The spectroscopic observations presented here were acquired during the 2017 August 21 total solar eclipse (TSE) with a three-channel partially multiplexed imaging spectrometer operating at extremely high orders (>50). The 4 R
⊙ extent of the slit in the north–south direction scanned the corona starting from the central meridian out to approximately 1.0 R
⊙ off the east limb throughout totality. The line widths and Doppler shifts of the Fe x (637.4 nm) and Fe xiv (530.3 nm) emission lines, characteristic of 1.1 × 106 K and 1.8 × 106 K electron temperatures, respectively, varied across the different coronal structures intercepted by the slit. Fe xiv was the dominant emission in the closed fields of an active region and the base of a streamer, with relatively constant 20–30 km s−1 line widths independent of the height. In contrast, Fe x emission exhibited broader (>40 km s−1) line widths in open fields, which increased with height, in particular in the polar coronal hole. Inferences of line widths and Doppler shifts were consistent with extreme ultraviolet (EUV) observations from the Hinode/EUV Imaging Spectrograph, as well as with the near-infrared Fe xiii 1074 nm line observed by Coronal Multichannel Polarimeter. The differences in the spectral line widths between distinct coronal structures are interpreted as an indication of the predominance of wave heating in open structures versus localized heating in closed structures. This study underscores the unparalleled advantages and the enormous potential of TSE spectroscopy in measuring line widths simultaneously in open and closed fields at high altitudes, with minimal exposure times, stray light levels, and instrumental widths.