Perception of nonadjacent tonic-key relationships

Abstract

The issue of structural nonadjacency in music and language was explored from a musical perspective in an experiment employing a stimulus-matching paradigm. The experiment measured the perceptual effect of a temporally nonadjacent key on the closure of a musical phrase; participants rated a stimulus-ending two-chord probe cadence for its closural properties. The temporal rate of decay of the nonadjacent key in memory was observed by varying the length of the intervening key area; that is, the key temporally adjacent to the probe cadence. Evidence emerged that listeners were able to hold the nonadjacent key in memory for over 10 seconds, indicating “global” nonadjacent harmonic perceptions. The study provides qualified evidence to support the notion that there are syntactic parallelisms between language and music, particularly in respect of nonadjacent key relationships.

Keywords

harmony language memory music nonadjacency

Music and language share profound similarities – both appear to be humanly universal, combinatorial and hierarchical. Parallels, or even overlaps, have been proposed between language and music in terms of developmental (McMullen & Saffran, 2004), cognitive (Sloboda, 1985) and neural processes (Koelsch & Siebel, 2005), as well as the ways in which each domain can be conceptualised (Jackendoff & Lerdahl, 2006).

These similarities notwithstanding, there are self-evident differences between language and music. Music typically employs complex structures in pitch and rhythm that are not intended to communicate semantic information, whereas language employs speech sounds that are timbrally differentiable, and that may be combined to communicate unambiguous information about complex matters. Neurological research provides evidence for some distinction in the neural substrates for language and music; deficit studies point to a double dissociation between the two faculties (Peretz, 2003). Moreover, despite theories suggesting that both language and music exhibit similar types of complex hierarchical structure in cognition, as Patel (2003) notes, while “long-distance syntactic dependencies are ubiquitous in language … the long-distance dependencies posited by music theory cannot simply be assumed to be perceived, and are instead better viewed as hypotheses subject to empirical test” (p. 675). This paper constitutes an experimental exploration of this last issue: the extent to which music perception exhibits similar types of long-range, nonadjacent dependency relationships to those of language.

Nonadjacent dependencies in language and music

Despite the proposal that there is a bias towards word adjacency on the grounds that it minimises cognitive load (Hawkins, 2001), a significant feature of language is that relationships between elements that are sequentially and temporally nonadjacent may have significance in perception and production. The functional identities of linguistic elements can depend on other, sequentially and temporally non-contiguous elements, as well as on immediate temporal context. This is perhaps most evident with relative clauses, where syntactic and semantic relationships exist between elements that are separated in time, and that have other linguistic structures interposed between them, yet can be easily accessible to language perceivers and producers. Such relationships can be thought of as exemplifying principles of recursion or hierarchy, which are believed to be central to the human language faculty (Hauser, Chomsky, & Fitch, 2002). For example, “Because the river flows past the house, Jack swims” may be expanded with the insertion of the nonrestrictive relative clause “which is green” to form the sentence, “Because the river flows past the house, which is green, Jack swims”. In this construction, the outer constituents are semantically enriched by the addition of the embedded clause. A constituent-structure tree of the sentence is shown in Figure 1; the inset is a structurally reduced version of the tree, showing the dependency relationships between the sentence’s constituent elements.

Figure 1.

Parsing tree of an English sentence in which the functional identities of some words depend on other sequentially and temporally nonadjacent words. Despite containing the sequence “green Jack swims”, the listener knows that “green” refers to “house”, not “Jack”. The dependence of the relative clause “which is green” on the noun phrase “the house”, and not “Jack”, is shown in the connections of the branches of the syntactic tree. S = sentence; NP = noun phrase; VP = verb phrase; AP = adverbial phrase; RC = relative clause; Conj = conjunction; Rel P = relative pronoun; N = noun; V = verb; A = adjective; Det = determiner.

