Perception of musical tonality as assessed by the probe-tone method. Willi R. Steinke, Lola L. Cuddy, and Ronald R. Holden, (Department of Psychology, Queen’s University at Kingston, Ontario, Canada K7L 3N6)

Introduction at comfortable listening levels, as determined by each subject. The purpose of the experimental research reported in this presentation was twofold: (1) to assess the reliability of the Probe-tone procedures. For the Probe-tone Melody test, probe-tone technique as a method of recovering listeners’ the melody used was the "March of King Laois" (from representations of the tonal hierarchy; and (2) to examine Johnston, 1985), an obscure 16th century Celtic tune, both sensory and cognitive accounts of the data by highly tonal in nature, characterized by simple elaborations comparing the relative success of selected predictor o f the tonic triad. The melody was played at a tempo of variables. MM = 100 (dotted half note) and lasted 12.2 seconds, and was followed, after a one-second pause, by a probe tone of The tonal hierarchy. Tonality is a function of the one second duration. Each of 12 probe tones in the hierarchical organization of pitch relationships. chromatic pitch set was presented twice, in random order Hierarchical pitch relationships exist at three interrelated for a total of twenty-four presentations of the melody ana levels, that of note, chord, and key, and involve increasing probe tone. The Yamaha TX81Z synthesizer was set to levels of abstraction. The concept of the tonal hierarchy factory present A15 (Wood Piano) while recording the describes the relationship among the single tones within a melody and probe tones. Subjects were required to rate, key. One single tone, the tonic, forms a reference point on a scale of 1 - 10, how well the probe tone fit in with the for all tones in the key. Each of the remaining tones is melody that came before it. A rating of "1" indicated a located in a hierarchical relationship with the tonic. It is poor fit and a "10" indicated a good fit. hypothesized that listeners relate individual tones to these reference tones in an ongoing fashion as music is heard, a For the Probe-tone Major and Minor Cadence tests, process that contributes to a sense of tonality. twenty-four major (IV-V-I) and twenty-four minor (iv-V-i) perfect cadences, of three seconds duration, was each The probe-tone method. The probe-tone method was first followed, after a one-second pause, by a probe tone of one used by Krumhansl and Shepard (1979) as an effective second duration. The cadences were played at a tempo of means of quantifying listeners’ responses to tonality. As MM = 110 (quarter note). Each of 12 probe tones in the generally applied (Krumhansl, 1990), subjects listen to a chromatic pitch set was presented twice, in random order, stimulus context, typically consisting of a short sequence of for a total of twenty-four presentations of each cadence notes or chords, or a scale or melody context, and then and probe tone. Each chord was constructed as a Shepard rate a following tone, the "probe tone", for degree of chord and consisted of fifteen notes spaced over six completion or goodness-of-fit with the context. The probe octaves. The probe tones were similarly constructed as tones consist of all possible tones from the 12-note Shepard tones and consisted of sine-wave components chromatic scale. The set of ratings, one for each of the 12 spaced at octave intervals. The Yamaha TX802 synthesizer probe tones, is called the probe-tone profile for the was set to produce sine tones for each chord tone and context. The profile is assumed to reflect the hierarchy of robe-tone note, with rise and decay times of 20 ms. each, stability of tones in the context. Where key-defining ubjects were required to rate the probe tone, c>n a scale contexts have been employed, the profile is thought to of 1-10, on how well it fit in with the preceding chord reflect the relationship between each probe tone and the pattern. A rating of "1" indicated a poor fit and a "10" tonal centre of the context. indicated a good fit. Method Results and Discussion The data for the probe-tone tests described below were All obtained probe-tone profiles resembled the collected as part of a larger study involving an extensive standardized profiles reported in the literature (Krumhansl, series of music and cognitive tests. 1990). The order of the ratings was consistent with music theoretic descriptions of the tonal hierarchy. Subjects Subjects. One hundred subjects participated in this study, generally rated the tonic note (C) the highest, followed by ranging in age from 18-40 years (mean = 27, SD = 6.2), the other notes of the tonic triad (E and G for the melody with years of formal education ranging from 7-22 years and the major-cadence contexts; Eb and G for the (mean = 15.6, SD = 2.7). Sixty-one subjects had little or minor-cadence context), the remaining diatonic notes, and, no music training, 22 subjects had moderate amounts of finally, the nondiatonic notes (see Figure 1). These results music training, and 17 subjects had high amounts of music suggest that each of the probe-tone contexts reliably