A new scheme for sinusoidal audio coding named multiple description spherical trellis-coded quantization is proposed and analytic expressions for the point densities and expected distortion of the quantizers are derived based on a high-resolution assumption. The proposed quantizers are of variable dimensions meaning that any number of sinusoids can be quantized jointly for each audio segment whereby a lower distortion is achieved compared to previously published scalar spherical quantizers. The quantizers are designed to minimize a perceptual distortion measure subject to an entropy constraint for a given packet-loss probability. In experiments, the performance of the quantizers is assessed and compared to the corresponding single description spherical quantizer and associated bounds under various conditions and is found to increase robustness towards packet-loss.