L O u I S   g o L d f o r D

The Orchestra as Auditory Scene:
String Scoring and Perceptual Grouping

UWM Peck School of the Arts — Milwaukee, WI — March 31, 2026

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Excerpts

excerpts

Today’s scores can be found at this QR code →
(also accessible by clicking on the QR code.)

https://einbahnstrasse.github.io/string-orchestration-perception/excerpts

String Family — Range

The orchestral strings span over 7 octaves — comprising the full orchestral range.

  • Violin: lowest string G3 (G below middle C); upper register extends well above E7.
  • Viola: lowest string C3; its typical writing reaches into the high E6–G6 range.
  • Cello: lowest string C2; upper register overlaps with violin’s middle register.
  • Double bass: lowest string E1 (or, down to C1 with a low C foot); upper register reaches into the 5th octave.

Violin range, by string (Blatter, 49)

Viola range, by string (Blatter, 56)

Cello range, by string (Blatter, 61)

Bass range, by string (Blatter, 67)

Unlike other families, the strings cover the
widest range within the orchestra, including some of the lowest & highest frequencies produced acoustically.

Registers + Timbres

  • The strings also feature extensive overlap in range between family members.
  • Overlap supports effective doubling and enables seamless handoffs of melodic lines across registers.
  • Timbres of string sounds are also unified across registers and across instruments:
  • i.e., the same pitch/octave, at the same dynamic & bowing will sound perceptually close whether played by a violin, viola, cello, or double bass.

Overlap in range of each string, on each instrument (source: Virtual Orchestration).

As a result, the entire string family can function
as a hyper instrument — a continuous range of pitches;
or, a single large instrument comprised of 4 instruments.

Dynamic Curves

  • Some orchestral families project louder or softer in different registers (e.g., the oboe becomes quieter and “thinner” as pitch climbs.)
  • The winds + brasses don’t achieve this unity of dynamic levels quite as easily.

Oboe dyanmic curve: loudness decreases across register (Blatter, 100).

String Dynamics

    Strings maintain consistent dynamics across registers and instrumental groupings, and are flexible within the orchestra:

    • capable of nuanced, expressive playing at extreme louds and softs;
    • an entire section can sound as quiet as a single player; a section fff can rival other families in the high registers;
    • transitions between dynamic levels can be rapid, acrobatic, and precisely controled

Grouping Effects

Because of their large range, overlap, and dynamic continuity,
strings can form unified masses or distinct layers.

Strings easily blend with themselves and with other families,

but they can also form clearly separate orchestral planes —

A group of strings may fuse into a single sonority,
or divide into separate musical entities.

In other words, strings naturally support
both perceptual integration and stratification.

(We’ll explore what these mean in a minute — don’t fret!)

Because the strings produce sound colors (timbres)
that can be so closely related, composers are free to
move fluidly between perceptual states.

Perception?

Okay, wait, what?!
What do we mean by perceptual states,
and why are they essential to string scoring practices?

Auditory Streams

Cognitive psychology describes how the brain perceives sound:

We organize sound into concurrent streams of activity.

We are constantly interpreting what we hear;
grouping musical elements by similarity, proximity, etc.

gestalt

source: Gestalt Principles in UX Design, Medium.com

Auditory Streams

excerpts

Streams are like our counterpoint: By listening,
we discern how many melodic voices we’re hearing,
and which notes belong to which voices.

This constant motion of sonic activity is called a stream.

At any moment, sonic events may be heard as one coherent audio source,
or as separate, simultaneous layers.

Stratification

Stratification occurs when sounds belong to different sources.

In the orchestra, differences in register, timbre, rhythm, or articulation
may cause us to separate sounds into distinct perceptual streams.

We then sense a coexistence of independent layers,

like: foreground, middleground, and background.

We can intentionally orchestrate stratification to build
contrast, structural hierarchy, etc.

Integration

Integration occurs when our brains group multiple sounds together
and hear them as belonging to the same source.

In the orchestra, similar pitch range, timbre, articulation,
and rhythmic timing encourage sounds to fuse together.

