Probe Tone Paradigm Reveals Less Differentiated Tonal Hierarchy in Rock Music

Our experiment and confirmatory analysis plan was pre-registered on Open Science Framework. These materials, including our raw data and analysis code, can be viewed at www.osf.io/btc3w.

Participants (n = 37) were recruited through introductory music theory courses at the University of Lethbridge. All participants were compensated for their participation with course credit. The sample reported a mean age of 21.30 years (SD = 2.37). Twenty-five participants reported their gender as “Female,” 12 reported their gender as “Male,” and 0 participants reported their gender as “Neither / Other.” Twenty-eight participants reported formal music training, with a mean duration of 6.95 years (SD = 5.79), and a mean age of onset of 10.04 years (SD = 5.54). Twenty participants reported currently playing music, with a mean time spent playing per week of 12.00 hours (SD = 11.64).

All stimuli were assembled in the Reaper 5.981 Digital Audio Workstation environment. All stimuli were composed using the Kontakt 5 sampling platform with MIDI instruments selected from Native Instruments’ Kontakt Komplete 11 libraries to best emulate classical or rock styles. Rock stimuli were produced using the Electric Sunburst MIDI instrument and Hi Gain Rock School amp setting to emulate an electric guitar. Classical stimuli were produced using The Grandeur MIDI instrument to emulate a grand piano.

Each excerpt consisted of a cadence (I - IV - V - I) that established the key context (see Figure 2), followed by a probe tone. The excerpt was played at 120 beats per minute (500 ms per beat). Each chord in the cadence lasted two beats (1,000 ms). Following the cadence, there was a one beat (500 ms) silence, followed by the probe tone, which lasted two beats (1,000 ms). The probe tone was always presented at a pitch height within the octave below the highest tonic pitch in the context (Figure 2). To create repetitions, the excerpts were presented in eight different keys (A, A♭, B, B♭, D, D♭, E, E♭). Combining this series of manipulations resulted in a total of 192 experimental excerpts (2 Styles x 12 Probe Tones x 8 Keys).

The experimental stimuli were presented on a computer running OpenSesame 3.1 (Mathôt, Schreij, & Theeuwes, 2012), and responses were collected via mouse click. Participants were tested in a quiet room, with sound presented using closed back headphones.

Trials were presented in two style blocks: Rock and Classical. The order of presentation of these blocks were counterbalanced between participants. Participants were not told the order in which the blocks would proceed. Before beginning the trial blocks, participants were given six practice trials chosen randomly from one of either the classical or rock block. Following the practice trials, participants were given the following instructions:

On each trial participants were given the following instructions:

The experimental session lasted approximately 30 minutes.

As a first step, we calculated intersubject correlations in order to quantify the degree of consistency in ratings across participants. A 24-point ratings vector was calculated for each participant (collapsing across Key, which was considered a repetition variable), providing an average rating for each of the 12 probe tones, in both styles. Correlations were then calculated across each of these participant vectors. The average intersubject correlation was r(22) = .40, p = .05, range [-.58, .97]. The average intersubject correlation was not meaningfully different between Classical, r(22) = .43, p = .04, range [-.84, .98], and Rock, r(22) = .43, p = .04, range [-.79, .98]. One can compare for reference, Krumhansl and Kessler (1982), who observed an average intersubject correlation of .59 for their major and minor tonal profiles, and Vuvan et al. (2011), who observed an average intersubject correlation of .27 for their minor tonal profiles. Thus, although there were significant differences between participants’ tonal profiles, our participants as a group showed a substantial amount of agreement in their tonal ratings for both classical and rock music. This agreement allowed us to calculate aggregate profiles for classical and rock, which were submitted to the correlation analyses reported below.

