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

Abstract

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 contextproperties 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 listener's 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.Background

Expectancy effects in memory for melodies.

“…In a different vein, Schmuckler (1989) had pianists complete different melodic and combined harmonic-melodic contexts and found that performers' productions mirrored expectancy judgments, with tones that had received high expectancy ratings in the previous perceptual studies produced more frequently than low expectancy tones. Subsequent analyses of these performances (Schmuckler, 1990) found that both global musical factors, such as tonal (e.g., Krumhansl & Shepard, 1979;Krumhansl & Kessler, 1982) and rhythmic (e.g., Palmer & Krumhansl, 1989) hierarchies, as well as local contextual factors, such as patterns of pitch and metrical information contained in the to-be-completed contexts, were all important factors in determining the content of these productions. One aspect of this work is that the majority of these studies have focused on the anticipation of the single next event in a sequence, or what Jones (1981Jones ( ,1982Jones ( , 1990) calls "expectancies," without examining anticipations of more extended, multi-event completions, or "expectancy schemes" (Jones, 1981(Jones, , 1982(Jones, , 1990; but see Schmuckler, 1990, for an exception).…”

Representation and execution of vocal motor programs for expert singing of tonal melodies.

“…Krumhansl and colleagues (Krumhansl, 1979(Krumhansl, , 1990Krumhansl & Kessler, 1982;Krumhansl & Shepard, 1979) have demonstrated that each musical key is associated with its own tonal hierarchy (see Figure 1). The tonic note ("do") is consistently rated as "fitting most closely with" a particular key.…”

Neuromagnetic responses to chords are modified by preceding musical scale

“…Krumhansl, with her colleagues, performed behavioral experiments to evaluate the tonal hierarchy of chords quantitatively using listeners' ratings for perceptual stability (Krumhansl & Shepard, 1979;Krumhansl & Kessler, 1982;Krumhansl, 1990). Their experimental paradigm is called the "probe-tone method", which has been widely used in the field of music psychology (Cuddy & Badertcher, 1987;Steinke et al, 1997;Leman, 2000).…”