Instead of separate instruments, the listener
perceives a single composite sonority.

We can integrate for blend, mass, and timbral cohesion.

Fusion

source: Kelly Fitz, CERL Sound Group

  • Here, sound components “fuse” together into a distinct color (timbre) that we might recognize as “trumpet.”
  • The ear parses a single timbre rather than discrete layers.
  • This is done by adding sine waves together to make the trumpet sound.
  • But prior to sine waves, we obtained fusion by adding instruments together.

Divisi (Divided)

We can change the sound of the string section simply by altering:

how many string players are sounding at any given time.

This alters the section’s perceived:

  • size
  • presence
  • tone color

Same notes — but different qualities entirely!

In the String Section

Changing the number of players doesn’t just change loudness

It changes tone qualities within the section, like:

  • how full it feels;
  • how thin or dense it feels;
  • whether we hear the strings in
    the foreground or background

Charles Koechlin

Koechlin

Charles Koechlin (1867–1950) was a French
composer, orchestration theorist, and author of a
highly detailed 4-volume Treatise on Orchestration.

He treated sound as something physical:
not just notes, but mass, density, space.

Koechlin’s orchestration is less a rule-based scoring practice,
focusing instead on the effects of instrumental combinations.

Volume vs. Intensity

What happens when we change the size of the string section?

In Koechlin’s view, “volume” is not the same as loudness:

Volume = the apparent size of a sound

how wide, spacious, or extensive it feels

Intensity = the strength or loudness of a sound

(Loudness and size, therefore, are different attributes.)

Large vs. Small

What is a “large” sound, anyway?! — Year’s later, we can validate what Koechlin could sense...

source: Chiasson (2017) — measuring the most salient features of acoustic instruments

Large Sound Small Sound
Intensity (loudness) high low
Spread of Energy narrow peak broad hill
Low frequency energy strong weak

How to Score “Volume”

Turns out: “Size” depends on spread, loudness, and presence of low frequencies.

  • low frequencies contribute to greater size
  • Bass + harmonic partials seem to enlarge a sound, making it coherent & weighty
  • But, size is not just a function of number of players...

Stay Out of the Mud!

  • Overlapping instruments in all different registers, with unrelated pitch and rhythmic content can lead to muddiness and masking of higher frequency energy,
  • reducing clarity; we’ll get a broad hill (like the one on the right) instead of a narrow peak, which will sound small rather than large.
  • So, size needs to be carefully orchestrated with similarity considerations...
  • (See today’s assignment for more information...)

Volume vs. Intensity

A sound can be:

  • large but soft, meaning it can have both...
    • high volume (size) and ↓ low intensity (loudness)
  • or small but fierce / mighty...
    • low volume (size) and ↑ high intensity (loudness)
  • ...or somewhere in between!

Cosmic Density

To illustrate this, Koechlin considers celestial stars of varying density:

A flute in its low register can sound large and diffuse,
like a red giant — a large star with its matter spread out.

  • high volume (size) and ↓ low intensity (loudness)

An oboe’s middle register can sound compact and concentrated,
like a white dwarf, with its mass compressed into a small space.

  • low volume (size) and ↑ high intensity (loudness)

Transparency vs. Density

Transparent:high volume (large size) and ↓ low intensity

perception of — warm, diffuse, receding sound

Dense:low volume (small size) and ↑ high intensity

perception of — bright, compact, proximate, forward sound

Depth

Dense sounds tend to be heard in front.

Think: solo or small group expressive nuance

Transparent sounds tend to fall behind.

Think: section in unison, or a tutti chorus-like effect

Review

Orchestration shapes perceived volume, intensity, and spatial presence,
creating a continuum from transparent to dense textures.

attribute transparent dense
how it hits large, soft small, fierce
volume ↑ high ↓ low
intensity ↓ low ↑ high
descriptors warm, diffuse bright, compact
spatial position distant, background proximate, foreground
“deep space” red giant white dwarf
woodwind analogy low flute middle oboe

Divided Strings

When we divide string sections into smaller groups, Koechlin cautions:

extreme divisions (divisi) can produce “almost weightless sounds”

Dividing the string section:

  • reduces mass, fullness
  • reduces homogeneous sound
  • reduces the chances of blending
  • but, increases individual presence

Also, risks sounding thin.

