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Audio scoping for srmech — 2026-05-09 cross-domain absorption round

Round: Audio (DSP / music / speech / spatial / EMDR-bilateral) Date: 2026-05-09 Method: Dual-agent research pattern (feedback_dual_agent_research_pattern.md)

Headline findings

  1. Audio instantiates every row of §3.5 cross-manifold table. Euclidean grid → spectrogram (STFT); sphere S² → HRTF / ambisonics; flat torus T² → periodic loops; triangle mesh → 3D acoustic-cavity meshes; general graph → microphone-array beamforming + Tonnetz key-relationship graph. Strongest evidence to date that the cross-manifold framing is load-bearing.
  2. Spectrogram is a 2D image → all graphics-domain primitives (heat-kernel blur, Perona-Malik bilateral, DoG, Varadhan SDF, anisotropic, Helmholtz wave, power-spectrum noise, reaction-diffusion) port directly with only an eigenvalues: field swap. Heat-kernel blur on spectrogram = noise reduction; Perona-Malik on spectrogram = harmonic-percussive separation; DoG on spectrogram = onset detection.
  3. Music theory IS cyclic-group theory. Z₁₂ chromatic scale = direct sibling of chess Z_640 / ephemerides Z_{2³²}. D₁₂ key-and-transposition = direct sibling of chess D₄ board symmetry. Tonnetz key-relationship graph = direct sibling of ephemerides 52-body resonance graph. AudioPhase12BIP is the audio-domain SkPhase9BIP cousin — same architecture, different alphabet.
  4. Bilateral audio is directly load-bearing for the EMDR project's mission. Audio as a peer modality alongside motor + LED, under the same UTLP-coordinated catalogue + bilateral-coordination machinery. Operators required (alternating tones, binaural beats, isochronic tones, music-driven panning, cardiac-coherence pacing at 0.1 Hz) are all closed-form g(λ) catalogue entries. Hardware cost: ~$2–5 BOM (PCM5102 / MAX98357 / UDA1334 I²S DAC). Potentially the shortest-path proof-of-concept for srmech on the project's actual mission.
  5. AMSC literature_curated already covers DSP knowledge. RBJ EQ Cookbook → literature_curated. ISO 226 equal-loudness, ERB / Bark / A-weighting curves, Moore-Glasberg masking, MPEG psychoacoustic model, codec specifications (MP3 / AAC / Opus tables) — all standard literature_curated fits. HRTF / RIR archives, speech corpora (TIMIT / LibriSpeech / VCTK / Common Voice), music corpora (FMA / MAESTRO / MUSDB) → binary_archive. No new ingestion machinery needed.
  6. Config-vs-substrate ratio: ~80/20. Most audio DSP is closed-form g(λ) — EQ, denoising (Wiener, spectral subtraction, MMSE-LSA), reverb, pitch-shift, ambisonic encoding. Substrate primitives are state-dependent or coupled (compressors / limiters, auto-tune, neural vocoders, source separation, AEC, ANC).

Operator counts

  • Audio manifolds: 13 (main agent) / 24 (sub-agent) — sub-agent broader enumeration; both cover the load-bearing core
  • Transforms: ~25 (main) / 27 (sub) — DFT/FFT, MDCT, STFT, CQT, NSGT, wavelets, gammatone, Mel/Bark, modulation spectrogram, cepstrum, MFCC, chroma, spherical harmonics, KLT, etc.
  • Closed-form g(λ) operators: 50+ (main) / 75+ (sub) across 8–11 thematic groups: EQ family, denoising family, reverb / convolution family, pitch / time family (phase vocoder), Hilbert / analytic-signal family, spatial / spherical-harmonic family, modulation / synthesis family, coding / quantisation family, fingerprinting / chroma family
  • Substrate primitives: 25 (main) / 26 (sub) — compressor / limiter / expander, auto-tune, adaptive filtering (LMS / NLMS / RLS / Kalman), AEC, ANC, RNNoise / DeepNoise, onset / beat detection, pitch detection, source separation (NMF / ICA / RPCA / Demucs / Spleeter), Karplus-Strong, waveguide synthesis, modal synthesis with feedback, WaveNet / SampleRNN / diffusion-on-spectrogram, Griffin-Lim, MSM / DTW, etc.
  • HDC cyclic groups: 9 (main) / 12 (sub) — Z₁₂ chromatic, Z₂₄ quartertones, Z₇ diatonic, Z₃ circle-of-fifths (Camelot wheel), Z_b beat cycles, Z₁₂ × Z_b chroma×beat, Tonnetz Z₁₂×Z₁₂ torus, Z₁₃₂ keyboard span, vocal-tract phoneme cycle, Shazam-style Z_n × Z_n peak-pair fingerprint, room-mode index (l,m,n)

