Kotoński-Inspired State-Event Generator — User Guide

Scope

This script is not a reconstruction of Kotoński's compositional method and does not recreate the original source recordings, studio procedures, or a specific realization of AELA. It combines historically informed preset constraints with an engine-specific finite-state controller.

The result is best understood as a finite-state event field: state memory controls ranges for event duration, onset interval, register, amplitude, and material tendency; transitions change that state after a user-defined number of events.

Quick start

1. Run Kotonski_FSM_Event_Generator.praat. No input Sound is required.
2. Choose one of the five ready-made fields or Custom Finite-State Field.
3. Set Duration, Sample rate, Number of events, Global amplitude, transition controller, state hold, and Spatial mode.
4. Open Edit state / sound details to change frequency range, IOI multiplier, attack/release, noise bandwidth, seed, and material preference for each state.
5. Run the script. Event/state data are realized first, then globally time-scaled so the latest event end lands exactly on the requested Duration.
6. The generated Sound remains in Praat. If enabled, a realization-score page is drawn after rendering.

Four engine states

The states are compositional classes invented for this engine. Each state defines ranges rather than one fixed event.

For general presets, an event's normalized register position is drawn randomly inside the state's range, clipped to 0–1, then mapped logarithmically into the current effective frequency range.

For the Etude-inspired serial grid, state ranges still provide the local duration/amplitude boundaries, but positions inside those ranges are selected by deterministic rotating parameter indices rather than by random draws.

State memory and transition controllers

The current state is retained for State hold events. Only after that many events has been generated is a transition decision made. The four available controllers are:

Cycle

Palindrome

Adjacent aleatoric

At each transition decision: 30% remain in the current state, 35% move toward the lower neighbor, and 35% toward the upper neighbor. At the boundaries, the attempted outward move is reflected inward.

Directed aleatoric graph

Audio materials

Each event receives one of three rendered source classes. A state material code of Mixed chooses between them stochastically: 44% tone, 34% noise band, 22% metallic transient.

1. Tone

A sine event at the realized center frequency, with a random starting phase and the event envelope.

2. Noise band

A local-duration Gaussian-noise Sound is filtered with Praat's Hann pass-band filter. The nominal bandwidth receives a random factor of .65–1.35. The filtered fragment is RMS-normalized locally before event scaling and is then mixed at half the event's nominal amplitude.

The passband is bounded to 20 Hz at the bottom and 0.45 × Fs at the top. A small smoothing width is derived from the actual passband width.

3. Metallic transient

Three inharmonic decaying sinusoids are combined at frequency ratios:

The event center is limited so the 2.13× component remains within safe sampling headroom. The upper components use relative amplitudes .45 and .28, and the complete metallic source receives an exponential decay before the common event envelope.

Safe event envelope

Attack and release are cosine-shaped. For short events, each side is independently limited to at most 45% of the realized event duration, preventing the user-specified attack/release values from overrunning a very short event.

Timing, overlap, and density

Event duration and IOI are independent. The next onset advances by the current event's IOI, not by its duration. Events can therefore overlap naturally when duration exceeds IOI.

Exact-duration normalization

After all events have been realized, the script measures the latest raw event end and applies one common time scale:

Every onset, event duration, and IOI is multiplied by this same factor. Relative temporal proportions and overlap relationships are preserved, while the latest event ends exactly at the requested Duration.

What IOI Density multiplier really does

The advanced IOI density multiplier multiplies raw IOIs before final time normalization. Values below 1 make raw onsets closer together; values above 1 spread them farther apart.

Overlap compensation

After time normalization:

The gain is applied to every event together with Global amplitude and the event's own amplitude value. It is an energy-compensation heuristic for dense overlap, not loudness normalization.

Frequency handling and sampling headroom

The script uses safeTop = 0.45 × sample rate.

General modes

If the requested Frequency maximum exceeds safeTop, the complete minimum/maximum range is scaled by one common factor:

This preserves the ratio between the range boundaries. If common scaling would push the lower boundary below 20 Hz, the script stops and asks for safer settings.

AELA-inspired 25-Hz field

AELA mode is treated differently because the 25-Hz arithmetic spacing is the historical constraint being preserved. Frequencies are rounded to the nearest 25 Hz, and the upper boundary is truncated rather than proportionally scaled.

