Tessellation is the tiling of textures (link is a dictionary definition). To explain, imagine that you have a block that has a physical space of 256x256x256, a nice, large-sized cube. You apply a 64x64 texture on it. The texture is repeated 16 times on the block per side (totalling 96 repeats). If you scaled the texture to half (0.5), the texture would be repeated 64 times on the block per side (384 total). This is because the texture takes half as much space on the same-sized object and it needs to be tiled more to get this. On the other hand, however, if you scaled the texture to double (2), the texture would be repeated 4 times on the block per side (24 total).

To get finely-scaled textures, use models. For a 0.25 scale, have the texture space coverage 4 times that of the physical size of the particular polygon(s) being mapped. That is, if you have a 256x256 polygon, have the texture space cover 1024x1024 pixels. For odd scales, like 0.375 (3/8), just take the physical size and divide by the scale size (this would give 682.66666... pixels of coverage).