Cross-pollination with already-absorbed srmech primitives

The §3.5 cross-manifold table extends — audio instantiation column:

Manifold Audio instantiation
Euclidean grid + Neumann BC Spectrogram (2D STFT)
Sphere S² HRTF / ambisonics — Y_l^m basis with l(l+1) eigenvalues
Flat torus T² Periodic-loop sample; periodic-rhythm pattern
Triangle mesh 3D acoustic-wave simulation on irregular geometry
General graph Microphone array; Tonnetz; key-relationship graph

Direct primitive ports (graphics → spectrogram):

  • Heat-kernel blur on spectrogram → noise reduction / envelope estimation (anisotropic σ_t and σ_f independent)
  • Perona-Malik on spectrogram → harmonic-percussive separation (Fitzgerald 2010)
  • DoG on spectrogram → onset detection
  • Sharpen / Laplacian on spectrogram → transient enhancement
  • Anisotropic-tensor diffusion on spectrogram → smoothing along harmonic ridges (vocal-formant tracking)
  • Helmholtz wave on spectrogram → procedural texture generator
  • Power-spectrum noise (audio variant) → 1/f pink, 1/f² brown, blue, violet, log-normal, log-banded — direct sibling of graphics §3.1 power-spectrum noise; same P ∈ {1, 1/√λ, 1/λ, √λ} menu

EMDR-project-specific opportunities (strong direct connection)

Bilateral audio as a peer modality alongside motor + LED:

  • Alternating tones (250 Hz–1 kHz, hard-pan L/R, 0.5–2 Hz alternation matching motor frequency range) — closed-form (Transform = trivial, λ = bilateral_phase, g = pan(t))
  • Alternating clicks / pulses — sharper attention than tones for some clients
  • Pink-noise burst alternation — spectrally rich, less fatiguing over 20-min sessions
  • Music-driven bilateral panning — energy-preserving rotation g_L(t) = cos²(π f_alt t), g_R(t) = sin²(π f_alt t)
  • Binaural beats (carrier f_L = 200 Hz, f_R = 204 Hz → 4 Hz beat via frequency-following response)
  • Isochronic tones — (1 + cos(2π f_pulse t)) · cos(2π f_tone t); mono-speaker compatible
  • Cardiac-coherence pacing tones — 0.1 Hz amplitude-modulated soft pink noise (EMDR_Slow_BLS_Research_Frontier.md sub-0.5 Hz frontier)
  • Coherent multi-modal stimuli — single phase signal drives motors + audio + LED; polyrhythm via Z₂ × Z₃ × Z₆ = Z₁₂ LCM cycle
  • HRV biofeedback tones — adaptive (substrate primitive); pace adjusts to user's RMSSD

Disability-accommodation dimension (per feedback_disability_accommodation_dimension.md, sub-agent caught this):

  • Aphantasia: bilateral audio gives non-visual cue (user can't visualise moving spot but hears alternation) — direct accommodation
  • Visual impairment / blindness: audio becomes primary modality; motor + audio is inclusive design
  • Hearing impairment: motor primary, audio adds redundancy; bone-conduction transducers a future-direction accommodation
  • Photosensitivity / migraine: audio + motor with no visual flicker
  • Cognitive load (ADHD / executive-function differences): audio coordination removes visual-attention demand of tracking moving spot

