What 345 Gigahertz Buys: Resolution, Nulls and Scattering Across Three Observing Bands

Moving a horizon-scale array from 86 to 345 gigahertz improves the Earth-baseline fringe spacing from 56.4 to 14.1 microarcseconds, a factor of 4.01, and shrinks the interstellar scattering angle toward Sagittarius A* from about 160 microarcseconds to 9.9 microarcseconds under the wavelength-squared law. The first visibility null of the M87* ring moves inward to 3267 kilometres at 345 gigahertz, bringing more station pairs across it. Those gains are real and quantifiable, and they are purchased with a smaller field of regard: atmospheric coherence times shorten, receiver noise rises, and the number of stations that can operate at the highest band is smaller. Weighed on the numbers computed here, 345 gigahertz is the band in which the photon-ring signatures and the scattering floor both become accessible, while 230 gigahertz remains the band of maximum baseline count. The case for simultaneous dual-band observing follows directly. Computed from stated scalings; simulated, not measured.