Nucleosomes in all eukaryotic cells are organized into higher order structures that facilitate genome compaction. Visualizing these organized structures is an important step in understanding how genomic DNA is efficiently stored yet remains accessible to information-processing machinery. Arrays of linked nucleosomes serve as useful models for understanding how the properties of both DNA and protein partners affect their arrangement. A number of important questions are also associated with understanding how the spacings between nucleosomes are affected by the histone proteins, chromatin remodelers, or other chromatin-associated protein partners. Contrast variation small angle X-ray scattering (CVSAXS) reports the DNA conformation within protein-DNA complexes and here is applied to measure the conformation(s) of trinucleosomes in solution, with specific sensitivity to the distance between and relative orientation of linked nucleosomes. These data are interpreted in conjunction with DNA models that account for its sequence dependent mechanical properties, and Monte-Carlo techniques that generate realistic structures for comparison with measured scattering profiles. In solution, trinucleosomes segregate into two dominant populations, with the flanking nucleosomes stacked or nearly equilaterally separated, e.g. with roughly equal distance between all pairs of nucleosomes. These populations are consistent with previously observed magnesium-dependent structures of trinucleosomes with shorter linkers.