RESEARCH NOTES

Representations of music

2025-04-14 · Alun @Atopos
#Music#Philosophy

Chapter 1: Representations of music↗

Music is not only sound. It also enters notation, analysis, memory and emotion. The same music can leave different kinds of traces:

Table 1. Different traces of the same music
Representation Example
Score Written notes, rhythms and performance directions
Audio A record of a performance or studio production
Musical analysis An account of harmony, rhythm or form
Evoked memories A listener’s connections between music and personal experience

These traces are not interchangeable. A score does not record every detail of a performance, and a recording does not explain why a listener is moved.

1.1 Acoustic, auditory and graphemic↗

The course follows Babbitt’s (1965) distinction between three levels:

Table 2. Babbitt’s distinction as presented in the course
Level Focus
Acoustic Sound signals detectable by a microphone or other equipment
Auditory Perceptual and cognitive representations and associations formed by a listener
Graphemic Notational systems such as scores

A classical semiological question follows: can something be represented without knowing what it means? Sometimes it can. A microphone can capture sound, which can be compressed into MP3 and played back, without first understanding its emotional significance. Preserving sound is different from preserving the whole experience of hearing it.

1.2 Music as subject and object↗

Music can be an object of description, but also an experience through which something else appears: a melody may recall a period of life, while notation and recordings make it available as an object that can be revisited.

Even a listener’s brain image does not escape this distinction. Common fMRI uses signals related to blood oxygenation to study brain activity during tasks. It is not a moving picture of memories and emotions themselves. Interpreting activity as evidence of a particular experience requires experimental design and independent evidence.

Chapter 2: An ellipsis, and what description leaves open↗

“What does music represent?” Sometimes the answer resembles an ellipsis.

Here, the ellipsis need not mark an absence of content. It can leave meaning unfinished. An “umm…” may signal hesitation, interruption or a search for words. Music’s relation to language need not be a translation of one fixed meaning into another set of signs.

2.1 A crescendo without notes↗

The lecture discusses a crescendo sign Schumann left in Henriette Voigt’s guestbook. Detached from particular pitches and a passage to perform, the sign can still suggest growth, approach or an unfolding emotion. Its effect depends on context, rather than a fixed dictionary of correspondences. This is a reading of the example offered in the course, not proof of Schumann’s sole intention.

“Semiotic surplus” provides a way to discuss such correspondences that resist exhaustive description. It need not mean a code that will eventually be solved, or that every interpretation is equally justified.

2.2 Unable to begin, or unable to finish saying↗

The course distinguishes the “untellable” from the “ineffable”: language may stop before an experience, or keep proliferating without exhausting it. Jankélévich’s discussion of music leans toward the latter. These are philosophical positions, rather than experimentally established cognitive stages.

A long analysis written after a symphony can still leave something unsaid. That need not make the analysis a failure: description may change the next listening, rather than settle the work once and for all.

2.3 Notation participates in experience↗

Drawing on Dahlhaus, the lecture questions an “audibility criterion”: why should only sounds actually produced count as material for musical experience? Notation can evoke imagination in silence; a complex texture need not be heard in full at once; reading and listening can influence one another. This reconsiders the range of musical materials without declaring hearing obsolete.

Defamiliarization rearranges familiar signs, drawing attention to habits of notation. A complex analytical diagram may also organize an experience that exceeds immediate listening, although complexity does not make a diagram or its music inherently profound. The course’s spectralist example adds another distinction: conventional notes can help organize timbres formed from multiple frequency components. A score should not simply be equated with an exhaustive transcription of a spectrum.

Chapter 3: A structure to communicate, or a recipe to perform?↗

A recipe offers an intuitive example. “Add 50 grams of flour” and “add enough flour until the batter is smooth” both guide action, specifying different things at different levels of precision. Descriptive and prescriptive do not mean precise and vague: the question is what a representation describes, or what it asks a performer to do, in its particular use.

The course uses Oscar Peterson’s boogie-woogie as an example. Notes written with equal values can be performed unequally according to stylistic convention. Readers bring knowledge of a musical tradition as well as the ability to decode written durations. This does not justify a general dismissal of notation as inaccurate, or a claim that real music exists only in improvisation.

3.1 Production, listening and musical materials↗

The course draws on Molino’s tripartition to distinguish different starting points for musical description:

Table 3. Molino’s tripartition as presented in the course
Perspective Object of description
Poietic Actions, reasoning and decisions involved in creation and production
Esthesic Listening, reception and musical experience
Neutral Materials and structures considered without defining them through creative intention or listener response

“Neutral” names an analytical level. It does not mean that the analyst makes no choices, or that a table exhausts a work.

Chapter 4: What does a representation choose?↗

The “musical surface” is not always the sound most immediately available to hearing. Relative to a particular representational system, it is the material taken as a detailed starting point: a score for a classical performer, a melody with chord symbols for a jazz improviser, or unprocessed audio for a recording engineer.

The course lists several further parameters:

  • Expressive completeness and structural generality: how much specific detail can be retained, and how general a structure can be expressed? “Completeness” is not confined to emotion.
  • Hierarchicity and associativity: are relationships organized mainly in levels or through cross-connections?
  • Intrinsic uncertainty: what can remain unspecified, and how is that uncertainty made visible?
  • Symbolic and continuous: are events and notes the organizing units, or is the sound signal the main object? A digital implementation still involves sampling and quantization.
  • Prescriptive and descriptive: does the material guide action in this setting, or record a musical phenomenon?

