Context effects on tempo and pleasantness judgments for Beatles songs

Rashotte, Matthew A.; Wedell, Douglas H.

doi:10.3758/s13414-011-0255-y

Context effects on tempo and pleasantness judgments for Beatles songs

Published: 13 January 2012

Volume 74, pages 575–599, (2012)
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Context effects on tempo and pleasantness judgments for Beatles songs

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Matthew A. Rashotte¹ &
Douglas H. Wedell²

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Abstract

Context effects on tempo and pleasantness judgments of different tempos were demonstrated in three experiments using Beatles songs. In Experiments 1 and 2, we explored how listening to versions of the same song that were played at different tempos affected tempo and pleasantness ratings. In both experiments, contrast effects were found on judgments of tempo, with target tempos rated faster when context tempos were slow than when they were fast. In both experiments, we also showed that the peak of the pleasantness rating function shifted toward the values of the context tempos, reflecting disordinal context effects on pleasantness relationships. Familiarity with the songs did not moderate these effects, and shifts in tempo ratings did not correlate with shifts in most pleasant target tempos when context was manipulated within subjects. In Experiment 3, we examined how manipulations of context tempos for one song affected judgments of the same song as compared with judgments of other more or less similar songs. For tempo ratings, contrast effects transferred to ratings of a similar song, but for pleasantness ratings, assimilative shifts of ideals were found only for the same song and not for similar songs. This pattern of results was supportive of independent bases for the two context effects.

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The literature on context effects in judgment provides strong support for the assertion that recently experienced stimuli can shift judgments of and preferences for the currently experienced stimulus (for reviews, see Parducci, 1995; Wedell, Hicklin, & Smarandescu, 2007), as explained in detail below. Given these pervasive effects, one would expect that altering the features of recently experienced musical clips would likewise affect feature judgments and liking for subsequent music. For instance, the tempo of a presented musical clip may be judged fast or slow, depending on the recent set of tempos one has experienced. Furthermore, the most pleasant tempo for a song may change as a function of the tempos one has recently experienced for that song. In a set of three experiments, we investigated how manipulating tempo for Beatles songs affects both judgments of tempo and tempo pleasantness. We investigated tempo because it has been demonstrated to be an important determinant of how songs are evaluated (Deutsch, 1999; LeBlanc, Colman, McCrary, Sherrill, & Malin, 1988; LeBlanc & McCrary, 1983), and it is a feature of the music that can be digitally altered with minimal disturbance of other musical attributes such as pitch, loudness, or timbre. In our studies, we attempted to determine whether context effects found in other domains extended to the domain of music in ways not previously demonstrated (i.e., Parker, Bascom, Rabinovitz, & Zellner, 2008), as well as how context effects on tempo judgment relate to context effects on judged pleasantness of tempo. Before describing these experiments, we will first review the nature of the context effects we will be examining and how these may apply to judgments of tempo and pleasantness for musical clips. The present research builds on the framework described by Wedell and Pettibone (1999), who explored how the nature of context effects on judgments depends critically on the relationship of the judgment scale to the underlying stimulus attribute. Figure 1 illustrates the two types of relationships and the corresponding anticipated context effects. In panel A, judgments describe the magnitudes of a given attribute across various stimuli, such as judging the tempos of different pieces of music. In this case, the expected relationship between judgments and stimulus values is monotonic (or ordinal) such that faster tempos receive higher judgments than slower tempos. For ordinal relationships between judgments and attribute values, the anticipated effect of context is contrast: The same tempo should be judged faster in the context of slower tempos than in the context of faster contexts. Contextual contrast is well explained by Parducci’s (1995) range-frequency theory of judgment, according to which the judged value of a stimulus is dependent on its rank in the distribution (the frequency principle) and its value relative to the minimum and maximum stimuli brought to mind at the time of judgment (the range principle).

The range-frequency judgment model can be expressed as follows:

$$ {{\text{J}}_{ik}} = {{\text{C}}_{\text{MIN}}} + \left( {{{\text{C}}_{\text{MAX}}} - {{\text{C}}_{\text{MIN}}}} \right) \left[ w\left( {{{\text{S}}_i}--{{\text{S}}_{{\text{MIN}},k}}} \right)/\left( {{{\text{S}}_{{\text{MAX}},k}}--{{\text{S}}_{{\text{MIN}},k}}} \right) + \left( {{1} - w} \right)\left( {{\text{Ran}}{{\text{k}}_{ik}}--{1}} \right)/\left( {{{\text{N}}_k}--1} \right)\right] , $$

(1)

where J_ik is the judgment of stimulus i in context k on a scale bounded by rating categories C_MIN and C_MAX, w is the relative weighting of the range principle, S_i is the context-independent value of stimulus i, S_MIN,k and S_MAX,k are the minimum and maximum values brought to mind that define the range of context k, rank_ik is the rank of stimulus i in context k, with 1 and N_k representing the minimum and maximum ranks in context k. Range-frequency theory predicts how shifts in the distribution (via shifts in range or relative frequencies) produce shifts in judgments that reflect contrast effects (Parducci, 1995).

In panel A of Fig. 1, the low context set includes four values that are lower than the values of the three target stimuli, which are common to both distributions (targets are shown as circles, whereas squares signify contextual values). Including these lower values will extend the range downward and increase the percentile ranks of the targets, thus displacing judgments upward. Conversely, the high context will extend the range upward and decrease the percentile ranks of the targets, displacing judgments downward. Such contrast effects are found for a wide variety of stimuli and judgments (for reviews, see Parducci, 1995; Wedell et al., 2007).

