In current musicological research, considerable attention is given to the description of melodic structure and pitch organization. But it is problematical that the analytical concepts and terminology of the Common Practice Era are largely inadequate for meaningful description of melody of Asia and medieval Europe. For most traditions of melody in Asia and medieval Europe, there is some sort of developed system of theory, but each system is limited to the repertory it describes. Consequently, the comparative study of melody in these fields has been seriously hampered, and much published research in melody has had to concern itself with the formulation of analytical approaches more than the actual study of melody. This study attempts to resolve this problem by offering for consideration an analytical model, the acoustic melodic formula, that is of use in the comparative study of melodic structures and formulas in Asia and medieval Europe. The acoustic melodic formula is a structural design consisting of three conjunct intervals, namely, a lower perfect fourth, a middle third of varying intonation, and an upper third, also of varying intonation. In addition to identifying the acoustic melodic formula in Japan, Korea, central Asia, and Jewish, Byzantine and Latin chant, this study also investigates how such melodies have additional tones--melodic embellishments--added to them through folk improvisation and artistic elaboration.