Observed CN and HCN intensity ratios exhibit subtle variations in extreme galaxy environments.

We use both new and archival ALMA data of three energy lines each of CN and HCN to explore intensity ratios in dense gas in NGC 3256, NGC 7469, and IRAS 13120-5453. The HCN (3-2)/HCN (1-0) intensity ratio varies in NGC 3256 and NGC 7469, with superlinear trends of 1.53$\pm$0.07 and 1.55$\pm$0.05, respectively. We find an offset to higher HCN (3-2)/HCN (1-0) intensity ratios (~0.8) in IRAS 13120-5453 compared to NGC 3256 (~0.3-0.4) and NGC 7469 (~0.3-0.5). The HCN (4-3)/HCN (3-2) intensity ratio in NGC 7469 has a slope of 1.34$\pm$0.05. We attribute the variation within NGC 3256 to excitation associated with the northern and southern nuclei. In NGC 7469, the variations are localized to the region surrounding the active galactic nucleus. At our resolution (~700 pc), IRAS 13120-5453 shows little variation in the HCN intensity ratios. Individual galaxies show nearly constant CN (2-1)/CN (1-0) intensity ratios. We find an offset to lower CN (2-1)/CN (1-0) intensity ratios (~0.5) in NGC 3256 compared to the other two galaxies (~0.8). For the CN (3-2)/CN (2-1) intensity ratio, NGC 7469 has a superlinear trend of 1.55$\pm$0.04, with the peak localized toward the active galactic nucleus. We find high (~1.7) CN (1-0)/HCN (1-0) intensity ratios in IRAS 13120-5453 and in the northern nucleus of NGC 3256, compared to a more constant ratio (~1.1) in NGC 7469 and non-starbursting regions of NGC 3256.