Panel B of Fig. 1 presents a nonmonotonic (disordinal) relationship between judgments and attribute values, with judgments rising with increased value up to a point and then decreasing. This type of single-peaked function is typical of judgments related to pleasantness, such as attitude judgments (Eagly & Chaiken, 1993). The attribute value at which the function peaks is referred to as an ideal point, reflecting the most pleasant attribute value (Coombs, 1964). Research exploring context effects on ideal points has primarily examined preference-related judgments in perceptual domains and has overwhelmingly found that the ideal point shifts toward the values of contextual stimuli (Hicklin & Wedell, 2007; Pettibone & Wedell, 2007; Riskey, Parducci, & Beauchamp, 1979; Wedell & Pettibone, 1999; Wedell, Santoyo & Pettibone, 2005; although for an exception, see Cooke, Janiszewski, Cunha, Nasco, & de Wilde, 2004). Panel B of Fig. 1 illustrates the typical context effect on ideals, with the ideal point, defined by the peak of the curve, shifting toward lower values in the low context and higher values in the high context. Note that these shifts produce a disordinal interaction in which pleasantness relations reverse for some targets. For example, in panel B of Fig. 1, the lowest target is rated higher than the highest target in the low context, but this relationship is reversed in the high context.

Judgment-mediated predictions

Although the range-frequency theory explanation of contextual contrast is well accepted, opinions about the origins of the assimilative shift of ideals are somewhat less settled. Wedell and Pettibone (1999) described two potential processes that might underlie this effect. The first they referred to as judgment mediated, according to which the contrastive shifts in the judgment of the attribute drive the assimilative shifts of ideal points. The long arrows in panel A of Fig. 1 help to illustrate this idea. In this example, the ideal is assumed to be defined by a fixed point on the attribute judgment scale. The ideal point then corresponds to different stimulus values. As illustrated in panel A, the elevated judgment function for the low context results in a lower ideal point than the relationally lower judgment function for the high context. According to the judgment-mediated model, the two types of context effects—contrast in judgment and assimilation of ideals in pleasantness—should show a close correspondence.

The judgment-mediated model can be expressed within a Gaussian ideal-point framework as follows:

$$ {{\text{A}}_{ik}} = a + b{ \exp }\left[ { - c{{\left( {{{\text{J}}_{ik}}--{{\text{J}}_{\text{IDEAL}}}} \right)}^2}} \right], $$

(2)

where A_ik is the attractiveness judgment of stimulus i in context k on the designated rating scale, c is a discriminability parameter reflecting how quickly the function rises and falls, J_ik is the contextual judgment of the stimulus from range-frequency theory, and J_IDEAL is the judgment value deemed ideal. The constants a and b linearly transform the attractiveness judgment from a 0–1 scale to the rating scale. Equation 2 describes a normal curve function that peaks at the stimulus whose judged value is equal to the ideal judged value. For many domains, the ideal should fall toward the center of the judgment scale, reflecting the avoidance of extremes. Presumably for song stimuli the ideal will vary with the type of music. For example, a sad song might have a slower ideal tempo than a happy song. Consistent with this idea, research by Quin and Watt (2006) demonstrates that people have different ideal tempos for different types of songs.

One interpretation of the judgment-mediated model is that the contrastive shifts on judged tempo reflect shifts in perceived tempo, so that the tempo perceived as the ideal corresponds to an objective tempo that is shifted toward the contextual set of values. An important implication of the judgment-mediated model is that contrastive shifts in descriptive evaluations should correlate with assimilative shifts of ideals derived from pleasantness judgments. We come back to this point when discussing the prototype model of these effects.

Prototype based predictions

An alternative to the judgment-mediated interpretation is the idea that shifts in the ideal point may be driven by a process that is independent of shifts in the attribute judgments. One such candidate process proposed by Wedell and Pettibone (1999) was that ideals were in part determined by the prototypical value for the stimulus, where the prototype is often represented by the average of experienced values (Reed, 1972). Linking the ideal to the prototype is consistent with demonstrations that the average of faces is judged more attractive than the constituent faces (Langlois & Roggman, 1990). More relevant to the domain of music, Repp (1997) demonstrated how the average of musical performances (i.e., averaging of MIDI recordings) was judged higher in quality than nearly all the constituent performances, although it was judged lower in individuality. Further support for the concept of abstracting an average is provided by the work of Ariely (2001), who demonstrated that averages can be computed quickly and used in perceptual estimation. Extraction of a running average is also consistent with early theories of context effects, such as Helson’s (1964) adaptation level theory.

More generally, the literature on categorization provides ample evidence that the graded nature of categories (found in typicality judgments, inductive inference, truth verification, etc.) can be explained in terms of the distance of a stimulus from the category prototype (Homa, 1984). However, within this literature, there is a debate concerning whether prototypes are encoded in memory and updated with each new experience or whether category exemplars are encoded and retrieved at the time of judgment (Nosofsky & Zaki, 2002). Hintzman (1986) demonstrated how exemplar models account for prototype effects by constructing a prototype from the retrieved exemplars. An advantage of exemplar models is that they can account for contextual effects that prototype models cannot, since context may be used to recruit the particular exemplars used to extract a prototype. Because shifts in ideals occur rapidly with shifts in context for both unfamiliar and familiar stimuli (Pettibone & Wedell, 2007; Wedell & Pettibone, 1999; Wedell et al., 2005), we posit a prototype model in which the prototype is constructed based on the retrieved exemplars, with recent exemplars weighted more heavily than older exemplars.