Ways to Divide

Some methods of distributing players across lines, managing volume & intensity:

method what players do notation
By Desks (stands) Each stand divides: outer player on upper note, inner takes lower 2 voices on 1 staff (div. or div. a 2)
Split in Half Half the section plays; inner
stand partners silent (tacet)
Half, la metà, la moitié, die Hälfte
Expanded
(3+ groups)
Section divided into >2 groups; fewer players per line div. a 3 or a 4+ on a single staff, or additional staves “Divide by stand”
Double Stops
(non divisi)
Each player performs multiple notes simultaneously Multiple noteheads on 1 stem marked non divisi
Chamber
(soli divisi)
A subset of the section plays,
then divides among given lines
Marked “soli” (e.g., 8 soli divisi)

La Traviata, mm. 1–7

trav opening

Overture opens with a 4-part chorale harmonization

scored for 1st and 2nd violins

8 soli divisi — 8 players from 1sts + 8 players from 2nds

4 independent voices, each one executed by 4 players

Perceptual result:

  • more dense:low volume (size) and, perhaps, ↑ high intensity (loudness)
  • sounds more proximate or intimate; nuanced cues from individual playing
  • spatially, seems more concentrated and in the foreground
  • with 4 on each part, this passage avoids sounding too thin

La Traviata, Tutti (m. 8+)

trav m. 8

From m. 8, 1sts & 2nds return to Tutti unision
lines, joined by viola & cello harmonies

What’s actually going on here?...

  • ↑ more violinists on each melodic part
  • introduces subtle chorus-like delays
    and microtuning differences
    • pyschoacoustic cues: “This mass is now larger...”
  • impression of a receded, more generic sound
    • ↑ increased conditions for fullness and blend (Koechlin)
    • e.g., violins can blend better with violas and cellos
  • ↑ greater transparency

La Traviata, m. 18

trav opening

At m. 18, the unison melody is made
even more transparent...

  • 1st violin melody is joined by viola & cello
  • viola & cello no longer harmonizing
  • ↑ more cellists as they move to Tutti

La Traviata, m. 18

trav opening

And, as a result...

  • 1st violin, viola, & cello integrate into their
    own perceptual layer, creating a fusion
  • wow!
  • despite the melody scored in 3 octaves...
  • Doubling in octaves enhances transparency
    by promoting fullness and volume:
  • More mass is spread out across multiple registers
  • La Traviata, m. 18

    trav opening
    • At the same time, the orchestra has also
      stratified into 3 concurrent layers:
      1. melody: 1st violin, viola, cello
      2. chordal accompaniment:
        2nd violin, horns, upper winds
      3. bass: double bass, bassoon
    • why this works: similarity of timbre, register, onset, and articulation
      leads to fusion within layers, and a separation between them
    • Interestingly, the strings are now distributed across all 3 layers,
      rather than sounding as a single family

    La Traviata, m. 18

    trav opening

    This is not a coincidence; violins don’t just
    miraculously fuse with cellos and violas...

    It’s the result of Verdi’s careful preparation:
    the management of size (volume), intensity
    (loudness), similarity of musical materials,
    fullness, and transparency.

    Review

    Now, we can add 2 more lines to our table...

    attribute transparent dense
    how it hits large, soft small, fierce
    volume ↑ high ↓ low
    intensity ↓ low ↑ high
    descriptors warm, diffuse bright, compact
    spatial position distant, background proximate, foreground
    “deep space” red giant white dwarf
    woodwind analogy low flute middle oboe
    chance of blend? ↑ high ↓ low
    scoring method full sectional, unison sound solo or divisi

    Ravel, m. 1

    trav opening

    Listen to the opening of Ravel’s Alborada del gracioso.