Similar recursive principles to the sentence in Figure 1 have been proposed with respect to tonal-harmonic music of the common practice period (c. 1600–1900). Schenkerian theory advances the idea that structurally significant events (pitches and chords) govern surrounding, subordinate events, referred to as elaborations or prolongations (Schenker, 1935/1979). Lerdahl and Jackendoff’s Generative Theory of Tonal Music (GTTM, 1983) recast Schenker’s theories within a linguistic and cognitive framework. In GTTM, and Lerdahl’s later Tonal Pitch Space Theory (2001),four partially inter-dependent analytical domains are employed in order to determine how an ‘ideal’ listener might parse a piece of tonal music: grouping structure, metrical structure, timespan reduction, and prolongational reduction. Within each domain a series of preference rules establishes the parsing which best conforms to a set of well-formedness criteria – a process that results in the generation of hierarchically structured representations, intended to encapsulate different aspects of a listener’s experience of the work. With the exception of metre, within each hierarchical representation, structurally significant relationships are depicted as holding between non-terminal and nonadjacent elements.

Although several aspects of Lerdahl and Jackendoff’s theory have received empirical support – Deliège (1987) showed that GTTM’s grouping (segmentational) principles were strongly predictive of listeners’ responses – a number of other studies have provided only qualified validation for the idea that music is hierarchically structured in cognition (see Cook, 1987; Deliège, Mélen, Stammers, & Cross, 1996; Dibben, 1994; Serafine, Glassman, & Overbeeke, 1989; West-Marvin & Brinkman, 1999). In a series of experiments, Emmanuel Bigand, Barbara Tillmann and their collaborators explored the temporal scope of listeners’ sensitivities to aspects of tonal musical structure (for an overview, see Tillmann & Bigand, 2004). Bigand and Pineau (1997) used both probe tone (Krumhansl, 1990) and priming (Bharucha, 1987) paradigms to study the ways in which chord progressions might be experienced as key defining. Bigand, Madurell, Tillmann, and Pineau (1999) replicated and extended this research over three experiments using a priming paradigm, comparing their results with the predictions of Bharucha’s (1987) connectionist model of musical cognition, MUSACT. In their first experiment, different (global) harmonic contexts were found to affect the processing of the last chord of a sequence even when immediate local-key contexts were held constant, which they proposed could be due to “spreading activation” (of the type provided in Bharucha’s model). In their second experiment they varied the length of the contexts from two to five chords, and found that the effect of the context diminished to zero as length was reduced. Their third experiment employed slightly longer sequences and used targets that varied in the extent to which they were likely to be expected. Having demonstrated that the structures which listeners are sensitive to depend on temporally extended sequences of musical events, Bigand et al. concluded that “global context effects result primarily from activations accumulated in the system when the target chord occurs” (p. 195).

In a related study, Bigand and Parncutt (1999) used more temporally extended musical sequences to explore whether listeners’ judgements of musical tension could be accounted for on the basis of both GTTM and Parncutt’s (1989) sensory-psychoacoustic principles. A specially composed sequence was employed, in addition to two versions of Chopin’s Prelude in E major (all of which incorporated several modulations). In three experiments, listeners were required to rate the degree of musical tension experienced after hearing versions of each piece that increased in length by one chord on each presentation. In this way the cumulative effect of the harmonic structure of the pieces on listeners’ judgements were assessed.

Bigand and Parncutt (1999) found that GTTM accounted well for listeners’ judgements, but this appeared to derive not from listeners being sensitive to large-scale relationships in the music in the ways depicted in the model, but rather because the model privileged the local cadencial (key-defining) structures to which listeners responded most directly. A further experiment by Bigand and Parncutt explored the issue of sensitivity to large-scale structure versus sensitivity only to local relations. In brief, pairs of chords were presented that occurred sequentially in Chopin’s E Major Prelude; their results did not significantly differ from those obtained when the piece had been presented in successively longer segments. They therefore inferred that “the hierarchic model was active in the previous experiments because it captured the influence of local harmonic structures rather than the influence of global structures” (p. 250). In short, whilst finding cadences and modulations to be salient, they concluded that their study did not support the notion that listeners integrated these structures into larger musical forms.

