Differentiable Articulatory Copy-Synthesis of Biphonic Singing

Sygyt is a Tuvan style of biphonic singing in which a low vocal drone is sustained while a high harmonic is selectively amplified in the 1--3\,kHz region. Copy-synthesizing this effect remains challenging for articulatory models, since it requires fine control of narrowly focused resonances that standard low-dimensional tract parameterizations cannot easily reproduce. We address this problem with a differentiable Kelly--Lochbaum waveguide augmented with a sublingual second source, cubic B-spline tract parameterization, and spatially varying learnable damping, optimized end-to-end by gradient descent from audio. On 20 segments from two independent sygyt datasets (5 singers, 10 pitches), the proposed model reduces log-spectral distance by 30--38\% relative to an articulatory baseline, with the largest gains concentrated in the overtone region. Cepstral-envelope analysis further shows more accurate recovery of the merged formant structure characteristic of sygyt production. The model also outperforms a DDSP harmonic-plus-noise baseline with direct per-harmonic spectral control, suggesting that explicit acoustic structure is a useful inductive bias for overtone-singing copy-synthesis.