ZSM-23 (MTT) is a silicon-rich zeolite with one-dimensional, 10-membered ring channels, which has recently attracted interest as a promising catalyst in aromatic-free methanol-to-hydrocarbons conversion. To obtain a better understanding of the catalytic activity and ultimately to design a better catalyst, it is crucial to locate the active sites in the zeolite framework. This work investigates the tetrahedral aluminum framework sites in two zeolite H-ZSM-23 samples by experimental and computational ²⁷ Al NMR spectroscopy. ²⁷ Al MQMAS NMR experiments at six different magnetic fields (4.7-22.3 T) were utilized to resolve distinct Al sites. The detected tetrahedral framework Al sites were assigned to the specific tetrahedral sites in the crystal structure by DFT calculations of the ²⁷ Al chemical shieldings. A comprehensive investigation of the structural model, basis set, and exchange-correlation potential used in the DFT calculations was performed. Two avenues were pursued for calculating the ²⁷ Al isotropic chemical shifts: the isolated-sites approach where clusters are extracted from large supercells with high Si/Al ratios and an approach targeting lower Si/Al ratios with a fully periodic model. It is found that for the ZSM-23 zeolites with Si/Al = 24 and 37 investigated here, the latter approach gives the best agreement with experiment.