1. Introduction: The Bio-Acoustic Paradigm

Conchordal represents a fundamental divergence from established norms in generative music and computational audio. Where traditional systems rely on symbolic manipulation—operating on grids of quantized pitch (MIDI, Equal Temperament) and discretized time (BPM, measures)—Conchordal functions as a continuous, biologically grounded simulation of auditory perception. It posits that musical structure is not an artifact of abstract composition but an emergent property of acoustic survival.

This technical note serves as an exhaustive reference for the system's architecture, signal processing algorithms, and artificial life strategies. It details how Conchordal synthesizes the principles of psychoacoustics—specifically critical band theory, virtual pitch perception, and neural entrainment—with the dynamics of an autonomous ecosystem. In this environment, sound is treated as a living organism, a "Voice" possessing metabolism, sensory processing capabilities, and the autonomy to navigate a hostile spectral terrain.

The emergent behavior of the system is driven by a unified fitness function: the pursuit of Consonance. Agents within the Conchordal ecosystem do not follow a pre-written score. Instead, they continuously analyze their environment to maximize their "Spectral Comfort"—defined as the minimization of sensory roughness—and their "Harmonic Stability," or the maximization of virtual root strength. The result is a self-organizing soundscape where harmony, rhythm, and timbre evolve organically through the interactions of physical laws rather than deterministic sequencing.

This document explores the four foundational pillars of the Conchordal architecture, mirroring the Manifesto's two perceptual axes:

1. The Psychoacoustic Coordinate System: The mathematical framework of Log2Space and ERB scales that replaces linear Hertz and integer MIDI notes.
2. The Frequency Axis — the Auditory Landscape: The real-time DSP pipeline that computes Roughness ($R$) and Harmonicity ($H$) fields from the raw audio stream.
3. The Temporal Axis — the Emergent Meter: The coupled-oscillator model that forms a metrical percept from the ecosystem's own onsets.
4. The Life Engine: The agent-based model governing the metabolism, movement, and entrainment of the audio entities that inhabit both terrains.

2. The Psychoacoustic Coordinate System

A critical innovation in Conchordal is the rejection of the linear frequency scale ($f$) for internal processing. Human auditory perception is inherently logarithmic; our perception of pitch interval is based on frequency ratios rather than differences. To model this accurately and efficiently, Conchordal establishes a custom coordinate system, Log2Space, which aligns the computational grid with the tonotopic map of the cochlea.

2.1 The Log2 Space Foundation

The Log2Space struct serves as the backbone for all spectral analysis, kernel convolution, and agent positioning within the system. It maps the physical frequency domain ($f$ in Hz) to a perceptual logarithmic domain ($l$).

2.1.1 Mathematical Definition

The transformation from Hertz to the internal log-coordinate is defined as the base-2 logarithm of the frequency. This choice is deliberate: in base-2, an increment of 1.0 corresponds exactly to an octave, the most fundamental interval in pitch perception.

$$ l(f) = \log_2(f) $$

The inverse transformation, used to derive synthesis parameters for the audio thread, is:

$$ f(l) = 2^l $$

The coordinate space is discretized into a grid defined by a resolution parameter, bins_per_oct ($B$). This parameter determines the granularity of the simulation. A typical value of $B=48$ or $B=96$ provides sub-semitone resolution sufficient for continuous pitch gliding and microtonal inflection. The step size $\Delta l$ is constant across the entire spectral range:

$$ \Delta l = \frac{1}{B} $$

2.1.2 Grid Construction and Indexing

The Log2Space structure pre-calculates the center frequencies for all bins spanning the configured range $[f_{min}, f_{max}]$. The number of bins $N$ is determined to ensure complete coverage:

$$ N = \lfloor \frac{\log_2(f_{max}) - \log_2(f_{min})}{\Delta l} \rfloor + 1 $$

The system maintains two parallel vectors for $O(1)$ access during DSP operations:

• centers_log2: The logarithmic coordinates $l_i = \log_2(f_{min}) + i \cdot \Delta l$.
• centers_hz: The pre-computed linear frequencies $f_i = 2^{l_i}$.

This pre-computation is vital for real-time performance, removing the need for costly log2 and pow calls inside the inner loops of the spectral kernels. The method index_of_freq(hz) provides the quantization logic, mapping an arbitrary float frequency to the nearest bin index.

2.2 Constant-Q Bandwidth Characteristics

The Log2Space inherently enforces a Constant-Q (Constant Quality Factor) characteristic across the spectrum. In signal processing terms, $Q$ is defined as the ratio of the center frequency to the bandwidth: $Q = f / \Delta f$.

In a linear system (like a standard FFT), $\Delta f$ is constant, meaning $Q$ increases with frequency. In Log2Space, the bandwidth $\Delta f_i$ of the $i$-th bin scales proportionally with the center frequency $f_i$. This property mimics the frequency selectivity of the human auditory system, where the ear's ability to resolve frequencies diminishes (in absolute Hz terms) as frequency increases. This alignment allows Conchordal to allocate computational resources efficiently—using high temporal resolution at high frequencies and high spectral resolution at low frequencies—without manual multirate processing.

2.3 The Equivalent Rectangular Bandwidth (ERB) Scale

While Log2Space handles pitch relationships (octaves, harmonics), it does not perfectly model the critical bands of the ear, which are wider at low frequencies than a pure logarithmic mapping suggests. To accurately calculate sensory roughness (dissonance), Conchordal implements the Equivalent Rectangular Bandwidth (ERB) scale based on the Glasberg & Moore (1990) model.

The core/erb.rs module provides the transformation functions used by the Roughness Kernel. The conversion from frequency $f$ (Hz) to ERB-rate units $E$ is given by:

$$ E(f) = 21.4 \log_{10}(0.00437f + 1) $$

The bandwidth of a critical band at frequency $f$ is:

$$ BW_{ERB}(f) = 24.7(0.00437f + 1) $$

This scale is distinct from Log2Space. While Log2Space is the domain for pitch and harmonicity (where relationships are octave-invariant), the roughness calculation requires mapping spectral energy into the ERB domain to evaluate interference. The system effectively maintains a dual-view of the spectrum: one strictly logarithmic for harmonic templates, and one psychoacoustic for dissonance evaluation.

3. The Frequency Axis: The Auditory Landscape

Music cognition treats consonance not as a property of notation but as a percept with two distinct components. Sensory dissonance is a bottom-up sensation: when two partials fall within the same critical band on the basilar membrane, their interference is heard as beating and roughness—a phenomenon present for any listener, musical training or not. Tonal fusion is a structural percept: partials standing in harmonic relation are bound by the auditory system into a single tone with a single (possibly virtual) pitch, heard as one voice rather than many. What musicians call consonance is the integration of the two—low roughness and strong fusion. The small-integer ratios celebrated since Pythagoras are properties of the stimulus; the harmony itself is constructed in the listener.

Both components have quantitative models. Helmholtz located dissonance in beating; Plomp and Levelt measured its dependence on critical bandwidth, yielding the roughness curve that peaks at roughly a quarter of a critical band and vanishes beyond it. Fusion runs through Stumpf's Tonverschmelzung to Terhardt's virtual pitch: the auditory brainstem, phase-locked to temporal fine structure, matches incoming partials against harmonic templates and infers the fundamental that best explains them—even when that fundamental is physically absent. The two mechanisms are separable: a sound can be smooth yet unfused, or fused yet rough.

Conchordal adopts this account literally. The system runs a cochlear front end on its own sound, computes a Roughness field and a Harmonicity field over the entire frequency axis, and integrates them into Consonance—a terrain whose peaks are where a new tone would fuse and whose valleys are where it would grate. Nothing in the system knows an interval name or a ratio; agents feel only this terrain. Section 4 applies the same move to time: just as harmony is computed from a model of the cochlea rather than imposed, meter is computed from a model of beat perception rather than scheduled.

The "Landscape" is the central data structure in Conchordal. It acts as the shared environment for all agents, a dynamic scalar field representing the psychoacoustic "potential" of every frequency bin. Agents do not interact directly with each other; they interact with the Landscape, which aggregates the spectral energy of the entire population. This decouples the complexity of the simulation from the number of agents ($O(N)$ vs $O(N^2)$).

The Landscape is updated every audio frame (or block) by the Analysis Worker. It synthesizes two primary metrics:

• Roughness ($R$): The sensory dissonance caused by rapid beating between proximal partials.
• Harmonicity ($H$): The measure of virtual pitch strength and spectral periodicity.

Both metrics are normalized to the $[0, 1]$ range. The rest of this chapter follows the analysis pipeline in order: Section 3.1 builds the log-frequency spectrum (NSGT), Sections 3.2 and 3.3 derive the Roughness and Harmonicity fields from it, and Section 3.4 integrates the two into the Consonance terrain that agents actually climb.

3.1 Non-Stationary Gabor Transform (NSGT)

To populate the Log2Space with spectral data, Conchordal uses a custom implementation of the Non-Stationary Gabor Transform (NSGT). Unlike the Short-Time Fourier Transform (STFT), which uses a fixed window size, the NSGT varies the window length $L$ inversely with frequency to maintain the Constant-Q property derived in Section 2.2.

3.1.1 Kernel-Based Spectral Analysis

The implementation in core/nsgt_kernel.rs utilizes a sparse kernel approach to perform this transform efficiently. For each log-frequency band $k$, a time-domain kernel $h_k$ is precomputed. This kernel combines a complex sinusoid at the band's center frequency $f_k$ with a periodic Hann window $w_k$ of length $L_k \approx Q \cdot f_s / f_k$.

$$ h_k[n] = w_k[n] \cdot e^{-j 2\pi f_k n / f_s} $$

These kernels are transformed into the frequency domain ($K_k[\nu]$) during initialization. To optimize performance, the system sparsifies these frequency kernels, storing only the bins with significant energy.

During runtime, the system performs a single FFT on the input audio buffer to obtain the spectrum $X[\nu]$. The complex coefficient $C_k$ for band $k$ is then computed via the inner product in the frequency domain:

$$ C_k = \frac{1}{N_{fft}} \sum_{\nu} X[\nu] \cdot K_k^*[\nu] $$

This "one FFT, many kernels" approach generates a high-resolution, logarithmically spaced spectrum without the cost of calculating a separate DFT for every band or using recursive filter banks. The current instrument runtime constructs a 96-bin-per-octave analysis space from 55 Hz to 8 kHz; Log2Space itself supports other positive, ordered bounds for experiments and tests.

3.1.2 Real-Time Temporal Smoothing

The instantaneous band powers $p_k = |C_k|^2$ exhibit high variance due to the stochastic nature of the audio input (especially with noise-based agents). To create a stable field for agents to sample, the RtNsgtKernelLog2 struct wraps the NSGT with a temporal smoothing layer.

It implements a per-band leaky integrator (exponential smoothing). Crucially, the time constant $\tau$ is frequency-dependent. Low frequencies, which evolve slowly, are smoothed with a longer $\tau$, while high frequencies, which carry transient details, have a shorter $\tau$.

$$ y_k[t] = (1 - \alpha_k) \cdot p_k[t] + \alpha_k \cdot y_k[t-1] $$

where the smoothing factor $\alpha_k$ is derived from the frame interval $\Delta t$:

$$ \alpha_k = e^{-\Delta t / \tau(f_k)} $$

This models the "integration time" of the ear. It is only the first perceptual stage: the smoothed power is subsequently converted into a sparse subjective-intensity density before the Roughness and Harmonicity kernels read it.

3.1.3 From NSGT Power to Subjective Intensity

SpectralFrontEnd (core/landscape_spectral.rs) does not pass the smoothed NSGT power directly to the Landscape kernels. For each hop it:

1. Converts per-bin power to power density using the Log2Space-aligned ERB cell widths.
2. Extracts significant spectral peaks, preserving their integrated mass rather than treating every analysis bin as an independent partial.
3. Applies an A-weighting power gain and the compressive exponent loudness_exp to each peak mass.
4. Scatters the resulting masses back onto a sparse Log2Space-aligned subjective-intensity density and applies a second leaky normalization with time constant analysis.tau_ms.

The resulting subjective_intensity scan—not raw $|C_k|$ or raw NSGT power—is the common input to the Roughness and Harmonicity computations below. Its integral is retained separately as loudness_mass.

3.2 Roughness ($R$) Calculation: The Plomp-Levelt Model

Roughness is the sensation of "harshness" or "buzzing" caused by the interference of spectral components that fall within the same critical band but are not sufficiently close to be perceived as a single tone (beating). Conchordal implements a variation of the Plomp-Levelt model via convolution in the ERB domain.

3.2.1 The Interference Kernel

The core of the calculation is the Roughness Kernel, defined in core/roughness_kernel.rs. This kernel $K_{rough}(\Delta z)$ models the interference curve between two partials separated by $\Delta z$ ERB-rate units. The default Sethares core peaks near a quarter ERB-rate unit; the reference-normalization stimulus uses a separation of 0.25 ERB.