    How many layers do you hear?

    So, what’s actually happening?...

    • Strings are all in pizzicato: dry attack, quick decay
    • Harps provide a similar articulation,
      reinforcing the same qualities of attack and decay
    • Careful control of doublings, register
    • These are sources with different physical properties
    • But coordinated in time, envelope, and spectrum

    Result

    trav opening
    • Not harp alone
    • Not strings alone
    • Not a stratified, layered texture
    • Instead, we hear a single, unified sound object:
    • A plucked, percussive, rapidly decaying timbre
    • Playing many notes: a kind of 2-part oompah
      structure, between bass and chords
    • Perceptually: this is like a guitar

    Target Sounds

    trav opening
    • The target sound here is not “strings” or “harp”
    • The target is a guitar-like sound
    • The strings are used to approximate that target
    • This is a goal-directed process:
    • Written parts are a specific means, not an ends;
    • The intension is not to “use orchestral colors,”
      but to evoke a specific sound
    • Ravel specifically sought to evoke the sound
      of the guitar in this example.

    Grouping

    trav opening

    The guitar is a hyper instrument: a virtual guitar
    consisting of string instruments that are added together.

    How this is achieved:

    • Onset synchrony: attacks align precisely
    • Envelope similarity: shared plucked decay
    • Compatibility: overlapping frequency regions
    • Balanced intensity: no source dominates
    • The sounds are fused into one perceptual object

    Ravel, m. 98

    trav opening

    Here is an emergent timbre: Its combined identity
    is not reducible to individual instruments.

    • Background: higher pitches fade out progressively,
      lowering overall brightness and orchestral “fade.”
    • Foregrounded pizzicato: 1st & 2nd violins, upper
      violas & cellos, and harps
    • Here, higher strings also progressively drop out, lowering brightness.
    • Snare and cymbal do not fuse with the strings and xylophone
      due to their inharmonic, noisy, unpitched timbres,
      despite all instruments playing identical rhythms.

    Natural Harmonics

    trav opening
    • Produced by lightly touching the string
      at specific points (nodes)
    • By suppressing the fundamental pitch, this
      isolates chosen upper partials
    • Common nodes: 1/2, 1/3, 1/4 of the string length
    • Resulting sound is:
      • lighter and less dense
      • reduced in low-frequency energy
      • often described as glass-like in timbre
      • highly transparent, promoting blend

    SUMMARY

    Today’s class covered the basics of string section grouping, phrasing, and harmonics.
    Next class will focus on:

    • Detailed bow strokes (e.g., détaché, martelé, spiccato, sautillé)
    • Vertical bowing (e.g., sul ponticello and sul tasto)
    • Col legno (e.g., battuto, tratto)
    • In-depth pizzicato discussion, incl. left hand and Bartòk pizz.
    • Contemporary approaches: e.g., Helmut Lachenmann’s friction techniques for strings

    Assignments

    These will also be posted under today’s date on Canvas/Moodle:

    assignment due link
    Revoicing a Chorale for Strings next class click here
    Madvillainy & Timbral Grouping in 3 weeks click here
    L O u I S   g o L d f o r D
    w o R K s 2 0 2 6

    Louis Goldford — Structure + Emergence in Recent Works

    UWM Peck School of the Arts — Milwaukee, WI — March 31, 2026

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    me-and-grandma

    bio

    me-and-grandma
    Grandma was pretty great.