Within our prototype model, we represent the ideal point as an average of recent and older memories as follows:

$$ {{\text{S}}_{{\text{IDEAL}},{\text{k}}}} = z{\mu_k} + \left( {{1} - z} \right){\mu_0}, $$

(3)

where S_IDEAL,k is the stimulus value representing the ideal point in context k, z is the relative weighting of the recent context k, μ_k is the mean of the stimulus values in context k, and μ₀ is the mean of the stimulus values prior to the current context. Equation 3 provides a conceptual framework for our use of the term prototype, but several aspects of the model are left unspecified. First, it is not clear what constitutes the recent context. It could be the last few trials, or it could be a more extensive set of trials. Second, the model does not specify how frequency might affect weighting. If the prior prototype, μ₀, is based on a higher number of instances, will the weight of the current context, z, be reduced? If so, one would expect familiarity with the stimuli to reduce contextual dependence, although in many domains this does not seem to be the case (O’Reilly, Leitch, & Wedell, 2004; Perrett, 1971). We examined this issue in Experiments 1 and 2 by including a measure of song familiarity in our analyses.

The prototype model then can be expressed as follows:

$$ {{\text{A}}_{ik}} = a + b{ \exp }\left[ { - c{{\left( {{{\text{S}}_i}--{ }{{\text{S}}_{{\text{IDEAL}},k}}} \right)}^2}} \right], $$

(4)

where the A_ik is the attractiveness judgment of stimulus _i in context k, c is a discriminability parameter of the normal curve function, S_i is the context-invariant scale value of the stimulus, and S_IDEAL,k is the stimulus value deemed ideal according to the average of recent and prior experiences as described in Eq. 3. Once again, a and b are scaling constants that relate the 0–1 judgment to the rating scale being used. By comparing Eqs. 2 and 4, one can see that the judgment-mediated model is based on contextually altered stimulus values and a constant ideal, whereas the prototype model is based on contextually independent scale values and an ideal that is altered by the recent set of stimuli. Although the predictions of the two models will often be very similar, a key difference is that the judgment-mediated model entails shifts in pleasantness when attribute judgments shift, but the prototype model does not.

If attribute contrast and ideal-point assimilation derive from different processes, then it should be possible to find circumstances in which the two effects are dissociated. Although Wedell and Pettibone’s (1999) research showed a moderate correlation between these effects, subsequent research has provided evidence for dissociation. For example, Wedell et al. (2005) demonstrated that participants in their sample who held highly negative self-appraisals of body image did not show the assimilation of ideals effect on body image evaluation, even though they did show the usual contrast effect on judgments of thinness. Likewise, Pettibone and Wedell (2007) demonstrated that when evaluations were prompted by labels for stimuli learned in the same encoding context, large contrast effects occurred for feature judgments with no accompanying shifts in ideals for pleasantness judgments. In two other experiments in which context was manipulated within subjects, Pettibone and Wedell showed that contextual contrast did not significantly correlate with ideal-point assimilation. Thus, there is mounting evidence for an independent basis for these two effects.

Overview of experiments

In the present article, we report three experiments exploring how these two types of context effects apply to judgments of Beatles music. Using music by The Beatles resulted in different levels of song familiarity across our sample of undergraduate participants, enabling us to address the question of how different levels of song familiarity affect contextual judgment. For instance, will high and low familiarity listeners show the same degree of contrast effects and ideal-point pleasantness shifts? If so, this would be evidence for the powerful effect of recently experienced contextual stimuli on these judgment processes. We manipulated the tempo of Beatles songs using computer software and created fast and slow tempo contexts. Embedded in these contexts were target tempo clips that included one with the original tempo of the song. The effects of contextual clips were assessed with these target clips. Prior research has shown that tempo judgments follow an ordinal relationship with tempo but that pleasantness judgments follow a single peaked relationship, with an intermediate tempo being rated most pleasant (Holbrook & Anand, 1990; Quin & Watt, 2006). Accordingly, we predicted that participants would show contrast effects on tempo judgments, with target tempos being judged faster in the slow tempo context than in the fast tempo context. We also predicted that participants would show assimilation of ideal points toward the mean of the recently experienced contextual clips. For example, the participants in the fast context should rate a faster target tempo as more pleasant than should participants in the slow context. However, song familiarity may moderate these contextual effects in listeners.

Our experimental designs also provided some tests of the judgment-mediated model of assimilation of ideals. In Experiments 1 and 2, we shifted context within subjects so that the magnitude of the contrast effect in tempo ratings and the assimilation of ideals effect in pleasantness ratings could be gauged for each participant. The judgment-mediated model predicts a significant correlation between these effects, given their common basis. The prototype explanation of ideal-point assimilation does not. In Experiment 3, we also provided a test of these two models by examining the transfer of context effects across different target songs. Typical models of contrast predict effects that generalize to similar stimuli but not to dissimilar stimuli (Brown, 1953; Zellner, Rohm, Bassetti, & Parker, 2003), so the judgment-mediated model would predict transfer to songs high in similarity for both tempo and tempo pleasantness judgments. A prototype explanation of assimilation of ideals would be expected to be more song specific, since ideal point comparisons would likely be based on recruitment of various instances of the same song. Thus, although contrast may extend to similar songs, assimilation of ideals may be song specific according to the prototype view.

