One rule · three voices · two readers

Sonic absence

01 / 24Phrase

Volume 28% 0:00

Ready

Finite Rule 30 / phrase 01

Center · readyRight · readyLeft · ready

● attack · ○ rest · / gap · × late · □ gateRow 160

Arrangement

Scale

Tempo104 bpm

Chord gravity55%

Voice paths

Column 0

Depth 5

Depth 12

Compose the conditions

Tuning

Tonic

Spectrum

Fundamental partial

Include the root

Timing

Pulses11 / 16

Cycle length16 steps

Swing54%

Echo32%

Center work per step

Interlock the cycles Moving phrase contour

Your interval steps

Your phrases

0 attacks · 0 late values · 0 marks

Live phrase

Inspect receipts

Step	Voice	Deadline	Command	Later

Ready · press Play

What is sound? What is music to a computer?

This room begins with one active cell. Rule 30 turns it into a history; three paths select values from that history. Values become gates and pitches only after a composer supplies timing, a scale, registers, tuning, envelopes and an instrument. You can change those decisions while the rule stays fixed. The distinction matters: the computation constrains the material, while its use as music remains a practice.

Three encounters with the same event

Instrument shows the score and its causes. Signal samples the audio graph and draws the measured waveform and spectrum. Listener makes fallible estimates from those samples. A separate score reader has access to commanded symbols. These are different situations of knowledge. The listener receives neither the Rule 30 cells nor the pitches the instrument intended to produce.

A physical sound can involve vibration, a medium and a receiving body. Here the observable is a digital signal before a loudspeaker. Samples are dimensionless amplitude values; they are not a measurement of pressure in your room. The signal can be rendered while nobody hears it. It can be perfectly periodic and still fail to reach you if the output device is disconnected. Computational access and an encounter through hearing come apart.

A question you can change

Music adds relations across time, distinctions learned within practices, a use, and the possibility of a listener taking something as significant. No threshold on amplitude, regularity or tonal fit settles all of that. Here, ask what a particular reader can preserve and what it discards. Play an arrangement, remove a voice, change the listener's memory, then offer your own sound or scale. Your account of music is not graded by the apparatus.

The eight arrangements are compositional proposals. The measurements test programs on finite inputs. Neither supplies evidence of machine experience or a universal definition of music. The philosophical dispute over what constitutes music remains open; Andrew Kania's account maps several competing positions.

What this take records, and what it cannot

The record separates exact cells at deadlines, later knowledge, musical settings, issued audio commands, synthesis partials, model predictions, acoustic feature snapshots, your marks and your written account. A record can establish that two runs used the same finite procedures. It cannot establish that they were identical encounters for a person.

Select a completed phrase to inspect its original receipts. A known-value replay is a distinct counterfactual, retaining the original take. Download record preserves both. Export phrase renders up to thirty-two issued steps through an OfflineAudioContext at a fixed 28% output gain, including tails; a missed command stays missed in that original render. Each command retains its instrument settings, although the export does not reconstruct gain changes made between steps. The render is an audio file you can hear independently of the live timing. It does not re-record your room or include an imported file.

A rendered phrase also remains in a local audio player with a Save WAV link. This lets you listen or save it when a browser does not complete the initial download. The preview is separate playback; it is not measured again by the live reader. New take clears the preview.

Marks are moments you chose to keep. Their timestamps are not measures of attention, emotion, consciousness or musical competence. The free account can refuse the supplied frame. Nothing in the application grades it. Downloads stay on your device until you decide to share them.

Playing, stopping and listening

Press Play to open audio. The default take has 768 eighth-note steps, divided into twenty-four phrases of thirty-two steps. At 104 beats per minute its grid lasts about 3 minutes 42 seconds. The last tails can ring a little longer. Changing tempo changes that duration; nothing is streaming from another server.

Play is a gesture that permits the browser's audio context to run. Pause stops current sources and delay feedback immediately; Continue keeps the score position and receipts. New take clears the take and its listener history but keeps your control settings. A hidden tab pauses and requires another Play gesture. Escape stops unless a contextual panel is open, in which case it first closes that panel.

