Carol L. Krumhansl

Quantification of the hierarchy of tonal functions within a diatonic context.

Listeners rated test tones falling in the octave range from middle to high C according to how well each completed a diatonic C major scale played in an adjacent octave just before the final test tone. Ratings were well explained in terms of three factors. The factors were distance in pitch height from the context tones, octave equivalence, and the following hierarchy of tonal functions : tonic tone, other tones of the major triad chord, other tones of the diatonic scale, and the nondiatonic tones. In these ratings, pitch height was more prominent for less musical listeners or with less musical (sinusoidal) tones, whereas octave equivalence and the tonal hierarchy prevailed for musical listeners, especially with harmonically richer tones. Ratings for quarter tones interpolated halfway between the halftone steps of the standard chromatic scale were approximately the averages of ratings for adjacent chromatic tones, suggesting failure to discriminate tones at this fine level of division. The study of perceived pitch and of the perceived relations between tones differing in pitch has generally been approached from one of two quite different traditions: the psychoacoustic and the musical. The psychoacoustic approach has typically focused on simple, physically specifiable properties of tones isolated from any musical context— properties of frequency, separation in log frequency, or simplicity of integer ratios of frequencies. The results of such studies have provided some precise information about how the ear responds to isolated tones or tones in random sequences. We believe that they have been less informative with regard to how the listener perceives tones in organized musical sequences. Music theory suggests that the perception of such sequences may rely on the listeners sensitivity to different and structurally richer principles associated with tonal and diatonic organization. Such principles are useful in explaining the cognitive phenomena of reference point, motion, tension, and resolution that underlie the dynamic force of virtually all tonal music. They have, however, been subjected to relatively little systematic laboratory investigation or quantitative formulation.

Mental representations for musical meter.

Investigations of the psychological representation for musical meter provided evidence for an internalized hierarchy from 3 sources: frequency distributions in musical compositions, goodness-of-fit judgments of temporal patterns in metrical contexts, and memory confusions in discrimination judgments. The frequency with which musical events occurred in different temporal locations differentiates one meter from another and coincides with music-theoretic predictions of accent placement. Goodness-of-fit judgments for events presented in metrical contexts indicated a multileveled hierarchy of relative accent strength, with finer differentiation among hierarchical levels by musically experienced than inexperienced listeners. Memory confusions of temporal patterns in a discrimination task were characterized by the same hierarchy of inferred accent strength. These findings suggest mental representations for structural regularities underlying musical meter that influence perceiving, remembering, and composing music.

The representation of harmonic structure in music: Hierarchies of stability as a function of context

Abstract The ability to appreciate most Western music presupposes cognitive structures capable of abstracting an underlying harmonic structure from a complex string of musical events. In this paper we provide a description of the listeners knowledge of hierarchies of harmonic stability. The organization of harmonic information may be summarized by six principles. Three of these principles—Key Membership, Intrakey Distance and Intrakey Asymmetry—govern harmonic organization independent of context. Three principles—Contextual Identity, Contextual Distance and Contextual Asymmetry—govern harmonic organization in the presence of a tonal context. Chords that are members of the same key are represented in a hierarchy of stability that is independent of context. Chords from different keys are represented in a hierarchy of stability that is dependent upon the prevailing context. Two different experimental tasks were used to provide convergent evidence for these principles: 1) multidimensional scaling of chords in the absence of any context or in the presence of different tonal contexts, and 2) recognition memory for chords in random and tonal contexts. It is suggested that harmonically stable chords function as cognitive reference points for the system as a whole. The importance of representations of hierarchies of harmonic stability is discussed with respect to generative accounts of musical competence.

Rhythm and pitch in music cognition.

Rhythm and pitch are the 2 primary dimensions of music. They are interesting psychologically because simple, well-defined units combine to form highly complex and varied patterns. This article brings together the major developments in research on how these dimensions are perceived and remembered, beginning with psychophysical results on time and pitch perception. Progressively larger units are considered, moving from basic psychological categories of temporal and frequency ratios, to pulse and scale, to metrical and tonal hierarchies, to the formation of musical rhythms and melodies, and finally to the cognitive representation of large-scale musical form. Interactions between the dimensions are considered, and major theoretical proposals are described. The article identifies various links between musical structure and perceptual and cognitive processes, suggesting psychological influences on how sounds are patterned in music.