The implementation uses a Sethares difference-of-exponentials core, a small directional masking asymmetry, a center-suppression dip, and an optional neural Gaussian component. With $u=|\Delta z|/\kappa$:

$$ S(\Delta z) = G,\max(0, e^{-bu} - e^{-cu}),A(\Delta z) $$

$$ M(\Delta z) = \left(1-e^{-\Delta z^2/(2\sigma_{sup}^2)}\right)^p, \qquad N(\Delta z)=e^{-\Delta z^2/(2\sigma_n^2)} $$

$$ K_{rough}(\Delta z)=(1-w_n),S(\Delta z)M(\Delta z)+w_nN(\Delta z) $$

Here $A(\Delta z)$ is the exponentially decaying positive/negative-side asymmetry controlled by mix_tail and tau_erb. The default $w_n=0$ selects the cochlear Sethares path. $M(0)=0$ suppresses self-roughness for a single pure tone; raising $w_n$ deliberately fills that dip with the neural component.

3.2.2 Convolutional Approach

Calculating roughness pairwise for all spectral bins ($N^2$ complexity) is computationally prohibitive for real-time applications. Conchordal solves this by treating the Roughness calculation as a linear convolution.

1. Mapping: The Log2Space-aligned subjective-intensity density from Section 3.1.3 is mapped onto a linear ERB grid.
2. Convolution: This density $A(z)$ is convolved with the pre-calculated roughness kernel $K_{rough}$.

$$ R_{shape}(z) = (A * K_{rough})(z) = \int A(z-\tau) K_{rough}(\tau) d\tau $$

The result $R_{shape}(z)$ represents the raw "Roughness Shape" at frequency $z$. To convert this to a normalized fitness signal, Conchordal applies a physiological saturation mapping.

3.2.3 Physiological Saturation Mapping

Raw roughness values from the convolution have unbounded range. Rather than hard-clamping, Conchordal uses a saturation curve that models the compressive nonlinearity of auditory perception. This mapping converts reference-normalized roughness ratios to the $[0, 1]$ range.

Reference Normalization: The system maintains reference values $r_{ref,peak}$ and $r_{ref,total}$ representing "typical" roughness levels. The reference-normalized ratios are:

$$ x_{peak}(u) = \frac{R_{shape}(u)}{r_{ref,peak}} $$

$$ x_{total} = \frac{R_{shape,total}}{r_{ref,total}} $$

The Saturation Parameter: The parameter roughness_k ($k > 0$) controls the saturation curve's shoulder. The reference ratio $x = 1$ maps to:

$$ R_{ref} = \frac{1}{1+k} $$

Larger $k$ reduces $R_{01}$ for the same input ratio. $k$ belongs to the sensation model and is set only in the configuration; how much roughness is minded is a valuation, changed from scenarios through set_roughness_aversion (Section 3.4).

Piecewise Saturation Mapping: The normalized roughness $R_{01}$ is computed from the reference-normalized ratio $x$ as:

$$ R_{01}(x; k) = \begin{cases} 0 & \text{if } x \leq 0 \ x \cdot \frac{1}{1+k} & \text{if } 0 < x < 1 \ 1 - \frac{k}{x+k} & \text{if } x \geq 1 \end{cases} $$

This function is continuous at $x = 1$ (both branches yield $\frac{1}{1+k}$) and saturates asymptotically to 1 as $x \to \infty$. The piecewise structure ensures linear response for low roughness (preserving sensitivity) while compressing extreme values (preventing saturation).

Numerical Safety: The implementation handles edge cases robustly:

• $x = \text{NaN} \to 0$
• $x = +\infty \to 1$
• $x = -\infty \to 0$
• Non-finite $k$ is treated as $10^{-6}$

Agents seeking consonance actively avoid peaks in the $R_{01}$ field.

3.3 Harmonicity ($H$): The Sibling Projection Algorithm

While Roughness drives agents away from dissonance (segregation), Harmonicity ($H$) drives them toward fusion—the creation of coherent chords and timbres. Conchordal introduces a novel algorithm termed "Sibling Projection" to compute this field. This algorithm approximates the brain's mechanism of "Common Root" detection (Virtual Pitch) entirely in the frequency domain.

3.3.1 Concept: Virtual Roots

The algorithm posits that any spectral peak at frequency $f$ implies the potential existence of a fundamental frequency (root) at its subharmonics ($f/2, f/3, f/4 \dots$). If multiple spectral peaks share a common subharmonic, that subharmonic represents a strong "Virtual Root".

3.3.2 The Two-Pass Projection

The algorithm operates on the Log2Space spectrum in two passes, utilizing the integer properties of the logarithmic grid:

1. Downward Projection (Root Search): The current spectral envelope is "smeared" downward. In scatter form: every bin $i$ with energy adds evidence to the bins $i - \log_2(k)$ for integers $k \in {1, 2, \dots, N}$ (its candidate roots). The implementation uses the equivalent gather form—each bin collects evidence from the positions where its harmonics would lie:

   $$ Roots[i] = \sum_k A[i + \log_2(k)] \cdot w_k $$

   On the log-frequency grid, $\log_2(k)$ is a constant bin offset (non-integer offsets are interpolated). $w_k$ is a weighting factor that decays with harmonic index $k$ (e.g., $k^{-\rho}$), reflecting that lower harmonics imply their roots more strongly than higher ones. The result Roots describes the strength of the virtual pitch at every frequency.

2. Upward Projection (Harmonic Resonance): The system then projects the Roots spectrum back upwards. If a strong root exists at $f_r$, it implies stability for all its natural harmonics ($f_r, 2f_r, 3f_r \dots$).

   $$ H[i] = \sum_m Roots[i - \log_2(m)] \cdot w_m $$

Emergent Tonal Stability: Consider an environment with a single tone at 200 Hz.

• Step 1 (Down): It projects roots at 100 Hz ($f/2$), 66.6 Hz ($f/3$), 50 Hz ($f/4$), etc.
• Step 2 (Up): The 100 Hz root projects stability to 100, 200, 300, 400, 500... Hz.
  • 300 Hz lies a perfect fifth above the 200 Hz tone (3:2).
  • 500 Hz lies a major tenth above it (5:2): an octave plus a major third.

No interval name appears in the code. The peaks follow from H's integer-ratio templates, a model of periodicity-based fusion; the integer prior is built into the kernel, not discovered by it. An agent at 200 Hz creates a "gravity well" at 300 Hz and 500 Hz, inviting other agents to form a major triad in open position (2:3:5).

3.4 Consonance: Integrating the Fields

With $R_{01}$ and $H_{01}$ in hand, Consonance is derived in two layers: a Consonance Kernel that fuses the two observables into a single fitness score, and a set of representation transforms that reshape that score for its different consumers in the Life Engine (Section 5).

Layer 1 — Consonance Kernel (bilinear family):

$$ C_{score} = a \cdot H_{01} + b \cdot R_{01} + c \cdot H_{01} R_{01} + d $$

Default coefficients: $a = 1.0$, $b = -1.35$, $c = 1.0$, $d = 0.0$. Because $b < 0$, roughness acts as a penalty; because $c > 0$, high harmonicity attenuates that penalty (the interaction term $c \cdot H_{01} R_{01}$ partially cancels $b \cdot R_{01}$ when $H_{01}$ is large). The bilinear family subsumes the earlier $\alpha H - wR$ formulation as the special case $c = 0$.

The director's set_roughness_aversion(w) multiplies the roughness terms $b$ and $c$, and the density $\rho$ below, by $w$ (default 1, which leaves the configured values bit-exact). $w$ is clamped to $[0, 100]$ and non-finite values are ignored. $w = 0$ makes valuation ignore roughness. Larger $w$ penalizes roughness more when the configured kernel penalizes it at every harmonicity ($b \le 0$ and $b + c \le 0$, true for the defaults). $R_{01}$ itself, as sensed and displayed, does not change.

Layer 2 — Representations:

Name	Formula	Range	Meaning
$C_{score}$	$aH + bR + cHR + d$	$(-\infty,+\infty)$	raw fitness from the kernel
$C_{level01}$	$\sigma(\beta(C_{score} - \theta))$	$[0,1]$	base sigmoid level; habituation drive and un-eroded view
$C_{density_mass}$	$\max(0,;H_{01}(1 - \rho R_{01}))$	$[0,+\infty)$	base density mass before erosion
$C_{density_pmf}$	$\text{normalize}(C_{density_mass}^{eff})$	$[0,1],;\Sigma=1$	normalized global view retained in Landscape
$C_{energy}$	$-C_{score}$	$(-\infty,+\infty)$	energy for minimization
$C_{score}^{eff}$	$\theta+(C_{score}-\theta)(1-h)$	$(-\infty,+\infty)$	habituation-eroded score read by movement and prediction
$C_{level01}^{eff}$	$\sigma(\beta(C_{score}^{eff}-\theta))$	$[0,1]$	habituation-eroded level read by behavior and the listener
$C_{density_mass}^{eff}$	$(1-h)C_{density_mass}$	$[0,+\infty)$	habituation-eroded mass read by density placement

where $\sigma(x) = 1/(1+e^{-x})$, $\beta$ controls sigmoid steepness (default 2.0), and $\theta$ is the sigmoid threshold (default 0.0). The density mass uses a separate $\rho$-kernel with coefficients $a{=}1, b{=}0, c{=}{-}\rho, d{=}0$; $\rho$ (consonance_density_roughness_gain, default 1.0) controls how strongly roughness suppresses density placement.

Spawn samples a range-local distribution. By default, a SpawnStrategy::Field slices the requested frequency range, derives target-specific local mass from the effective views, masks occupied bins, and normalizes only that local vector. A zero-mass range falls back to an unoccupied-uniform distribution and then to full-range uniform if every bin is occupied. Peak placement chooses the target extremum deterministically, or the nearest field-score target when tension is specified. The global $C_{density_pmf}$ remains a normalized Landscape representation exercised by core tests.

The root configuration key birth_surrogate = true enables optional body-density evaluation for Field placement; it is disabled by default. For each candidate fundamental, a direct model of the selected renderer estimates the body's subjective-intensity density. Density placement integrates that density against the effective target mass over ERB cells, divides by the body's in-band mass, and uses the result as the local birth weight. Peak placement integrates the target score instead. All candidates are evaluated within the same hop; equal body recipes reuse their preparation while occupancy and spacing are updated after each birth. Range-local normalization and the zero-mass fallbacks remain in force. Unsupported bodies and recipes use the existing terrain-only placement (the supported conditions are listed in Section 5.1.1).

The birth option is independent of body-aware metabolism (Section 5.2); both can be enabled together. The excitation renderer supports Field placement and frequency proposals for Sine and the supported Harmonic recipes; Modal retains terrain-only placement. With the legacy renderer, the option also affects supported final respawn evaluations. Random retains 16 proposals and resamples their non-negative scene scores. Hereditary selects one parent and keeps the maximum-level choice among 16 proposals. PeakBiased keeps its terrain-peak proposals, parent bias and local search grid, but uses integrated body scores for its final weights and local search when supported. The integrated score is converted to level with the same configured sigmoid as the terrain; minimum-level rejection therefore retains its scale and threshold. Unsupported policy/body combinations use the existing point evaluation. With the excitation renderer, final respawn selection, local search and minimum-level rejection retain point evaluation because native final-selection distributions have not been conformed.

The author adopted a maximum total-variation distance of 0.1 from the rendered-and-analyzed selection distribution for each supported measured body condition. The value is an author acceptance rule chosen to include the measured Sine result (about 0.095); it is not derived from the psychoacoustic model. For the legacy renderer, the bound was checked only at the measured points in saved Consonance/Density fixtures: 104 groups of seven candidates near 440 and 1800 Hz, at 48 kHz with hop 512, in silence and other-only Sine 440 Hz, Sine 660 Hz and Harmonic 330 Hz environments. These fixtures have no occupancy, spacing or tension. For the excitation renderer, the corresponding 64 Sine/Harmonic groups were checked against native candidate PCM, keeping the saved terrain and realized mode ratios fixed. The guarantee is limited to the supported conditions in those fixtures; it does not extend to arbitrary parameters or environments, Peak placement or final respawn distributions. Legacy final respawn selection has the separate measured scope below.

Legacy final respawn evaluation uses the same author rule of total-variation distance at most 0.1. Saved rendered candidate scores were passed through the existing Random and Hereditary selectors, with the seven measured frequencies repeated cyclically to form 16 proposals; the supported measured conditions reached maxima of 0.095963 and 0, respectively. PeakBiased was checked with 16 terrain-derived proposals from its existing generator and the default parent bias and local search (0.50-semitone radius, 0.05-semitone step), around 440 Hz in the other-only Harmonic 330 Hz environment. At 48 kHz with hop 512 and 72-hop body observations, its complete final distribution included 158 rendered candidate frequencies per body condition; the supported conditions reached a maximum of 0.025876. These results cover those saved measurements and that bounded PeakBiased case, not arbitrary parameters, environments or proposal sets. Conditions exceeding the author rule retain point evaluation; the policy-specific supported domains are listed in Section 5.1.1.

There is also a distinct, per-Voice adaptation mechanism. AdaptationContext tracks fast boredom and slow familiarity over the shared fundamental-occupancy field and adds a candidate-specific score adjustment during pitch selection. It coexists with the Landscape-level habituation below: adaptation is agent-relative memory; habituation is a shared perceptual erosion field.