The volume control changes digital output gain. It cannot know your system volume or acoustic level. Start at a comfortable device volume. A recording of note commands establishes what the program asked the audio graph to do; a digital render establishes samples. Neither records what you heard.

A rule becomes a score through choices

Rule 30 updates each binary cell with left XOR (center OR right). Its seed has one active cell and zeros outside its expanding cone. The center path can move between columns −24 and +24; the edge paths move inward by a chosen depth. An edge strip follows a characteristic direction and can be computed at fixed width in this finite apparatus. Center values use a full cone with an intentionally limited work allocation.

A selected one opens a candidate note. Five neighboring bits encode an integer from 0 to 31. The arrangement maps that integer into a scale degree, register and accent. A chord bias can redirect it toward three scale degrees; nearest-octave voice leading limits unnecessary register jumps. Rhythm gates can withhold an otherwise eligible note. The original selected value and the eventual command are recorded separately.

Necessity and composition

The rule determines a bit history once its initial condition is fixed. It does not determine an instrument or a musical culture. Mapping a high bit to a high note would be another legitimate procedure; reversing that mapping would be another. Here you can supply a scale and change the paths. The resulting differences are consequences of explicit mappings, rather than proof that the bits contained a hidden composition.

The rings show one thirty-two-step phrase. Solid points are issued attacks, small open points are known rests, slashes are omitted values, crossed points missed computation deadlines, and squares are withheld rhythm gates. A central field draws actual finite Rule 30 cells. It is a score display, not a sound-pressure image.

Eight ways of composing the same computation

Glass garden puts a Dorian field through a glass lead, a plucked edge and a lower harmonic voice. Small ratios combines a fixed five-limit tuning with a strongly chord-biased lattice. Three against four gives the voices twelve-, sixteen- and twenty-step cycles on the same eighth-note grid. A missing root removes each fundamental partial from harmonic synthesis. Bent bronze couples an inharmonic bell spectrum with Phrygian pitch choices. Unmoored breaks fixed subdivisions with deterministic timing offsets and chromatic degrees. Night figures uses harmonic-minor material and swing. Room to breathe distributes a few attacks across longer gaps.

Selecting one changes future musical decisions. The old score records and the listener's learned transitions remain. This makes a change of arrangement a small encounter with expectation: a reader trained by one passage can meet another without being reset. New take starts the comparison again from the same finite seed.

These are eight authored transformations, not eight outcomes extracted by the cellular rule alone. Harmony, articulation and voice leading are imposed procedures. Their usefulness has to survive listening. An exact calculation cannot certify that an arrangement is worth hearing.

Mode, harmony and voice leading

A mode selects interval steps relative to a tonic. Dorian has a minor third and major sixth; Phrygian adds a flattened second; Lydian puts an augmented fourth into a major collection; harmonic minor raises its seventh. The pentatonic collection here uses steps 0, 2, 3, 7 and 10. These names specify the implemented collections. They do not reproduce the full melodic practices associated with every use of a name.

Chord gravity biases future degrees toward a moving three-degree set. The harmony follows the scale-degree sequence 1, 4, 5, 1, 6, 4, 2, 5, changing every two phrases. This is a composed trajectory. It introduces longer relationships than a single row of cells. The moving contour adds a register change in later phrases; nearest-octave voice leading chooses a pitch near the voice's previous commanded note within a bounded register.

Turning gravity down exposes more direct bit-to-degree material. Turning it up supplies a stronger common scaffold. The result asks where coherence is coming from: the recurrence of cells, a fixed scale, a progression, register continuity, rhythm, or the listener's memory. These supports can cooperate. The instrument does not offer a clean causal experiment on human expectations because you hear several supports at once.

A mode is not synonymous with a key. The acoustic reader compares its accumulated chroma against major and minor profiles only. A Dorian passage may resemble one of those profiles and receive that label. That is an observable failure of the available vocabulary, not a reason to rename your mode.

