PARTICIPANTS

29 undergraduates from the University of North Carolina at Greensboro's School of Music, Theater and Dance participated in return for a snack of their choice. All participants were enrolled in either the Bachelor of Music, the Bachelor of Music Education, or the Bachelor of Arts in Music programs. Median age was 20, and the group included 15 men, 13 women, and 1 genderqueer individual. Participants indicated the number of years they had studied music (0-5, 5-10, 10-15, 15+; for analysis purposes, these were coded using 4 random variables for each possible option), whether they had "some degree of absolute pitch," and their primary instrument.

MATERIALS AND PROCEDURE

All auditory stimuli were presented using in-house software written in MaxMSP (Zicarelli, 1998). Participants interacted with an external Apple Pro keyboard and listened with noise isolation headphones. The MIDI velocity value was set at 100 for the duration of the test, but participants were allowed to adjust the volume to their comfort level before the test began. MIDI patch 0 ("acoustic grand piano") was used throughout. The test was conducted in a soundproofed booth, and at the end participants were debriefed on the purpose of the experiment. Pitch height was randomized for each participant, with the program choosing a number between 45 and 65, using that number as the central MIDI pitch, and generating the experiment's pitch material from that central note. MaxMSP tracked the keystrokes for participants' tapping: a tap on a pulse was defined as occurring any time between the program's initiation of a pitch and the initiation of the following pitch.

The test proceeded in two parts, the tonal orientation and the forced-choice task. The tonal orientation included a I-IV-V7-I progression played three times, with each chord lasting 900 milliseconds. The voicing of the three chords was neutrally represented as three ordered sets, [0, 7 16], [-7, 9, 17], and [-5, 11, 17], where the central MIDI pitch is added to each number to create the sounding pitch sets (i.e., 0 represents the key's tonic pitch, 7 would be the dominant pitch seven semitones above, -7 would be the subdominant pitch 7 semitones below; the changing pitch level of the tonic changes the pitch level of the whole progression.)

In the forced choice task, participants heard a melody consisting entirely of two oscillating pitches. In order to mitigate the effect of leaps on accent perception, only pairs of scale degrees separated by whole-step were used. There were four instances of scale-degree pairs: ^1-2, ^2-3, ^4-5 and ^5-6 (in C major: {C-D}, {D-E}, {F-G}, and {G-A}, respectively). This distribution allowed us to control for biases toward lower or higher pitches: in two of these cases, the more stable/probable degree is lower, and in two it is higher. In order to not introduce bias toward the initiating pitch, the switchback pattern was randomized (i.e., ^1-2-1-2… versus ^2-1-2-1…), and the melody faded in over 7 seconds by adding a compounding value of 15 to each of the first 20 MIDI onsets' velocities. The crescendo began immediately after the tonally-orienting chord progression. When velocity reached 300, the value was constant for the remainder of the experiment. Fade-in began immediately after the orientation. The inter onset intervals (IOIs) were 350 milliseconds, (a tempo chosen to encourage duple groupings; London, 2004), and each note's duration was 315 milliseconds. Participants were asked to tap the spacebar on which of the two pitches they heard as the stronger pulse. The test ended when the participant had tapped 21 times. Participants were given at least one test version of the experiment; their responses were only recorded once they indicated that they understood the instructions and were comfortable with the tasks.

Participants were each given 3 trials after a single practice trial, with parameters randomized between each trial and the tonally-orienting chord progression occurring before each; each participant's session took approximately 3 minutes. Preference for a pulse was defined as tapping on a pitch more than 14 times (or > 66% of taps). Given the literature surrounding tonal/metric hierarchies, we hypothesized that participants' preference for more-stable pitches would yield an 80% effect size: given that a relatively strong effect was hypothesized, we aimed to recruit between 25 and 30 participants, a sample size in which a strong effect would be visible. The null hypothesis was that stability had no effect on the participants' behavior, and the pulses on which they tapped would follow a 50/50 – a p(.5) – distribution: following a two-tailed binomial distribution, fewer than 10 or more than 19 positive responses would be sufficient to reject this hypothesis with greater than 95% confidence. Given that the hypothesized effect was 80%, testing 29 recruited participants gave a power of 89.1% against a null hypothesis of p ≤ .05.

PARTICIPANTS

48 undergraduates and graduate students enrolled in music programs at UNCG participated in return for a variable cash sum. Median age was 20, and 28 participants identified as women, 19 as men, and 1 as genderqueer. Students who participated in the previous experiment were allowed to participate in this experiment. (Anecdotally, there seemed to be much overlap between participation in this, the previous, and subsequent studies; however, given that each participant was anonymized in our dataset, specifics concerning any participation overlap are not available. Note that, given the small number of genderqueer participants, it would be especially difficult to retain their anonymity in repeated tests.) Participants again indicated their years of musical training and whether they had absolute pitch.