3.5 Landscape-Level Habituation

Consonance is not treated as an inexhaustible place. When [psychoacoustics.habituation] is enabled, HabituationField maintains a per-bin state $h_i\in[0,1]$ for both the ecology's habitat analysis and the ListenerTwin's presentation analysis. The raw drive combines the base consonance level $L_i$ with a fresh common-root projection $P_i$:

$$ d_i^{raw}=L_iP_i, \qquad d_i=\frac{d_i^{raw}}{d_i^{raw}+r_{ref}} $$

The state relaxes asymmetrically toward that drive:

$$ h_i(t+\Delta t)=a h_i(t)+(1-a)d_i, \qquad a=e^{-\Delta t/\tau} $$

with $\tau=\tau_e$ when the drive exceeds the current state and $\tau=\tau_r$ otherwise. satiation_sec and recovery_sec are the times to reduce the discrepancy from the respective equilibrium by 90%, so the implementation uses $\tau_e=T_s/\ln 10$ and $\tau_r=T_r/\ln 10$. The sustained-drive equilibrium depends on drive strength; after complete withdrawal it is zero. The effective score relaxes toward the neutral sigmoid threshold $\theta$, while density mass is eroded multiplicatively, as shown in the table above.

The default is enabled=true, with satiation_sec=5.0, recovery_sec=8.0, and ref_drive=0.25. Explicit enabled=false is an exact identity: every effective view equals its base view bit-for-bit. When enabled, movement, prediction, metabolism, respawn, density placement, and the listener read effective views; the UI terrain and diagnostics intentionally retain the un-eroded base views. Habituation belongs to the sensation and in-performance listener model; Rhai provides no switch for it. Scientific controls use explicit enabled=false.

With --report, an additional habituation_scan record at each generated second carries fmin_hz, bins_per_octave, n_bins, and the habitat's state_scan, raw_score_scan, and eff_score_scan. The arrays share fixed Log2Space coordinates and are serialized from borrowed slices. This permits a fixed region to be followed through withdrawal; the older per-hop tracked_bin remains the moving raw-score maximum.

4. The Temporal Axis: The Emergent Meter

Music cognition distinguishes three layers of musical time. Rhythm is the surface: the actual pattern of onsets as they occur. Pulse (the tactus) is the perceived regular beat a listener taps along to—already an inference, since the surface rarely contains it explicitly. Meter is the hierarchical organization of that pulse: nested periodicities (subdivision, beat, measure) with alternating strong and weak positions. Crucially, meter in this sense is a percept, not a notation. A time signature is an instruction; meter is what a listener's brain constructs from the sound—and constructs even from sound that was never notated.

This percept has well-studied dynamics. It takes a few cycles of evidence to establish (beat induction); once established it persists through syncopation, gaps, and silence, with events heard against the induced grid rather than destroying it; and it is plastic, re-locking when the input tempo drifts. Neural resonance theories (Large and colleagues) explain these properties mechanistically: populations of neural oscillators entrain to acoustic onsets, and the self-sustaining dynamics of the oscillation—not the stimulus itself—carry the pulse across interruptions.

Conchordal uses this structure in an engineering mechanism. It eschews the concept of a master clock or metronome; time is structured by an emergent meter—a self-sustaining beat oscillator with adaptive integer-ratio layers—that listens to the ecosystem's own onsets and forms a metrical percept from them. Voices, in turn, entrain their onset timing to this perceived pulse with per-voice coupling strengths (Section 5.4). Rhythm is therefore a closed perception–action loop: nothing schedules a beat; a beat condenses out of the population's behavior and then attracts it. This is the temporal mirror of the harmonic landscape (Section 3): just as consonance is not imposed but computed from a model of the cochlea, meter is not imposed but computed from a model of beat perception.

4.1 The Meter Core: An Adaptive Integer-Ratio Hierarchy

The default Events input and the presentation-side ListenerTwin meter use acoustic onset recurrence. An opt-in Continuous input for the existing production meter is selected by the top-level temporal_meter_t2 = true (default false). It reads raw habitat T2 directly and shares the beat, fast onset detector, PLV, integer layers, shaping and output state with the Events mechanism. It does not add a second production meter.

MeterNetwork (core/meter.rs) combines a self-sustaining beat oscillator with acoustic recurrence corroboration. Its amplitude retains the forced Hopf equation, while phase advances freely between detected onsets:

$$ \dot r = \alpha r + \beta r^3 + F_a,g,s(t)\cos\varphi, \qquad \dot\varphi=\omega $$

Here $g=1+\mathrm{stability}$, $\alpha=1$ and $\beta=-1$. The unforced radius tends to 1, so the beat continues through gaps. Production drive combines the habitat bus's DorsalStream spectral flux with habitat-routed phonation onset strengths. Presentation-only Voices do not directly reinforce this meter.

At detected onset $j$, the meter measures phase error $\epsilon_j$ before correcting its prediction. It adjusts the current period $T$ using the preceding error and corrects phase using the current error:

$$ T^+=T^-\left(1+\eta_p g\frac{\sin\epsilon_{j-1}}{2\pi}\right), \qquad \varphi^+=\varphi^- -\eta_\varphi g\sin\epsilon_j. $$

The gains $\eta_\varphi=0.6$ and $\eta_p=0.1$ come from the Large & Jones (1999) simulation. The meter retains detected acoustic onset times for $H=2\times2,\mathrm{s}+60,\mathrm{ms}=4.06,\mathrm{s}$, covering two maximum candidate intervals and the confirmation tail. Three possibly nonadjacent onsets corroborate a lag $p$ when successive spacings agree within $w(p)=\min(0.2p,60,\mathrm{ms})$, reusing the acoustic participation window. Lags are ranked by $R(p)=M(p)/N$, where $M$ is triangular, chronological one-to-one matching mass between the history and its shift by $p$, and $N$ is the full history's event count, common to all candidates. An already accepted lag remains in this comparison. Histories whose adjacent intervals all agree within the existing window retain the previous adjacent-interval confirmation path. From the corroborated rate $f_o=1/p$, the meter considers $f_r=r f_o$ for $r\in{1,1/2,1/3,1/4,2,3,4}$ within the continuous beat band, normally 0.5–4 Hz. Ideal nested event trains give support $S_r=\min(r,1/r)$: shared events divided by their union. Thus a faster candidate cannot win solely because its PLV also aligns with every input onset.

Candidates are ranked by $S_r W(f_r)$. The cultural prior is $W=(1-s)+sP$, with $s=\mathrm{clamp}(\texttt{meter_stability},0,1)$. Here $P$ falls linearly with log-frequency distance from the preferred center to either band edge. The center is the arithmetic mean of an explicit temporal_basin, or 2 Hz in the default band. The default depth 0 gives flat weighting within the band; greater depth favors an in-band tactus nearer the center. With an explicit basin, the center restoring term uses the same depth and is reduced by preceding beat confidence. This is an engineering rule based on neural resonance structure, rather than a numerical transplant of a published oscillator network.

The first adoption anchors phase zero to its onset, clears evidence in the old coordinates, and does not count that onset as evidence for itself. Subsequent corroboration sets the resulting tempo without resetting phase; the event correction and remaining hop advance also update the unwrapped beat count. An established beat survives whole missing beats: an interval compatible with two, three or four current periods retains the established tactus. This resolves the ambiguity in favor of persistence and cannot separately identify a sudden integer-factor slowdown from missing onsets.

Subdivision phases are $2\varphi,3\varphi,4\varphi$; measure phases divide the unwrapped beat count by 2, 3 or 4. Each layer retains separate phase-coherence or accent evidence. Faster-than-band input can therefore be read as subdivision of an in-band beat. Independent noninteger tempi and adaptive inter-oscillator coupling are outside this implementation.

Perception vs production. The runtime uses this same mechanism in two instances. The production meter listens to the habitat bus and guides Voice behavior. The ListenerTwin meter listens to presentation audio and supplies beat confidence to the UI and report. DCC pressure uses presentation-derived consonance tension, rather than beat confidence directly.

Continuous habitat recurrence

Continuous input retains the native 30×4 signed hop means without group attribution or component weights. It forms positive rises only from two consecutive, known hops with the same filter reset origin. Within the existing 4.06-second history, native-hop lags compare component-wise minimum and maximum masses; their intersection/union ratio proposes recurrence. A flat profile does not induce a beat. Interior strict peaks may use the fixed local quadratic vertex, reevaluated against the actual linearly interpolated overlap. The accepted lag wins a tie, followed by the shorter grid lag. The existing integer aliases and cultural prior choose the tactus.

T2 proposes recurrence; actual habitat flux and executed onset reinforcement supply phase and intensity. A proposal received at a hop end can be adopted only at a subsequent fast onset. Initial adoption clears old confirmation evidence and contributes no confidence. Once adopted, each issued future source-hop component prediction freezes its lag, source support and target. Only coordinates known in both prediction and later observation contribute, once, to predicted, observed and matching masses. Late evidence retains its source age. Known silence can disagree with a positive prediction; missing evidence contributes no disagreement.

Raw frames are computed once in the analysis thread and sent through a bounded, preallocated queue, independently of the group arrival adapter. Playback does not wait on this queue; overflow records a missing interval. Offline rendering waits for the current source-hop result at the fixed end cut, after fast advancement and before state publication and the next forecast. Physical source time, availability and receipt remain distinct. A source gap restarts the recursive filters and breaks unsupported differences/interpolation, while the accepted meter coordinate and bounded history persist. Configuration, bus, sample-rate, hop or feature-unit changes require an explicit coordinate reset. Filter origin and the group's existing continuity epoch are not the raw configuration epoch.

4.2 Beat Confidence: Phase and Pattern Recurrence

The following event-count confirmation describes Events input. Until an interval hypothesis has first been corroborated, the meter accumulates no beat, subdivision or measure evidence: all three confidences and the subdivision/measure ratios are zero (unknown). The oscillator and onset-event corrections continue during this interval. After corroboration, subsequent detected onsets contribute unit phasors at their predicted phases before correction. Their leaky resultant length divided by their leaky count is the phase-locking value (PLV). A single-position history retains $\mathrm{PLV}\times\mathrm{presence}$. Evidence decays with a 2.5-second time constant; measure accents use 6 seconds. Stability lowers the presence thresholds but preserves the confidence ceiling of 1. The initial adoption contributes no phasor. Subdivision evidence combines its harmonic coherence with $\tfrac12(1-\mathrm{beat\ PLV})$, keeping a beat-only input from certifying its harmonics as subdivisions.

After first adoption, each subsequent onset issues a prediction at its then-current basic lag $t_i+p$. Issued targets are not rewritten when tempo changes. Future onsets and targets match one-to-one within $w(p)$, with triangular timing weight. After their windows close, leaky predicted, observed and matching masses give $J=M/(N_p+N_o-M)$. These are fresh post-confirmation masses; the confirming onset supplies neither a prediction nor confidence evidence. If a retained adjacent interval is shorter than $p-w(p)$, the history contains multiple positions and beat confidence reads $\max(\mathrm{PLV},J S_r)\times\mathrm{presence}$. This supports recurrence of a pattern without requiring every event to occupy the same phase. Subdivision and measure evidence keep their existing phase and accent rules.

Confidence describes phase coherence or confirmed pattern recurrence with accumulated evidence. After initial corroboration, a chance cluster in irregular input can still produce a temporary rise; confidence alone does not certify a unique tempo. In silence the oscillator continues while evidence and presence decay. Phase zero remains the predicted onset and is not shifted again by subtracting the mean onset-phasor angle.

For Continuous input, the future component comparisons accumulate matching $M$, predicted $Q$ and observed $O$ with the existing persistence decay. Where $Q+O-M>0$, the recurrence support is $S_R=\rho M/(Q+O-M)$, with the existing integer-alias profile $\rho=\min(r,1/r)$. Beat confidence is $\operatorname{clamp}{[0,1]}(\max(\mathrm{PLV}{fast},S_R),\mathrm{presence}_{fast})$; undefined support is omitted rather than treated as a negative observation. Initial seed confidence remains zero. The continuous branch uses defined subsequent support rather than the event multi qualification. The score does not condition recurrence mass on beat phase and does not certify a correct phase or a posterior probability. Missing fast input advances time without updating the onset baseline or variance; the oscillator and existing evidence decay continue.

4.3 From Meter to Modulation: NeuralRhythms

NeuralRhythms::from_meter_state (core/modulation.rs) projects the metrical state onto the modulation bands consumed by voice behavior:

• Delta ← the beat (tactus): phase and tempo of the pulse. Its phase drives env_open, a cosine gate that sharpens the articulation envelope toward the downbeat as confidence rises and leaves it open when the beat is uncertain.
• Theta ← the subdivision: the note-rate band that the breath oscillator (Section 5.5) locks to.
• Delta/Theta precision (alpha) equals beat confidence; prediction error (beta) is its complement.
• Measure carries its own phase, frequency and confidence, with measure_ratio identifying the detected grouping. Its phase origin follows the observed strong-onset phasor. No detected grouping yields a neutral, zero measure band; the optional measure_accent strength coupling consumes this band.

4.4 Composer Priors: Shaping the Temporal Terrain

The director can bend the terrain the pulse forms on—never schedule it—via MeterShaping (set from Rhai):

• meter_stability(v) — attractor depth in $[0,1]$. Scales amplitude and event correction, and lowers the existing evidence-presence thresholds. It changes how readily the meter commits without raising the confidence ceiling. The same depth directly weights the preferred tempo: higher values favor an integer-ratio reading closer to the basin center, or 2 Hz without an explicit basin. The default is 0 (neutral).
• temporal_basin(min_hz, max_hz) — a continuous tempo-prior band. Seeds the beat at its arithmetic center and confines candidate adoption and frequency adaptation to the band. At stability 0 there is no additional center preference or restoring pull. At higher stability, candidate preference and confidence-weighted restoring grow in direct proportion to the depth.