Pulse, meter, swing and interlocking cycles

Tempo names the quarter-note grid. Each computational step occupies an eighth note. Swing delays alternate steps while retaining the duration of each pair. At 50% the pair is even; at roughly 67% its onset spacing approaches a two-to-one division. In Free timing, neighboring bits supply an additional bounded delay instead. No onset is sampled from an unrelated random track.

Lattice rhythm distributes a selected number of pulses as evenly as possible within a cycle. Twelve-, sixteen- and twenty-step cycles can recur together after 240 steps, though their note gates still depend on the underlying bits. The cycles share one subdivision here: this is interlocking periodic structure on a grid, not independent continuously drifting tempi.

The distribution is related to the evenly spaced family discussed in Godfried Toussaint's rhythm paper. Spacing alone does not supply performance accent, dance, historical context or a claim to reproduce a named tradition. The algorithm here has a declared rotation for each voice and an extra gate from the score.

A beat can have more than one account

The listener estimates pulse from detected spectral changes, then compares integer-multiple alignments across candidate periods from 48 to 180 bpm. A half-time or double-time estimate may fit nearly as well. Fewer attacks, overlapping tails and syncopation can destabilize it. A beat estimate is not a measure of meter; grouping into bars needs further assumptions and evidence. The grid's known tempo stays visible separately from the estimated pulse.

Mode, harmony and voice leading

A silence has causes the samples cannot recover

The ledger keeps a known zero, an omitted value, an unavailable value, a closed voice and a withheld rhythm gate distinct. A zero belongs to the declared score: the computation supplied a rest. An omission is an authored gap. An unavailable value missed the work deadline. A closed voice suppresses a known command. A rhythm gate withholds an eligible note according to another periodic rule.

Those causes can all produce the same zero-valued digital output after their tails decay. The acoustic reader has no access to the causal ledger. It labels a frame inactive when RMS energy falls below your threshold. Turning that threshold up can label a quiet audible signal inactive. Turning it down can retain a nearly vanished tail. Inactivity under a criterion and absolute digital zero are separate conditions.

Silence as a temporal relation

A rest can preserve meter, mark a phrase boundary or make a return more consequential. The signal alone supplies its duration; an account of those uses needs a context. Your room may also remain acoustically active while the digital graph is zero. This page does not capture that room: it never opens a microphone.

Irwin Kremen's account of Cage's 4′33″ score describes duration and changing environmental sound as part of the work. Here the operational question is narrower: what is absent from this channel, and what kind of evidence would identify why? A digital zero cannot identify a performance situation by itself.

Three voices, three access paths

Center, right edge and left edge are different selections from the same history. Moving a path changes which cells it encounters. It does not change the law. At the same row, a neighboring cell can be a rest when the original cell was a note. This is a useful intervention because the new score must answer to a particular difference in the material.

Opening or closing a voice changes musical participation. Closed voices retain their sampled values and silence reason in the ledger. The audio listener receives the resulting mix, including ringing tails and echoes. It cannot identify which absent voice you deliberately closed from digital silence alone.

The voices are panned left, center and right, but the analyser reads their downmixed signal. Stereo separation can help a human follow strands while collapsing them for this reader. The score reader follows only the center voice. A polyphonic pitch estimate may therefore disagree with the center's commanded note without either record being corrupt.

Pitch, interval and the cost of a tuning

Equal temperament assigns each semitone the frequency ratio 2 to the power 1/12. Twelve steps make an exact octave. A four-semitone major third is 400 cents, where cents measure 1200 times the base-two logarithm of a frequency ratio. The fixed five-limit table uses 5/4 for that third: approximately 386.314 cents. The difference is about 13.686 cents. The Pythagorean table uses 81/64: approximately 407.820 cents.

Choose the same scale and change tuning. The cell gates and named scale degrees persist; oscillator frequencies change. The ratio table is anchored to the chosen tonic and does not adapt to each chord. A five-limit table cannot promise pure intervals between every pair of degrees, especially after changing harmonic context. A fixed compromise is part of this instrument's character.

