Harmoniformula

Harmoniformula is a conceptual framework used in music theory and computational composition to describe and quantify harmonic relationships. It encompasses a family of expressions that assign a numerical value to a harmonic event—such as a chord, progression, or voice-leading situation—so that consonance, functional harmony, and stability can be analyzed or guiding-generation of music can be performed. The term is often employed in algorithmic composition, music information retrieval, and pedagogical contexts to compare harmonies and to steer automated music generation.

In its typical form, a harmoniformula expresses a function H that takes inputs such as a set of pitch classes P, a chord type T, a key K, and optionally a voice-leading or rhythmic state V, returning a score s in a chosen range (for example [0,1] or a real-valued vector). A common instantiation combines components for consonance of intervals, fidelity to functional harmony in the given key, and voice-leading efficiency. A simple representation might be H(P, T, K, V) = wC · consonance(I) + wF · functionalFit(T, K) − wL · leadingCost(V), with nonnegative weights wC, wF, wL.

Applications include guiding algorithmic composition, ranking candidate harmonies in music-generation systems, and teaching harmony by providing a measurable metric. Limitations include subjectivity in consonance judgments, cultural variation in harmonic taste, and the need for calibration to match stylistic goals. Harmoniformula is related to concepts in musical set theory, tonal analysis, and optimization-based music generation.

See also: musical set theory, harmony, algorithmic composition, music information retrieval, tonal function.