Events versus time in the perception of nonadjacent key relationships

Abstract

Increasing the duration of an intervening key has a negative effect on memory for the original, nonadjacent key. Evidence suggests the recollection of a key only remains for 20 seconds after modulation to a new key section. But factors other than time might influence the perception of nonadjacent key relationships. By using a probe-cadence paradigm, this study tested whether time or the number of musical events (chords) determined the deterioration in memory of the global effect of nonadjacent keys. Stimuli were constructed in three parts: (a) a major key was established through a standard chord progression; (b) an intervening section, either 6 or 9 seconds in duration and formed from either four or six chords, was introduced in 12 possible keys; and (c) a short pause was followed by the probe cadence in the original key—that is, the key at (a). Fifty-one participants were asked to estimate the amount of harmonic closure they perceived at the probe cadence. Results confirmed previous findings of significant negative effects of time on the residual influence of the nonadjacent key. However, there were no significant effects of number of events. This provides evidence that it is the length of time, not the number of musical events in an intervening modulation that determines the recollection of the original key.

Keywords

Harmony memory music nonadjacency perception

Introduction

If we now consider that, in addition, the return to the tonic coincides with the formal conclusion—as it does in this consequent—and that it thus signifies a return to the harmonic point of departure, we see that the motion has reached its goal: form as well as harmony have closed their circle; and for this reason we call such a conclusion a full close, a perfect cadence. (Schenker, 1954, p. 217)

This quotation by Heinrich Schenker calls to mind the longstanding preoccupation within theory and analysis communities that tonal-harmonic music of the common-practice period is best or correctly viewed as a holistic, circular process. In this conceptualization, a crucial element is the structural juxtaposition of key regions—usually, outer relationships having the greatest hierarchical significance. That said, the extent to which nonadjacent key relationships are perceived by those who do not possess absolute pitch (the majority) is a moot point, which in turn suggests that musical coherence may be due to factors other than, or in addition to, key relationships, particularly those that are nonadjacent. Which is to say, the idea that musical unity is instantiated through (long-range) harmonic relationships may be, for most people, an illusion. Similarly, localized harmonic perceptions are deeply influenced by immediately preceding events (Temperley, 2007, p. 89), just as modulation is perceptually shaped by the overarching tonal structure. An example of global harmonic contexts shaping our musical experiences is the perceptual asymmetry of the circle of fifths proposed by Cuddy and Thompson (1992).

With respect to Cuddy and Thompson (1992), in traditional music theory, keys are organized into a circle of fifths: a geometric representation of key relationships in which keys are arranged into a circle, each separated musically by a distance of a fifth (see Figure 1; Piston, 1978). Neighbouring keys are thus constructed of the same notes, all except for one. Perceptually, this is the closest and most consonant interval after the unison and octave (Laitz, 2012, p. 9).

These keys are spaced evenly in either direction, but our perception of the modulation is asymmetrical; movement in a clockwise direction is judged as significantly closer in musical “distance” than counter-clockwise modulations (Cuddy & Thompson, 1992). This may be due to familiarity—clockwise modulations are used more often in music than counter-clockwise (Cuddy & Thompson, 1992). The higher probability of modulation in this direction may cause listeners to judge these keys as more related and thus the distance traversed as smaller. The same patterns are not seen in single voice sequences (Thompson, 1993; Thompson & Cuddy, 1989, 1992, 1997; for summary see Krumhansl, 2000), suggesting there are specific factors in play that impact perception. Though increasing the amount of harmonic information directly influences our perception, it remains unclear from these studies which other factors may have an effect and how long the original key maintains its influence after modulation.

In Cook (1987), one of the earliest studies on structural perception, the cognition of large-scale tonality within music was explored. In his study, participants were randomly presented with six excerpts from the Classical period (circa 1750–1820) written for solo piano. Each excerpt was presented in two versions: the original, nonmodified excerpt in a single key, and one that was modified such that the last few measures were transposed to a different key. Participants were asked to compare these two versions and choose one based on preference for various characteristics (expressiveness, coherence, pleasure, and sense of completion). Perhaps surprisingly, only the two shortest excerpts prompted any preference from the participants, suggesting that listeners had difficulty perceiving tonal structures past approximately one minute (Cook, 1987). However, this study only took into account the entire excerpt and not the modified section itself, providing little distinction between local and global effects. This and similar, related research has sparked work into nonadjacent key relationships (Akiva-Kabiri, Vecchi, Granot, Basso, & Schön, 2009; Granot & Jacoby, 2011; Karno & Konečni, 1992).

