There is a growing and urgent need for an overarching conceptual framework that encompasses and harmonises the world's diverse moral values. However, existing research presents a puzzle: evolution has equipped humans with a range of innate moral instincts; yet moral values vary considerably across cultures. How can these perspectives be reconciled? We explore the theory that morality is a 'discrete combinatorial system', in which innate moral 'elements' are combined to create new culturally-specific moral "molecules". Starting with a "periodic table of ethics", we use conceptual analysis to identify the universe of possible moral molecules, and review the literature to identify which have already been analysed and which remain to be explained. We then use survey techniques from social psychology to investigate the relationship between moral elements and molecules, from a cross-cultural sample of participants in Japan, Russia, China, Argentina, UK and Saudi Arabia. Our results will: advance our understanding of the philosophical, psychological and cultural basis of moral values, and illuminate the process by which new moral values are created. By identifying what we have in common, and explaining why we differ, the project will help people of different cultures and backgrounds to live in greater harmony.