Trauma-informed audio environment design (per feedback_trauma_informed_defensive_scope.md):

  • Soft-onset / soft-offset envelopes (avoid startle response)
  • Bandwidth-limited (no aggressive high-frequency content)
  • Sub-A-weighted-loudness limits (perceptually safe per IEC 61672)
  • No abrupt panning (smooth bilateral alternation, not L/R discrete)
  • Post-session quiet ramp

First-principles cautions (framework-edge)

  • Phase matters in audio. g(λ) must often be complex-valued (delays, all-pass, comb filters). The (Transform, λ_k, g) decomposition extends naturally — g maps to ℂ rather than ℝ — but substrate must support this.
  • Time-varying g(ω, t) for chorus / flanger / phaser. Framework extends but is not yet articulated in §3.0 sketch.
  • Real-time vs offline. Offline FFT-of-whole-signal fits config; real-time block-by-block needs substrate-primitive scheduling (overlap-add / overlap-save / sliding-DFT).
  • Sample-rate dependence. Physical-frequency g(λ) parameters re-bind per sample-rate.
  • Perceptual vs physical eigenbasis. Audio's "right" basis is often perceptual (Mel / Bark / ERB / cochlear) rather than linear. Cross-manifold framing handles this; choosing per task is design.
  • EMDR sub-100ms latency budget. Most operators work in 10ms blocks; some don't (CQT reassignment).
  • Z₁₂ / D₁₂ caveat for non-12-EDO music. Microtonal (24-EDO, 31-EDO, just intonation) needs different modular arithmetic. Non-pitched percussion lives in rhythm-graph world.

Comparison: main-agent vs sub-agent

Dimension Main-agent (with conversation context) Sub-agent (independent fresh-read)
Manifold count 13 24 (broader; added cepstral / wavelet plane / pitch helix / spherical shell / loudspeaker line / non-rectangular plate / auditory-nerve graph / score graph / Q-factor / beam-pattern manifolds)
Filter family Bundled (low-pass / high-pass / band-pass / shelving / peaking) Explicit (Butterworth Nth, Chebyshev I/II, elliptic / Cauer, Bessel, Linkwitz-Riley)
Closed-form ops 50+ 75+
Substrate ops 25 26 (added Griffin-Lim explicit, neural vocoder HiFi-GAN / Vocos, Weighted Prediction Error WPE, self-organizing maps, voice conversion)
HDC groups 9 12 (added Z₂₄ quartertones, Z₃ Camelot, Z_n×Z_n fingerprint, Z₁₃₂ keyboard, vocal-tract phoneme, room-mode index)
Citation discipline Loose Strong (RBJ Audio EQ Cookbook 2003 by name)
Hardware specifics "needs care for latency" I²S DACs (PCM5102 / MAX98357 / UDA1334), ~$2–5 BOM, 512-sample real-time DCT on ESP32-C6
Disability-accommodation memory Missed Applied
Trauma-informed memory Missed Applied
Phase-mattering caveat Caught Implicit only
Time-varying g(ω, t) framework extension Caught Listed but not articulated as gap
Real-time vs offline scheduling Caught Light treatment
Sample-rate re-binding Caught Not surfaced
Z₁₂ caveat for non-12-EDO Caught Mentioned but not flagged
AudioPhase12BIP naming Implied Named explicitly
AMSC mode taxonomy Flat list Structured 7 mode classes

Convergent core (both reached independently): all 6 headline findings above. The differences are at the margin of enumeration breadth and citation specificity vs framework-edge cautions.

Takeaways landed in master srmech notebook

  • §3.5 cross-manifold table: audio instantiation column added
  • §4.2 calibration: audio profile is ~80/20 (similar to graphics)
  • §5.2 absorption-round subsection: headline findings + link to this file
  • §1.5 future-notebook candidates: audio row added (project-mission relevance — direct EMDR fit)