In contrast to the studies outlined above, Thompson (1986) presented results that suggest that listeners are sensitive to temporally extended relationships in the harmonic domain. In his experiment, following modulation to the key of the dominant, there was a more persistent influence of the original key than when the modulation was to the subdominant. Thompson and Cuddy (1992) and Cuddy and Thompson (1992) extrapolated from Thompson’s original study, proposing that modulations in the direction of the subdominant were more likely to “overwrite” the initial key than modulations in the direction of the dominant. Following the dominant modulation, “Probe-tone profiles … reflected both the tonal hierarchy of the initial key and the tonal hierarchy of the final key” (Cuddy & Thompson, 1992, p. 57; emphasis added).

In sum, there is mixed empirical evidence to indicate that the operation of hierarchical principles in music perception are either of the same order of complexity, or are extended over similar durations, as in language. Moreover, the finding that only trained musicians appear to be sensitive to such types of structure in music (Bigand et al., 1999), suggests that this competency may be acquired through formal training rather than enculturative processes of the type that underpin language acquisition.

Present study

The aim of the present study was to test the sensitivity of participants with two levels of musical experience to “global” key structure. Consequently, participants were presented with stimuli in which the influence of rhythm, melody and voice leading were minimised. The perception of nonadjacent key relationships was investigated by asking participants to judge two-chord phrase-ending cadences (referred to as probe cadences) for their closural properties. By “phrase-ending cadences” we refer to authentic V-I cadences, two-chord progressions by which the harmonic goals of phrases are defined.

Measuring the perception of nonadjacent key relationships presents two challenges. First, the method used must disambiguate the effect on the probe cadence of a nonadjacent key from that of an intervening key. Second, the method must be able to detect potentially weak nonadjacent-key effects on the perception of tonal closure. The potentially weak effect of the nonadjacent key was addressed by using relatively large numbers of stimuli. The method employed to disambiguate the effect of a nonadjacent key from the intervening key on the perception of tonal closure used the following stimulus-matching paradigm.

Stimulus-matching paradigm

Non-modulating phrases were paired with modulating phrases that were identical in every respect (duration, number of chords, chord function and order, adjacent key and probe cadence) except for the nonadjacent key of the modulating phrases. The effect of the nonadjacent key of the modulating phrase was calculated by subtracting a rating of tonal closure for the probe cadence of the non-modulating phrase from that of the matching modulating phrase.

The phrase pairing in Figure 2 shows how the effect of the nonadjacent key, C major, of the modulating phrase can be measured with respect to the intervening key, D♭major. For example, if on a 7-point scale a participant’s tonal closure rating is 3 for the non-modulating phrase and 5 for the modulating phrase, the effect of the nonadjacent key of the modulating phrase (the only element differentiating the two phrases) is the difference between the two ratings: 5 − 3 = 2. That is, the nonadjacent key of the modulating phrase, C major, has a positive effect (+2) on the tonal-closure rating of the probe cadence. We hypothesised that a significant difference between the probe cadence ratings of the modulating and non-modulating phrase pairs, that is, the residual of the two phrases’ ratings, would be indicative of the nonadjacent key being retained in memory during the statement of the intervening key, and therefore a measure of perceptual nonadjacency.

Figure 2.

Measuring the effect of the nonadjacent key of C on the perception of tonal closure in a phrase that modulates from C to D ♭, and closes with a cadence in C. The closure rating of the non-modulating phrase was subtracted from that of the modulating phrase.

Method

Participants

Participants were 35 adults (17 females) with two distinct levels of musical experience, henceforth referred to as musicians and nonmusicians. There were 17 musicians and 18 nonmusicians. The musicians included 9 females and 8 males aged from 20 to 27 years old (mean = 22; SD = 2.19); nonmusicians included 8 females and 10 males aged from 20 to 28 years old (mean = 24; SD = 3.02).

Musicians in the study were overwhelmingly involved in Western classical music, had received on average over 10 years’ formal musical training, and practised/played/performed an average 9 hours per week. Musicians’ practical involvement in classical music was not reflected in their listening habits however, which showed a 53% – 47% split between classical and popular styles, and which was on average for 12.4 hours per week. Nonmusicians in the study had received on average only 1.5 years’ formal musical training and were not active players and/or singers. On average, at least 10 years had elapsed since 56% of nonmusicians had played an instrument; the remaining 44% had never played an instrument. The nonmusicians’ listening habits showed a 81% – 19% split in favour of popular music over classical, and which was on average for 11.5 hours per week.