The basin has a second role: it initializes metric() Voices at the same sanitized arithmetic center, independently of stability. Without a basin, their intrinsic starting rate remains 2 Hz. The final basin declaration applies to every metric Population created by place() or create(), including declarations after wait(); it is one scene initial condition, not a timed change. Entrained/steady/flow retain their separate bodily scale, 2 Hz unless intrinsic_rate(hz) is supplied, and explicit pulse(rate_hz) retains its rate. Initial Voice phases remain independent, and shared-beat coupling stays zero until sound confirms a beat. Respawn reads the Population template rather than a parent's current clock rate.

These operations shape an emergent process without placing a beat grid; the listener's tempo adaptation remains confined to the declared band.

5. The Life Engine: Agents and Autonomy

The "Life Engine" is the agent-based simulation layer that inhabits the two terrains established above—the consonance landscape (Section 3) and the emergent meter (Section 4). It manages the population of "Voices," handling their lifecycle, sensory processing, and actuation (audio synthesis).

5.1 The Voice Architecture

The Voice struct (life/voice.rs) is the atomic unit of the ecosystem. It is composed of several components:

• An AnySoundBody actuator (synthesis backend).
• An ArticulationWrapper (wrapping an ArticulationCore).
• A PitchController (wrapping a PitchCore).
• A PhonationEngine that manages note-level timing and command queuing.
• An optional ToneAdsr envelope for attack-decay-sustain-release shaping.
• Lifecycle and metabolism tracking (energy, age, perceptual context).

The Voice itself acts as an integration layer, managing the control-plane signals that coordinate the components without coupling them directly.

5.1.1 The SoundBody (Actuator)

The BodyMethod enum defines three synthesis body types, each projecting a distinct spectral footprint onto the Landscape:

• Sine: A pure sine tone via a single oscillator. Minimal spectral interference; useful as anchors and calibration probes.
• Harmonic: A complex tone with a TimbreGenotype governing its partial structure. Parameters include:
  • stiffness: Inharmonicity coefficient (stretching the partial series).
  • brightness: Spectral slope (decay of higher partials).
  • comb: Even harmonic attenuation.
  • damping: Energy-dependent thinning of upper partials. A slow spectral-energy envelope tracks the excitation (fast attack, ~0.5 s release) and darkens the tone as drive fades. Its floor bounds the relative partial balance; it does not create a free tail in the excitation renderer.
  • vibrato_rate / vibrato_depth: LFO-based pitch modulation.
  • jitter: 1/f pink noise FM strength for organic fluctuation.
  • unison: Detuned copy amount for chorus-like thickening.
  • mode: Harmonic (integer multiples) vs. Metallic (non-integer ratios).
• Modal: Resonator-based synthesis via ModalEngine, supporting arbitrary mode frequency ratios and decay times. Mode patterns can be specified as harmonic, odd harmonics, power-law, stiff string, or custom ratios.

Sound generation is dispatched through the AnyBackend enum:

• Oscillator(OscillatorBank): A struct-of-arrays layout for cache-efficient additive synthesis. Handles Sine and Harmonic bodies. Pitch refresh occurs every 64 samples; motion/vibrato refresh every 8 samples.
• Resonator(ModalEngine): A Damped Modified Coupled Form resonator bank. Handles Modal bodies. Mode coefficients are rebuilt every 64 samples on pitch change.

The default renderer retains the legacy body response. The optional excitation renderer separates shaped excitation from body radiation (Sections 5.1.3 and 6.1). Sine and Harmonic respond immediately to composer ADSR and the existing onset transient, with no free radiation after effective Off. Sine retains its additive onset boost (gain 0.2, maximum 1, time constant 80 ms); Harmonic retains its 80 ms drive response and onset spectral burst. Modal retains mode-specific free decay, impulses and noise drive, including radiation after Off. Explicit body motion remains effective, with zero as its default.

Sine and Harmonic share the legacy f32 partial-rotation kernel, without per-sample normalization. Pitch and motion retain their 64- and 8-sample refresh clocks. The carrier has the same floating-point drift as the legacy kernel. Isolated constant-level holds can match legacy PCM bits, while excitation multiplication order and handle scheduling can still change the complete waveform. Effective Off still stops oscillator radiation; Modal keeps its existing free response.

Body parameters change the emitted spectrum and therefore the shared Landscape. Movement samples that terrain at a fundamental frequency. Birth placement and supported final respawn selections have the optional body-density evaluation described in Section 3.4. Metabolism can also use a body's representative density to evaluate its current position against an environment with its own sound removed (Section 5.2). This option is disabled by default. Timbre inheritance is not implemented.

The birth surrogate requires a body factory to declare direct-model conformance for the selected renderer. The current Sine implementation is supported. Harmonic requires zero motion and one active unison copy. With the legacy renderer, Modal requires one active unison copy and brightness exactly 1. Native Modal is unsupported because its radiation is not shaped by output ADSR and persists after Off. A single copy results from zero spread or unison = 1. Controls ignored by a body's renderer are ignored in this decision too. Other Modal brightness values, randomized mode recipes used by Harmonic or Modal, unsupported factories and inputs outside the model's bounded domain use the existing terrain-only birth path. A replacement renderer receives no surrogate capability by default. These conditions identify the implemented fast path; its numerical guarantee remains limited to the saved measurements in Section 3.4.

Body-aware metabolism uses the factory's declaration of conformance for the selected renderer and obtains its density by rendering and analyzing a representative Tone with that renderer. It does not apply the birth surrogate's stricter recipe conditions. Factories that do not declare this capability use the existing point-based metabolism. The excitation renderer supports Sine and Harmonic body metabolism; Modal retains point-based metabolism.

Final respawn body evaluation is enabled only with the legacy renderer and adds policy-specific restrictions to this shared body capability. With the excitation renderer, all bodies retain point evaluation at final selection; the supported Sine/Harmonic Field proposals remain body-aware. Random uses point evaluation for Sine and LandscapeDensity recipes. Hereditary uses point evaluation for LandscapeDensity and LandscapePeaks recipes. PeakBiased supports legacy Harmonic bodies with implicit modes or terrain-derived LandscapeDensity/Peaks recipes; Sine, Modal and explicit fixed-ratio recipes keep point evaluation. These runtime domains identify the implemented paths; their numerical guarantees remain limited to the measured conditions in Section 3.4.

5.1.2 The Core Stack

Behavior is split into three focused cores plus the PhonationEngine, each defined in a separate file:

• ArticulationCore (When/Gate) — life/articulation_core.rs: Manages gating and envelope dynamics. Three variants exist:

  • KuramotoCore: Coupled "breath" oscillator with a normalized energy/vitality model, rhythm coupling modes (TemporalOnly, TemporalTimesVitality), rhythm reward (metabolism bonus for phase match), and autonomous attack capability. It entrains its envelope to the meter-derived rhythm bands (Section 4.3). Energy is fixed to the 0–1 domain; the stored composing parameters are nominal endurance_sec and optional recovery_sec, while runtime rates are derived once at voice construction.
  • SequencedCore: Fixed-duration gate patterns.
  • DroneCore: Sustained output with optional sway modulation.

• PitchCore (Where) — life/pitch_core.rs: Proposes the next target in log-frequency space. Two implementations:

  • PitchHillClimbPitchCore: Local search over the consonance terrain. Parameters: neighbor_step_log2, tessitura_gravity, landscape_weight, move_cost_coeff, move_cost_exp, and a single search temperature (0 = greedy settling; higher accepts downhill moves via a Metropolis rule). Occupancy/crowding: crowding_strength, crowding_sigma_cents. Leave-self-out analysis supports ApproxHarmonics and ExactScan modes.
  • PitchPeakSamplerCore: Probabilistic peak sampling with window_cents, top_k, sigma_cents, random_candidates, and the same search temperature (softmax over candidates).

• PhonationEngine — life/phonation_engine.rs: Manages note-level command scheduling. Issues ToneCmd (On, Off, Update) to the ScheduleRenderer. Uses a gate grid (ThetaGrid) for onset bookkeeping and note-off placement. Configuration is via PhonationSpec:

  • When: Once (single trigger), Pulse { rate_hz, sync, social } (repeated triggers on the adaptive gate clock), or Coupled(CoupledTimingSpec) — explicit synchronization or bodily acoustic participation (Section 5.4).
  • Duration: WhileAlive, Gates(n), Field { hold_min_theta, hold_max_theta, curve_k, curve_x0, drop_gain }.

5.1.3 The Sound Pipeline

Audio rendering is handled by ScheduleRenderer (life/schedule_renderer.rs), which maintains a BTreeMap<ToneKey, RoutedTone> of active tones, each routed to one of two buses (Section 6.2): the habitat bus (analyzed as the landscape's environment) and the presentation bus (what the audience hears).

The Tone struct (life/sound/tone.rs) combines:

• A backend (AnyBackend: OscillatorBank or ModalEngine).
• An optional RenderModulator for articulation envelope shaping.
• An ADSR envelope: linear attack ramp, exponential decay to sustain level, constant sustain, linear release ramp.
• Smoothed pitch and amplitude transitions with configurable time constants.
• Continuous drive for sustained excitation.

The PhonationEngine emits ToneCmd commands; the ScheduleRenderer creates, updates or releases Tones and mixes their radiation per bus. The legacy renderer keeps its output ADSR. In the excitation renderer, ADSR and articulation shape the input, with no second ADSR applied to body output. An Off request starts the specified release ramp; effective Off is its endpoint. Sine and Harmonic then radiate known zero, while Modal continues its free response. A zero-second release uses the existing minimum of one sample.

In the excitation renderer, pitch Updates address open handles, including their release interval, and retain carrier phase or resonator state. Closed handles reject Updates and future kicks; Modal tails keep their last coefficients. A new On creates a separate Tone that may overlap retained radiation. Ownership and routing remain attached to each source generation. Effective Off and disposal are distinct: closed states are retired when the summed residual bound for their source generation reaches the renderer threshold. A silent open handle is not disposed merely for being silent.

With body-aware metabolism enabled, either renderer also captures each supported Voice's habitat PCM by (id, generation). Subtracting it from the habitat mix gives that Voice's environment. Presentation-only audio and other generations are excluded from its own signal. The shared mix is analyzed continuously. Each Voice's environmental PCM history is retained; its analysis advances on its turn, accounting for the intervening hops in one update rather than restarting from a finite window.

5.1.4 Control-Plane Signals: Planned and Error

The Voice coordinates its cores through two orthogonal signals rather than direct coupling:

• Planned: The PitchCore proposes a target (TargetProposal), and the Voice maintains the "planned" state—next target frequency, expected jump distance, and salience. This represents the agent's intention.
• Error: The Voice computes the discrepancy between the SoundBody's current pitch and the planned target (signed cents, absolute cents). This represents the result of prior actions and is available for observation. Importantly, the PitchCore does not read the error signal—search remains decoupled from feedback.

This separation keeps each core focused: PitchCore explores the landscape, ArticulationCore shapes the envelope, and the Voice orchestrates timing and state transitions.

5.2 Lifecycle and Metabolism

Agents in Conchordal are governed by energy dynamics modeled on biological metabolism. The LifecycleConfig defines two modes of existence:

• Decay: A transient articulation whose envelope decays with a configured half-life. This models plucks and percussion without exposing a redundant energy scale.
• Sustain: A living articulation with energy normalized to $[0,1]$.
  • Endurance: endurance_sec is the nominal energy-depletion time at zero field fit, with no attacks or recovery. The derived basal rate is $1/(T_e(1+p_d))$, where $T_e$ is endurance and $p_d$ is dissonance_penalty; this keeps zero-fit endurance fixed while allowing good fit to extend life.
  • Continuous recovery: Optional recovery_sec is the time to refill energy from 0 to 1 at a viability signal of 1, with drain and attacks disabled. The derived rate is $1/T_r$.
  • Attack economy: attack_cost_fraction and attack_recharge_fraction are fractions of normalized capacity applied per full-strength attack; consonance scales the recharge term.
  • Rhythm Reward: An optional MetabolismRhythmReward multiplies the recharge contribution for phase-matched attacks, configured via rho_t and the AttackPhaseMatch metric.

Energy depletion disables retriggering and starts the envelope tail. Reports therefore distinguish configured endurance, energy-depletion time, and observable lifetime.

By default, energy updates use the effective consonance level at the Voice's fundamental. Optional body-aware metabolism instead evaluates the current position against the environment after subtracting the Voice's own sound. It averages the effective consonance score over the representative body's subjective-intensity density, weighted by ERB cell widths and normalized by in-band mass, then applies the existing score-to-level sigmoid. The current-position density is retained per Voice and rebuilt when the fundamental, recipe, generation or analysis settings change.

The [body_metabolism] configuration section enables this path with enabled = true; updates_per_hop, observation_frames and representative_hold_sec must be specified explicitly. Omitting the section or setting enabled = false keeps point-based metabolism. With render_prototype = true, Sine and Harmonic use native representative Tones and source-PCM subtraction; Modal uses point-based metabolism. The author adopted updates_per_hop = 2 from comparison results; 2 is a configured update budget, not a constant of the psychoacoustic model.

