The present paper studies the chromaticity gamut of multi-color printing processes. Heptatone (7-color) printing - the most promising variant of multi-color printing - offers a significantly larger gamut than a conventional CMYK printing process, approaching CRT and film gamuts. The behavior of the process in the device-independent CIE-XYZ and CIE-Luv* colorimetric spaces is explored using the compound Neugebauer model developped for this purpose. A simple and straightforward Moiri-free separation process is proposed. The strong point of the proposed separation process is the fact that only 3 different screen layers are needed for any odd number of basic colors including black.