Consonance as Synchronization: a tonotopic bank of driven nonlinear oscillators (Milestone 1)

Working paper, Milestone 1 of a clean-room theory of musical consonance: consonance as synchronization. This record is deposited as the historical Milestone 1 document, frozen as written on 2026-10-01 — its claims, data, and honest accounting are unchanged. A tonotopic bank of 128 driven Stuart–Landau oscillators (f₀ log-spaced 5.5–440 Hz; all frequencies scaled ×1/10 from audio, a choice made before any interval results were seen) is driven by the partials of musical intervals. Dissonance is quantified as slow amplitude modulation of the oscillator envelopes (roughness/beating made operational); intervals are ranked by the median over the bank (median-D), adopted because the self-sustained bank is multistable and rare chaotic outliers corrupt the mean (documented via a 6-interval × 5-seed IC-robustness test). The bank reproduces the extremes of the Plomp–Levelt curve (P1, P5, P8 most consonant; m2, TT, m7 most dissonant) but reads equal-tempered thirds/sixths as dissonant. Falsifiable prediction: stretched inharmonic timbre collapses the perfect fifth from 2nd-most-consonant to 7th (dissonance +36%) while the octave moves only +5% — the fifth is the most inharmonicity-sensitive interval. Two real bugs found and fixed during the work are documented honestly in the paper and the lab notebook. Milestone 2 addendum (2026-11-09). Milestone 2 has since been published (DOI 10.5281/zenodo.23093208, linked below as this record's continuation) and revises Milestone 1 in three places, flagged here and in the accompanying addendum PDF rather than edited into the original text: (a) Milestone 1's claim that under the ×1/10 scaling "the dynamics depend only on ratios" is withdrawn (Milestone 2 §2: fractional tongue width scales ~inversely with f₀, so the scaling is a tongue-width knob, not a neutral change of units). (b) Milestone 1's diagnosis of the thirds/sixths failure as narrow-tongue hypersensitivity to equal-temperament mistuning is falsified: Milestone 2 §6 ran the just-intonation check Milestone 1 had deliberately deferred, and the thirds got worse under just intonation (m3 #11, M3 #13 of 13; P4 #12). (c) The calibrated blind listening pilot announced in Milestone 1 was prepared but abandoned before any data collection (Milestone 2 §8); no listening data exists. A further note: Milestone 1 states the stretched-fifth effect as a rank change (2nd → 7th, 5 seeds); Milestone 2 §7 re-reports it as an effect size (+37.0%, 95% CI [+31.5, +42.8], 20 seeds), which supersedes the rank form. The addendum PDF also carries the reference list and related-work note that the original paper lacked. PDF regenerated from source on 2026-11-09; content unchanged. The code in this record is the current version of the five Milestone 1 scripts, not a verified Oct 2026 snapshot (no version history survives; the files are byte-identical to the copies published with Milestone 2). Files: working paper (PDF, 5 pp., as written 2026-10-01), deposit addendum (PDF), code, run data, figures, and the lab notebook (consonance_lablog.md, the Milestone 1 record — truncated at the last entry before the Milestone 2 paper entry; later entries continue in the Milestone 2 record). License CC-BY-4.0.