Experiment 1

Experiment 1 was conducted to test whether manipulating tempos of a Beatles song, Sergeant Pepper’s Lonely Hearts Club Band (SP), would produce the two basic effects of context described in Fig. 1: contrast for tempo judgments and assimilation of ideals for tempo pleasantness judgments. Figure 2 presents the basic design of the experiment, which consisted of both between-subjects and within-subjects manipulations of context. The first two sets of ratings provide a between-subjects test of context effects and a gauge of the magnitude of these effects when only a single context has been presented. By reversing the contextual distribution for sets 3 and 4, we are able to examine how much contextual judgment changes despite expected carry-over effects from the first context.

Evaluating each participant in each context provides within-subjects measures of contrast on tempo judgments and assimilation of ideals on pleasantness judgments that can be used to test predictions of the judgment-mediated model. One way to interpret the judgment-mediated model is that changes in the tempo judgments reflect changes in the perceived tempo of the songs and not just mapping of stimulus values to response values. If this is the case, and the ideal preferred tempo remains constant, then contrast on tempo perception should produce assimilation of ideals in pleasantness ratings, as described by Eq. 2. Thus, the judgment-mediated model predicts that there should be a positive correlation between indices of contrast and assimilation of ideals calculated for each participant. Although previous research using a similar design has not found a significant positive correlation between these indices (Pettibone & Wedell, 2007), this proposition has not been tested with music stimuli.

Indeed there is evidence that perceived tempo may be sensitive to tempo context. Research using comparative judgments of short tone sequences has revealed that tempo perception adapts to global and local tempo contexts (Jones & McAuley, 2005; McAuley & Miller, 2007). For instance, the point of subjective equality for the same 500-ms tone sequences was inferred to be slower in a slow global context but faster in a fast global context. Although it is difficult to relate results from comparative to absolute judgments, this result provides support for the possibility of a perception-mediated effect. Alternatively, the work of McAuley and colleagues implies that tempo perception is mediated by a tendency to form and use a prototypical stimulus value based on the recent set of contextual values. This interpretation is consistent with the prototype model of pleasantness judgment we describe.

At the end of the four sets of ratings, participants in Experiment 1 rated their familiarity with the song (SP). Familiarity ratings provide a way to assess the degree to which previous exposure to the song might moderate context effects. Extant research suggests that tempo is stored with a high degree of accuracy for songs with which people are very familiar. Levitin and Cook (1996) asked people to sing songs they knew well and found that the majority came within 8% of the actual tempo. This result implies that it might be difficult to shift tempo pleasantness away from the original tempo for participants who are highly familiar with the song in our experiment. Moreover, research indicates that listeners can identify the original recording of a song from a tempo-altered version of a different performance of that song digitally altered to have the same tempo (Honing, 2006). Honing and Ladinig (2009) also found that identification of the original unaltered-tempo version increased with exposure to the musical idiom from which the songs were drawn. Thus, participants in our study who were highly familiar with the song may have been better able to distinguish the original from the altered tempo versions. These findings, taken together, suggest that familiarity might moderate context effects on tempo and pleasantness judgments in our studies, with reduced contextual effects expected for those who are most familiar with the music. However, none of these studies manipulated context; thus, it is unclear to what degree familiarity will be a moderator. Indeed, research in other domains of judgment suggests that exposure to and expertise with the stimulus domain only slightly reduces context effects of this kind (O’Reilly et al., 2004; Perrett, 1971).

Method

Participants and design

Participants were 83 undergraduates from the University of South Carolina who received course credit for volunteering. The experimental design was based on two different testing blocks. In the first block, participants were randomly assigned to either the fast or slow tempo context, so tempo context was manipulated between subjects. The slow tempo context consisted of seven clips with tempos of -30%, -27%, -24%, -21%, -18%, -15%, and -9% of the original. The fast tempo context consisted of seven clips with tempos of 30%, 27%, 24%, 21%, 18%, 15%, and 9%. Additionally, both sets included five target clips with tempos of -12%, -6%, 0%, 6%, and 12%. The original tempo (i.e., 0%) thus was included as a target. The resulting beats per minute (bpm) for each clip is shown in Table 1. Nine-point rating scales were used to make tempo and pleasantness ratings. As shown in Fig. 2, following the first block of testing, participants repeated the task with the other contextual set of song clips. This design allowed for assessment of contextual shifts within subjects, as well as of how changes in contrast scores across contexts related to changes in assimilation of ideals across contexts. As shown in Fig. 2, ratings of tempo (sets 1 and 3) always preceded ratings of tempo pleasantness (sets 2 and 4). Previous research has demonstrated that manipulating the order of these two tasks does not affect the magnitude of the context effects obtained (Pettibone & Wedell, 2007; Wedell & Pettibone, 1999; Wedell et al., 2005).

Table 1 Beats per minute for contextual and target songs

Full size table

Materials and apparatus

All experimental materials were presented on desktop computers with 17-in. monitors and audio headphones that covered the ear and provided a high-quality listening experience. We utilized the recently released digitally remastered Beatles compact discs from 2009. Tracks were copied to a computer using AVS audio converter 6.1 as WAV files. Bit rate was set at 1,411 kps, sample rate was 44,100 Hz, and sample size was 16 bit. The WAV files were then opened in Audacity 1.2.6 and edited. A 14.47 s section from the song SP served as the clip. The clip was taken from approximately 0:20 to 0:34 in the song and included the lyrics, “It was twenty years ago today, Sergeant Pepper told the band to play, they’ve been going in and out of style, but they’re guaranteed to raise a smile, so may I introduce to you.” The Beatles set the original tempo of this song at 95 bpm (Leonard, 1995). Using this clip, we created 18 tempo-altered clips with Audacity while holding constant other features of the song such as pitch and loudness. The clip was tempo transformed in Audacity using the “Change tempo without changing pitch” function. Each file was transformed by a percent change amount and was then exported as WAV files. The tempo manipulations systematically affected the length of the clip. When the speed of the original clip was increased by 30%, the clip’s duration was 11.13 s, and when the speed was decreased by 30%, the clip’s duration was 20.65 s. E-prime was used to administer the experiment and to collect tempo and pleasantness ratings.

