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The whiteness of your white depends on the fabric base chosen. The whitest whites are the poplin, sateen, and twill. The rest are varying degrees of off-white.
The richness of the blacks also depends on the fabric base. The polyesters (silky faille and the performance knit) provide the closest to true black. (Sample fabric image shows one of the polyesters.) Cotton poplin is the closest to black of the cottons. The rest will print closer to charcoal gray or "off-black."
If in doubt, order a test swatch.