Musicians were music undergraduate and graduate university students, and received no financial remuneration for their participation; nonmusicians were largely drawn from other departments of the university and were remunerated for their participation. No musician responded with an accuracy level greater than 67% in a pre-experiment 12-pitch identification test of absolute pitch; nonmusicians were not tested for absolute pitch.

Apparatus

Stimuli were produced using the programming language SuperCollider. “Shepard tones” (Shepard, 1964), consisting of superposed octave-related sinusoids with overall amplitude controlled by a Gaussian function, were used for the presentation of the stimuli. The technique produces tones with approximately equal overall pitch height and with no clear pitch maxima or minima, thereby diminishing voice-leading effects.

Stimuli

Probe-cadence ratings of tonal closure were obtained for phrases in which the length of the intervening key was systematically varied; that is, in which the number of events and therefore the elapse time between the nonadjacent key and probe cadence changed. The time between the nonadjacent key and probe cadence was altered by the addition of chords to the intervening key. The effect of temporal distance of the nonadjacent key on tonal closure was measured using the modulating/non-modulating stimulus-matching paradigm set out above. The nonadjacent key was induced using a four-chord sequence, I-IV-V-I, which from music-theoretic perspective is considered sufficient to induce a sense of key (Piston, 1978). The adjacent key followed immediately, was 2, 4, 6, 8, 10 or 12 chords long, and wrap-constructed so that it always began and ended with the same chords; see Table 1.

Table 1.

Wrap construction of intervening chord sequences.

Nonadjacent key	Intervening key (adjacent to probe cadence)		Probe cadence
Nonadjacent key	Chords	Chord #	Probe cadence
I-IV-V-I	vii^o-I	2	V-I
I-IV-V-I	vii^o-I-V-I	4	V-I
I-IV-V-I	vii^o-I-ii-IV-V-I	6	V-I
I-IV-V-I	vii^o-I-iii-vi-ii-IV-V-I	8	V-I
I-IV-V-I	vii^o-I-V-I-iii-vi-ii-IV-V-I	10	V-I
I-IV-V-I	vii^o-I-ii-IV-V-I-iii-vi-ii-IV-V-I	12	V-I

Note. Intervening chord sequences were always preceded by the four-chord nonadjacent key, and followed by the probe cadence.

In a pre-experiment pilot study exploring the effect on the probe cadence of different nonadjacent keys, the greatest effect was recorded when the nonadjacent key had a tonic relationship to the probe cadence. As a result, and in order to limit the potentially large scope of this study, only tonic nonadjacent key relationships were explored.

All possible major keys were used as the intervening key; each stimulus concluded with a probe cadence corresponding to the nonadjacent key,i.e. that had a tonic relationship to the nonadjacent key. This yielded 72 phrases: 12 intervening keys × 6 intervening key lengths (either 2, 4, 6, 8, 10 or 12 chords). A two beat rest followed the intervening key to help participants identify the probe cadence and focus attention on this part of the stimulus (for example, see Figure 2).

All stimuli, including probe cadences, were in major keys; minor keys were not explored. The tempo was 96 bpm; one chord was presented per beat (i.e. every 0.625 seconds). Between the end of the nonadjacent key to the start of the probe cadence the elapse times were: 2 (adjacent) chords = 2.50s; 4 chords = 3.75s; 6 chords = 5.00s; 8 chords = 6.25s; 10 chords = 7.50s; 12 chords = 8.75s.

Procedure

Participants were required to rate on a 7-point scale via a computer terminal the degree to which the probe cadence completed the preceding phrase, that is, the induced sense of tonal closure of the probe cadence: 7 for a very strong sense of completion, 1 for very weak. Five practice stimuli were presented to each participant prior to the experiment; experiment sessions lasted approximately 45 minutes. To control for order effects, each participant was presented with the stimuli in a different random order and transposition. Participants listened via headphones and adjusted the volume to a comfortable level before testing.

