Boundary colors are observed when light from a scene is dispersed by a prism or diffraction grating. We discovered that patterns with repeating black and white stripes can produce repeating bands of boundary colors with two hues. These hues are virtually constant as measured by chromaticity or CIELAB. We found seven cases of this kind using a new appearance model for boundary colors. The model correctly predicts that green and magenta bands recur as stripe widths and dispersion strength vary. The first green/magenta case in the sequence traces out an accurate ellipse in XYZ color space. Green and magenta bands are prominent in supernumerary rainbows and interference rings, and we explain why that might be the case. The explanation is based on an interesting property of the visible spectrum. In addition to the green/magenta cases, the other cases are orange/cyan, yellowish-green/purple, and yellow/violet. The success of the boundary color appearance model implies that bands are perceived as if the wavelength responses of the cones were essentially independent, which contradicts the actual behavior of cones. (c) 2014 Wiley Periodicals, Inc. Col Res Appl, 40, 135-146, 2015