Many composers and musicians use the theory of negative harmony to revitalize their music, sometimes even unconsciously. Quite surprisingly, this theory has not yet been discussed in the field of music processing. In this article, we address and present negative harmony from a mathematical perspective, considering it as a geometric transformation applied to the pitch space. We then analyze, for the first time, how it is possible to derive negative melodies, unveiling the not-bijective nature of the transformation. Our discussion is corroborated with examples drawn from diverse musical genres and forms, such as chorales and piano performances, offering new insights with the ultimate goal of fostering creativity. Finally, we have developed and made freely available an audio plug-in that applies such transformations in real time, providing a creative tool for musicians and composers who want to delve into and take inspiration from the “dark side of harmony.”