Tonal Hierarchies in the Music of North India

Cross-culturally, most music is tonal in the sense that one particular tone, called the tonic, provides a focus around which the other tones are organized. The specific organizational structures around the tonic show considerable diversity. Previous studies of the perceptual response to Western tonal music have shown that listeners familiar with this musical tradition have internalized a great deal about its underlying organization. Krumhansl and Shepard (1979) developed a probe tone method for quantifying the perceived hierarchy of stability of tones. When applied to Western tonal contexts, the measured hierarchies were found to be consistent with music-theoretic accounts. In the present study, the probe tone method was used to quantify the perceived hierarchy of tones of North Indian music. Indian music is tonal and has many features in common with Western music. One of the most significant differences is that the primary means of expressing tonality in Indian music is through melody, whereas in Western music it is through harmony (the use of chords). Indian music is based on a standard set of melodic forms (called rags), which are themselves built on a large set of scales (thats). The tones within a rag are thought to be organized in a hierarchy of importance. Probe tone ratings were given by Indian and Western listeners in the context of 10 North Indian rags. These ratings confirmed the predicted hierarchical ordering. Both groups of listeners gave the highest ratings to the tonic and the fifth degree of the scale. These tones are considered by Indian music theorists to be structurally significant, as they are immovable tones around which the scale system is constructed, and they are sounded continuously in the drone. Relatively high ratings were also given to the vadi tone, which is designated for each rag and is given emphasis in the melody. The ratings of both groups of listeners generally reflected the pattern of tone durations in the musical contexts. This result suggests that the distribution of tones in music is a psychologically effective means of conveying the tonal hierarchy to listeners whether they are familiar with the musical tradition. Beyond this, only the Indian listeners were sensitive to the scales (thats) underlying the rags. For Indian listeners, multidimensional scaling of the correlations between the rating profiles recovered the theoretical representation of scales described by theorists of Indian music.(ABSTRACT TRUNCATED AT 400 WORDS)

Independent temporal and pitch structures in determination of musical phrases.

In two experiments we addressed the roles of temporal and pitch structures in judgments of melodic phrases. Musical excerpts were rated on how good or complete a phrase they made. In Experiment 1, trials in the temporal condition retained the original temporal pattern but were equitonal; trials in the pitch condition retained the original pitch pattern but were equitemporal; and trials in the melody condition contained both temporal and pitch patterns. In Experiment 2, one pattern (pitch or temporal) was shifted in phase and recombined with the other pattern to create the pitch and temporal conditions. In the melody condition, both patterns were shifted together. In both experiments, ratings in the temporal and pitch conditions were uncorrelated, and the melody condition ratings were accurately predicted by a linear combination of the pitch and temporal condition ratings. These results were consistent across musicians with varying levels of experience.

A Perceptual Analysis Of Mozart's Piano Sonata K. 282: Segmentation, Tension, and Musical Ideas

The experiments reported here provide a perceptual analysis of the first movement of Mozart9s Piano Sonata in Eb Major, K. 282. The listeners, who varied in the extent of their musical training, performed three tasks while listening to the piece as it was reproduced from an expert performance. The first task determined how the music is perceived to be segmented, the second task determined how the experience of tension varies over time, and the third task determined what listeners identify as new musical ideas in the piece. These tasks were performed first on the entire piece and then on smaller sections from the beginning. These three aspects of music perception are coordinated with one another and correlate with various musical attributes. Judgments of section ends co- occurred with peaks in tension and slow tempos. Judgments of new musical ideas co- occurred with low tension levels and neutral tempos. Tension was influenced by melodic contour, note density, dynamics, harmony, tonality, and other factors. Judgments of large-scale section ends were less frequent than judgments of new musical ideas, but these were more nearly one-to-one on smaller time scales. A subsidiary experiment examined the extent to which tension judgments were influenced by performed tempo and dynamics. Listeners made tension judgments for four different versions of the piece: as performed, constant dynamics (with tempo as performed), constant tempo (with dynamics as performed), and constant tempo and dynamics. The tension curves were generally very similar, deviating only in a few regions containing major section ends. The results are considered in light of the metaphor of tension applied to music and the analogy between music and linguistic discourse.

Music: A Link Between Cognition and Emotion

Cognition and emotion are closely linked in music. The interplay between expectations and the sounded events is hypothesized to play a central role in creating musical tension and relaxation. The research summarized here is part of an ongoing program investigating how this dynamic aspect of musical emotion relates to the cognition of musical structure. Musical emotions change over time in intensity and quality, and these emotional changes covary with changes in psychophysiological measures. Perceptual studies support music-theoretic descriptions of musical structures that underlie listeners’ expectations. Cross-cultural comparisons suggest that certain psychological principles of expectation are quite general, but that musical cultures emphasize these differentially. A schema of temporal organization that relates episodes of tension and relaxation to musical form and expressive aspects of musical performance is described. Finally, some results suggest that the expression of emotion in music shares properties with the expression of emotion in speech and dance.

Acquisition of the hierarchy of tonal functions in music

The acquisition of the hierarchy of tonal stabilities in music is investigated in children of elementary school age. Listeners judge how good short tone sequences sound as melodies. The ratings show a pattern of increasing differentiation of the pitches in an octave range. The youngest listeners distinguish between scale and nonscale tones; older listeners distinguish between the tonic triad tones and other scale components. A group of adult listeners show octave equivalence and temporal asymmetries, with a preference for sequences ending on the more stable tones within the hierarchy. Pitch height effects do not interact with the age of the listener. These results are discussed in terms of the primacy of physical variables, novice-expert differences, and general cognitive principles governing the acquisition and development of internal representations of pitch relationships.

Infants' Perception of Phrase Structure in Music

A visual preference procedure was used to examine 6- and 41/2-monthold infants’ sensitivity to phrase structure in music. Sections of Mozart minuets were divided into segments that either did or did not correspond to the phrase structure of the music. Infants in both age groups listened significantly longer to the appropriately segmented versions. Their behavior accorded well with judgments of the same materials made by adults, suggesting that protracted musical experience may not be necessary to perceive phrase structure in music. Strong correlations were found between certain musical variables and the infants’ preferences for the musical passages, pointing to acoustic properties that may be important for defining musical phrases.