By “nonadjacent,” we refer to a temporal relationship between three key regions: (a) an original, starting key, (b) movement to a novel, second key, and (c) a return to the original key, which by virtue of (b) is temporally nonadjacent to (a). Such relationships are common in Western music, though they may vary in terms of duration; a phrase, section, movement or even an entire multimovement piece can be organized into nonadjacent structures (Laitz, 2012, pp. 371–384). Depending on the factors involved, the restatement of the original key is either perceived as a definite return to the tonic or as a new key altogether (Farbood, 2016).

Woolhouse, Cross, and Horton (2016) measured the effect of the nonadjacent key on the closure of a musical passage after varying lengths of time. Stimuli were based on the nonadjacent key template: a nonadjacent key section was first established through traditional Western harmony, the intervening section modulated to one of 12 major keys (as found on the circle of fifths in Figure 1), after which the stimulus ended on a probe cadence—a pair of chords with the harmonic equivalence of a period (V-I) or comma (I-V)—in the original key. Participants were asked to rate this (perfect authentic) cadence for its sense of completion using a Likert-type scale. In each trial, the intervening key was of varying length, lasting from 2 to 9 seconds in duration. Participants rated shorter trials as having significantly more closure than longer trials, suggesting the effects of the nonadjacent key deteriorate logarithmically as duration increases. In post-hoc analysis, Woolhouse et al. (2016) estimated that this effect lasted approximately 11 seconds in their experimental setup.

In a similar, subsequent study, Farbood (2016) extended the duration of the intervening key past the calculated value in Woolhouse et al. (2016). This time, participants were instructed to rate, on a sliding scale, the amount of tension felt (based on Lerdahl’s tonal tension model; Lerdahl & Krumhansl, 2007) as the stimulus progressed. Tension spiked when participants came across novelty in the stimulus, such as a modulation to a different key. The more novel the event, the more extreme the spike in tension. Thus, participants experienced a significant spike at the first modulation (from nonadjacent to intervening key), followed by a second spike as the stimulus modulated back to the original key. Farbood (2016) proposed that as tension decreased rapidly after the second spike, the second modulation was perceived as less novel. As such, the participants must have recognized the original key to some degree despite its shifting to an intervening key along the way. Farbood’s results confirmed this pattern: as the duration of the intervening key increased, so too did the amplitude of tension felt at the second modulation. These tension profiles extended the predicted duration of the effect of nonadjacent keys from 11 seconds (Woolhouse et al., 2016) to approximately 20 seconds (Farbood, 2016). Additionally, Firmino and colleagues have undertaken interesting work on the effect of modulation of chord sequences on perception of time in which modulation to more distantly related keys seems to produce subjective underestimations of the duration of stimuli (Bueno, Firmino & Engelman, 2002; Firmino & Bueno, 2008; Firmino, Bueno & Bigand, 2009).

Despite their focus on manipulating time, a possible limitation of the experimental designs in Woolhouse et al. (2016) and Farbood (2016) is that both modified the duration of the intervening key by adding or subtracting chords. In Woolhouse et al. (2016), a duration of 5 seconds, for example, would always comprise six chords while a duration of 2.5 seconds always comprised only two. Similarly, in Farbood (2016), chords, delivered as arpeggios, were repeated in direct proportion to the lengthening of the intervening key. In both instances, this created a possible confounding factor: it may have been the number of chords/events and not time that influenced the effect of the nonadjacent key. Conversely, both could have had some effect, as in Akiva-Kabiri et al. (2009). Our study sought to disentangle this issue.