Each hop updates at most the configured number of supported Voices in round-robin order. Per-Voice slots carry monotonically increasing visit numbers: the smallest numbers are selected first, and both visited Voices and newborns receive new numbers at the back. Other Voices keep their last body score. Until its first evaluation, a newborn uses the existing point score. Unsupported bodies and unavailable evaluations also use the point score; an unknown result is not treated as a known zero. These metabolism scores feed energy updates; life diagnostics and direct phonation gates retain their point evaluations. Metabolism alone does not change final respawn scoring; the independent birth option can enable the supported legacy-renderer body evaluations described in Section 3.4.

This mechanic creates a Darwinian pressure: Survival of the Consonant. Poor acoustic fit depletes energy; good fit can maintain or replenish it. The fit is a point level by default and a body-weighted level when the optional evaluation is available. With Landscape habituation enabled, a formerly supportive environment can lose effective value under sustained activity and recover after withdrawal, so survival depends on both acoustic fit and recent perceptual history.

5.3 Pitch Retargeting Logic

Agents are not static; they move through frequency space to improve their fitness. The execution layer applies a retarget gate (a zero-crossing of the meter-derived theta band, Section 4.3, plus an integration window) and then asks the PitchCore to propose the next target. Candidate evaluation reads the habituation-eroded score at the candidate fundamental. ExactScan recomputes a raw score after clearing the current fundamental bin, then applies the same local erosion before comparison. Body-aware metabolism leaves these point-based movement evaluations in place. Its energy changes can still affect subsequent movement through the existing energy-dependent behavior.

5.3.1 Pitch Application Modes

Three modes govern how a new pitch target is applied:

• GateSnap: Discrete pitch changes at sounded note boundaries. Gated phonation uses the target at onset; sustained participation retains the latest adopted target until a sounded opportunity.

• Glide: Smooth continuous pitch transition with a configurable time constant $\tau$. The SoundBody interpolates exponentially toward the target frequency, producing portamento effects. Suited for drone-like Voices or slow melodic movement.

• Rearticulate: For free-pitch Hold Voices without a participation clock, the default zero boundary releases the old Tone and attacks at each changed target's adoption sample. A positive rearticulate_above boundary instead slides at or below its distance from the last sounded onset.

For seek_consonance() voices the mode is resolved automatically from the phonation timing unless the script chooses explicitly: sustained voices (once()) glide, while re-attacking voices (pulse or coupled timing) snap at onsets. Explicit sustain with participation also resolves to Glide.

5.3.2 Crowding and Leave-Self-Out

The crowding system prevents agents from collapsing to identical frequencies. Both crowding (mutual repulsion) and pitch adaptation read one shared occupancy field: a Gaussian penalty centered on each occupied fundamental (raw f0), with width set by crowding_sigma_cents (default 60) and strength by crowding_strength. A pairwise split bias further prevents frequency degeneracy. No octave-equivalence (chroma) penalty is applied; octave relations act only through the consonance potential.

Pitch evaluation supports two leave-self-out approximations:

• ApproxHarmonics: Subtracts positive terrain-score contributions around assumed partial positions, using an exponential distance decay with a 24-cent scale and per-index weights 1/n. Explicit body ratios determine the positions when available; otherwise an integer harmonic series is assumed. The weights do not measure the rendered partial amplitudes.
• ExactScan: Clears one bin at the current fundamental in the processed subjective-intensity density, then recomputes H, R, and C. Upper partials remain, and another source's contribution in the cleared bin is removed too. The name refers to the historical mode; it does not provide exact source separation. If that bin has no positive finite density, evaluation falls back to ApproxHarmonics.

Neither mode reconstructs the audio of all other sources before spectral analysis. Both evaluate the resulting terrain at the candidate fundamental rather than averaging it over the candidate body's spectrum.

These timing-sensitive transitions and crowding evaluations are guarded by regression tests to prevent subtle breakage.

Retaining the Voice's articulation policy

For free-pitch sustained coupled timing with Rearticulate and a positive movement boundary, articulation_persistence(p) adds a private Base/Connect policy. Base uses the existing boundary and participation rules. While a Tone lives, Connect slides all adopted targets and intentionally withholds sounded opportunities, without a new Tone, onset metabolism or onset-context learning. Small adoptions and cost skips propose Connect; large adoptions and newly selected sounded opportunities propose Base. For 0 < p < 1, an opposing proposal retains the current policy with probability p; a matching proposal does not draw. Each planned opportunity keeps its decision until execution, independently of waiting hops. Entering Connect cancels pending pitch without changing last-onset memory; cancelled adoptions never replay and policy changes alone never sound.

The parameter is initial-only and inherited through templates; replacements start in Base with fresh performance state and a dedicated random stream. Default zero and endpoint one bypass this state and retain the existing path. Live mode changes reset Base; the same mode and boundary-only changes preserve it, and a zero boundary suspends its path. Finite Off, rest, tails, gaps and lifecycle constraints take priority, and a legal onset without a living Tone cannot be vetoed. Retention acts on both policies, so increasing p need not monotonically increase Connect time or reduce attacks. Its duration follows existing events, not seconds or beats; it is inertia without inferred cadence, contour, rest or phrase boundaries.

Extending a living Tone without pending pitch

tie(p) is an initial-only probability in free-pitch sustain plus metric/entrained/steady/flow with GateSnap or Rearticulate. At a selected legal opportunity, a pending target still attacks; a living Tone without one extends with probability p. Omission resolves to 1 for sustained metric and 0 for sustained entrained/steady/flow, where costs can omit opportunities. Explicit 0 retains attacks without tie state or draws; 1 extends eligible Tones without drawing. Intermediate values use a dedicated individual stream at execution, never during waiting. Small boundary-limited glides are eligible; small GateSnap adoptions remain pending and attack. This thins the existing opportunity sequence, without changing pitch, timing candidates, costs or skip. It is not an overall legato amount or phrase-boundary mechanism. Connect vetoes before tie; Base uses it only without pending pitch, leaving policy proposals and retention unchanged. Finite Off, tails/rest and lifecycle have priority, and no-Tone legal onsets pass. Templates carry the probability, not performance/RNG state. Builder order is independent; live Glide suspends tie and returning resumes it. There is no live probability setter. Inputs follow sanitize01; unsupported final forms warn and ignore.

5.4 Onset Timing: Synchronization and Participation

RhythmRelation distinguishes synchronized timing (metric()) from acoustic participation (entrained(), steady() and flow()). Both issue sound through the same PhonationEngine command path.

The presets keep distinct timing relationships. An opportunity is not an attack: phonation legality, lifecycle, rest and articulation can withhold onsets or extend a living Tone.

Preset	Keeps	May change	Does not guarantee	entrainment(x)
entrained()	Lifetime-fixed intrinsic bodily rate	Participation period follows supported recurrence weighted by proximity to that scale; costs select near-due timing, waiting up to one participation period, or skipping	Equal onset intervals, persistent differences between Voices' onset rates, or shared beat phase	Acoustic influence on adaptation and timing costs; omitted 0.5
flow()	Intrinsic scale for bounded renewal, without recurrence adaptation	Irregular renewal intervals, acoustic timing choices, waiting and skipping	A regular sequence, a beat, or a mean onset interval equal to the intrinsic period	Acoustic timing costs, not renewal-scale adaptation; omitted 0.05
steady()	Intrinsic period and later private due-time grid, subject to sample rounding	Sound or skip at due; execution constraints can remove onsets	An attack count, a pitch outcome, or following another Voice's time	Sound-or-skip costs only; omitted 0.5
metric()	Confidence-weighted attraction to the confirmed production beat and configured phase offset; independent phase before confirmation	Effective rate and phase; the clock free-runs before confirmation	Beat confirmation itself, exact phase coincidence, or independent noninteger tempo relations	Beat-rate and phase attraction; omitted 0.95

Setting entrainment(0) removes these acoustic timing influences; flow remains irregular. The meter supplies one beat and integer-ratio layers. Steady advances missed or illegal opportunities by whole intrinsic periods. Its initial sustained Hold onset is immediate, outside the later grid. These are initial-only presets; the last timing preset wins, with duration resolved separately.

Participation separates causal habitat observation from the body's due time. The observer projects fully observed recurrence cycles onto a roughly four-second horizon at 20 ms spacing. Recurrence contrast fades toward the adaptive baseline with a six-second time constant; energy beyond the horizon uses the observed mean. Future queries never enter the observation history. Known self habitat PCM is subtracted from the observed mixture before energy analysis. The external history is projected using both the previous shared recurrence projection and a local history predictor. Matching actual outcomes fit their bounded mixture for subsequent participation requests.

For entrained/flow, candidate cost combines squared displacement in participation periods, distance from experienced external energy shapes, and a three-band overlap integral. Context memory retains three-band external energy in two post-onset windows (2×3); candidate forecasts use the same windows. The default 64-point envelope proxy includes the duration rule's hold and the Voice's ADSR release. An optional footprint path uses 16 bins of body power approximated from a frozen representative-onset recipe, or an envelope proxy. Its worker is independent of the auditory-cognition observer; missing, stale or unsupported body results use the proxy. For Sine and Harmonic, the excitation renderer computes these 16 bins from native representative PCM and normalizes them to their peak; its identity is separate from the legacy analytic footprint. Native Modal remains unsupported (renderer-phase3) and uses the envelope proxy because its free radiation has different support. Legacy analytic Tone-energy forecasts remain unavailable in the excitation renderer. Actual-PCM observation, including T2 and the external/self-sound history predictor, continues through the rendered bus audio. Omitting costs one plus the number of consecutive voluntary omissions; an emitted onset resets that count. This cost is an action preference, not a metabolic reward. It prevents bounded acoustic costs from prescribing permanent silence, but does not establish musical quality. The envelope proxy omits additional body/modulator decay; neither energy estimate is an auditory masking or consonant-fusion model.

An optional T2 preprocessing path supplies accents from the actual audio of each observed bus. Its principle layer is a named composition of AMT 1.6 auditory components: 30 gammatone bands on the LTFAT erbspacebw(80,8000,1,1000) grid, half-wave rectification and a 1 kHz inner-hair-cell low-pass stage, five adaptation loops with limit=10, and four modulation outputs: LP 2.5 Hz, signed BP 5 and 10 Hz, and absolute BP $50/3$ Hz. Numerical checks on finite inputs establish agreement with the corresponding reference realizations. These component references are described in the AMT implementations of gammatone, ihcenvelope, adaptloop, and modfilterbank. The analysis worker derives coefficients from the actual sample rate and retains filter state across hops. An input gap starts a new cold state; support records include the input prefix on which the recursive filters depend.

Group attribution and event formation are author rules, separate from those auditory components. Existing NSGT assignments supply each group's fraction of the bus mass in each native band, including residual mass in the denominator. These fractions condition the whole-bus responses; groups do not have separate PCM streams or filter banks. The current rule takes signed hop means, freezes the first hop's fractions over four consecutive hops, and combines the positive component rises with explicit component weights and gain. A supported local peak above the explicit threshold creates an accent directly, with an explicit event-weight gain. It does not require an accent from the other acoustic detector. The event time and the later time at which it becomes available remain distinct. The same accent goes to the period estimator and next-arrival model, with credit retained by its owner and a reset when that owner changes. Missing PCM, unknown ownership or broken support suppress an event; supported zero remains known zero.

T2 is disabled by default. Its producer runs for raw production recurrence when temporal_meter_t2 = true, or for group events when [temporal_t2] is present. The raw meter input requires none of the group event parameters. Enabling the group event path requires the acoustic-group and period configurations and every T2 setting explicitly: component_weights, gain, threshold, weight_gain, window = "hop_mean", combination = "positive_component_rise", attribution = "first_hop_mass_fraction", and unknown = "suppress". The free numerical parameters have no selected values or defaults. Reference agreement establishes the preprocessing behavior; it does not select those parameters or establish a musical effect.

The policy can additionally use Periodic next-arrival forecasts from observed habitat groups to select a participation candidate. Using the observed period and last accent, each forecast fixes the next arrival time at issuance and represents it as a single right-continuous step. The arrival term is disabled by default; arrival = true in [temporal_onset_comparison] enables it with the configured auditory observation and period estimator. An omitted arrival_weight uses 1, placing arrival mismatch on the same scale as the context mismatch term by convention. Explicit finite, nonnegative weights remain supported. The existing participation coupling sets the strength of both terms; the unit weight is not a preprocessing constant.

Each decision uses one common set of active habitat groups with causal forecasts that cover every valid candidate window. A group is excluded as the acting Voice's own only when habitat routing, source and body generations, body evidence, prototype assignment and freshness agree. If this correspondence is unknown, the group is not excluded as self. For each candidate, the step's increment across its onset window gives a group arrival probability; their equal-weight mean is $P$. The additional cost is $\mathrm{coupling} \times \mathrm{arrival_weight} \times (1-P)$, favoring candidates near a predicted arrival.

Groups with unavailable periods, uncertain elapsed time, invalid clocks or insufficient forecast coverage are excluded. An empty common set leaves arrival unknown and applies no arrival term. A nonempty set with $P=0$ is known zero and incurs the weighted cost. Omission still uses the minimum candidate cost without the arrival term, so this term affects candidate selection rather than prescribing an omission.