Procedure

Participants were tested in groups of up to four in a large laboratory room with computers spaced about 2 m apart. Figure 2 shows how participants completed each step of the experiment. First, instructions informed participants that they would hear clips from SP by the Beatles played at different tempos. After each clip, participants would rate it in terms of tempo or pleasantness. Before any ratings were made, participants listened to the original tempo clip (i.e., 0%). Specifically, they were instructed to click on the mouse to hear the original unaltered portion of the song. Each block of the experiment was divided into two phases. In the first phase, participants rated each clip in terms of tempo on a 9-point scale anchored by 1 = Slow tempo and 9 = Fast tempo. During this phase, a total of 12 clips (five target and seven contextual clips) were presented to participants in random order. In the second phase, participants again heard the 12 clips in random order but rated each clip in terms of pleasantness on a 9-point scale anchored by 1 = not at all pleasant tempo to 9 = very pleasant tempo. After participants completed their first block of testing, they began the second testing block. This second block was identical to the first except that participants were assigned the opposite level of context. After completing the second block, participants gave a familiarity rating for SP on a 9-point scale anchored by 1 = not at all familiar to 9 = very very familiar.

Results

Results for between-subjects and within-subjects comparisons are reported in separate sections below. For each design, repeated measures ANOVAs were conducted on tempo and pleasantness ratings of the targets, with partial η² provided as a measure of effect size for significant effects. To aid in the theoretical interpretation of the results, we conducted model fits to the group mean tempo ratings and pleasantness ratings. Rather than engage in model testing of different parameterizations of the models, we estimated a simple version of each model that fit the data well and provided interpretable parameter values shown in Table 2. Additionally, we compared fitted ideal points with those predicted by the judgment-mediated model, as shown in Table 3. These modeling results are described in three separate sections. A final section of the Results is devoted to analyses of individual differences.

Table 2 Parameter values for range-frequency model and Gaussian ideal-point model fits

Full size table

Table 3 Comparison of judgment-mediated model-predicted ideals with inferred ideals (Experiments 1 and 2)

Full size table

Between-subjects comparisons

Participants were assigned to either the fast or the slow tempo context for their first two sets of ratings so that comparisons between context are also between-subjects comparisons for these data. Figure 3 presents the mean ratings for tempo (panel A) and pleasantness (panel B), along with the model fits. Both panels show large context effects consistent with predictions.

A 2 (context) × 5 (target) repeated measures ANOVA was conducted on tempo ratings of the five target tempos. The significant main effect of context, F(1, 81) = 95.5, partial η² = 0.541, p < .001, reflected the predicted contrast effect in which the same tempo was rated faster in the slow context than in the fast context. The significant main effect of target, F(4, 324) = 108.1, partial η² = 0.572, p < .001, simply reflected the fact that tempo ratings were highly sensitive to the actual differences in tempo between targets. The lack of a Context × Target interaction, F(4, 324) = 0.4, p > .05, indicated that the context effect did not significantly differ across targets.

A 2 (context) × 5 (target) repeated measures ANOVA was also conducted on pleasantness ratings of the five target tempos. The significant main effect of context, F(1, 81) = 33.4, partial η² = 0.292, p < .001, reflected higher pleasantness ratings for the target tempos in the slow context. The significant main effect of target, F(4, 324) = 23.0, partial η² = 0.221, p < .001, reflected the predicted curvilinear relation between pleasantness and tempo for the target values. The significant Context × Target interaction, F(4, 324) = 11.7, partial η² = 0.126, p < .001, was consistent with the predicted crossover interaction in which the peak of the pleasantness rating function was shifted to a faster target tempo in the fast context than in the slow context. This interpretation is supported by the statistically significant linear component of the interaction, F(1, 81) = 39.6, partial η² = 0.328, p < .001.

Although the most accurate way to assess ideal points for each participant is to fit Eq. 4 to each (see Wedell & Pettibone, 1999, for an example), this method is problematic in significance testing for two reasons. First, when the function is monotonic, the fitted value of the ideal point estimate is very unstable and may be extreme in magnitude. Second, because contextual values are asymmetric across conditions, artifacts may be introduced into the estimation process by the inclusion of different contextual values across conditions. A measure that does not suffer these problems is the most pleasant target tempo, which is simply the target tempo that is rated highest in pleasantness. If more than one target tempo shares the highest rating, then these tempo values are averaged together. Because only target tempos shared across conditions are used, the calculated value cannot reflect artifacts resulting from including different contextual values in estimation. Because this measure is restricted to be in the range of the target values (-12% to 12%), it will not produce extreme and unreasonable values associated with monotonic functions. However, for this same reason, it will not be as extreme as the true ideal point value when that value lies outside the target range. We conducted analyses on the most pleasant target tempos computed as a way to more directly infer changes in ideal points. A t test computed on this measure was significant, t(81) = 3.02, p < .01, with the most pleasant target tempo faster in the fast context (M = 7.28) than in the slow context (M = 2.37).