Version 1.6.1 also quantizes that safe upper boundary itself:

so sampling-headroom truncation cannot introduce a final frequency that falls between grid steps.

Presets

1. Etude-inspired Serial Parameter Field

The synthetic serial analogy uses deterministic rotating indices:

Duration and amplitude levels are interpreted inside the current state's ranges. The articulation-to-source mapping is an AudioTools invention; it is not presented as Kotoński's historical articulation table.

2. Microstructures-inspired Fragment Montage

In this mode, selected fragments are shortened by an additional random factor of .35–.75, while IOIs receive an additional random factor of .55–1.15. The result is a synthetic overlapping montage analogy, not a recreation of the original glass/wood/metal recordings.

3. AELA-inspired 25-Hz Sine Field

4. Sparse Point Field

5. Dense Mixed State Field

6. Custom Finite-State Field

Uses the values entered in the main form and optional advanced page. Historical special modes — serial grid, Microstructures fragment modifications, and AELA 25-Hz quantization — are off.

Controls

Spatial modes

Stereo gains use equal-power panning:

Output and level

Visualization — Partytura Realizacyjna

Version 1.6 deliberately presents the visualization as one realization-score page, not as an analysis dashboard. Every system uses the same horizontal time axis, so a vertical cut through the page refers to the same moment/event across parameters.

Head block

Shows preset, event count, requested duration, realized events/s, tone/noise/metallic counts, transition controller, state hold, spatial mode, and seed.

Montaż — event field

A log-frequency field shows the actual realized events as horizontal filled bars. Color indicates the engine's four state classes. Tone and metallic events appear as narrow frequency bars; a noise event's vertical height represents its realized bandwidth.

Tablice skal — four scale systems

The score contains four aligned ruled systems:

• WYSOKOŚĆ / height — 11 levels.
• DŁUGOŚĆ / length — 11 levels.
• DYNAMIKA / dynamics — 11 levels.
• ARTYKUL. / articulation — 6 levels.

For the Etude-inspired serial-grid preset, the first three systems show the actual generated serial-grid indices, while articulation shows its actual six-class index. For presets that do not use the serial grid, realized frequency, duration, and amplitude values are binned to the same 11-level display purely to keep one score grammar; the key explicitly says that those presets use no grid.

State ribbon

A colored strip beneath the parameter systems shows the realized finite-state trajectory across the common time axis.

v1.6.1 visual-range correction

The log-frequency bounds now use effective_min_Hz and effective_max_Hz after any sampling-headroom scaling. This keeps scaled low-frequency events inside the plotted score instead of calculating the visual range from stale pre-scaling values.

Historical basis and Further Reading

The historical statements retained in this guide are limited to points supported by archival, institutional, or scholarly collection sources.

Study on One Cymbal Stroke / Concrete Etude (1959)

POLMIC identifies Kotoński's 1959 Study on One Cymbal Stroke as the first autonomous tape composition created at the Polish Radio Experimental Studio and describes one recorded cymbal stroke transformed within a precisely planned structure. Unearthing the Music documents the source being filtered into six bands of different widths, transposed to eleven pitches, and organized with related duration and articulation scales. The present 11/11/11/6 grid is a structural analogy, not a reconstruction of that concrete-source workflow.

Microstructures (1963)

UNT Music Library metadata describes Microstructures as a montage built from recorded impacts on wood, metal, and glass: tape fragments were cut and assembled into chance sequences and loops/layers. This script substitutes synthetic tone/noise/metallic fragments and an FSM-controlled montage.

AELA (1970)

POLMIC and Map of Polish Composers date AELA to 1970. MoMA's Polish Radio Experimental Studio archive describes the work as a framework or “family of electronic pieces” using sine-wave material on a frequency scale from 25 to 10000 Hz in 25-Hz intervals, with aleatoric procedures. The AELA-inspired preset therefore uses sine tones only, retains a 25-Hz grid, and uses the engine's directed aleatoric state graph without claiming to reproduce a specific realization.

Verified online references:

• Polish Music Information Centre (POLMIC) — Włodzimierz Kotoński.
• Unearthing the Music — Electroacoustic Music in Poland (1957–1990).
• UNT Digital Library — Kotoński, Microstructures.
• MoMA Post — Polish Radio Experimental Studio scores and Aela.
• Map of Polish Composers — Włodzimierz Kotoński.