To understand how the possible confounds referred to above relate to memory processes, we must briefly review relevant research in this area. Memory begins in the ear itself, which transforms raw auditory stimulation into electrical energy, forming the first stage of memory called echoic memory (Craik & Lockhart, 1972). This is where “feature extraction” occurs and the brain begins to piece together elements such as timbre or musical notes without yet labeling them (Snyder, 2000). Leman (2000) is one model that uses this process to form an echoic image which can then be used in the inference of music key (Leman, Lesaffre & Tanghe, 2001). This feature extraction process feeds into short-term memory (STM) in two ways: directly through unlabeled perceptual awareness as well as indirectly through an identification process that first utilizes long-term memory (LTM; Craik & Lockhart, 1972; Snyder, 2000). Baddeley’s model of STM is perhaps the most widely known (Baddeley, 2003; Baddeley & Hitch, 2018; Schulze & Koelsch, 2012). It divides STM into three components: the phonological loop, the visuospatial sketchpad and the central executive (Baddeley, 2003). The phonological loop is responsible for processing auditory stimuli and maintaining activation of this stimulus in memory through a rehearsal process (Baddeley, 2003). However, there is some debate in music cognition circles on whether STM for music is included in Baddeley’s phonological loop or whether it has a tonal loop of its own (Berz, 1995; Pechmann & Mohr, 1992; Schulze & Koelsch, 2012). This phonological/tonal loop is where working memory (WM) and rehearsal for music resides (Snyder, 2000). According to Snyder, WM is where conscious awareness occurs. This is where we perceive and make conscious connections between features and stimuli within short periods of time. Nonadjacent key relationships most likely occur in the STM system by utilizing WM and the tonal loop.

With specific relevance to our current study, various models of memory have suggested a capacity limit to WM. For example, models have suggested that WM has a limited capacity depending on the type of stimulus (Berz, 1995; Craik & Lockhart, 1972; Snyder, 2000, pp. 53–56); it can span anywhere from two to nine items if they are perceived as separate events, and up to as many as 20 items if they are related, such as words that form a grammatically coherent sentence. According to Craik and Lockhart (1972), after this limit, items stored in a working memory buffer are replaced with newer items, and are thus no longer accessible. It is possible that the number of chords and/or events used in Woolhouse et al. (2016) and Farbood (2016) affected the representation of the original key in working memory by replacing the chords stored in a buffer with newer chords presented in the intervening key section. We sought to test whether memory for a previous key could be explained using a buffer model of finite capacity, consisting of musical events.

Present study

Specifically, the aim of this study was to test the perception and retention of global tonic-key structures in auditory stimuli containing intervening modulations. To this end, participants were presented with a musical phrase consisting of an initial key section, an intervening section in a different key, and a two-chord probe cadence (V-I) in the initial key, that participants rated for goodness of completion (as adapted from Woolhouse et al., 2016). The intervening key was modified so as to test the effects of time and events separately. While many things within a musical context may constitute a perceptual event, for our purposes, we define an event as a harmonic triadic chord. The rationale for this was due to the relationship between key induction (and its subsequent perceptual maintenance) and the functional organization of chords into well-formed sequences (Auhagen & Vos, 2000). At least, this is typically what happens, from a theoretical perspective, in real-world music of the common-practice period (Brown & Butler, 1981).

The intervening key consisted of either four or six chords that lasted for either 6 or 9 seconds in duration. In this way, an intervening section made of six chords lasting 6 seconds would consist of quarter-note chords, whereas one made of six chords but lasting 9 seconds would consist of half-note chords (see Figure 2). Table 1 shows a summary of all possible variations of the intervening key. By comparing these conditions, we were able to test the extent to which participants retained the initial key over time despite the presence of a distractor in the form of an intervening key, and, in turn, determine the effect of either time (T) and/or the number of events (E) within the modulation on the sense of closure.

Table 1.

Summary of the possible modifications to the intervening key.

Condition	Time (s)	Events
T₆E₆	6	6
T₉E₆	9	6
T₆E₄	6	4
T₉E₄	9	4

Experimental designs involving tonal induction pose inherent challenges. First, the nonadjacent key must be as salient as possible in order to reliably establish a “home” key through all stimuli equally. Second, the effects of key must be limited to the global effect of the nonadjacent key on the probe cadence rather than that of the more local intervening key. In order to correct for the limitation of key salience, the nonadjacent section was consistently constructed from a I-I⁶-ii⁶₅-V-I chord progression; this progression ensured that the nonadjacent key was established in accordance with the tenets of music theory (Piston, 1978).