To determine the effects of familiarity, we dichotomized the familiarity ratings and included this grouping factor in the analyses described earlier (six cases were excluded from the analysis because of missing familiarity rating data for these participants). Familiarity with SP varied widely across listeners (M = 4.16 and SD = 2.91). Participants were classified into the high familiarity group if their familiarity rating was 5 or greater (N = 35) and into the low familiarity group if their rating was less than 5 (N = 42). For neither the ANOVA on tempo judgments or on pleasantness judgments did familiarity interact with context. Thus, there was no evidence that context effects were moderated by familiarity with the song. Familiarity grouping did significantly interact with target values for the ratings of pleasantness, F(4, 292 ) = 4.09, partial η² = 0.053, p < .01. Examination of the means indicated that the high familiarity group rated the faster tempos more pleasant than the original tempo, but the low familiarity group did not. Thus, the interaction did not reflect any tendency for familiarity to increase tempo pleasantness for the original tempo version of the song.

Within-subjects comparisons

After rating tempo and pleasantness in one context, participants were exposed to the opposite context and rated tempo and pleasantness again. Comparing first and second block ratings then provides a within-subjects evaluation of context effects. Figure 4 presents the data for these comparisons, along with the model fits. Each panel presents the mean ratings from the same participants in the two different contexts. As seen in the left panels, strong contrast effects were found for these within-subjects comparisons, but clear carryover effects occurred as well. The magnitude of contrast was about half that found in the between-subjects manipulation. Comparing the tempo rating functions to the diagonal, one can see that the initial context produced ratings far away from the diagonal, but these ratings shifted only about halfway back when the opposite context was subsequently presented. The pleasantness ratings show a clear difference in the peak of the functions for the slow then for the fast condition, but less of a difference for the fast then for the slow condition. Consistent with the asymmetry of shifting found in the between-subjects comparison, it was more difficult to move the ideal point to slower target tempos after the fast context established faster target tempos as more pleasant.

Parallel ANOVAs were conducted on ratings across the two blocks so that context was a within-subjects factor. A 2 (order of context) × 2 (context) × 5 (target) repeated measures ANOVA conducted on tempo ratings of the target tempos revealed a large effect of context, F(1, 81) = 64.3, partial η² = 0.443, p < .001, reflecting a strong contrast effect on tempo ratings when context was manipulated within subjects. Although this effect was quite large (a mean difference of 0.73), it was less than half the size found in the between-subjects manipulation of context (a mean difference of 1.87), reflecting carryover effects of context from the first block. Further evidence of carryover effects was found in a significant main effect of order of context, F(1, 81) = 59.3, partial η² = 0.423, p < .001, with target ratings higher when the slow context occurred first than when the fast context occurred first. The only other significant effect was a main effect of target, F(4, 324) = 218.4, partial η² = 0.729, p < .001.

A 2 (order of context) × 2 (context) × 5 (target) repeated measures ANOVA conducted on pleasantness ratings of the target tempos revealed a large Context × Target interaction, F(4, 324) = 13.7, partial η² = 0.147, p < .001, reflecting the crossover interaction predicted by a shift in ideals toward contextual values. As predicted, the linear component of this interaction was significant, F(1, 81) = 19.0, partial η² = 0.190, p < .001. A significant main effect of order of context, F(1, 81) = 7.5, partial η² = 0.085, p < .01, reflected higher pleasantness ratings when the slow context was presented first. This is consistent with asymmetric shifts of ideals so that once the fast context established slower targets as unpleasant, they did not tend to be rated as pleasant with a shift to the slower context. Evidence for carryover effects comes from a significant Order × Target interaction, F(4, 324) = 2.9, partial η² = 0.035, p < .05. If the first context continued to influence the ideal when the second context was presented, then the differences in ideals associated with context should have depended on which context occurred first. Accordingly, the peak of the functions averaged across contexts was at a higher tempo value when the fast context occurred first rather than second. Additional significant effects included a main effect of context, F(1, 81) = 43.0, partial η² = 0.347, p < .001, reflecting higher overall pleasantness ratings in the slow context, and a main effect of target, F(4, 324) = 61.2, partial η² = 0.431, p < .001, reflecting the predicted single peaked shape of the pleasantness rating function. No other effects were statistically significant.

Although the three-way Order × Context × Target interaction was not significant for pleasantness ratings, there appeared to be an asymmetry in the shifting of pleasantness. Those starting out in the fast context did not shift their most pleasant target tempo downward much when encountering the slow context, but those starting in the slow context did shift their most pleasant target tempo upward to a greater extent when encountering the fast context. A t test comparing most pleasant target tempo when the slow context occurred first showed that these differed with context, t(42) = 2.49, p < .05, M _Slow = 2.37 and M _Fast = 5.86. However, this difference was not significant when the fast context occurred first, t(39) = 1.35, p > .05, M _Slow = 5.63 and M _Fast = 7.28.

Range-frequency model fits

The range-frequency model of Eq. 1 was fit to the group mean tempo ratings for the 2 (context) × 2 (context order) conditions shown in the left panels of Figs. 3 and 4. Because range and frequency values were highly correlated in this design, we simplified Eq. 1 by setting w = 1.0 and thus fit two parameters to each context, S_MIN,k and S_MAX,k, corresponding to the minimum and maximum values defining the subjective range in each context. This version of the model was fit using least-squares linear regression. Note that S_MIN,k and S_MAX,k are subjective values that we infer from the data on the basis of a scale-matching assumption (Parducci, 1995). Rather than fit an additive and multiplicative constant to transform internal judgments to a response scale, the scale-matching assumption posits that when the a stimulus corresponds to S_MIN,k it will be assigned the lowest rating category, C_MIN, and that when it corresponds to S_MAX,k, it will be assigned the highest rating category, C_MIN + (C_MAX – C_MIN). This scale-matching assumption is reflected in the parameterization of Eq. 1 and is used in a similar fashion when we describe predictions from the judgment-mediated model.

