Rhythm: One Coupling Continuum

Rhythm in conchordal is one coupling continuum on a shared emergent meter, not a set of independent clocks. The population drives a single production meter (a coupled-oscillator beat); each voice is a phase oscillator that entrains its onset phase to that emergent beat with a coupling strength. There is no externally imposed grid — coherence (or its absence) emerges from how tightly each voice locks to the meter the population itself drives.

The three rhythm “families” are just three regions of the continuum:

• metric: high coupling — a deep attractor, reads as a stable pulse.
• entrained: medium coupling — synchronization emerges over time, still drifts.
• flow: near-zero coupling — a free renewal process, non-metric texture.

Rhythm is part of the same ecology as consonance, viability, movement, and respawn: timing can affect survival, and survival reorganizes timing.

Director-level terrain

The director shapes the rhythmic terrain, symmetric to the consonance-field operations. These are soft priors, never a schedule — emergence still does the work:

• meter_stability(value) — attractor depth in [0,1]: how readily a pulse forms. It only deepens the basin for a real periodicity; it never fabricates a beat from non-metric input.
• temporal_basin(min_hz, max_hz) — the tempo region the emergent beat gravitates toward (the time-axis analogue of consonance(min, max)). It shapes the terrain; it does not place a beat, and it never forces a measure.

Per-voice presets and modifiers

The Tier-1 presets take no rate argument: metric(), entrained(), and flow(). The tempo region is a property of the terrain, set once at the director level, not per voice. They work on both a Material and a draft Participant.

Per-voice modifiers refine where on the continuum a voice sits:

• entrainment(strength) — coupling in [0,1], free (0) .. locked (1).
• rhythm_role("beat"|"subdivision"|"accent"|"texture") — the voice’s metrical job. accent emits a stronger onset that drives the shared meter harder, so a recurring downbeat can seed an emergent measure.
• microtiming(amount) — a signed beat-phase offset in [-0.5, 0.5]. 0.5 places a voice a half-beat off, reading as syncopation.

meter_stability(0.85);     // attractor depth: how readily a pulse forms
temporal_basin(1.8, 2.2);   // tempo region the emergent beat gravitates toward

let beat = harmonic()
    .metric()
    .rhythm_role("accent")  // a strong onset that drives the shared beat
    .cycles(2);

let entrained = harmonic()
    .entrained()
    .cycles(2);

let drift = harmonic()
    .flow()
    .cycles(1);

let offbeat = harmonic()
    .metric()
    .microtiming(0.5)       // a half-beat offset reads as syncopation
    .cycles(2);

place(beat, at(110.0));
place(entrained, consonance(110.0).peak().count(3));
place(drift, consonance(300.0, 1200.0).count(4));
place(offbeat, at(220.0));
wait(12.0);

Calls on the same axis are last-write-wins: the last timing mode and the last duration mode determine the final behavior. Modifiers are remembered and applied when their matching preset is selected, so entrainment(0.8).metric() and metric().entrainment(0.8) are equivalent. The same applies to duration_range(...).adaptive_duration() and the reverse order.

Explicit when/duration (Tier 2)

Below the presets sit explicit controls: once(), pulse(rate_hz), while_alive(), cycles(n), and adaptive_duration() (with duration_range, duration_curve, and shorten_on_drop for tuning).

Timing as survival (Tier 3)

Use rhythm_coupling_vitality(lambda_v, v_floor) and rhythm_reward(rho_t, "attack_phase_match") when timing should affect survival and reorganization, and rhythm_freq(freq_hz) to set the internal oscillator directly:

let pulse_voice = harmonic()
    .repeat()
    .pulse(2.0)
    .cycles(2)
    .rhythm_freq(2.0)
    .rhythm_coupling_vitality(0.8, 0.4)
    .rhythm_reward(0.4, "attack_phase_match");

place(pulse_voice, at(165.0));
wait(8.0);

Scaffolds (research controls)

The scaffold functions impose an external pulse for comparison assays:

set_scaffold_off();
set_scaffold_shared(2.0);
set_scaffold_scrambled(2.0, 17);

They are useful for demos and assays. They are not the rhythm-composition abstraction: composed rhythm should come from the continuum and the terrain.