training or were professional musicians. assessed subjects’ sense of tonality, and that all subjects evidenced a sense of tonality, regardless of level of music Apparatus. A Yamaha TX81Z synthesizer controlled by training. a Zenith Z-248 computer running 'TDX-Score" software was used to create the single-note stimuli for the Probe-tone It was noted that subjects with high music training Melody test. A Yamaha TX802 synthesizer controlled by roduced profiles in which ratings were more clearly an Atari 1040ST computer using "Notator" music Pifferentiated than subjects with little or no music training, processing software was used to create the "Shepard-tone" and correlations of the profiles with music theoretic stimuli for the Probe-tone Major and Minor Caaence tests. predictions were highest for subjects with high music Shepard tones and chords do not have a well-defined pitch training. Nevertheless, there was close correspondence heignt. Each tone contains sine-wave components between the profiles for the three training groups (average distributed over a multi-octave range under a half-cosine r = .93, all p < .001). amplitude envelope which approaches hearing threshold at the high and low ends of the range (Shepard, 1964). All We next examined psychoacoustic and musical correlates music sequences were recorded on audiocassettes and of the perceived tonal hierarchies. A number of predictor reproduced through the speakers of a portable tape player variables were derived and the amount of variance in the

- 85 - Mean Rating Mean Rating Mean Rating PROBE-TONE MAJOR CADENCE MAJOR PROBE-TONE PROBE-TONE MINOR CADENCE MINOR PROBE-TONE PROBE-TONE MELODY PROBE-TONE Probe tone tone Probe Probe tone tone Probe rb tone Probe - pitch. physiological basis for the theory of music of theory the for basis physiological Journal of Experimental Psychology: Human Perception and Perception Human Psychology: Experimental of Journal Performance, n mldc structures. melodic and samples of distributions statistical from obtained are values statistical of power roughness predictive the the tested set second from The example, for obtained, were of property acoustical was the tested variable predictors of set first predictor The each by for accounted profiles approach. variance in probe-tone profiles for all three contexts. contexts. three all for profiles probe-tone in variance The third set of predictors were derived from Parncutt’s Parncutt’s from derived were predictors of set third The Shepard, R.N. (1964). Circularity in judgments of relative relative of in judgments Circularity jMt (1964). R.N. Shepard, (1989). R. Parncutt, (1990). C.L. Krumhansl, (1985). J.C. Johnston, (1954). H.L.F. Helmholtz, these by assigned values The music. tonal of from properties also values. and Helmholtz the of (1885/1954) Values modifications bandwidth Helmholtz critical context. of probe musical the the calculations of between centre key of consonance the terms in and acoustical tone of tone These probe degree each 57). to p. the (1990, values assigned obtained Krumhansl in were predictors values table summary consonance a of from sets Six consonance. computed. ulse, 1885.) published, in the stimulus context. Three versions of the model were were model the of versions Three tested. context. stimulus the in each to value a assigns contexts, cadence the to specifically Kingston, Ontario: Queen’s University. Queen’s Ontario: Kingston, will model this of goodness-of-fit discussed. the be for reasons Possible sensory a greatest surprisingly, (containing version and, the One contexts, yielded context. cadence melody salience the the for for pitch of both success, model Parncutt’s 67). p. 1990, The Krumhansl, keys. (see minor music and tonal each of major which both with in frequencies occurred relative tone the probe were predictors l sbet; pn ice - o msc riig xs - x’s training; music low - - circles squares open (Open subjects; training. music all of levels by Melody and subjects Probe-tone for ratings probe-tone Mean 1. Figure context. diatonic a within Quantification function tonal (1979). of R.N. hierarchy the of Shepard, & C.L., Krumhansl, originally edition (Revised Dover. York: New trans!). & probe tone in terms of its spectral and virtual pitch weight weight pitch virtual and spectral its of terms in applies tone which probe model, This salience. pitch of model (1989) trace decay) consistently accounted for over 80% of the the of 80% over for accounted consistently decay) trace moderate music training; triangles - high music training.) music high - all triangles for training; music Cadences moderate Minor and Major Probe-tone for and 86 ^ora o te cutcl oit ofAeia 36, America, f o Society Acoustical the of ^Journal . m - New York: Oxford University Press. University Oxford York: New New York: Springer Verlag. Springer York: New , 579-594. 5, References The perceptual salience of melody of salience perceptual The Unpublished B.A. Thesis. Thesis. B.A. Unpublished Cognitive foundations o f musical f o foundations Cognitive amn: psychoacoustical A Harmony: n h estos oea a as tone f o sensations the On (A. J. Ellis, Ed. Ed. Ellis, J. (A.