Model fits are shown in the left panels of Figs. 3 and 4 as fitted lines, with a close correspondence between fitted and empirical values (R² = .993 for fits to the slow to fast condition, and R² = .996 for fits to the fast to slow condition). Parameter values estimated from the range-frequency model are shown in Table 2 and help interpret the effects of order reported earlier. When the slow context is judged first, a low minimum value defining the range is established that does not change much when the fast context is subsequently judged. When the fast context is judged first, a high maximum value defining the range is established that does not change much when the slow context is subsequently judged. Thus, the range-frequency model explains the carryover effects as resulting from the maintenance of an extreme range anchor that was established in the first context when judging targets from the second context.^{Footnote 1}

Prototype model fits

The Gaussian ideal-point model of Eq. 4 was fit to the group mean pleasantness ratings for the 2 (context) × 2 (context order) conditions shown in the right panels of Figs. 3 and 4. In fitting the Gaussian ideal-point model of Eq. 4, the additive constant (a) was set equal to 1, the lowest value on the rating scale, and three parameters were fit to each context. The value of b reflects the height of the pleasantness rating function, the value of c reflects the narrowness of the function, and the value of ideal estimates the tempo value corresponding to the peak of the function. The model was fit using iterative nonlinear regression with a least squares error function.

Model fits are shown in right panels of Figs. 3 and 4 as lines, with a close correspondence between fitted and empirical values (R² = .987 for fits to the slow to fast condition, and R² = .988 for fits to the fast to slow condition). Parameter values estimated from the Gaussian ideal point model are shown in Table 2. The ideal point values reported in Table 2 can be compared to the mean most pleasant target tempos reported earlier. As expected, the differences in inferred ideal points with context are generally larger than those reported for mean most pleasant target tempo. This is largely due to the restriction on the range of tempo values possible for the latter measure (between -12% and 12%, the slowest and fastest target values). As an example, note that the inferred ideal was 16.83 for the fast context (when judged first), which is beyond the target range.

Judgment-mediated model predictions

The judgment-mediated model predicts the ideal point location according to judged tempo values and an ideal judgment value. We examined this relationship more thoroughly by comparing predictions from the judgment-mediated model of Eq. 2 to ideal points inferred by fitting Eq. 4 to the data. Table 3 shows this comparison. According to Eq. 2, one free parameter, the ideal judgment value (J_Ideal), determines the location of the ideal point once judged tempo values (J_ik) are modeled. As described earlier, we successfully modeled these judged values using Eq. 1 with just two free parameters determining judgments in each context, S_MIN,k and S_MAX,k. Thus, based on these values, each context provides an estimate of J_Ideal. We averaged these estimates and used the single estimated value to predict ideal points as shown in Table 3. As can be seen, the predictions of the ideals are quite accurate for the first context encountered (i.e., the slow context in the slow to fast condition and the fast context in the fast to slow condition). However, the predictions for the ideal points for the second context encountered are not very accurate.

Individual differences analyses

The significant within-subjects effects of context enabled us to test the hypothesis that differences in judged tempo mediate the differences in the most pleasant target tempo at the individual level. If this were the case, then one would predict a significant positive correlation between the amount of contrast a participant shows in rating tempo across contexts and the amount of assimilation of ideals the participant shows in rating pleasantness across contexts. Contrast was computed for each participant by subtracting the mean of target ratings in the fast context from the mean of target ratings in the slow context. Assimilation of ideals was estimated for each participant by subtracting the most pleasant target tempo in the slow context from the most pleasant target tempo in the fast context. Inconsistent with the hypothesis of judgment-mediated effects on pleasantness, the correlation of these two context scores was close to zero, r = .02.

A potential problem with the use of a simple correlation to assess the correspondence between context effects on tempo judgments and pleasantness judgments is that the proposed relationship is dependent on assumptions about the tempo judgment functions. As shown in Fig. 1, the shift in ideal points predicted from panel A is based on parallel functions in low and high contexts. If the slopes of the functions change significantly across contexts, then the predicted shift in ideals can change as well. Furthermore, when comparing across participants, the steepness of the slopes of these functions should affect predicted differences in ideal points. Steeper functions will typically result in smaller shifts in ideals than flatter functions, all else being held constant. To assess these effects, we calculated for each participant the average slope across the two contexts and the difference in slopes across the two contexts based on the target tempo ratings. In a regression analysis predicting change in the most pleasant target tempo from difference in mean tempo ratings, we included these terms along with their interaction with difference in mean tempo ratings. None of the included terms significantly incremented R², and the model R² did not rise above .006, implying that the lack of correlation between these two measures was not moderated by individual slope differences or averages.

