky Way galaxy.

    Texture

    Painting engages techniques to create texture, rising to broad descriptions of style that actually describe structure: impressionism, cubism, pointillism. Musically, macro-structure is thought of as texture and form. Texture has been treated in broad descriptive categories: monody, homophony, polyphony, counterpoint, and more recently, sound mass, each focusing on the number of distinct parts, voices, or layers and how they interrelate. At the risk of invoking too many different metaphors, I like to think of the musical texture as a fabric.

    Other topics

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

    To read more, request a password from tc24@txstate.edu

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