Steady uses unchanged costs and weights. Arrival cost cannot change sound versus skip in its one-candidate policy because the skip comparison excludes it. Explicit sustain retains the current Tone on skips. All three pitch modes, movement boundary, tie (omitted zero), persistence and finite-duration rest use the existing articulation path; no adoption-time candidate is added, even in Glide. Respawn inherits policy and rate from the template with fresh performance state.

intrinsic_rate(hz) sets the founder bodily rate for entrained(), steady() and flow() before place() or create(), independently of builder order. The intrinsic period is 1/hz and remains fixed during life. This sets a bodily scale rather than commanding onset intervals or placing a shared beat. The same period feeds participation, finite note lengths (cycles, duration_range), rest(periods) and representative overlap hold, so note lengths and rests in seconds change together. Omission retains the existing 2 Hz path. Replacements read the Population template with fresh due, plan and policy state, without inheriting parental cadence. There is no live setter. Final entrained/steady/flow specifications require finite values in 0.01–200 Hz; invalid values are script errors before placement. These are execution protection limits, not a musically recommended range. Other final timing forms, including metric, pulse, repeat and once, warn and ignore the modifier even if its value is invalid. Flow's renewal intervals separately retain their 0.035–4 second limits, so extreme rates do not scale actual intervals proportionally. rhythm_freq remains an articulation-core oscillator control; proposal_interval remains a pitch-proposal interval.

Experience memory updates only after an emitted onset and both matching acoustic windows. The intrinsic period, acoustically adapted participation period, and sound duration have separate roles. An entrained Voice selects a supported recurrence near its intrinsic scale, weighted by a Gaussian affinity with a half-octave width. Coupling and recurrence support control the adaptation rate, with two intrinsic periods setting the time constant. Unavailable references relax the cadence toward the intrinsic pace. These support values and constants are engineering choices, not validated human beat confidence.

Cadence updates preserve the remaining fraction of a future, uncommitted cycle and never target a shared onset phase. Each observation is used once; future evidence and changes to already selected actions are rejected. Chosen waits do not train the cadence. Flow keeps the intrinsic scale for clustered renewal instead of adapting it to recurrence. Acoustic context still affects waiting and omission, so executed intervals can change. An internal switch to flow preserves a committed candidate and restores the intrinsic scale for subsequent intervals. It also clears the cadence-observation timestamp, so returning to entrained timing does not count time spent in flow as elapsed adaptation time.

Hold lengths and their overlap preview use the configured intrinsic period, independently of cadence adaptation. Thus cycles(n) does not stretch a sound when the acoustic recurrence slows; flow retains its existing threefold hold multiplier. ADSR release remains in seconds. Later tempo observations do not reschedule an existing note-off. Candidates respect the actual-onset 200 Hz ceiling, and amplitude and viability gates still decide whether to emit an onset.

Forecasts are built only for pending decisions, and observed external contexts feed subsequent candidate comparisons. Sustained-note termination, causal effect estimation and action-value learning are not implemented.

Observed external RMS history, indexed by past age and known coverage, is also frozen with the decision-time evidence. The context-distance term compares external energy in the two experienced windows.

For explicit synchronization, onset timing is generated by the CouplingClock (life/phonation_engine.rs): a per-Voice phase oscillator that offers an onset opportunity at each integer crossing of its phase. Its effective rate blends an intrinsic renewal rate with the shared beat:

$$ f_{eff} = (1 - \ell), f_{int} + \ell, f_{beat}, \qquad \ell = \kappa \cdot c $$

where $\kappa$ is the voice's coupling strength (entrainment, 0–1) and $c$ is the meter's beat confidence (Section 4.2)—so a voice can only lock as strongly as the meter is believed. A phase pull drags the oscillator's crossings toward the beat phase (optionally offset by microtiming):

$$ \dot{\phi} = f_{eff} \left(1 + \ell K ,\mathrm{err}(\phi_{beat} - \phi)\right) $$

where $\mathrm{err}(\cdot)$ is the wrapped phase error in cycles ($[-0.5, 0.5]$) and $K$ a fixed pull gain chosen so the rate factor stays positive—the phase always advances, only faster or slower.

This phase-attraction mechanism serves synchronized timing. Increasing coupling for an entrained/steady/flow participant instead increases its response to acoustic context; it does not switch the participant into this clock.

Each onset carries a strength set by the voice's rhythm_role—beat 1.0, subdivision 0.7, accent 2.5, texture 0.85—and these strengths feed back into the production meter's drive. A recurring accent therefore drives the meter harder, allowing a downbeat (and eventually a measure) to be induced by the population rather than declared. There is no externally imposed grid anywhere in this loop.

The optional measure_accent(amount) couples detected measure structure back to onset strength. Its multiplier is 1 + 0.35 * amount * confidence * cos(phase), evaluated at each actual onset. The measure phase is measured relative to the circular mean of the observed accents, rather than the arbitrary origin of the accumulated beat count. An undetected measure produces no modulation; the default amount is zero. This path schedules no new onset and sets no beats-per-measure value. Production rhythm_observation records expose the measure phase, frequency, confidence and ratio used by the voices; listener observations remain separate.

Sustained beat synchronization

Explicit sustain() plus metric(), in either order, retains a live Tone and uses integer crossings of the existing CouplingClock as sounding opportunities. The first Hold onset is immediate. Free-pitch GateSnap/Rearticulate defaults to attacking a beat with a pending adopted destination and extending other beats, equivalent to tie(1). Explicit tie(0) re-attacks every legal crossing; other explicit probabilities keep their meaning. Fixed pitch and Glide still attack each crossing. Sustained entrained/steady/flow keeps omitted tie at 0, with cost-based omission. The resolved default also applies while a live mode switch enters the eligible range; tie remains initial-only. GateSnap and boundary-zero Rearticulate defer the latest adoption to a legal crossing. Positive boundaries, Base/Connect persistence, finite-duration rest, role strength, confirmed measure emphasis and microtiming share the existing articulation rules. Synchronization has no participation cost skip or committed waiting plan; suppressed crossings advance the clock without replay or onset metabolism/learning.

The shared beat is acoustically confirmed. Before confirmation coupling is zero, so the clock free-runs at the existing basin-centered rate with its independent initial phase. This combination does not place an external beat. Fixed pitch is supported as in sustained participation, while tie/persistence retain their free-pitch scope. Implicit Coupled tuning and standalone presets are unchanged.

5.5 The Breath Oscillator: Kuramoto Articulation

Independent of onset scheduling, the KuramotoCore ArticulationCore entrains each voice's envelope (its breath) to the meter-derived theta band, using a mean-field Kuramoto phase step:

$$ K_{eff} = \omega_{target} \cdot K_{global} \cdot s_\theta \cdot |\theta_{mag}| \cdot \theta_\alpha \cdot g_{env} \cdot a_{env} $$

where $\omega_{target}$ is the theta band's angular frequency, $K_{global}$ the scene-wide coupling gain (set_global_coupling), $s_\theta$ the voice's theta sensitivity, $|\theta_{mag}|$ and $\theta_\alpha$ derive from beat confidence, and $g_{env}$, $a_{env}$ are the envelope gate and amplitude. Helper functions kuramoto_k_eff() and kuramoto_phase_step() are exposed for external simulation (paper experiments). The energy/vitality subsystems interact with this coupling:

• Rhythm Coupling Modes: TemporalOnly (pure phase coupling) or TemporalTimesVitality { lambda_v, v_floor } (healthy agents synchronize more strongly).
• Rhythm Reward: an optional MetabolismRhythmReward (rho_t, AttackPhaseMatch) grants a metabolic bonus for phase-matched onsets, linking rhythmic conformity to survival.
• Autonomous Attack: self-triggered attacks when envelope-gate and confidence thresholds align.

6. System Architecture and Implementation Details

Conchordal is implemented in Rust to satisfy the stringent requirements of real-time audio (latency < 10ms) alongside heavy numerical analysis (NSGT/Convolution). The architecture uses a concurrent, lock-free design pattern.

6.1 Threading Model

The instrument conchordal and the separate offline conchordal-render binary support an optional excitation renderer. Enable it at the top level of the TOML configuration:

render_prototype = true

Omission or false selects the legacy renderer. The setting is a boolean and has no decay, rise, kick-gain or motion-scale subsettings. The instrument binary conchordal exposes no audio-file output. In either execution path, natural Finish closes excitation and waits for retained body radiation to retire. Offline rendering then closes the WAV. Headless execution exits; the GUI waits for user exit by default and feeds silence to the ring after Finish, or exits when wait_user_exit = false. This is generator completion; no additional device or ring-drain wait is introduced.

The application creates four primary thread contexts, plus the GUI event loop:

1. Audio Thread (Real-Time Priority):

   • Managed by cpal in audio/output.rs.
   • Constraint: Must never block. No Mutexes, no memory allocation.
   • Responsibility: Pops mono samples from a lock-free ring buffer and copies them to all output channels. A Limiter (soft-clip or peak-limiter) is applied in-place on the interleaved output.

2. Analysis Thread (Background Priority):

   • Defined in core/analysis_worker.rs, running AnalysisStream from core/stream/analysis.rs.
   • Responsibility: Receives habitat-bus hops (time-domain chunks), runs the NSGT to produce a log2 power spectrum, then computes both the Harmonicity field (Sibling Projection) and the Roughness field (ERB-domain convolution) in a single pipeline.
   • Update Cycle: When analysis is complete, it sends the updated Landscape snapshot back to the worker thread via a bounded SPSC channel.

3. Listener-Analysis Thread:

   • Runs the ListenerTwin perception pipeline on presentation-bus hops.
   • Responsibility: Models what an audience member perceives—including its own habituation field and the perception meter's beat confidence—for the UI, the headless report, and the DCC pressure coupler.

4. Worker Thread (Simulation Loop):

   • Named "worker" in app.rs.
   • Responsibility: Runs the main simulation loop. Each iteration: merges analysis results into the current Landscape, dispatches Conductor events, advances the Population (pitch retargeting, articulation, metabolism), renders audio via ScheduleRenderer (which processes PhonationBatch vectors of ToneCmd and maintains the Tone pool), drives the production MeterNetwork from habitat flux and the population's own onsets, and pushes mono samples into the ring buffer for the audio thread.

5. App/GUI Thread (Main):

   • Runs the eframe/egui visualizer.
   • Responsibility: Handles user input, visualizing the Landscape (ui/plots.rs), and displaying simulation metadata. It receives UiFrame snapshots from the worker thread via a bounded channel.

6.2 Data Flow

To maintain data consistency without locking the audio thread, Conchordal uses a multi-channel update strategy for the Landscape. Rendered audio is split across two buses: the habitat bus (the environment the ecosystem senses) and the presentation bus (what the audience hears). A drone can be routed to the habitat bus only—shaping the landscape without being presented.

1. The Worker Thread renders audio per bus and sends each habitat hop to the Analysis Thread; presentation hops go to the Listener-Analysis Thread.
2. The Analysis Thread runs the NSGT + subjective-intensity + Roughness + Harmonicity pipeline and sends the resulting raw Landscape snapshot back.
3. The Worker Thread merges the analysis result into the current LandscapeFrame, recomputes the base Consonance representations, advances the ecology's HabituationField, and writes the effective views. A separate habituation state is advanced on listener-analysis results.
4. The Worker Thread drives the production MeterNetwork with the habitat onset flux (DorsalStream) combined with the phonation onset strengths of habitat-routed voices; the resulting MeterState is projected into landscape.rhythm via NeuralRhythms::from_meter_state.
5. The Community evaluates the effective Landscape for pitch selection, metabolism, spawn, respawn, and Voice lifecycle.
6. When DCC coupling is enabled, tension_pressure = tension_level * coupling_strength produces a bounded temperature bonus that feeds the Voices' pitch search. Listener tension already includes resolvability; the coupler applies no second factor. The default coupling strength is zero, so this path is behaviorally inert unless explicitly enabled.
7. The PhonationEngine emits ToneCmd batches; the ScheduleRenderer creates, updates, or releases Tone instances accordingly and renders the selected body response into each bus (Section 5.1.3).
8. Rendered presentation audio is pushed into a lock-free ring buffer consumed by the Audio Thread.

This decoupled architecture ensures that the audio thread always sees a consistent stream of samples, even if the analysis thread lags slightly behind real-time. The analysis thread processes all hops in-order to maintain NSGT time continuity.

6.3 The Conductor: Scripting with Rhai

The Conductor module acts as the interface between the human artist and the ecosystem. It embeds the Rhai scripting language, exposing a tiered API for controlling the simulation.

The API follows four explicit lifetimes: a PopulationSpec is a reusable pre-placement definition, a Population is the stable population identity created by place(), a Voice is one living member, and the runtime Community aggregates all Populations sharing the Landscape. The authoritative, always-current reference is the Script Reference book (docs/rhai_book, published under /docs/rhai/); this section summarizes the conceptual tiers only. There is no Species object; PopulationSpec is the configuration unit.

6.3.1 PopulationSpec Configuration

A PopulationSpec begins with a preset and is refined through method chaining. It contains founder Voice defaults together with population-level lifecycle, viability, and respawn policy:

Presets: sine(), harmonic(), saw(), square(), noise(), modal(). variant(parent) clones an existing PopulationSpec for modification.