Given the single peaked nature of the pleasantness functions, one may ask to what degree are individual participants well characterized by the fits to the group mean. Assuming that all individuals follow a single peaked function, the correlation between an individual’s rating function and the group function will decrease as the difference in peaks increases, and in extreme cases, it can be close to -1.0. To evaluate the correspondence between individual and average rating, we computed the correlation between each participant’s rating function and the mean rating function within each order × context condition. Figure 5 presents the cumulative proportions for these correlations in each of the four conditions. Two important observations can be derived from this figure. First, there is a high degree of agreement between individual and averaged data for the first distribution encountered. For the slow–fast order, the median correlation was .844 for the slow context, with 88% having r > .60. Similarly, for the fast–slow order, the median correlation was .895 for the fast context, with 90% having r > .60. However, the agreement of individual rating functions to the average rating function diminishes for the second set judged, presumably reflecting individual differences in the tendency to shift ideals with context. For the slow–fast order, the median correlation was .593 for the fast context, with 45% having r > .60. For the fast–slow order the median correlation was .667 for the slow context, with 63% having r > .60

Discussion

In Experiment 1, we clearly demonstrated evidence for two types of context effects operating on judgments of Beatles music: contrast for tempo ratings and assimilation of ideals for pleasantness ratings. Contrast effects were consistent with predictions of range-frequency theory (Parducci, 1995) and may be attributed to either shifts in ranks or ranges across context. Because ranks and stimulus values were highly correlated, we fit a simplified version of the range-frequency model that depended only on range values by setting w = 1 in Eq. 1. This model fit the mean ratings well, indicating that the shift in ratings is consistent with the two contexts bringing to mind different ranges of contextual values at the time of judgment. The range-frequency modeling also provided a simple explanation of the observed carryover effects on ratings of tempo. When adjusting to a new context, the range anchor extends quickly to accommodate the new extreme tempo values being presented, but the opposite range anchor does not recede, even though these extreme values are no longer being presented. This tendency to rapidly extend the range but only slowly retract the range has long been noted in the contextual judgment literature (Parducci, 1956). The lack of a significant interaction of context effects on tempo judgments with song familiarity suggests that these effects are independent of familiarity.

In Experiment 1, we demonstrated that the most pleasant tempo at which Beatles music is played changes with the manipulation of contextual tempos: The most pleasant tempo was faster in the fast context than in the slow context. This pattern of effects is consistent with previous research in other domains (Riskey et al., 1979; Wedell & Pettibone, 1999; Wedell et al., 2005). Ideal point shifts in Experiment 1 appeared to exhibit some asymmetry. First, even in the between-subjects condition that was designed to maximize context effects, the ideal did not move below the original tempo value, whereas it moved quite strongly to a faster tempo value. Furthermore, carryover effects from the within-subjects design appeared asymmetric as well for pleasantness ratings. The most pleasant target tempo readily shifted to a faster tempo when the initial context was slow. However, the most pleasant target tempo did not shift to a significantly slower tempo when the initial context was fast. We investigated this asymmetric finding further in Experiment 2.

Somewhat surprisingly, familiarity was not a moderator of context effects for either tempo or pleasantness judgments. Previous research has shown fairly accurate remembered tempos for familiar songs (Levitin & Cook, 1996) and an ability to discriminate the original tempo from a tempo-altered version that increases with familiarity with the song idiom (Honing & Ladinig, 2009). These two findings provided a basis for the prediction that context effects might be reduced for participants who are more familiar with the song, since they would have a more stable representation in memory. This was not the case for either tempo or pleasantness judgments. Furthermore, the significant Familiarity × Target interaction on pleasantness judgments indicated that those more familiar with the song preferred a version that was faster than the original, whereas those less familiar with the song did not. Thus, there did not appear to be any special preference for the original for those more familiar with the song; indeed, the opposite was found.

The within-subjects manipulation of context also provided for a test of the judgment-mediated model of ideal point shifts. Because participants judged tempo and pleasantness in both fast and slow contexts, indices of contrast on tempo judgments and of most pleasant target tempo on pleasantness judgments could be calculated and compared. If contextual shifts in judged tempo cause corresponding changes in pleasantness as described in Eq. 2, then there should be a positive correlation between magnitude of contrast and magnitude of assimilation of ideals. However, this correlation was very small and not significant, consistent with prior research on judgments of schematic faces (Pettibone & Wedell, 2007). Regression analyses support the conclusion that the lack of correlation was not due to differences in the slopes of judgment functions between and within participants.

One interpretation of the lack of correlation between these two effects is simply that the judgment-mediated model fails to account for shifts in ideals. Alternatively, it may be that the judgment-mediated model fails only to account for shifts in ideals when contexts change within subjects, possibly because of different factors affecting carryover for these two types of judgments. The fit of the judgment-mediated model to the data described in Table 3 supports this alternative interpretation. The judgment-mediated model predicted shifts in ideal points well for the first distribution judged, but not for the second distribution judged. The reduced correlations between individual and group ratings for the second distribution (shown in Fig. 5) suggests that participants may be somewhat idiosyncratic in whether they shift ideal points with the shift in context.

Experiment 2

In Experiment 2, a faster tempo Beatles song was used to investigate ideal point shifts in tempo preference. Paperback Writer (PBW) was chosen because it has an original tempo speed of 156 bpm (Leonard, 1994). We tested whether a faster song would produce more symmetrical ideal-point shifts. If participants do not shift toward slower than normal tempo values in the slow context using a faster tempo song, then it may be that musical stimuli produce inherently asymmetrical context effects. Such asymmetry may be the result of a generally positive correlation between tempo and liking for the song (LeBlanc et al., 1988, although see Geringer, 2010, for an exception). On the other hand, if participants shift equally toward slower and faster than toward original tempo values, we will conclude that musical stimuli can indeed produce symmetrical context effects for tempo. Another possibility is that the asymmetry might reverse, with participants more willing to shift to a slower tempo than a faster tempo for fast-paced music. This result would be consistent with Geringer, who found a preference for faster versions of slow paced songs and slower versions of fast paced songs. It would also be consistent with Moelants’ (2002) assertion that there may be a preferred tempo centered near 120 bpm.