MATERIALS AND PROCEDURE

The same hardware and software was used as in the previous experiment. To focus attention, the test was presented as a game of chance in which participants were told they would "have the chance to win between 1 and 3 dollars by identifying strong beats." Participants then received a baseline of $1, with 10 cents added for each keystroke on the more frequent pitch, receiving a maximum of $3, the details of which were explained to the participants in a debriefing after the test. Again, participants practiced the tasks at least once before engaging in the recorded test.

The test progressed in three parts: an exposure, an audiating task, and a forced-choice task. For the exposure, participants heard an algorithmically composed pitch sequence lasting five minutes, consisting only of the two notes of the tritone. To control for the possibility that height affected judgments, each participant heard one of two possible "height cases," with higher and lower pitches occurring more frequently in the exposure session, respectively. In each, one pitch had a threefold greater likelihood of being generated than the other. Transposition level was randomized with the program choosing the lower note between MIDI pitches 45 and 65, and the other pitch generated 6 semitones higher. IOIs were 450 m.s., each note had a duration of 200 ms, and MIDI velocity was set at 120. To avoid boredom, foster associations between the exposure and metrical accent, and to practice the forced-choice task, participants were given a "dummy task" – tapping the spacebar during the exposure to group the pitches they heard into metrical groupings, switching between groups of 2 and groups of 3 as they saw fit.

After five minutes, participants removed the headphones and the exposure melody continued to be played over the computer's speakers such that both participant and test administrator could hear it. Participants were then asked to sing the pitch that they heard as more stable of the two. A successful response was recorded if the participant sang or hummed the more frequent pitch; if any other pitch was sung or the response was inaudible, the response was recorded as unsuccessful.

For the forced-choice task, participants used the headphones to listen to a melody that oscillated between the two members of the tritone, fading in as in Experiment 1. They were instructed to tap the spacebar on the alternating note they heard as the stronger pulse. After 30 taps, the test ended. Each of the participant's taps was recorded, and a successful trial was defined as tapping 20 times ( > 66%) on one of the two pitches.

The increased number of participants reflects both a concern that the previous experiment's hypothesized effect may have been too high and that exposure to a non-tonal stimulus may produce less reliable participant responses. We therefore hypothesized that 2/3 (66.67%) of our participants would respond positively to the stimulus. Our null hypothesis again was represented by a p(.5) two-tailed binomial distribution; with 48 participants, 96% of the probability mass is accounted for between 17 and 31 responses, inclusive. Given the participation, the hypothesized effect size yields a power of 55.1%. Additionally, we believed that participants would be strongly drawn to associate the more frequent pitch with stability, and hypothesized an 80% effect positive response rate, yielding a power of 99% against a null hypothesis of p ≤.05.

PARTICIPANTS

28 undergraduates from the UNCG's School of Music, Theater and Dance participated in return for $10. Median age was 20, with 16 men, 11 women, and 1 genderqueer participant. Hardware and software were the same as in Experiments 1 and 2, and again we did not exclude students if they had participated in the previous experiments.

MATERIALS AND PROCEDURE

The experiment progressed in three steps: practice, exposure, and the forced-choice task. A fully-diminished seventh chord (set class [0369]) was chosen as the underlying set since it is both maximally symmetrical and tonally ambiguous when appearing on its own. For each participant, a central pitch between MIDI pitches 45 and 65 was randomly chosen, and the fully-diminished seventh chord was generated by adding three minor thirds above that pitch. For instance, if MIDI pitch 60 (middle C) was chosen, the four pitches would be 60, 63, 66, and 69 (or C, D♯, F♯, and A). This chord is tonally ambiguous in that it could function as a leading-tone seventh chord (vii°7) in four different keys: in the spelling given above, the chord could be in the key of D♭/C♯, E, G, or B-flat.

To practice, the participants heard randomly generated pitches of a fully-diminished seventh and were given the practice task of tapping the spacebar on alternate pitches, entraining to the pulse using groups of two notes. This practice task occurred twice, once without headphones and once with the headphones on.

During the exposure, participants listened to a probabilistically-generated string of pitches from the underlying set. We divided the new larger set into two subsets: the pitches of one of the constituent tritones would have a probability three times greater than those of the other tritone. This allowed for two height cases, with either the pitches of the lower tritone (i.e., [C, D♯, F♯, A]) or higher (i.e., [C, D♯, F♯, A]) being generated more frequently. Following Loui (2012), participants listened to the stimulus for 30 minutes. They were instructed to be attentive, and to not fall asleep, use their phones, or do any other work. To mitigate boredom effects, participants were provided with coloring books, crayons, and colored pencils to use if they desired.