As the musicians were drawn from an academic music institution, we instructed this group not to treat the experiment as an examination of aural acuity. That is, they were informed that this was not a test in which there were right or wrong answers, and not to attempt consciously to “think through” the modulations. Our intention was to avoid the formation of rating strategies that may have skewed the results.

Data and analysis

After testing, the stimulus presentation order was unscrambled and re-transposed so that the probe-cadence key was always C major. Using the standard deviation and participants’ mean ratings, individual ratings were normalised and re-expressed as z-scores. Mean residual values per intervening key length were calculated for each participant. These means were used in a two-way mixed factorial ANOVA to explore the effect of intervening-key length (2, 4, 6, 8, 10 or 12 chords) and musical experience (musician, nonmusician), and possible interactions between the two factors. Mauchly’s test of sphericity indicated that the assumption of sphericity had not been violated.

Results

Musicians’ and nonmusicians’ mean residual values in Figure 3 show the effect of the nonadjacent key as the intervening key was increased from 2.50 to 8.75 seconds, that is, from 2 to 12 chords. In the ANOVA, the within-participant factor intervening-key length was highly significant (F_5,198 = 5.345; η² = 0.111; p < .001). Pairwise comparisons using Tukey’s Honest Statistical Difference (HSD; Miller, 1981) showed a number of significant differences between the six different intervening key lengths; principally, pairwise significance existed between the outer ranges; that is, 2 and 4 chords versus 8, 10 and 12. The between-participants factor musical experience was also highly significant (F_1,198 = 8.281; η² = 0.034; p < .005). However, despite a significant difference in the performance of the two groups (overall the musicians were more sensitive to the nonadjacent key), the interaction intervening-key length by musical experience was not significant: F_5,198 = 1.541; n.s.

Figure 3.

Musicians’ and nonmusicians’ mean residual values showing the effect on tonal closure of the nonadjacent key as the intervening key increased from 2 to 12 chords. Musicians’ and nonmusicians’ line x-axis intercepts are 10.32s and 11.47s respectively.

Post hoc analysis

Logarithmic trend curves were found to model the mean residual values effectively, producing R² values of .91 for musicians, and .79 for nonmusicians. In order to calculate the hypothetical time at which the effect of the nonadjacent key ceased, that is, the duration of the nonadjacent key in memory, we forward-extended the trend curves until they crossed the x-axis, the point at which y was equal to zero. Musicians’ trend curve crossed the x-axis at 10.32 seconds, nonmusicians’ at 11.47 seconds (see Figure 3).¹ To verify whether there was a statistically significant effect of nonadjacent key, particularly when the intervening key was extended to 12 chords, we entered the per-participant means of each intervening key length into t-tests in which the comparison array was constructed of zeros (representing no effect of non-adjacent key). All but one of the p values for these tests showed either significant or marginally significant effects of the nonadjacent key, the one exception being for the nonmusicians’ per participant means for the intervening key extended to 12 chords.

This experiment measured the changing effect of a nonadjacent key, and extrapolated its longevity in memory from the rate of decreasing effect. Logarithmic trend curves modelled the decreasing effect of the nonadjacent key, producing relatively high R² values, particularly for the musicians (.91). Nonadjacent-to-probe cadence key relationships were limited to the tonic.

Conclusion

Two main findings emerge from this study. First, nonadjacent harmonic material can be experienced as related – the prior existence in a musical phrase of the cadence key positively affected the sense of closure of the phrase. It seems, therefore, that at least some of the “long-distance syntactic dependencies posited by music theory” (Patel, 2003, p. 675) can indeed be perceived. Second, over time there is a decrease in the extent to which the key-defining attributes of initial events exert an influence on later events. The rate of decrease was sufficiently slow as to suggest that the nonadjacent key was experienced globally, i.e. as influencing the perception of latter events across relatively long musical phrases (ca 10 seconds). It remains to be seen whether the perception of real musical examples that present instances of key establishment, modulation, and initial key re-instantiation conform or go beyond the limits suggested by the present results.