The spectrum changes the question

Two fundamentals alone do not determine every interaction between complex tones. Their partials can align, beat, or form other relations. The bell's inharmonic partials change which intervals produce those interactions. Sensory roughness also does not exhaust harmonic function, tension, learned style or a listener's preference. William Sethares's tuning-and-timbre work makes this dependence on the spectrum concrete.

The reader folds spectral bins into twelve pitch classes referenced to A = 440 Hz. It therefore brings equal-tempered categories to all three tuning systems. A microtonal displacement can be rounded away; a category boundary can amplify a small shift. The display exposes that simplification rather than silently calling it hearing.

An instrument is a changing spectrum

Each attack sums sine partials, shapes amplitude through an attack and decay, pans it, and optionally sends it into a short feedback delay. The glass arrangement assigns different spectra to the three voices. Selecting another family gives all voices that family while retaining their registers and durations. Strings uses integer harmonics with descending amplitudes; Bell uses ratios 1, 2.76, 5.4 and 8.93; Air uses a soft, sparse harmonic spectrum. These are compact synthetic instruments, not physical instrument models.

Timbre extends beyond a static spectrum. The attack can reveal an event that a long decay obscures. Echo makes a past event remain acoustically present after its score step ended. The plotted centroid is the power-weighted mean of frequency bins in the measured band. The plotted flatness compares geometric and arithmetic mean power. Neither is a complete model of brightness or noisiness as heard.

Replacing a spectrum while keeping gate and pitch decisions fixed makes a consequential comparison: the score reader can retain its pattern, while the acoustic reader obtains different features. If its key label changes, that change may arise from the instrument's partials entering pitch-class bins, rather than from a new harmony. A computer's representation determines what an instrument change can mean to it.

A pitch can outlive its fundamental

Removing the fundamental keeps the higher partials. In a harmonic family, partials at 2f, 3f, 4f and later integer multiples can still share a period corresponding to f. A periodicity estimator can find that period even when the spectrum has little or no energy at f. This is a finite signal property. It does not establish what every human will hear.

Try A missing root, then visit Signal and Listener. The spectrum has peaks above the nominal frequency. The autocorrelation search asks which lag makes the sampled waveform resemble itself. The result can suggest a lower frequency than the strongest spectral peak. In a polyphonic mix, it can instead settle on an octave error or fail to find a clear lag.

Removing a fundamental from Bell does not turn it into a harmonic series. Its inharmonic ratios lack the same shared period. The intervention has a different consequence because the particular spectrum differs. Tonal labels from summed spectral bins remain especially fragile in this comparison.

Pulse, meter, swing and interlocking cycles

A beat can have more than one account

Too late to play, still possible to know

The center cone spends a chosen number of cell updates per score step. This quota is deliberately imposed. It is not the computer's benchmark, a theorem about Rule 30, or a lower bound on every way of finding a particular cell. The edges use exact narrow strips; the center uses an expanding full cone.

Hold the work or reduce the budget. Once the score reaches beyond the computed row, a center value becomes unavailable. Catch up computes forty-eight future rows immediately. Know the past computes the remaining finite cone and adds late knowledge. Neither action retroactively issues the missed note.

Replay with known values creates a separate take using the original paths and musical settings. An added note belongs to that counterfactual. It does not revise the original encounter. This is one way to make epistemic absence audible without pretending that a calculation can repair a lived deadline.

Mode, harmony and voice leading

A sample is an amplitude with an index

Signal reads a 4096-sample window from the audio graph after output gain and compression. At 48 kHz the window spans about 85 milliseconds and FFT bins are about 11.72 Hz apart. The actual browser sample rate is displayed. The waveform shows amplitude against sample position; the spectrum shows the magnitude of frequency bins. Horizontal scales have different units.

RMS averages squared amplitudes and takes their square root. dBFS is 20 log10 of that RMS, relative to full-scale digital amplitude. It is not dB SPL in air and cannot report listening safety. The frequency analyser's windowing and smoothing alter the estimate. The renderer rejects oscillator partials near its Nyquist limit rather than requesting ultrasonic components.