Choosing a representation also means choosing which differences to preserve and which can, for now, be set aside.

Chapter 5: Pitch, lines and visual arrangements↗

5.1 Giving pitch a position↗

Scales provide discrete pitch relations; a monochord makes relationships between string length and pitch demonstrable; staff lines give pitches visual positions.

Early medieval neumes often indicated melodic contour as an aid to recalling familiar chants. Heightened neumes made relative height more explicit; reference lines and clefs stabilized how positions were read. Staff practices associated with Guido of Arezzo were an important development. Four-line and five-line staves should be distinguished from the Guidonian hand, a hand-based aid to remembering solmization; the hand is not another name for a four-line staff. Developing polyphony also increased the importance of rhythmic coordination and notated durations.

5.2 Improvisation and instrument notation↗

Figured bass supplies a bass line and figures indicating intervals and harmonic realization above it, leaving choices of voicing to the performer. A jazz lead sheet generally offers melody and chord symbols, guiding performance like a sketch. It is not equivalent to the numbered notation known as jianpu in Chinese.

Tablature can encode strings, frets or action positions, connecting notation to instrument construction, tuning and bodily movement. Baroque dance notation makes bodily movement through space an object of inscription. Notation does more than place abstract pitches on paper.

5.3 Graphic notation: the image need not precede the sound↗

Examples in the lecture include:

Table 4. Dates of music in the lecture examples; images may have later dates
Composer Work Date of the music
Brian Eno Music for Airports 1978
John Cage Fontana Mix 1958
George Crumb Makrokosmos I, No. 12, “Spiral Galaxy” 1972
Iannis Xenakis Metastasis 1953–54
György Ligeti Artikulation 1958

These images need not have the same purpose. In particular, the familiar colored listening score for Artikulation was made by Rainer Wehinger from an analysis of the recording and published in 1970. It should not be mistaken for a set of instructions Ligeti wrote before composing the work in 1958. The ICST work archive documents this distinction. The date of the music is different from the date of an image later made to represent it.

Chapter 6: What do digital formats preserve?↗

6.1 Symbolic events and sampled audio↗

Table 5. Digital formats distinguished by their objects, not by the presence of file structure
Object Common formats or systems Emphasis
Symbolic musical materials MIDI, Humdrum’s **kern, MEI Notes, events, structures or documentary semantics, depending on the format
Audio signals WAV, MP3 and others Encoded sound over time, with different fidelity and compression choices

Calling the former structured and the latter unstructured conflates two questions. Audio usually lacks explicit note and chord annotations, but WAV is itself a structured file container and can hold more than one audio encoding.

For common PCM sampling, a simplified expression is:

x[n]=Q ⁣(s ⁣(nfs)).x[n]=Q\!\left(s\!\left(\frac{n}{f_s}\right)\right).

Here, s(t)s(t) is a continuous-time signal, fsf_s the sample rate and QQ quantization. This omits practical steps such as filtering before sampling. It simply shows why digital audio is not the infinitely continuous sound signal itself.

6.2 MIDI and piano rolls↗

MIDI, introduced in 1983, is first a standard for communication between electronic instruments and devices. A pitch–time plane is a common display, rather than the full content of MIDI messages. MIDI 1.0 messages also include velocity, controllers and pitch bend.

For discussion, a note event can be summarized as:

ei=(pi,tion,tioff,vi).e_i=(p_i,t_i^{\mathrm{on}},t_i^{\mathrm{off}},v_i).

Here, pip_i is a note number, tiont_i^{\mathrm{on}} and tiofft_i^{\mathrm{off}} its onset and offset, and viv_i its onset velocity. This is a convenient event representation, not the raw MIDI byte format or a complete account of its messages. MIDI records events rather than full audio; the resulting timbre also depends on the receiving instrument. An ordinary note number does not itself preserve enharmonic spellings such as F♯F^\sharp and G♭G^\flat.

“Piano roll” also needs a distinction. Historical perforated rolls recorded performances, but the fidelity of dynamics, pedaling and microtiming depends on the system and its recording and playback conditions. A digital workstation’s piano-roll view is an event visualization. Limitations of the historical medium do not automatically become defects of that view.

6.3 Humdrum, MEI and Verovio↗

Humdrum is a framework for representation and processing; **kern is one of its text representations for core information in common-practice Western notation. Its emphasis differs from MEI, which uses XML structures to encode musical documents, their semantics and notational features.

Verovio is an engraving tool centered on MEI. It can generate outputs such as SVG and import or convert several other formats. Encoding a document and turning that encoding into readable notation are related but distinct tasks.

6.4 Sonic Pi: code as performance material↗

Sonic Pi brings algorithms and sound generation into a live-coding environment. Its Ruby-based domain-specific language, educational uses and Raspberry Pi background provide useful entry points. The central idea is that code can be changed while the performance unfolds.

The program is both a set of sound-generating rules and material the performer can manipulate. The boundary between representing music and making it becomes less stable once again.

Adapted from Yannis Rammos’s Representations of Music lecture (10 March 2025) for EPFL’s Digital Musicology (DH-401).