TAKING H ARMONY I NTO A CCOUNT : T HE E FFECT OF H ARMONY ON M ELODIC P ROBABILITY C LAIRE A RTHUR Ohio State University PROBABILISTIC MODELS HAVE PROVED REMARKABLY successful in modeling melodic organization (e.g., Huron, 2006a; Pearce, 2005; Temperley, 2008). However, the majority of these models rely on pitch information taken from melody alone. Given the prevalence of homophonic music in Western culture, however, sur- prisingly little attention has been directed at exploring the predictive power of harmonic accompaniment in models of melodic organization. The research presented here uses a combination of the three main approaches to empirical musicology—exploratory analysis, model- ing, and hypothesis testing—to investigate the influence of harmony on melodic behavior. In this study a com- parison is made between models that use only melodic information and models that consider the melodic information along with the underlying harmonic accompaniment to predict melodic continuations. A test of overall performance shows a significant improve- ment using a melodic-harmonic model. When individ- ual scale degrees are examined, the major diatonic scale degrees are shown to have unique probability distribu- tions for each of their most common harmonic settings. That is, the results suggest a robust effect of harmony on melodic organization. Perceptual implications and directions for future research are discussed. Received: June 5, 2015, accepted August 20, 2016. Key words: melodic probability, melodic modeling, melodic expectation, harmony, scale-degree distributions M USICAL EXPECTANCY IS A FREQUENT TOPIC of interest in the music theory and music perception literature. Many models of melodic expectancy have been proposed over the past several decades. Two early theoretical models in partic- ular have been highly influential to the fields of music theory and psychology, specifically those of Meyer (1956) and Narmour (1992). Each of these models is highly complex and comprehensive in scope, with insights drawn from observations of hundreds of musical examples, as well as acute musical intuitions. A testament to the influence of these theories is the large body of work that has attempted to simplify, quantify, test, or otherwise expand upon them, most notably: Cuddy and Lunney (1995), Krumhansl (1995), Larson (2004), Lerdahl (2001), Margulis (2005), Pearce and Wiggins (2006), and Schellenberg (1996, 1997). (For a review of expectation literature, see Pearce & Wiggins, 2006; Temperley, 2012.) The majority of these models focus on the evaluation of pitch information taken from the melody alone (e.g., pitch height, interval size, con- tour, etc.). However, while the pitch domain has received the greatest attention, research has also estab- lished the importance of rhythm and phrasing in con- tributing to melodic expectation. For example, rhythmic information can help predict the location of phrase end- ings (Jusczyk & Krumhanl, 1993, Krumhansl, 2000; Krumhansl & Jusczyk, 1990; Palmer & Krumhansl, 1987), and pitches located near phrase endings will have an increased probability to move towards their note of resolution (Aarden, 2003; Pearce, 2005). Given the prev- alence of homophonic music (i.e., melody with accom- paniment) in Western musical cultures, an obvious avenue for further exploration in models of melodic organization would be that of harmonic context. In other words, in modeling melodic expectancy, it may prove beneficial to examine melody not just as isolated lines, but as lines embedded in a harmonic context. While some scholars have considered the effects of har- mony on musical expectations in experimental settings, it has typically been investigated in isolation, such as studies examining the ‘‘perceived relatedness’’ of har- monies (Krumhansl, Bharucha, & Kessler, 1982; Bhar- ucha & Krumhansl, 1983; Bharucha & Stoeckig, 1986; Bharucha, 1987). One paper that has investigated the expectations of melody and harmony combined is that of Schmuckler (1989). Schmuckler’s results are some- what counterintuitive; based on the results from three studies he proposes that melody and harmony have independent effects on musical expectations. However, as will be further discussed in the conclusion, Schmuck- ler’s unusual finding was never replicated. Although the processes underlying expectation are complex and multifaceted, research has suggested that Music Perception, VOLUME 34, ISSUE 4, PP. 405–423, ISSN 0730-7829, ELECTRONIC ISSN 1533-8312.  2017 BY THE REGENTS OF THE UNIVERSITY OF CALIFORNIA ALL RIGHTS RESERVED. PLEASE DIRECT ALL REQUESTS FOR PERMISSION TO PHOTOCOPY OR REPRODUCE ARTICLE CONTENT THROUGH THE UNIVERSITY OF CALIFORNIA PRESS ’ S REPRINTS AND PERMISSIONS WEB PAGE, HTTP:// WWW. UCPRESS . EDU/ JOURNALS . PHP? P¼REPRINTS . DOI: https://doi.org/10.1525/ MP.2017.34.4.405 The Effect of Harmony on Melodic Probability 405