Body: amp(v), freq(v), brightness(v), spread(v), unison(n), modes(pattern), adsr(a,d,s,r), send(bus) (habitat/presentation routing).

Pitch: anchor() (hold the voice at its pitch; implied by freq(hz)), seek_consonance() (climb the consonance terrain; the apply mode is then resolved automatically—sustained voices glide, re-attacking voices snap at onsets—unless overridden via pitch_apply_mode("gate_snap"|"glide"|"rearticulate")), pitch_core("hill_climb"|"peak_sampler"), glide(v), landscape_weight(v), neighbor_step_cents(v), tessitura_gravity(v), temperature(v) (one search-stochasticity knob shared by both cores; 0 settles greedily — this is the movement-tension knob: a hot search keeps a voice restless and straying off consonance, cooling it resolves), move_cost(v), proposal_interval(sec), global_peaks(n), ratio_candidates(n), plus peak-sampler knobs (window_cents, top_k, sigma_cents, random_candidates).

For a free-pitch Hold Voice without participation, pitch_apply_mode("rearticulate") with the boundary omitted or zero couples each changed adopted target to one onset. At its sample time the old Tone begins release and a new Tone attacks at the new pitch. A positive rearticulate_above(cents) measures net displacement from the last actual onset: strictly above the boundary attacks, at or below it glides with glide(tau), retaining that selection until the next adoption. Exact Log2Space centers use bin-distance in cents; other endpoints use continuous log2 distance without rounding or epsilon. Earlier legal attacks in the same output hop provide the reference, while cancelled requests do not update actual onset memory. The boundary is a composer parameter; it defaults to zero, sanitizes negative or nonfinite values to zero and imposes no upper limit. Outside Rearticulate, a call warns and is ignored. Live boundary changes cause no attack and affect the next adoption. Replacement Voices inherit the boundary, not the parent's last-onset pitch. Anchored Voices remain locked.

Unchanged targets, rejected proposals and steps without proposals create no extra onsets. Glide retains legato movement. Live mode changes preserve the sounding Tone, create no onset by themselves and cancel unrendered articulation requests. Free-pitch Gated Rearticulate is a script error at final placement, independent of builder order, and before live writes. Use Hold with sustain, or Glide/GateSnap for Gated phonation. Attacks and release tails follow the existing synthesis, energy and habitat-perception paths.

Explicit sustain() with entrained(), steady() or flow(), in either builder order, combines sustained sound and participation opportunities. Waiting or skipping retains the Tone. The omitted mode is Glide: sounding releases the old Tone and attacks at that sample's body pitch. In entrained/flow, a pitch adoption offers one legal candidate using the unchanged costs, tie order and committed plans; unselected movement glides, and coincident adoption and clock onset emit one attack. Steady offers no adoption-time candidate and retains only its due-time opportunity.

Explicit GateSnap with free pitch instead holds one adopted target. Later adoptions replace it; only a sounded participation opportunity consumes it, releases the old Tone and attacks at the target pitch. With no pending target, the current pitch is re-attacked. Waiting and skipping retain pitch and pending target, without sliding or expiry. This mode offers no extra adoption-time candidate and leaves participation costs and skip unchanged. At the same sample, adoption precedes opportunity; a future adoption cannot affect an earlier onset. Release, death and removal cancel pending targets. Each emitted attack enters energy and acoustic paths once. Prediction retains the existing finite representative footprint.

With sustained participation, explicit Rearticulate uses the last actual onset pitch to classify each adopted target. At or below a positive distance boundary, it cancels any old pending target and starts gliding immediately, without an attack. Above the boundary, it stops the glide, holds body pitch and replaces the single pending target. Only a sounded opportunity consumes that target, jumping and attacking there; without a target it attacks at current body pitch. That pitch can differ from the preceding onset during a glide. Both attacks update actual onset memory. Waiting and skipping retain sound and pending state while existing glides continue. Same-sample adoption precedes opportunity; no adoption-time candidate is added, and the boundary does not filter clock attacks. Zero or omission matches GateSnap, including zero-distance adoption. Without participation, Rearticulate attacks at adoption; with participation, it attacks at sounded opportunities.

Live Glide ↔ GateSnap ↔ Rearticulate changes cancel pending attacks, selected glides and unrendered control records, retaining the Tone and the controller's target. Returning to Glide follows that target at the next control update; GateSnap and Rearticulate wait for later adoptions. Repeating the same mode retains pending state. A boundary change retains the selected behavior until the next adoption. Replacement Voices inherit the resolved controls with fresh performance state. Implicit WhileAlive or while_alive() alone does not select sustained participation. Single presets and sustain with metric, pulse or repeat retain their existing meaning. Participation presets remain initial-only.

With rest(), explicit sustained participation also retains an explicit finite duration from cycles(n) or adaptive_duration() and its modifiers, independently of builder order. Each sounded note ends with its scheduled normal Off while the Voice remains alive. Tails are retained, and new attacks are prohibited until the renderer confirms completion of all Tones with the same source ID and generation. From that completion, rest() waits one intrinsic bodily period; rest(periods) waits the composer's multiple of the period measured then. With a known period, zero waits only for tail completion. Unknown periods or unfinished tails keep waiting without a fallback or timeout. Negative and nonfinite values sanitize to zero, with no upper limit on finite nonnegative values.

The end of the rest permits participation but emits no forced onset. Existing candidates, costs and skip rules are retained, and intentional suppression is not learned as a cost-based skip. GateSnap retains the latest pending target through sounding, tails and rest until the next sounded opportunity; Glide does not update released tails. Rearticulate processes adoptions through release and rest using the same small-target cancellation and large-target deferral. The last actual onset remains its reference until the next attack; body glides never retune released tails. Lifecycle endings take precedence. rest and finite duration are initial-only controls, inherited by replacements with fresh performance state. Missing finite duration or timing outside explicit sustain plus entrained/steady/flow is a placement error before writes. All three pitch application modes are available. Explicit while_alive() clears finite intent. Absence of rest retains existing behavior. Every note in this form has a finite end; per-note selection of sustain versus release is not implemented.

Crowding: avoid_neighbors(strength) (default sigma) / avoid_neighbors(strength, sigma_cents), crowding_target(same, other), leave_self_out(bool), leave_self_out_mode("approx"|"exact"), leave_self_out_harmonics(n).

Brain/Phonation: brain("entrain"|"seq"|"drone"), sustain(), repeat(), once(), pulse(rate), pulse_lock(depth), social(coupling); duration via while_alive(), cycles(n), adaptive_duration(), duration_range(min,max), duration_curve(k,x0), shorten_on_drop(gain); finite sustained participation with rest() / rest(periods).

Rhythm (Section 5.4): metric() selects shared-beat attraction; entrained(), steady() and flow() select acoustic participation. entrainment(v) changes the influence within that intention. microtiming(v) offsets the synchronized target only. temporal_basin shapes the production meter and initializes metric bodies at its center; intrinsic_rate(hz) sets the separate founder bodily scale of entrained/steady/flow, otherwise 2 Hz, and changes note lengths and rests in seconds together. Articulation controls remain separate: rhythm_freq(v), rhythm_coupling_vitality(lambda_v, v_floor), and rhythm_reward(rho_t, "attack_phase_match").

Lifecycle/Viability: endurance(sec), optional recovery(sec), attack_cost_fraction(v), attack_recharge_fraction(v), consonance_viability(low, high), dissonance_penalty(v), and phonate_when_viable() (withhold the first onset until the viability window opens).

Respawn: respawn_random(), respawn_hereditary(sigma_oct), respawn_consonance(), respawn_capacity(n) (maximum living membership; founder count by default and never lower than it), respawn_settle(placement), respawn_min_c_level(v), respawn_background_death_rate(v).

6.3.2 Mode Patterns

Modal synthesis mode patterns are specified via constructor functions with optional modifiers:

• harmonic_modes(), odd_modes(), power_modes(beta), stiff_string_modes(stiffness), custom_modes(ratios), modal_table(name), landscape_density_modes(), landscape_peaks_modes().

Modifiers: .count(n), .range(min, max), .spacing(d), .gamma(g), .jitter(cents), .seed(s).

6.3.3 Placements

Placements determine the founder Voices' initial frequency allocation when a PopulationSpec enters the ecosystem. A field-relative placement names a target — consonance, dissonance, edge (the consonance/dissonance boundary), gap (low-intensity registers) — realized as a density cloud by default (.density()) or a deterministic extremum with .peak(); consonance(root) takes a harmonic window, the others an absolute (min, max) range. Field-agnostic placements are random(min, max) (log-uniform) and the geometric at(freq) / line(start, end). Modifiers: .count(n), .range(min_mul, max_mul), .spacing(d) (minimum ERB distance), and Consonance-only .tension(degree), which targets an in-range field-score step below the strongest peak.

6.3.4 Population Placement and Live Control

• place(population_spec, placement): Immediately schedules founder Voices at the current cursor and returns their stable Population.
• release(population): Terminally closes the Population and marks its current members for fade-out; later patches are ignored.

place() is the sole definition/runtime boundary; there is no public draft Population. Initial body, behavior, lifecycle, and respawn methods exist only on PopulationSpec. Population exposes only live patches—such as pitch, amplitude, and timbre updates—and release. A Population retains its population_id while member voice_id and generation values change through death and respawn.

6.3.5 Control Flow

• wait(sec): Emits pending live patches, then advances the timeline cursor.
• flush(): Emits pending live patches without advancing the timeline.
• seed(n): Sets the random seed for reproducible runs.
• section(name, callback): Marks a named scene boundary; Populations created within the callback are automatically released when the section ends.
• play(callback): Executes a scoped block—Populations created inside are released on exit.
• parallel([callbacks]): Runs multiple blocks concurrently (timeline branches), advancing the cursor to the latest endpoint.

6.3.6 Director Operations

Scene-global terrain shaping, on both axes:

• Harmonic terrain: set_roughness_aversion(w), set_pitch_objective("consonance"|"dissonance"). Both change valuation, not the sensed $R_{01}$ / $H_{01}$.
• Temporal terrain: meter_stability(v), temporal_basin(min_hz, max_hz) (Section 4.4).
• Interaction: set_global_coupling(v) scales agent interaction strength.

Scenario Parsing: Scenarios are loaded from .rhai files. This separation allows users to compose the "Macro-Structure" (the narrative arc, the changing laws of physics) while the "Micro-Structure" (the specific notes and rhythms) emerges from the agents' adaptation to those changes.

7. Case Studies: Analysis of Emergent Behavior

The following examples, derived from the samples/ directory, illustrate how specific parameter configurations lead to complex musical behaviors.

7.1 Case Study: Three Timing Intentions (samples/07_heartbeat.rhai, 08_murmuration.rhai, 09_rain.rhai)

The three samples exercise the separate intentions described in Section 5.4.

1. Metric (07_heartbeat.rhai): explicit synchronization to the production beat. The dedicated downbeat Voice remains because synchronization is the subject of the demo.
2. Entrained (08_murmuration.rhai): bodily participation using acoustic context. Gated attacks use ordinary consonance recharge, without a phase-match reward.
3. Flow (09_rain.rhai): clustered bodily renewal with weak acoustic participation. Pitch still follows the consonance field.

Samples 08 and 09 have no dedicated synchronization accompaniment.

7.2 Case Study: Drift and Flow (samples/research/drift_flow.rhai)

This compact research fixture demonstrates live Population patches and repeated field-relative placement; it does not demonstrate autonomous drift.

1. Explicit patch: A sustained anchor enters at C2 (65.41 Hz), while a second sustained Voice enters at C#3 (138.59 Hz). The script then patches that Voice directly to 220 Hz with population.freq(220.0) and releases it.
2. Field query: Five one-Voice swarms are placed in sequence with consonance(130.0).peak().range(1.0, 4.0), demonstrating repeated deterministic queries against the live field.
3. Terrain change: The anchor is finally patched to F2 (87.31 Hz), changing the field after those placements.

Autonomous settling is demonstrated by samples/05_settling.rhai.

7.3 Case Study: Emergence and Resolution (samples/12_emergence_and_resolution.rhai)

The closing integration sample combines a habitat-only harmonic root, a metric colony, and a temporary non-metric flow Population. It has no dedicated beat-carrier Voice. The colony's own onsets drive the shared production meter, while the hidden sustained root supplies a pitch reference to the Landscape.

The colony enters at 2.3 s. At 11.7 s, the Scenario raises its search temperature and shifts the root upward; flow enters at 15.0 s. At 20.3 s, the Scenario cools the search, explicitly enables Glide, returns the root, and reduces flow amplitude. Flow is released at 23.6 s, followed by a further colony amplitude reduction at 24.9 s and the remaining releases. These are scheduled macro operations; individual pitch searches, onsets, viability, and consonance-biased respawn remain local processes.

“Tension” and “resolution” name the intended arc, not a verified perceptual outcome. The resulting harmonic development and closure require listening judgments for the rendered conditions.

8. Conclusion

Conchordal establishes a foundation for Bio-Mimetic Computational Audio. By replacing the rigid abstractions of music theory (notes, grids, BPM) with continuous physiological models (Log2Space, ERB bands, neural oscillation), it creates a system where music is not constructed, but grown.