What a spectrum loses

A magnitude spectrum discards phase. Different signals can share those magnitudes; a finite time reversal preserves the DFT magnitudes while reversing order. A whole-passage histogram also discards the sequence in which pitches occurred. The instrument can make music from ordering that these summaries cannot recover.

Finite windows trade temporal specificity for frequency resolution. A short attack can spread across bins. A long tail can make two events appear to coexist. The plots expose these estimates, with samples and frequency axes, rather than pretending to be a score. Their behavior follows the Web Audio specification.

A sample is an amplitude with an index

What a spectrum loses

Periodicity is a candidate, not a score

The pitch estimator subtracts the sample mean and compares the waveform to delayed copies of itself. It normalizes each comparison by the energy of the two segments. It seeks an early strong local peak, with a fallback strongest-lag search over candidate frequencies from 70 to 1100 Hz. Parabolic interpolation gives a finer lag estimate than an integer sample position alone.

A strong repeated pattern supports a period in this window. It does not identify a named note, a voice, a key or an expressive gesture by itself. Closely related candidate lags can correspond to octave alternatives. Several voices can produce beating, interference or a composite pattern that is not any one source's fundamental.

The finite checks use digital zero, a sine at 440 Hz and a harmonic pair at 880 and 1320 Hz. Success on those fixtures warrants only that narrow result. Music files, low notes below the search range, inharmonic bells, transients and changing polyphony can resist the procedure. A blank estimate is a legitimate answer when the available representation has insufficient evidence.

An instrument is a changing spectrum

Let the reader meet your own sound

Choose an audio file from your device. The browser decodes it locally and plays it through the same output and analyser, with synthesis paused. There is no upload, microphone request or server processing. File size is limited to 25 MB and playback to the first ninety seconds. Codec support depends on your browser. The reader does not receive a title, score, genre or embedded tags as model input.

A new source clears acoustic history to keep its measured window distinct from the instrument's previous signal. The score reader is inactive for files because no commanded note alphabet is available. Returning to the instrument resumes the original take after another Play gesture. Its historical ledger survives.

A recording can contain environmental noise, speech, percussion, mixed harmony or deliberate near-silence. Failures of a twelve-class template and a monophonic periodicity estimator on those inputs are useful constraints on the apparatus. They do not disqualify your file as music.

Does the computer listen?

Calling this a listener identifies a functional role: it receives a signal, retains a history, and responds differently when its input changes. That role can be specified and tested. A statement about an experience of sound requires another argument. The moving display supplies no such argument.

The acoustic reader has amplitude samples and magnitudes. The score reader has commanded symbols. A participant can have physical hearing, cultural knowledge, memories, bodily timing, purposes, and the freedom to attend elsewhere. These access conditions differ before anyone makes a claim about intelligence. An exact score receipt can explain a missing command that the acoustic features cannot infer. A listener can hear a phrase ending that the receipt never represents.

Use, recognition and responsibility

A machine can compute relations useful to a musical task without defining the task's value. For an onset alarm, energy and novelty may suffice. For performance timing, period estimates may help but need error handling. For deciding whether a sound is music in a particular situation, the people and practices that supply that situation matter. The representation does not automatically acquire those practices because it has a detailed numerical output.

Try a sound the composer did not choose. Change the threshold until the reader loses it; change the memory until a tonal account stabilizes or dissolves. You can reject its categories and write your own account below. That account is saved locally with the take. There is no computed score for whether your account is correct.

Does the computer listen?

Use, recognition and responsibility

A tonal template brings its own musical world

The acoustic reader folds measured spectral power between 60 and 2200 Hz into twelve nearest equal-tempered pitch classes. Exponential memory accumulates those classes. It compares the result with rotated major and minor probe-tone profiles using Pearson correlation. The best fit and the margin to the next fit are displayed. Correlation is not a posterior probability or a percentage of understanding.

