We introduce a novel mosaic synthesis algorithm for musical style transfer using the autocorrelogram as a feature map. We decompose the autocorrelogram feature map sparsely in a decaying sinusoid basis, using that decomposition as an interpolation scheme in feature space. This efficiently provides gradient information in the mosaicing optimization, including gradients of the challenging time-scale parameters, which are usually computationally intractable for discretely sampled signals. The required calculations are straightforward to parallelize on vectorprocessing hardware. Our implementation of the method provides good quality output and novel musical effects in example tasks by itself and can also be integrated into alternative mosaicing methods.