    bio

    • Raised in St. Louis, Missouri
    • Studied piano, saxophone, flute, clarinet, improvisation, composition, and arranging
    • Undergraduate degrees in Composition and Economics
    • My “Econ Days” — inspired my thinking in terms of statistical trends, models, forecasting, data visualization & sonification
    with-fd
    TAIPEI, Taiwan
    with-fd me-and-st
    with-fd me-and-st
    with Flâneur Daguerre — with Sabu Toyozumi
    TAIPEI, Taiwan
    • 2009-2012
    • Primarily worked as a freelance saxophonist
    • Founded experimental improvising ensemble Flâneur Daguerre
    • Fostered collaborations within Taiwan's richly diverse music scene: jazz, free improvisation, rap, and hip hop musicians
    with-fd me-and-st
    with Flâneur Daguerre — with Sabu Toyozumi
    TAIPEI, Taiwan
    • First pieces with real-time electronics
      in MaxMSP & Supercollider
    • Learned studio recording and post-production techniques
    • First pieces for acoustic instruments based on synthesis processes & algorithms
    at-cu
    Masters
    • 2012-2015
    • Expanded vocabulary of playing techniques
    • Gained facility with real-time electronics
    • Focused on offline synthesis techniques
      and computer-assisted composition (CAO)
    • First pieces of mixed music
    at-cu
    Doctorate
    • 2016-2024
    • Continued pursuit of a personal,
      timbral language focusing on temporal resolution and microtiming
    • IRCAM Cursus in 2018-2019
    • Teaching Fellow at Columbia University’s
      Computer Music Center
    • Worked with Carmine Cella on his Orchidea software for computer-assisted orchestration
    • Research-Creation Grant from the ACTOR timbral research project (McGill University)

    Musical Concerns

    Psychoacoustics

      • auditory illusion
        • when the brain is convinced it hears a sound that isn't physically present
      • fusion of sonic constituents
        • blending of multiple sound sources into a single, unified sonic event or timbre
      • sound morphologies
        • how we represent or describe the evolving shapes and structures of sounds
    E m e r g e n c e
    gestalt

    source: Gestalt Principles in UX Design, Medium.com

    Gestalt

    the sensation of a whole modeled as a clear sum of perceivable component parts, or “constituents,” that share properties with some totality

    Emergence, unlike the gestalt, refers to a property’s [...] statistical change over time, and therefore lends itself to computational analysis and a dynamic conception of musical form, rather than a traditional representation of musical form as a static and unchanging or monolithic entity...”

    —Louis Goldford,

    Emergence in the Music of
    Pierluigi Billone and Georges Aperghis

    gestalt

    source: Goldford, Emergence in the Music of Pierluigi Billone and Georges Aperghis, DMA diss.

    dynamical systems

    • representations of musical turbulence
    • modeling non-linear ebb + flow
      • in musical time & pitch,
      • in trajectories of spatialized sounds,
      • in swirling, eddying currents between orchestral aggregates and layers,
      • or in the momentary flux of perceptual audio descriptors

    Quantification

    • metrical discretizing
      • How do we reduce the inherent complexity of continuous and irrational “fluid” rhythms?
      • And package them into sensible meters with readable subdivisions?
      • While preserving the integrity of the original musical source material — its textural and timbral properties?
      • This is the pursuit of a practical symbolic solution.

    Transcription

    • especially of “complex sounds”
    • i.e., “paradoxical” or “unstable” sounds
    • their mimesis by acoustic instruments
      • a natural extension of transcribing
        jazz + free music as a saxophonist

    Orchestration

    2 paradigms:
    1. historical, syntactical
      • Served Western music for generations.
      • Best for orchestrating pure timbres or pitched musical materials, but not for noise or complex timbres in instrumental settings.
      • White noise arrived late to the orchestra; percussion imitating Ottoman Janissary bands (e.g., Mozart, Abduction from the Seraglio, 1782)
      • We assign antiquated terms to the effects we perceive; e.g., “spacing” fails to account for basic timbral properties.
    adler1 adler2
    Samuel Adler, The Study of Orchestration

    Orchestration

    2 paradigms:
    1. historical, syntactical
    2. target-based, algorithmic
      • Uses computation to find instrumental matches that are “best fit” to imitate the specific qualities of “target” source sounds (e.g., ambient field recordings).
      • Especially well suited to resolve noisier or complex and abstract sound sources.
      • next slide: brief demo of an orchestration “workspace...”

