We advocate the idea of a training-free texture classification scheme. This we demonstrate not only for traditional texture benchmarks, but also for the identification of materials and of the writers of musical scores. State-of-the-art methods operate using local descriptors, their intermediate representation over trained dictionaries, and classifiers. For the first two steps, we work with pooled local Gaussian derivative filters and a small dictionary not obtained through training, resp. Moreover, we build a multi-level representation similar to a spatial pyramid which captures region-level information. An extra step robustifies the final representation by means of comparative reasoning. As to the classification step, we achieve robust results using nearest neighbor classification, and state-of-the-art results with a collaborative strategy. Also these classifiers need no training. To the best of our knowledge, the proposed system yields top results on five standard benchmarks: 99.4% for CUReT, 97.3% for Brodatz, 99.5% for UMD, 99.4% for KTHTIPS, and 99% for UIUC. We significantly improve the state-of-the-art for three other benchmarks: KTHTIPS2b - 66.3% (from 58.1%), CVC-MUSCIMA - 99.8% (from 77.0%), and FMD - 55.8% (from 54%).