Ratings were submitted to repeated measures ANOVA, with Style (Classical, Rock) and Probe Tone (1–12) as within-subjects factors. There was no significant main effect of Style, F(1, 27) = 0.36, p = .55, GES = .004, indicating that the average rating across all probe tones was equivalent for Classical and Rock. As predicted, there was a significant main effect of Probe Tone, F(1, 27) = 80.88, p < .001, GES = .60, indicating substantial variability in ratings across probe tones. Finally, as predicted, there was a significant interaction between Style and Probe Tone, F(1, 27) = 8.50, p = .007, GES = .06. This interaction suggests that the pattern of probe tone ratings (i.e., the tonal hierarchy) differed between Classical and Rock (Figure 3).

Further characterizing this Style by Probe Tone interaction, the classical tonal hierarchy consisted of a larger spread of values (SD = 0.86; range = 2.72) than the rock tonal hierarchy (SD = 0.79, range = 2.63). This difference is consistent with the theoretical description of the rock profile being less differentiated than the classical profile.

To explore whether musicianship had an effect on our observed results, we submitted the ratings to a repeated measures ANCOVA with Style (Classical, Rock) and Probe Tone (1–12) as within-subjects factors, and years of self-reported formal music training as a covariate. The results were identical, with no main effect of Style, F(1, 27) = 0.36, p = .55, GES = .004, a significant main effect of Probe Tone, F(1, 27) = 80.88, GES = .60, and a significant Style x Probe Tone interaction, F(1, 27) = 8.50, p = .007, GES = .06. A second ANCOVA in which age of onset of formal music training was substituted for years of training again yielded the same pattern of results, with no main effect of Style, F(1, 27) = 0.36, p = .55, GES = .004, a significant main effect of Probe Tone, F(1, 27) = 80.88, GES = .60, and a significant Style x Probe Tone interaction, F(1, 27) = 8.50, p = .007, GES = .06. Thus, musicianship did not play a meaningful role in the effects of style observed in these data.

To further characterize the differences between our classical and rock tonal hierarchies, we ran a series of correlation analyses that compared our classical and rock profiles to each other, as well as other tonal hierarchies that have been previously published (Table 2). These tonal hierarchies included four probe tone rating profiles from behavioral experiments and six frequency of occurrence profiles from corpus analyses. The four behavioral profiles were the major profile from Krumhansl and Kessler (1982) and the three minor profiles from Vuvan et al. (2011). The six corpus profiles were major and minor profiles for each of a rock melody corpus, a rock harmony corpus, and a classical corpus, all reported by Temperley and de Clercq (2013).

As a first step, we collapsed ratings for each style and probe tone across all participants to obtain a “classical profile” and a “rock profile” from our data (Figure 3). Our classical and rock profiles were highly correlated, r(10) = .93, p < .001. Thus, although the significant Style x Probe Tone interaction suggests that the classical and rock profiles differ meaningfully from one another, they also reflect a shared underlying Western tonal structure, the shape of which can be seen in Figure 1.

Next, we correlated our classical and rock profiles with the previously published tonal hierarchy profiles described above. These correlations allowed us to better describe the differences between the classical and rock profiles. Then, to confirm these descriptive differences using inferential statistics, we calculated correlations matrices for each participant (classical and rock profiles correlated with each of the five previously published tonal hierarchy profiles described above). The correlations in these participant matrices were transformed using Fisher’s r to z transformation to obtain normally distributed z scores, and then these z scores were submitted to paired samples t tests to reveal whether the classical and rock profiles differed significantly in their correlations to each of the test profiles.

Please note that only the analyses involving the Krumhansl and Kessler (1982) and the Vuvan et al. (2011) profiles were pre-registered and were assessed with critical p = .05. The analysis with Temperley and de Clercq’s (2013) profiles were considered exploratory and were assessed at critical p = .05/6 tests = .008.

Correlations with Krumhansl and Kessler (1982) Major Profile We predicted that Krumhansl and Kessler’s major profile better reflects a classical music context than it does a rock music context. This prediction was confirmed descriptively, with the Krumhansl and Kessler profile correlating better with our classical profile than our rock profile (Table 2). However, a paired samples t test performed on our participants further substantiated this claim, with participants’ classical profiles correlating significantly higher with the Krumhansl and Kessler major profile than did their rock profiles, t(36) = 2.31, p = .03, d = 0.38. Figure 4 shows that this effect is subtle, but systematic.