The paper "Conchordal: Emergent Harmony via Direct Cognitive Coupling in a Psychoacoustic Landscape" (arXiv:2603.25637) validated the psychoacoustic landscape as an effective ALife terrain through controlled experiments demonstrating self-organization, selection, synchronization, and hereditary accumulation. These results confirm that the Roughness-Harmonicity-Consonance pipeline and the Kuramoto entrainment model produce musically coherent emergent behavior under a range of initial conditions.

Version 0.4.0 integrates the paper findings into the instrument and adds the temporal axis of the architecture: the fixed rhythm filterbank is replaced by an emergent meter (a forced limit-cycle oscillator with corroborated acoustic recurrence and phase/pattern confidence), voice timing is expressed as synchronized (metric) or acoustic-participation (entrained, flow) intentions (Section 5.4), and the composer's temporal control is reduced to terrain priors (meter_stability, temporal_basin) that shape where a pulse forms without ever scheduling one. A dual-bus design separates the habitat (what the ecosystem senses) from the presentation (what the audience hears). Landscape habituation is enabled by default. A simulated ListenerTwin feedback path can raise pitch-search temperature; its coupling remains zero by default.

The technical architecture—anchored by the Log2Space coordinate system and the "Sibling Projection" algorithm—provides a robust mathematical foundation for this paradigm. The use of Rust ensures that these complex biological simulations can run in real-time, bridging the gap between ALife research and performative musical instruments.

Chapter 9 closes the document with a condensed ledger of the Manifesto's commitments: what is discharged and what remains open. The design decisions behind each row, and what the implementation taught back, are kept in the repository's design ledger rather than in this note.

9. Manifesto Correspondence and Open Problems

The Manifesto declares commitments; this chapter records which of them the current implementation discharges and which remain open. It describes the instrument as built. The design decisions, numerical registrations and revision history behind each row are kept in the repository's design ledger, docs/design-notes/technote-ledger.md, which preserves the former numbering of this chapter (§9.2–§9.4).

9.1 The Ledger

Manifesto commitment	Mechanism	Section	Status
Generation without symbolic intermediaries	Log2Space + landscape; no note names, scales, or time signatures anywhere in the engine	§2–4	Implemented
Frequency-axis terrain (cochlea/brainstem models)	Roughness, Harmonicity, Consonance kernels	§3	Implemented
Temporal-axis terrain (neural oscillation)	Emergent meter: forced limit cycle, default onset recurrence or optional continuous T2 recurrence for tempo adaptation; fast input updates phase and intensity, and confidence does not certify phase-origin accuracy. metric keeps explicit synchronization; entrained, steady and flow use a bounded acoustic observer and a bodily participation policy; steady fixes due and chooses sound or skip	§4, §5.4	Partial. Persistence of temporal relations across all conditions is open; measure-accent coupling is opt-in
Landscape variability (culture, individual, unknown principles)	consonance kernel coefficients, set_roughness_aversion, default-enabled habituation erosion	§3.4–3.5, §6.3.6	Partial. Cultural tuning systems are not yet absorbed
Adaptation and expectation	Per-Voice AdaptationContext, ecology/listener HabituationField, short-term recurrence and energy forecasts feeding habitat participation	§3.5, §5	Partial. Relational memory, phrase/scene expectation and action-value learning are open
Acoustic life: perception, metabolism, autonomy	The Voice: articulation-life cores, normalized energy, time-domain endurance/recovery, viability	§5	Implemented
Population: niches, symbiosis, terrain deformation	Crowding, respawn, the closed loop	§5	Implemented
No central conductor	Local perception only; one shared meter reads habitat recurrence and fast phase/intensity evidence, with optional continuous T2 recurrence	§4–5, §7	Implemented. Dedicated beat carriers appear only in explicit synchronization demonstrations (sample 07)
Scenario as macro direction	Director terrain operations	§6.3.6	Implemented as authorial composition
Temporal structure grounded in auditory cognition	Default-disabled temporal_meter_t2 feeds whole-habitat continuous T2 recurrence into the production meter; group accents and Periodic arrival costs have separate default-disabled settings	§5.4	Partial. Continuous recurrence, accent and arrival mechanisms are implemented. Production recurrence does not require group assignment and retains causal support and explicit unknowns; group arrival retains owner credit. Group-event numerical parameters have no defaults; an omitted arrival weight uses 1
DCC stage two: biosignal closed loop	ListenerTwin pressure can feed pitch-search temperature when [dcc] coupling is enabled	§4.1, §6.2	Simulated loop implemented, off by default; the physical biosignal loop is open
Cognition coupled to the sound actually presented	Separate presentation analysis; missing hops invalidate observations and suspend DCC pressure until a complete window is available	§6.2	Implemented. Physical-device overload validation is open
Excitation and body radiation	Optional excitation renderer in the instrument and offline binary: immediate Sine/Harmonic response and Modal free decay, with separate Off and disposal	§5.1, §6.1	Implemented as an opt-in; the default remains the legacy renderer
Music as a living performance	The instrument exposes no audio-file output; the separate conchordal-render binary supports offline study	§6	Implemented as a binary boundary
Dissolution of roles; spatial landscapes; heredity of timbre; other domains	Hereditary respawn exists as assays	—	Horizon

9.2 Open Problems

• Cultural tuning systems and individual hearing profiles as landscape parameters.
• Persistence of temporal relations across performance conditions for entrained and flow.
• Phrase, section and long-context memory, held as research outside the instrument's core.
• Cognitive retention and interference, and stream identity in overlapping sound.
• The physical biosignal loop of DCC stage two.
• Real-time acceptance under device overload and large populations.
• Native Modal remains unsupported for body-aware birth/metabolism and representative-onset footprints. Legacy analytic Tone-energy forecasts remain unavailable in the excitation renderer.

Appendix A: Key System Parameters

Parameter	Module	Unit	Description
bins_per_oct	Log2Space	Int	Resolution of the frequency grid (typ. 48-96).
sigma_cents	HarmonicityParams	Cents	Width of harmonic peaks. Lower = stricter intonation.
roughness_k	LandscapeParams	Float	Saturation parameter for roughness mapping. Default: $(1/0.7) - 1 \approx 0.4286$ (so $x=1$ maps to $\approx 0.7$).
kernel.a	ConsonanceKernel	Float	Harmonicity coefficient (default 1.0).
kernel.b	ConsonanceKernel	Float	Roughness coefficient (default -1.35; negative penalizes roughness).
roughness_aversion	LandscapeParams	Float	Valuation weight on the roughness terms $b$, $c$ and density $\rho$; set by set_roughness_aversion. Default 1.0.
kernel.c	ConsonanceKernel	Float	Interaction coefficient (default 1.0; positive attenuates roughness penalty at high harmonicity).
kernel.d	ConsonanceKernel	Float	Bias term (default 0.0).
beta	ConsonanceRepresentationParams	Float	Sigmoid steepness for $C_{level01}$ (default 2.0).
theta	ConsonanceRepresentationParams	Float	Sigmoid threshold for $C_{level01}$ (default 0.0).
consonance_density_roughness_gain	LandscapeParams	Float	$\rho$ in density kernel $H(1-\rho R)$ (default 1.0).
habituation.enabled	HabituationParams	Bool	Enable Landscape erosion; configuration default true. Explicit false makes effective views bit-identical to base views.
habituation.satiation_sec	HabituationParams	Seconds	Time to reduce the discrepancy from a sustained-drive equilibrium by 90% (default 5.0).
habituation.recovery_sec	HabituationParams	Seconds	Time to recover 90% after drive withdrawal (default 8.0).
habituation.ref_drive	HabituationParams	Float	Half-saturation drive in the habituation transfer function (default 0.25).
loudness_exp	LandscapeParams	Float	Compressive exponent applied to A-weighted peak power in the subjective-intensity front end (default 0.23).
tau_ms	LandscapeParams	Milliseconds	Leaky normalization time constant after peak extraction ([analysis].tau_ms).
stability	MeterShaping	0.0-1.0	Beat attractor depth (meter_stability): scales entrainment forcing and tempo learning.
basin_hz	MeterShaping	Hz pair	Scene tempo region (temporal_basin): seeds and confines beat-frequency learning; its center initializes metric bodies independently of stability.
coupling	CoupledTimingSpec	0.0-1.0	Acoustic-context influence for participation; shared-beat attraction for synchronization (entrainment).
flow_depth	CoupledTimingSpec	0.0-1.0	Renewal clustering of free-running onsets (0 = regular).
steady	CoupledTimingSpec	boolean	Non-flow participation with fixed intrinsic period and due as its only candidate.
microtiming	CoupledTimingSpec	cycles	Signed beat-phase offset of the lock target.
temperature	PitchHillClimbPitchCore / PitchPeakSamplerCore	Float ≥ 0	Search stochasticity shared by both pitch cores; 0 settles greedily, higher explores. Musically the movement-tension knob (high = restless/straying off consonance, 0 = settled).
crowding_strength	PitchHillClimbPitchCore	Float	Strength of frequency-space crowding avoidance.
crowding_sigma_cents	PitchHillClimbPitchCore	Cents	Width of crowding penalty Gaussian (default 60).
leave_self_out	PitchHillClimbPitchCore	Bool	Whether to subtract own spectral contribution during evaluation.
endurance_sec	LifecycleConfig::Sustain	Seconds	Nominal energy-depletion time at zero field fit, with attacks/recovery disabled.
recovery_sec	LifecycleConfig::Sustain	Optional seconds	Time to refill normalized energy 0→1 at a full viability signal.
attack_cost_fraction	LifecycleConfig::Sustain	Normalized energy / attack	Capacity spent by a full-strength attack.
attack_recharge_fraction	LifecycleConfig::Sustain	Normalized energy / attack	Maximum capacity restored by a fully consonant attack.
dissonance_penalty	LifecycleConfig::Sustain	Float ≥ 0	Extends well-fit lifetime while preserving the zero-fit endurance contract.
dcc.coupling_strength	DccConfig	0.0-1.0	Strength of ListenerTwin tension feedback; default 0.0 (behaviorally off).
dcc.max_temperature_bonus	DccConfig	Float ≥ 0	Maximum pitch-search temperature added by listener pressure (default 0.10).
attack_step	KuramotoCore	Float	Envelope attack step size.
decay_rate	KuramotoCore	Float	Envelope decay rate.

Appendix B: Mathematical Summary

Consonance Kernel (bilinear):

$$ C_{score} = a \cdot H_{01} + b \cdot R_{01} + c \cdot H_{01} R_{01} + d $$

Consonance Level (sigmoid representation):

$$ C_{level01} = \frac{1}{1 + e^{-\beta(C_{score} - \theta)}} $$

Consonance Density Mass ($\rho$-kernel):

$$ C_{density_mass} = \max(0,; H_{01}(1 - \rho R_{01})) $$

Landscape habituation and effective views:

$$ d_i=\frac{L_iP_i}{L_iP_i+r_{ref}}, \qquad h_i(t+\Delta t)=a h_i(t)+(1-a)d_i, \quad a=e^{-\Delta t/\tau_{rise/fall}} $$

$$ C_{score,i}^{eff}=\theta+(C_{score,i}-\theta)(1-h_i), \qquad C_{density_mass,i}^{eff}=C_{density_mass,i}(1-h_i) $$

$$ C_{level01,i}^{eff}=\frac{1}{1+e^{-\beta(C_{score,i}^{eff}-\theta)}} $$

Roughness Saturation Mapping (from reference-normalized ratio $x$ to $R_{01} \in [0,1]$):

$$ R_{01}(x; k) = \begin{cases} 0 & \text{if } x \leq 0 \ x \cdot \frac{1}{1+k} & \text{if } 0 < x < 1 \ 1 - \frac{k}{x+k} & \text{if } x \geq 1 \end{cases} $$

where $k$ is roughness_k (default $\approx 0.4286$). The function is continuous at $x=1$ and saturates to 1 as $x \to \infty$.

Time-domain lifecycle (normalized energy $E\in[0,1]$):

$$ b = \frac{1}{T_e(1+p_d)}, \qquad \Delta E_{basal} = -b,[1+p_d(1-C_{level01}^{eff})],\Delta t $$

$$ \Delta E_{recovery} = \frac{V(C^{eff})}{T_r},\Delta t, \qquad \Delta E_{attack} = -f_c + f_r C_{level01}^{eff}m_r $$

where $T_e$ is endurance, $T_r$ is recovery, $p_d$ is the dissonance penalty, $V(C^{eff})$ is the viability-window signal, $f_c/f_r$ are attack cost/recharge fractions, and $m_r$ is the bounded rhythm-reward multiplier.

Harmonicity Projection (single-path Sibling Algorithm):

$$ Roots[i]=\left(\sum_k k^{-\rho}A[i+\log_2(k)]\right)^{\gamma} $$

$$ H[i]=\max\left(0,;\sum_m m^{-\rho}Roots[i-\log_2(m)] -(1-w_{diag})\left(\sum_{k=1}^{K}k^{-2\rho}\right)A[i]\right) $$

The implementation then applies the optional absolute-frequency TFS gate and, by default, peak-normalizes the scan.

Roughness Convolution: $$ R_{shape}(z) = \int A(\tau) \cdot K_{rough}(z-\tau) d\tau $$