The method follows the profile comparison described by Krumhansl and Schmuckler. Krumhansl's account connects it to experimentally measured tonal hierarchies. Temperley's reconsideration examines alternative profiles and temporal segmentation. This room uses a compact spectral approximation, rather than either full symbolic implementation.

The categories supply assumptions about what can count as a key. Major and minor are available; Dorian, non-octave scales and unpitched musical practices are not. Strong harmonics can contribute pitch classes absent from the commanded fundamentals. A stable label can therefore be a stable misdescription. Several seconds of signal and some chroma diversity are required before a label is shown, but that gate cannot certify correctness.

Changing the memory span changes the time over which the template asks for coherence. Short memory follows a local passage; longer memory carries earlier material into a modulation. Neither is the unique correct duration of musical attention. The choice is exposed because it changes what this reader can claim.

A silence has causes the samples cannot recover

Silence as a temporal relation

Pulse, meter, swing and interlocking cycles

A beat can have more than one account

A tonal template brings its own musical world

Expectation has an alphabet and a history

The score reader follows the center voice's commanded pitch classes and a thirteenth symbol for no command. It deliberately collapses several silence causes that the ledger keeps separate. A first-order transition table remembers a bounded number of recent transitions. Every possible next symbol receives a half-count prior so novel events have finite probabilities.

The program computes P(next | previous) before adding the new transition. Surprise is −log2 P. A low-probability event costs more bits under this model; repeated transitions can become cheaper. This is a statement about a declared predictive code. It is not a measure of how much you enjoyed a note or whether you found it meaningful.

Research using IDyOM studies musical predictability and uncertainty with substantially richer models and listener experiments. The little transition learner here is not IDyOM and has no training corpus. It begins with its prior and learns only from this take. It does not know cadence, voice separation, phrase function, performance history or your expectations.

A memory you can intervene on

Forget the listener clears future inference but leaves existing prediction receipts. Changing memory limits future transitions. A familiar return after a reset can be novel for this reader even if you remember it. Conversely, a repeated symbol can become statistically unsurprising while its musical use changes completely. These comparisons show where the alphabet and memory constrain the claim.

Expectation has an alphabet and a history

A memory you can intervene on

Expectation has an alphabet and a history

A memory you can intervene on

A silence has causes the samples cannot recover

Silence as a temporal relation

A tonal template brings its own musical world

Expectation has an alphabet and a history

A memory you can intervene on

Does the computer listen?

Use, recognition and responsibility

What this take records, and what it cannot

Evidence, limits and the open encounter

The finite program tests check Rule 30 arithmetic, tuning ratios, pulse distributions, prediction timing, sampled pitch fixtures, spectral time-reversal ambiguity, immutable records and interruption behavior. Actual browser review checks operation and layout. Offline audio verifies rendered samples. Those are separate kinds of evidence.

Thirteen independent engine checks and thirteen extension checks pass, with 13,759 extension comparisons. Twenty browser lifecycle conditions pass, including cancellation of a pending start and a synthetic hidden-tab event. All eight arrangements render nonzero, finite stereo samples at 48 kHz with peaks below 0.115 at the tested gain. Desktop and narrow-screen review checks the controls and contextual readings. These results apply to the reviewed program and fixtures.

The acoustic model is small, untrained and explicitly limited. It is not a source separator, speech recognizer, automatic score extraction system, psychoacoustic model or classifier of music. Its tonal vocabulary is culturally narrow. Its pulse estimate is ambiguous. Its pitch estimate can fail on the music this same instrument generates.

The work offers one subject, a finite computed score; one consequence, distinct observers lose distinct relations; one rejected alternative, a universal numerical music score; and one limit, no reader here certifies musical meaning or experience. Whether the instrument is rewarding to play, and what another person understands or resists without explanation, require reception. A passing test leaves those questions open.

Sonic absence

The measured signal

Listen to your own sound

What each reader retains

Acoustic reader

Score reader

Your account

Your phrases

The measured signal

Listen to your own sound ?

What each reader retains

Acoustic reader

Score reader

Your account ?

Your phrases

Listen to your own sound

Your account