Automatic Functional Harmonic Analysis

Abstract

Music scholars have been studying tonal harmony intensively for centuries, yielding numerous theories and models. Unfortunately, a large number of these theories are formulated in a rather informal fashion and lack mathematical precision. In this article we present HarmTrace, a functional model of Western tonal harmony that builds on well-known theories of tonal harmony. In contrast to other approaches that remain purely theoretical, we present an implemented system that is evaluated empirically. Given a sequence of symbolic chord labels, HarmTrace automatically derives the harmonic relations between chords. For this, we use advanced functional programming techniques that are uniquely available in the Haskell programming language. We show that our system is fast, easy to modify and maintain, robust against noisy data, and that its harmonic analyses comply with Western tonal harmony theory.For ages, musicians, composers, and musicologists have proposed theories regarding the structure of music to better understand how it is perceived, performed, and appreciated. In particular, tonal harmony exhibits a considerable amount of structure and regularity. The first theories describing tonal harmony date back at least to the 18th century (Rameau 1722). Since then, a rich body of literature that aims at explaining the harmonic regularities in both informal and formal models has emerged (e.g., Lerdahl and Jackendoff 1996). Such models have attracted numerous computer music researchers to investigate the automation of the analysis and generation of harmony. Most of these theories, however, have proven to be very hard to implement (e.g., Clarke 1986). We are not aware of a model that has a working implementation that effectively analyzes tonal harmony and deals robustly with noisy data, while remaining simple and easy to maintain, and scaling well to handle musical corpora of considerable size. In this article we present HarmTrace (Harmony Analysis and Retrieval of Music

A functional approach to automatic melody harmonisation

“…In this section we introduce the harmony model of harmtrace, and how chord sequences are parsed to fit this model. This is mostly restating previous work (De Haas et al 2011Haas et al , 2012Haas et al , 2013Magalhães and De Haas 2011), adapted to the purposes of FHARM.…”

“…Due to space constraints we had to omit some specifications for diatonic chains of fifths, borrowings from the parallel mode, and the Neapolitan chord. For the full specification of the model, we refer the reader to De Haas et al (2013).…”

“…HARMTRACE automatically derives the harmonic function of a chord in its tonal context given a sequence of symbolic chord labels (De Haas et al 2013;Magalhães and De Haas 2011). Among other applications, these functional annotations can be used to improve the estimation of harmonic similarity of two chord sequences (De Haas et al 2011), and to improve chord recognition from audio (De Haas et al 2012).…”

Augmenting Music Sheets with Harmonic Fingerprints

“…The notation, however, omits the explicit representation of the relationship that exists between the individual notes and their location within the overarching musical structure [11]. While understanding these complex relationships is of immediate interest for the musician [6], such an understanding typically requires analyzing the score and thus, a certain level of musical expertise [7,17]. The understanding of the harmonic structure of the score allows for faster learning of new musical pieces and enhances musical memory and should ideally be more accessible to novices.…”

Understanding the structure of musical compositions: Is visualization an effective approach?

“…This is a time-consuming process, especially when large corpora have to be analyzed. 1 It is worth to note that the knowledge of music theory and composition techniques is essential to understand the melodic and harmonic structures of musical compositions.…”