Correlations with Vuvan, Prince, and Schmuckler (2011) Parallel Minor Profiles We predicted that the rock profile would have a higher correlation with the parallel minor tonal hierarchies than would the classical profile. Interestingly, this prediction was not confirmed descriptively, with the classical (major) profile showing higher correlations with Vuvan et al.’s (2011) minor profiles, regardless of which minor type—natural, harmonic, or melodic—was tested (Table 2).

As can be seen in Figure 5, paired samples t tests performed on our participant correlations further substantiated this result, with participants’ classical profiles correlating significantly higher than their rock profiles with the parallel natural minor, t(36) = 2.71, p = .01, d = 0.45, harmonic minor, t(36) = 4.17, p = .0002, d = 0.69, and parallel melodic minor, t(36) = 4.27, p = .0001, d = 0.70.

Correlations with Temperley and de Clercq (2013) Profiles Finally, we correlated our classical and rock profiles with Temperley and de Clercq’s (2013) six corpus profiles (rock melody major, rock melody minor, rock harmony major, rock harmony minor, classical major, classical minor). We predicted that our empirically derived rock profile should be better correlated with the statistics of actual rock music than our classical profile, and vice versa. Furthermore, we expected that our rock profile would show a higher correlation with the minor corpus profiles than would the classical profile.

Our predictions were not borne out by the data. As can be seen in Table 3, the rock corpus profiles correlated almost equally with our classical and rock ratings. A paired samples t test performed on our participant correlations further substantiated this observation, with no significant difference in correlations between participants’ classical and rock ratings and the rock melody major distribution, t(36) = 0.31, p = .76, d = 0.05, the rock melody minor distribution, t(36) = 0.36, p = .72, d = 0.06, or the rock harmony minor distribution, t(36) = 0.78, p = .44, d = 0.13. There was a marginally significant difference for the rock harmony major distribution, t(36) = 2.91, p = .006, d = 0.48, such that correlations were slightly higher for the classical profile than for the rock profile. Interestingly, our behavioral profiles seem to reveal a greater degree of differentiation between rock and classical than do the corpus profiles (Figure 6), which may underlie the lack of correspondence observed in the current analyses.

With regard to the classical corpus profiles, our classical ratings appeared to correlate better than our rock ratings with both the classical major and minor corpora. However, these nominal differences were not borne out by paired comparisons. There was no significant difference in correlations between participants’ classical and rock ratings and the classical major distribution, t(36) = 2.23, p = .03, d = 0.37, or the classical minor distribution, t(36) = 1.13, p = .26, d = 0.19.

In the current experiment, listeners heard short excerpts that primed a major tonality in either the classical or rock style. Participant responses were in high agreement with one another, providing evidence that the aggregated tonal hierarchy profiles measured for classical and rock are reasonably generalizable across individuals. As predicted, the profiles for the two styles were distinct, with a less differentiated hierarchy for rock compared to classical, but also reflecting a shared underlying Western tonal structure. Correlation analyses revealed that the classical profile was significantly better correlated than the rock profile with the major ratings profile from Krumhansl and Kessler (1982) and the minor ratings profiles from Vuvan et al. (2011). However, the classical and rock ratings profiles did not correspond well to distributions found in existing major and minor classical and rock corpora from Temperley and de Clercq (2013).

Our central hypothesis, that the rock tonal hierarchy is less differentiated than the classical tonal hierarchy because of rock’s more permissive tonal structure, was confirmed. Moreover, listeners’ style-specific representations can be evoked using a simple timbral cue, as the classical and rock excerpts were identical except for the instrument they employed. In previous work Vuvan and Hughes (2019) demonstrated that reducing the number of style cues available to listeners weakens the distinction between tonal representations for classical and rock. Thus, in the current experiment, the successful instantiation of distinct tonal hierarchies for classical and rock with minimal stylistic manipulation is notable.

