Recovery of the tonal hierarchy: Some comparisons across age and levels of musical experience

Abstract

Two experiments examined the recovery of the tonal hierarchy from three melodic patternsthe major triad, the major scale, and the diminished triad. In the probe-tone technique, for each pattern, each of the 12 tones of the chromatic scale was rated as a completion note for the pattern. Pattern tones and probe tones were synthetic complexes of octave partials, amplitudeweighted according to Shepard (1964). First-through sixth-grade children participated in the first experiment, adults with three levels of musical experience in the second. For all subjects, the probe-tone ratings for the major-triad pattern indicated recovery of the full tonal hierarchy. For the major-scale pattern, children and adults successfully differentiated tonal function within the scale. Adults, however, showed greater sensitivity to key organization than did the children and were less influenced by pitch proximity. The diminished-triad pattern conveyed no musical meaning to the children and was tonally ambiguous for the adults. The importance of the major triad in establishing a sense of key is underscored. As patterns depart from this prototype, recovery of the tonal hierarchy may depend on the degree to which musical knowledge (intuitive and formal) is applied. This paper explores listeners' abstraction of the pitch structures conveyed or implied by melodic patterns in tonal music. It examines the extent to which the tonal hierarchy described by music theory and perceptual experiments may be recovered from different melodic patterns. Adults and first-through sixth-grade children with three levels of musical experience were tested.It is generally agreed that the composition and appreciation of "tonality," although an extraordinarily complex human activity in its fullest expression (Browne, 1981), involves a hierarchically organized system of pitch relationships. Basic features of the system can be found in standard music texts (e.g., Piston, 1962; Ratner, 1962) and their psychological counterparts in recent theoretical treatments (e.g., Bharucha, 1984;Deutsch & Feroe, 1981;Dowling, 1978;Krumhansl, 1983;Shepard, 1982). The system is structured at several interrelated levels. First, descriptions of pitch relationships usually include the notion of determinate pitch sets and the assignment We thank C. L. Krumhansl, Cornell University, for discussions, advice, and encouragement. We also thank the Frontenac County Board of Education and the staff of Lord Strathcona Elementary School, especially R. Galbraith and John Gallienne, for permission to test their students and for kind cooperation throughout the study. Daniel Scheidt and Lise de Kok provided cheerful and invaluable research assistance. The data were previously reported in an honors thesis submitted to the Department of Psychology, Queen's University, by Betsy Badertscher. Research was supported by an operating grant from the Natural Sciences and Engineering Council of Canada and an award from the Advisory Research Committee of Queen's University. Requests for reprints should be sent...

Expectancy in melody: Tests of children and adults.

“…The other variable (tonal hierarchy) accounted for differences in the perceived stability of the various test tones in the key of the melody. After a key is established, even children as young as 6 years of age judge do (the most stable tone in a key) to fit better with the key than ti (an unstable tone; Cuddy & Badertscher, 1987). The variable consisted of the quantified values provided by Krumhansl (1990, Table 2.1, p. 30).…”

Harmonic Closure: Music Theory and Perception

“…Listeners who know tonal style in general seem to hear the goal notes of the tonic, mediant, and dominant as more stable than the nongoal notes of the supertonic, submediant, and leading tone. Much recent work attests to the cognitive reality of this phenomenon (Castellano, Bharucha, &c Krumhansl, 1984;Krumhansl, 1979Krumhansl, , 1983, although disputes continue over how scale-step recognition is established and the extent to which such recognition pervades the perception of a given musical composition (Butler, 1989(Butler, , 1990Cuddy & Badertscher, 1987;Krumhansl, 1990). Howsoever these disagreements are eventually resolved, the listener's sense of scale step is purely learned.…”

Perceptual Tests of an Algorithm for Musical Key-Finding.

“…Although not directly answering this question, a number of psychological studies over the years have used the Krumhansl-Schmuckler algorithm to quantify the tonal implications of the stimuli in their experiments. For example, Cuddy and Badertscher (1987) used a variant of the Krumhansl-Schmuckler algorithm to determine the tonal structure of ratings provided to the 12 tones of the chromatic scale when these tones were presented as the final note of melodic sequences. In a similar vein, Takeuchi (1994) used the maximum key-profile correlation (MKC) of the KrumhanslSchmuckler algorithm to (successfully) predict tonality ratings and (unsuccessfully) predict memory errors for a set of melodies.…”