Woolhouse et al. (2016) demonstrated an effective method of separating global from local effects by comparing the ratings for a modulating stimulus (e.g., key X-Y-X; where the final X refers to the key of the probe cadence) to a non-modulating stimulus (e.g., key Y-Y-X). If the ratings were significantly different, the modulating stimulus was presumably affected by both global and local structures, while the non-modulating sequence was only affected locally. By subtracting them from each other, the only factor left is the global effect. This was, indeed, corroborated by the results of Woolhouse et al. (2016), providing evidence that participants’ perceptions at the point of the probe cadence were significantly influenced by the original key, despite the presence of an intervening modulation of varying length.

There were two main areas of interest in the present study: the length of time spent in the intervening key and the number of events (chords) it contained. This led to six possible hypotheses as illustrated in Table 2. The first hypothesis was that increasing the amount of time spent in the intervening key would have a negative effect on the sense of completion of the probe cadence, hereon identified as T- (i.e., T negative). This means that spending more time in a novel key decreases the global effect of the nonadjacent key, thus lowering ratings for completion of the probe cadence. In contrast, time could have a positive effect, hereon called T+ (i.e., T positive), or no effect whatsoever, in which case we refer to it as simply T (i.e., T neutral). The same three hypotheses were applied to number of events: increasing the number of events in the intervening key could have a negative effect, a positive effect, or no effect on the capacity of the probe cadence to complete the musical phrase (E-, E+, E respectively).

Table 2.

Summary of proposed hypotheses.

Hypothesis ID	Description
T-	Negative effect on closure of greater duration of the intervening key
T+	Positive effect on closure of greater duration of the intervening key
T	No effect of duration of the intervening key
E-	Negative effect on closure of more events within the intervening key
E+	Positive effect on closure of more events within the intervening key
E	No effect of number of events within the intervening key

Method

Participants

A total of 51 undergraduate students (17–21 years of age, mean: 19, SD: 0.79; 46 biologically female) participated in the experiment. Determined by their level of formal musical training and engagement in music, the cohort was divided into two groups: “musicians” and “non-musicians.” Based on this categorization, there were 21 musicians, all of whom had five or more years of musical training and were currently playing a musical instrument (average: 6.86 years; SD: 1.71), and 30 non-musicians. Participants were drawn from a variety of departments at McMaster University and were rewarded for their participation with a course credit under the McMaster Psychology, Neuroscience and Behaviour student research-pool system.

Apparatus

Stimuli were generated in MuseScore2 and programmed into an online web module using HTML5 and JavaScript. The stimuli, however, were not “online,” or completed by people in their homes. Rather, the stimuli were presented to participants in the lab setting in which no other persons were present except for the experimenter; extraneous noises were imperceptible. The stimuli were presented through AKG K 172 HD headphones, which have a frequency range of 18 Hz–26 kHz. Each participant adjusted the headphone volume to a comfortable level prior to the first trial of the experiment session. Responses were entered by adjusting a slider programmed into the web module.

Stimuli and procedure

The stimuli employed the default grand piano timbre in MuseScore. They were exported from MuseScore as mp3 files and digitally mastered in Audacity, an open-source audio editing program. Each stimulus had the same intensity and dynamic range. A total of 48 randomly transposed stimuli were created for this experiment (four conditions, 12 key modulations). These stimuli were then presented in a different randomized order to each participant. Modulations spanned from no modulation to an 11-semitone modulation between the nonadjacent and intervening keys. Each key progression was used for all four of the experimental conditions. Conditions were determined using two independent variables: (a) number of events and (b) duration (in seconds) of the intervening key. The events in consideration were defined as the number of chords used in the intervening key progression (Figure 2). Two of the experimental conditions had 4 events and two had 6 events in the intervening key. Out of these, intervening keys could last either 6 or 9 seconds.