The motivation for using this minimal stylistic manipulation was to keep our stimuli as controlled (in terms of pitch, rhythm, number of onsets and durations) as possible. This control allows us to make a stronger claim about the contribution of top-down knowledge about the pitch structure of different styles. It is possible that the distortion applied to the guitar could have affected the listener’s perception of the rock tonal hierarchy in a meaningful way, given its impact on the presence of various partials heard throughout the harmonic series. However, we find no evidence in our data that listener ratings for the rock stimuli were less reliable than those for the classical stimuli. One could indeed hypothesize that distortion is the sole reason for the differentiated tonal hierarchies in our experiment. We argue, however, that its presence was a necessity for conveying a sense of rock’s style, in which distorted electric guitar is a hallmark. To tease apart the degree to which guitar distortion is responsible for conveying this sense of style is a difficult and necessary question that we hope to engage in future research.

Overall, our results indicate that participants have clearly distinguishable representations of the classical and rock tonal hierarchies, and that these representations can be activated with a single stimulus cue (in this case, timbre). That said, it is possible that expanding the number of stylistic cues presented to listeners might produce more divergent mental representations for the classical and rock styles, and show a more divergent pattern of correlations with the comparison profiles we tested in the current experiment.

Discourse in music theory scholarship dealing with harmony in popular music has produced varied opinions with regard to its overlap with common-practice repertoire. Walter Everett (1999, 2004) among others, embraces a more unified approach to tonal practice in both rock and common-practice music. Other scholars, such as Ken Stephenson (2002), Allan Moore (Moore & Martin, 2018), Alf Björnberg (2007), and Phillip Tagg (2014) have argued that rock’s tonal system is meaningfully distinct from that demonstrated by common-practice repertoire. More recently, computational analyses of various rock corpora (Acevedo, 2017; Burgoyne, Wild, & Fujinaga, 2011; de Clercq & Temperley, 2011; Temperley & de Clercq, 2013) have suggested a tonal system that resembles that used in common-practice music, but with some important differences. Notably, the flattened seventh scale degree occurs more frequently in rock music than it does in common-practice repertoire (Temperley & de Clercq, 2013). This result is reflected by listener judgments of chords (Vuvan & Hughes, 2019). The results of the current study expand this account to show that the listener representations of the tonal hierarchy in rock music are less differentiated than in classical music.

As noted above, our rock and classical profiles were equally correlated to the Temperley and de Clercq (2013) corpus profiles. Given that these authors’ major key rock profile was only strongly differentiated from a standard classical profile for certain tones (i.e., the flattened-seventh scale degree) and that our style primes did not contain this scale degree, it is possible that our rock primes sounded more like weak representations of classical music than a strong representation of rock music. It is possible that tone distributions based on larger more representative corpora of rock and classical music might correspond more clearly with our ratings profiles.

Also unexpected was the higher correlation between the Vuvan et al. (2011) minor key profiles and our classical profile than with our rock profile. Given that our primes provided an unambiguously major-key context, the rock profile’s weaker correlation to the Vuvan et al. minor-key profile makes sense. Absent the modal mixture that rock music usually employs, participants may have heard the rock primes as only weakly depicting the style. In this case, their judgments would have been guided by the bottom-up input which was strongly major. Thus, one goal of future work will be to elucidate which and how many stylistic cues are required to elicit various theorized aspects of pitch structure in rock music. Another important objective will be to test our paradigm using minor key primes in order to better understand the way that modes are represented by listeners in rock contexts.

Some of our recent work (Hughes & Vuvan, 2018) has already demonstrated that increasing the number of stylistic cues in a musical prime can produce stronger differentiation between listener responses to classical and rock music. The current study thus adds to a growing body of scholarship finding evidence for listener representations of pitch structure that are highly sensitive to stylistic context. This line of research contradicts the idea that music from the common-practice era is representative of all Western musics, and challenges music cognition researchers to explore style-appropriate stimuli and models of pitch structure for their experiments.

This work draws on research supported by the Social Sciences and Humanities Research Council.