Twelve years ago the occasional BMInt writer Nathaniel Eiseman implemented an “Algorithmic Approach to Melodic Harmonization” as an honors thesis to satisfy requirements of the Tulane music and mathematics departments. Wondering if he could combine mathematics and music in a relatively accessible and potentially useful way, he proved that by using the tenets of probabilistic inference and codified domain knowledge he could automate the harmonizing of melodies in the style of a four-part chorale characteristic of the German Baroque. Will readers tell us how AI, Chat GPT and so forth have advanced the field after reading the complete paper HERE and playing the examples? Some excerpts from his paper follow. (FLE)

The ultimate purpose of this thesis is to design an algorithmic framework that allows a computer to do exactly what Bach did: with nothing but a melodic line as input, provide the alto, tenor, and bass voices. This automatic harmonization process is based upon two procedurally distinct subroutines. First, harmonies are selected probabilistically based on a variety of contextual factors including each melodic pitch’s position within its phrase and the notes and harmonies preceding it. The alto, tenor, and bass are then deterministically assigned pitches based on the selected harmony, such that rule violations are minimized.

Given a sequence of melodic pitches, the system developed herein supplies the three other voices of the chorale in a way that produces aurally pleasing harmonic progressions and satisfies the rules of four-part writing. This is accomplished by the interface between a probabilistic process that selects the harmonies for these progressions based on data obtained from the chorale harmonizations by Johann Sebastian Bach and a deterministic process that voices a sequence of four-part chords given melodic pitch and information about the harmonic progression specified by the first process. … Undoubtedly, computers are capable of generating chorale harmonizations that are semantically correct. The question is whether, if supervised by the rules of counterpoint and instructed by analysis of Bach’s harmonic language, they can satisfactory resolve the defective spots. The ultimate question is whether computer harmonization can sound good.

The  example below compares Bach’s harmonizations with my algorithmic results.