The nonadjacent key was established using a I-I⁶-ii⁶₅-V-I progression in which each chord was delivered at 80 bpm; the nonadjacent key therefore lasted 3.75 seconds. The intervening adjacent key was wrap-constructed so that it always began and ended with the same chords (V-I), minimizing any ambiguity as to the key it was in. Each stimulus ended with a probe cadence in the initial, nonadjacent key. The probe cadence consisted of two chords (dominant and tonic), which typically occur at the end of a piece in the tonal-harmonic idiom. A two-beat rest, lasting 1.5 seconds, separated the intervening key from the probe cadence; this, we assumed, would draw attention to the probe. Together, the two-beat rest and probe cadence lasted 3 seconds (1.5 for the two-beat rest; 1.5 for the probe). Due to time constraints and in order to avoid participant fatigue, only major keys were used in this experiment. The texture of the stimuli was homophonic (rather than polyphonic, for example) as this simplified the classification of events (e.g., chords versus overlapping melodies) and because chords can be used to readily establish keys (Cuddy & Thompson, 1992; Thompson & Cuddy, 1992).

Participants were asked to rate the probe cadence for its sense of tonal closure using a Likert-type scale of 1–7 (from “not at all” to “strong sense of closure”). The experiment lasted for approximately 25 minutes.

Results

To minimize the differences in rating strategies between participants, raw scores were normalized by converting each rating into z-scores for each participant separately. A repeated-measures 4-way mixed analysis of variance (ANOVA), with Time, Events, and Transposition as within-subject factors, and Musicianship as the between-subject factor were run on the dependent variable. Within Time there were two levels (6 vs 9 seconds spent in the intervening key); within Events there were two levels (4 vs 6 chords); and within Transposition there were 12 levels (12 major keys). The assumption of sphericity was not violated.

The main effect of Time was highly significant (F_{1, 50} = 36.247, p < 0.005, $ω^{2} = 0.014)$ however, the main effect of number of Events did not reach significance (F_{1, 50} = 2.976, p = 0.0846). There was no significant interaction between Time and Events (F_{1, 50} = 0.012, p = 0.912). With regards to Table 2, finding no significant effect of Events provides evidence for the E hypothesis (neutral). Furthermore, there was a significant negative effect of spending more time in the intervening section on the sense of completion (providing evidence for the T- hypothesis). This means that the probe cadence became less structurally viable the greater the duration of the intervening, distractor key. There was no significant effect of musicians when compared to non-musicians (F_{1, 50} = 0, p = 1). Transposition did reach significance (F_{11, 50} = 48.266, p < 0.005, $ω^{2} = 0.175)$ providing evidence that local harmonic structures affected participants’ ratings of the stimuli, as was expected.

Mean differences

Results were further explored by subtracting the means of conditions, as seen in Table 3, in which Column A lists the possible comparisons between the various conditions. For example, Row 1, T₆E₆ – T₉E₆, represents a comparison between stimuli in which the duration of the intervening key was 6 seconds (T₆), consisting of six chords (E₆), and stimuli in which the duration of the intervening key was 9 seconds (T₉), consisting of six chords (E₆). Column B identifies the factor (Time and/or Events) that differs between the two stimuli. For example, in the case of T₆E₆ – T₉E₆, time changes (6 vs 9) while the number of events/chords is held constant (6 vs 6). Column C lists the differences (residuals) between the two types of stimuli. For example, the mean difference when T₉E₆ stimuli were subtracted from T₆E₆ stimuli (i.e., T₆E₆ – T₉E₆) was 0.21; see Cell C1. The values in Column C are shown graphically in Figure 3. Columns D, E, and F in Table 3 show which hypotheses are supported depending on the mean differences between two types of stimulus (shaded cells). For example, T₆E₆ – T₉E₆, Row 1, yielded a positive value of 0.21; as Cell E1 indicates, this positive value is consistent with the T- Hypothesis, that is., increasing the duration of the intervening key has a negative effect on closure (similarly, see also T₆E₄ – T₉E₄ and Cell E6). As shown by the values in Cells D2 and D5, the results are also consistent with the hypothesis that changing the number of events has a neutral effect on closure (E Hypothesis). And, following on from this, the value associated with T₉E₆ – T₆E₄ (-0.15, Cell C4) is more likely to be due to the negative effect of increasing time (T- Hypothesis) than number of events (E- Hypothesis); similarly, see also Cell C3 associated with T₆E₆ – T₉E₄. These hypotheses were further supported by a Tukey’s Honest Significant Difference (Tukey HSD) in which all comparisons were significant except for those in Rows 2 and 5 in which the changing factor was Events (see Figure 3 for more details).

Table 3.

Summary of comparisons between the various conditions. Shaded cells indicate supported hypotheses.

