A functional approach to automatic melody harmonisation

Abstract

Melody harmonisation is a centuries-old problem of long tradition, and a core aspect of composition in Western tonal music. In this work we describe FHARM, an automated system for melody harmonisation based on a functional model of harmony. Our system first generates multiple harmonically well-formed chord sequences for a given melody. From the generated sequences, the best one is chosen, by picking the one with the smallest deviation from the harmony model. Unlike all existing systems, FHARM guarantees that the generated chord sequences follow the basic rules of tonal harmony. We carry out two experiments to evaluate the quality of our harmonisations. In one experiment, a panel of harmony experts is asked to give its professional opinion and rate the generated chord sequences for selected melodies. In another experiment, we generate a chord sequence for a selected melody, and compare the result to the original harmonisation given by a harmony scholar. Our experiments confirm that FHARM generates realistic chords for each melody note. However, we also conclude that harmonising a melody with individually well-formed chord sequences from a harmony model does not guarantee a well-sounding coherence between the chords and the melody. We reflect on the experience gained with our experiment, and propose future improvements to refine the quality of the harmonisation.

Automatic Functional Harmonic Analysis

“…With the automatic annotation techniques that we present here, this can be done quickly, even for large corpora possibly containing errors. Additionally, HarmTrace could aid in (automatic) composition by generating sequences of chords, generating harmonically realistic continuations given a sequence of chords, or automatically harmonizing a melody (Koops, Magalhães, and De Haas 2013).…”

Functional generation of harmony and melody

“…Hybrid models usually try to combine these two approaches: the deterministic part creates a context in which a musical piece can be explored, and a stochastic part that tries to creatively find interesting patterns within this context. An example of such a hybrid system is that of Koops et al (2013), which is capable of harmonising a given melody through the aid of a functional model of tonal harmony. The given input melody is analysed and appropriate chords are selected for each note.…”

“…To ease the understanding of musical concepts for programmers, we accompany our description with illustrative code snippets of how to encode each musical concept in Haskell. Since FCOMP follows a line of previous work (Magalhães and De Haas 2011;Koops et al 2013), this section restates some parts of earlier work adapted for the current context.…”

Grammar-based automated music composition in Haskell

“…The HarmTrace package, written in Haskell, builds on Rohrmeier's grammar to automate harmonic analysis [15]. FHarm, a later system that also uses Haskell, addresses the task of melodic harmonization using HarmTrace to filter out results that best match a particular harmonic model [13]. A fundamental difference between our system and FHarm is that FHarm harmonizes an existing melody, whereas our system performs composition from scratch and does not currently address any melodyspecific features.…”

“…Each measure contains a different mapping of the same example. From left to right, they are: block trichords (Equation 10), an OPC-space mapping of those trichords(Equation 11), block jazz chords from our jazz space (Equation 12), and those jazz chords mapped through OPC-space (Equation13). …”