High-resolution X-ray diffraction of high-purity multiwall carbon nanotubes has been performed and unusual diffraction physics was observed. Fourier analysis confirms that the multiwall nanotubes are made of concentric cylinders and that there is a non-uniform distribution of inner tube diameter. The interference effect discussed in this paper is unique for concentric tubes and in contrast to nanotubes that are scroll-like or made up of irregular grains.