	A	B	C	D	E	F
	Comparison:T_nE_n – T_nE_n	Changing factor	Mean difference	Negligible difference	Positive difference	Negative difference
1	T₆E₆ – T₉E₆	Time	0.21	T	T-	T+
2	T₆E₆ – T₆E₄	Events	0.06	E	E+	E-
3	T₆E₆ – T₉E₄	Both	0.28	T and/or E	T- and/or E+	T+ and/or E-
4	T₉E₆ – T₆E₄	Both	−0.15	T and/or E	T+ and/or E+	T- and/or E-
5	T₉E₆ – T₉E₄	Events	0.07	E	E+	E-
6	T₆E₄ – T₉E₄	Time	0.22	T	T-	T+

Post-hoc analysis: Intervening key modulation

A post-hoc analysis of the data indicated some unexpected trends in terms of intervening key modulation (see Figure 4). On average, stimuli that modulated were rated negatively for closure in comparison to non-modulating sequences (e.g., stimuli in the key of C major throughout). That said, modulations up a minor second and fourth from the nonadjacent key were rated relatively highly. On the face of it, this is contrary to multidimensional maps of key relatedness, such as Krumhansl and Kessler (1982), in which keys related by a fourth and a fifth are closer than a minor second (see also Krumhansl, 1985; Lerdahl, 2001, pp. 110–112).

Discussion

Increasing the duration of an intervening key significantly diminished the global effects of the nonadjacent key. However, global effects of the initial, nonadjacent key appear not to have been affected by the number of events in the second, interpolated key. These results disentangle the confounds of previous studies (Farbood, 2016; Woolhouse et al., 2016), which covaried the duration and number of events (i.e., chords) of the intervening key, and show that duration is the critical factor. Moreover, this finding appears to be generalizable to the population at large, as there was no significant difference between musicians and non-musicians in our study.

Although Farbood (2016), in one of her experiments, presented the intervening key as a repeating single arpeggiated chord of variable length, the fact remains that participants are likely to have heard this as multiple events constructed from a repeating ostinato figure. Arguably, therefore, the confound discussed in the Introduction, in which number of events increased with duration of intervening key, was not addressed in her study. That said, Farbood (2016)—unlike Woolhouse et al. (2016), who only found an effect up to approximately 12 seconds—extended this to approximately 20 seconds. Farbood’s study, therefore, represents a subsequent advancement in the field. The unique contribution of the study presented in this paper, however, is that we now have a clearer idea of the relative roles played by events versus time, with the latter carrying significantly more weight.

There could be several alternative explanations for finding no effect of number of events (chords). In our design, we assumed that each chord was experienced in a unitary manner—that is, as a separate event. However, what constitutes a single, perceptual event in music is a highly subjective and complex matter and could include a chord, a phrase, or even an entire passage (Snyder, 2000, pp. 12–15, 53–56). Clearly, this depends on an individual’s ability to “chunk” musical information (Snyder, 2000, p. 54) and whether they hear chords in a well-formed sequence as belonging indivisibly to one another. We confess that we did not test this musical perception, nor, indeed, would we know how to do this unequivocally. As a result, we applied a straightforward mapping between chord and event based on the assumption that participants were aware of an auditory change between each chord.

Another possibility is that the difference between four and six events was too small to affect memory in a meaningful way. It may be that the number of events falls short of wholly replacing the representation of the original key. As the chords in the intervening key are related harmonically, it is possible that they are being perceived as connected—similar to when words form a sentence—and thereby increase memory capacity to ~20 items (Craik & Lockhart, 1972). Future studies should expand the number of events in this paradigm to thoroughly test whether a significantly higher number of events has a negative impact on working memory capacity. That being said, the current results do not support the buffer model of musical memory presented in the Introduction (Berz, 1995; Craik & Lockhart, 1972; Snyder, 2000), in which newer chords replace the representation of previous chords in memory.