Post hoc analysis extended the trend curves forward until they crossed the x-axis, the hypothetical limit of the memory for the nonadjacent key.² From musicians and nonmusicians’ trend curves it was deduced that nonadjacent-key effects lasted over 10 seconds, well beyond the perceptual present (in the region of 5 seconds; Fraisse, 1984). Although musicians’ residual values were significantly higher than nonmusicians’, the equal duration of the nonadjacent key in memory for both groups suggests that musicians and nonmusicians do not employ different memory processes.

Figure 3 also reveals considerable variability in the data. For example, nonmusicians’ mean residual value is greater at 6.25 seconds than at 5 seconds; musicians’ value is greater at 8.75 seconds than at either 7.5 or 6.25 seconds. While these apparent anomalies are difficult to explain, the likely cause is due to the sources of experimental variance being considerable. For example, the values in Figure 4 are residuals, calculated by subtracting ratings for a non-modulating phrase (one source of variance) from ratings for a modulating phrase (another source of variance). The values are therefore subject to two sources of variance, rather than merely one, potentially leading to relatively noisy data. It is reasonable to suppose that the variability in the data may have been reduced and cleaner patterns revealed had greater numbers of participants been employed. Despite these difficulties, clear evidence emerged that musically trained and untrained listeners were able to hold in memory, at some level, the pitches of the nonadjacent key to the extent where harmonic relationships were established over relatively long musical phrases.

Figure 4.

Parsing-tree representation of the experiment stimuli in which there were tonic-to-tonic nonadjacent effects. The strength of the effect that the nonadjacent key had on perceptions of tonal closure in listeners’ ratings suggests that the intervening key may have been embedded within the ambit of the outer keys, and therefore hierarchically subordinate.

The results of Cook (1987) and of West-Marvin and Brinkman (1999) indicate that there is an upper limit of around 30 second for trained musicians with respect to the maintenance of key effects in music. However, unlike Cook and others, we do not propose that the apparent time limits on the perception of tonal closure in our experiment demonstrate that nonadjacent-key relationships have no cognitive reality over longer timescales. It may be that experimental paradigms that effectively expand memory capacity, for example through repeated listening or by including melodic material, would reveal sensitivities to nonadjacent-key relationships over far longer timescales than we have shown.

Music and language syntax

In a similar way to the parsed sentence in Figure 1, tonal-harmonic music can be analysed as a dependency tree in which shorter sub-branches, representing subordinate elements, terminate at longer main branches, representing superordinate elements. Adopting the approach of Lerdahl and Jackendoff (1983), foremost is the terminal branch, almost invariably the tonic, to which all other branches lead, either directly or indirectly. Implicit in this representation is the notion that most musical events are understood structurally with reference to the tonic, and therefore are hierarchically subordinate to it. Moreover, the structural characteristics of the parsing tree imply that there are constraints on the types of dependency relationships permitted in tonal music; the terminal branch could not be a subdominant harmony, for example.

Despite the overall mixed empirical evidence for hierarchy set out in the opening section of this paper, arguably given our findings there is some justification, in terms of dependency trees, for representing the tonic nonadjacent key as being connected to the terminal branch of the closing tonic cadence (see Figure 4).

Supported by our experiment’s finding, Figure 4 is comparable to the parsing tree of the sentence used in Figure 1: the tonic-to-tonic nonadjacent-key relationship (equivalent to, “Because the river flows past the house, Jack swims”) creates a unitary, overarching structure into which an adjacent key (equivalent to, “which is green” or any relative clause, like “which is falling down” or “built last fall”) can be embedded.

Of course, it is possible that tonal musical is not bound by the same types of structural constraints as language; for example, music, unlike language, does not present semantically decomposable information (Cross, 2005), and therefore may not require similar structural devices in order to create coherence. Moreover, the reasons for embedding in music are likely to be different from those in language. Whereas in language, embedding can lead to semantic enrichment (additional, contextual information in the form of relative clauses, for example), in tonal music, embedding may derive from culturally and historically contingent aesthetic preferences for complexly patterned yet closural structures.