    Transom (2024)

    ensemble + electronics

    Themes

    • Inspired by Pruitt-Igoe federal housing project in St. Louis (my hometown)
    • Contrasts so-called “modernist failure” and “postmodern excess”

    History + Myth

    • Pruitt-Igoe: Built 1954 but demolished 1972 — seen as the “death of modern architecture” (Charles Jencks)
    • Cold War military testing site: zinc cadmium sulfide exposure
    • Failure of the project was wrongly blamed on Black residents.
    • The project’s demise is now understood as systemic neglect & racism

    Architectural Models

    • Architectural geometry is used to generate the work's harmonies using physical modeling synthesis
    • Blueprints from Pruitt-Igoe buildings (“modernist failure”) and the Frank Gehry Residence (“postmodern excess”)
    • Each set of blueprints is treated as a virtual acoustic model — a resonator.
    • Physical models of each building drives musical structure + synthesis

    Broad Applicability

    the wider appeal of these tools

    Formant Synthesis

    • Models resonant frequencies of the vocal tract to produce vowel-like timbres
    • Used to structure gestures around vowel formants and explore speech research
    • Bridges voice science, vocal music pedagogy, and audio engineering
    • Singer-songwriters, producers, and engineers can use vowel formants to fine-tune their EQ, mix clarity, and balance

    Spectral Analysis & Resynthesis

    • Breaks down sound into frequency components for compositional reuse
    • Used for high-resolution modeling of life-like sound sources
    • Enables realistic timbres as well as glitch-friendly timbres
    • Crosses into jazz, electronica, as well as academic research

    Audio Feature Extraction + Machine Learning

    • Extracts perceptual and mathematical characteristics (e.g., brightness, spectral centroid)
    • Guides composition with perceptual data
    • Drives recommendation engines, adaptive game scores, and AI production tools
    • Forms the backbone of smart EQ, intelligent mixing and mastering tools

    Interactive Environments

    • Visual programming languages like MaxMSP for real-time sound/media interaction
    • Used for experimental works and intermedia performance environments
    • Supports custom tools for improvisation, installation art, live visuals
    • Bridges DSP, gestural mapping, and creative coding

    Audio-Visual Tools

    • Jitter, Processing, and TouchDesigner link sound and image in real time
    • Used to create audiovisual analogs between structure, gesture, and form
    • Extends sonic material into visual modalities for immersive performance
    • Widely used in video art, AR/VR/XR

    Modular Synthesis

    • Patchable modules allow for flexible, nonlinear signal paths
    • Users now can start learning modular virutally before investing in expensive hardware
    • Bespoke sound design and exploratory instrument-building
    • Cross-genre appeal: pop, ambient, techno, sound art
    • Embodied, intuitive interface supports curiosity-driven exploration
    • Teaches us to work within limits

    Audio Spatialization

    • Techniques for positioning/moving sound in physical or virtual space
    • Used in gesture-driven immersive setups
    • Binaural production now enables widespread, affordable immersive listening systems
    • Core to VR/AR/XR, cinematic sound design with Dolby Atmos, museum installations, site-specific works
    • Bridges musical form with perception, architecture, and accessibility technologies

    Repertoire

    Au-dessus du carrelage de givre (“Above a Frost-Tiled Floor”) (2019) tenor, electronics, video 9' Benjamin Athanase, IRCAM
    Tell Me, How Is It That I Poisoned Your Soup? (2019) ensemble + electronics 11' Talea Ensemble
    Mauvaise foi (2022) soprano, ensemble, electronics, and reactive lighting 11' Alice Teyssier, International Contemporary Ensemble
    Audiendum Extimate (2018) 2 perc., 2 pno., transducers 11' Yarn/Wire
    Mémoire involontaire (2017) string quartet 16' JACK Quartet

    Au-dessus du carrelage de givre (2019)

    tenor, electronics, video

    Tell Me, How Is It That I Poisoned Your Soup? (2019)

    ensemble + electronics

    Mauvaise foi (2022)

    soprano, ensemble, electronics, and reactive lighting

    Audiendum Extimate (2018)

    2 perc., 2 pno., transducers

    Mémoire involontaire (2017)

    string quartet