With respect to our post-hoc analysis investigating the intervening keys, one possible explanation for relatively high ratings for modulations up a fourth is that the stimulus, taken as a whole, created a relatively well-formed harmonic structure: I (nonadjacent key)–IV (intervening key)–V-I (probe cadence). Which is to say, participants heard the intervening modulation as a predominant preparation for the following probe cadence. Modulations up a minor second being positively rated may relate to the concept of tritone substitution within a chromatic harmonic context. For example, in jazz, the dominant harmony is frequently swapped for the flattened supertonic—that is, the harmony having a tritone relationship (Cataldo, 2018). If this scenario is at play in our stimuli, the intervening key could arguably have been perceived as a dominant prolongation (Caplin, 1998, p. 77), thus creating a coherent harmonic sequence: I (nonadjacent key)–♭II (intervening dominant substitution/prolongation)–V-I (probe cadence). That said, were this to have been the case, modulations which explicitly stated the dominant should have been rated relatively highly, but this was not the case. And thus, we are left to assume that there may have been some subtle voice-leading effects pertaining to certain modulations, such as the raised minor second, which we did not fully anticipate.

More specifically, we hypothesize that the reason for the poor ratings of the fifth are due to the intervallic relationships in the chord progressions between the intervening key and the probe cadence. In isolation, the probe cadence should be perceived as V-I in the nonadjacent key. However, due to the intervening key being the dominant, the first chord of the probe cadence may have been interpreted as the tonic of the dominant key and not the dominant of the original tonic key. This might have created a heightened sense of unexpectedness within the stimuli and speaks to the necessity for carefully controlling all aspects of the participants’ experiences. Indeed, voice leading can have a profound effect upon musical perceptions. For example, Huron (1993), in a study investigating the derivation of the rules of voice leading from perceptual principles, found that most rules in traditional Western voice-leading practices can be accounted for by perceptual principles such as Toneness or Masking principles. The Toneness principle, for example, maintains that complex tones are easier to separate and identify than pure tones, suggesting that even something as simple as timbre can have an impact on perception. Moreover, he suggests that music following conventional voice-leading practices is experienced as more pleasing to participants, and thus, has an aesthetic quality.

While the issues discussed above do not in any way negate the core findings of our study, future research should, as a minimum, be mindful of local voice-leading effects and attempt to ameliorate, or at least account for, their influence where possible. Indeed, the negative ratings for a majority of modulations may have been due to awkward voice leading. For example, many stimuli had relatively large leaps in the bass at the point of modulation, which could have sounded awkward or jarring to participants (e.g., see Figure 2: stimuli T₆E₄ and T₉E₄, chords 5 to 6). We assume that had our approach been more aesthetically pleasing than logical/scientific, as suggested by Huron (1993), participants may have responded more favorably overall.

Conclusion

The significant effect of time and non-significance of number of events provides support for the findings of Woolhouse et al. (2016) and Farbood (2016). In their exploration of the duration of musical memory, time spent in the intervening key was prolonged by increasing the number of chords (or “events”) in that section. This addition provided a possible confounding factor: that the number of events had a negative effect on key retention. The present study extended this research by investigating both time and number of events. Based on current results, we can be confident that, to the extent to which this study tests the factor, including more chords in a sequence did not interfere with the intended tests.

There remain some limitations to the current study that can be addressed in future research. As discussed in the previous section, the number of events may not have been extensive enough to interfere with working memory. It should be noted that despite rather small differences in both time and number of events, the manipulation of time was enough to result in highly significant differences. This provides compelling support for previous studies even if the possibility yet remains for events to be of some interference on a larger scale. Future experiments should expand on this factor and fully test events as a possible intervening factor with the goal of decreasing unexplained variance in the present data.

A second limitation relates to the stimuli themselves. As with many psychological studies of music, the current stimuli are not particularly representative of everyday music; in our quest to control the factors involved, musical stimuli were purposefully constrained. As a result, numerous other musical dimensions, such as melody and rhythmical activity—that is, features pertaining to the musical surface—could be explored from the perspective of nonadjacency.

The decrease in participants’ ratings as the intervening key duration increases could, and perhaps should, be taken into account by theorists, analysts, and perception researchers when studying relatively sophisticated musical excerpts and stimuli. In other words, the effect of musical memory over relatively short time spans, particularly for novel stimuli, may have significantly impacted musical perceptions in numerous empirical studies.

Footnotes

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research is generously supported by a Partnership Development Grant (#890-2014-0126) from the Social Sciences and Humanities Research Council of Canada.

ORCID iD

Joanna Spyra

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