Not only may the motivations for embedding in language and music be different, but so too may be the cognitive processes and brain systems involved in each domain. As mentioned in the opening section, evidence from cases of congenital amusia has been used to propose a degree of dissociation between musical and linguistic abilities (Ayotte, Peretz, & Hyde, 2002), although Aniruddh Patel has argued that common cognitive and neural resources are likely to be employed across the two domains in processes of syntactic integration (Patel, 2003, 2007; see also Williamson, Baddeley, & Hitch, 2010). Our findings are consistent with the view of Patel, in that sensitivity to long-distance key dependencies suggests that syntactic processes are operational in the experience of music.

Within Western tonal music it is likely that aspects of both temporal span and harmonic relatedness will affect whether syntactic relationships are perceived between nonadjacent elements. Traces of the initial key in a listener’s perceptions will progressively be reduced to core tonal relationships (of sequentially ordered tonic-to-tonic, for example) as a second key gradually replaces or overwrites the first. Hence, only presentation of material that re-instantiates those core relationships will cue the initial key, and lead to the experience of a dependency relationship between temporally nonadjacent key regions.

The present study was limited in a number of respects. For example, we did not set out to measure the relative contributions on tonal closure of nonadjacent versus adjacent keys. This was for the following reason: it is not known what memory processes operate with respect to long-range structural connections in music. For example, a nonadjacent key may be held in memory as a continuous trace that decays over time, increasingly masked by additional events in the perceptual present, for instance, as in connectionist models (and as suggested in Bigand et al., 1999). Alternatively, a nonadjacent key may be reactivated if its functional identity is cued by appropriate chords occurring later in a progression. Given that this issue remains unexplored, our approach was primarily to isolate the effect of the nonadjacent key, and to describe its influence on tonal closure over specific durations. Our paradigm led to the adjacent key literally being subtracted from the equation; using an exhaustive set of adjacent keys ensured that the data represented the general operation of nonadjacent tonic key relationships. The ways in which the nonadjacent and adjacent keys separately and together impact listeners’ perceptions requires considerable further experimentation, as does elucidation of the memory processes involved in the perception of relationships between nonadjacent musical events.

Our experiment was also constrained in that the stimuli were largely devoid of melody – a feature that music theory suggests should bear significantly on the perception of nonadjacency in music. For example, in sonata form, following a (modulating) development section, earlier harmonic events are recapitulated in conjunction with thematic material. Although evidence has been found for an effect of long-term auditory memory for thematic material (Levitin, 1994; Pollard-Gott, 1983), resolution of the possible interactions between harmony, melody and numerous other dimensions of music requires further experimentation.

One question that naturally arises from our study is whether harmonic nonadjacency is affected by the absolute time that elapses between the initial presentation of a key and its later re-instantiation or the number of intervening events (chords). Our experiment did not test this, rather, elapse-time and the number of intervening chords were proportional, and therefore could not be treated as separate factors. In addition, in an attempt to investigate nonadjacent-key relationships in music perception we presented relatively simple isochronous harmonic progressions. Future experiments are required to explore the role of voice leading and other musical parameters in the experience of structural relationships in music, perhaps building on the earlier work of Thompson and Cuddy (1992). Moreover, the experiment reported here used the total available range of intervening (adjacent) key relationships. A detailed understanding of which core tonal-harmonic relationships underlie the experience of nonadjacency is likely to require a more restricted range of intervening keys, as hinted at in Horton (2002), and Cuddy and Thompson (1992). Finally, the extent to which musical materials can be embedded at multiple hierarchical levels requires empirical attention before conclusions can be drawn as to whether long-distance syntactic dependencies are of the same type, or have the same structural and temporal elaborateness, in music as in language.

Footnotes

Acknowledgements

The authors wish to thank Nick Collins for programming the experiments in Supercollider, Brian Glasberg for discussions regarding data processing, and John Hawkins for his many helpful suggestions. Thanks are due also to Patrick Rebuschat and Martin Rohrmeier for their assistance with respect to parsing the sentence used in . Finally, thanks go to Michael Barone, Morwaread Farbood, Tommi Himberg, Nikki Moran, Chris Nash, Nicholas Rogers, Neta Spiro, and Joanna Spyra for comments made on earlier drafts of this paper.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was supported by a grant from the UK Arts and Humanities Research Council (AHRC APN18519).

Notes

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