After the exposure session, participants heard an algorithmically generated series of pitches from the same fully-diminished seventh set, now alternating between pitches of the subsets heard more and less frequently in the exposure, randomly choosing one of the notes from each subset. (Using our C-based set, the series would alternate between [C or F♯] and [E♭ or A].) Again, to control for bias toward the initiating pitch, the subset heard first was randomized, and the series faded in as in earlier experiments. The participants were instructed to choose which alternating pulse they heard as the stronger pulse, and to tap the spacebar on that stronger pulse. (Our choice of having two frequent and two infrequent pitches was informed by this task: were participants to hear a single more frequent pitch, each alternating pulse in the forced-choice task would have returned to that single pitch. Participants could have then identifies the same-different-same-different melodic contour, obscuring our findings' relationship to our experimental question.) After 30 taps, the test ended and results were recorded. Again, a successful trial was defined as 20 or more taps on one of the pulses (> 66%).

We hypothesized two potential distributions: a strong distribution resulting from exposure (80% expected positive response) and a weaker effect (66.67% expected positive response). The null hypothesis, a 50% distribution, would have a 97.2% confidence interval between 8 and 20 positive responses. This results in a power of 94.6% given a hypothesized 80% distribution, and a power of 41.7% given a hypothesized 66.67% distribution.

PARTICIPANTS

33 undergraduates from the University of North Carolina at Greensboro's School of Music, Theater and Dance participated in return for a snack of their choice. The median age was 21, and the group included 22 men, 9 women, and 2 genderqueer individuals, allowing for participation overlap with previous experiments. The same hardware and software were used as in previous experiments.

MATERIALS AND PROCEDURE

The stimulus was based on that of Experiment 1: an oscillating whole step, the lowest pitch of which was randomly generated between MIDI pitches 45 and 65. Both notes had IOIs and durations identical to Experiment 1. Two emphasis cases were introduced to induce a feeling of metric accent. Based on the above-cited work on objective rhythmicization, we differentiated the two pitches with velocities of a factor of 10, with one pitch set at MIDI velocity value 50 and the other at 500. The harmonization choices were based on the chords used to provide tonal contexts in Experiment 1, with each constituent note's velocity set at 100 but now with a duration of 900 m.s., ensuring that the sound would sustain over several repetitions of the oscillating pattern. Figure 4 schematizes the potential harmonizations available to the participants, transposed to C. In their non-transposed form (i.e., in relation to a C-D oscillating whole step), the harmonizing chords were G7, F7, and B-flat7. Each dominant seventh exists in only one key: that is, even though no tonic chord is sounded, the tonally-determinate nature of these dominant sevenths will suggest a tonal orientation. Here, the tonal orientations would be C (choice 1), B-flat (choice 2) and E-flat (choice 3), therefore harmonizing C-D as scale degrees ^1-2 (choice 1), ^2-3 (choice 2), or ^6-7 (choice 3). These three choices allowed us to control for the placement of the tonally stable pitch within the whole-step, with ^1 and ^3 being more stable than ^2, and with ^6 and ^7 similar within key profiles.

Fig. 4. The oscillating whole step heard by participants, and their harmonization choices, transposed to C

A potential confounding factor would be the participants' preference to align the louder pitch with the chord tones, a factor taken into account in the ensuing analyses. It was due to this concern that we did not include the other two whole-steps of the major scale, ^4-5 and ^5-6, since their harmonizations (in relation to a C-D whole step, C7 and D7, respectively) both placed one member of the dyad as the chord's root. We also voiced the dominant-seventh chords such that neither pitch of the sounding dyad would appear in the chord if at all possible: to this end, the G7 and F7 omitted the chordal fifths. Two major triads were used as the harmonization choices for the practice and intermediary tasks, one whose lowest pitch was the lower of the melody, one whose lowest pitch was the higher of the melody (C major and D major triads in relation to a C-D whole step).

Each participant engaged in 3 harmonization trials, with all triads preceded by a practice/intermediary task. Between all trials and practice/intermediary tasks, the oscillating whole step and harmonizing chords changed to a different (random) transposition. The practice/intermediary tasks asked participants to choose the triad that "better fits the pattern." By pressing the "1" and "2" keys, participants heard the lower and higher major triads, respectively. After hearing them as many times as they liked, a choice was made by pressing SHIFT-1 or SHIFT-2. The three harmonization trials progressed likewise. Upon hearing the whole step melody, participants tried different harmonizations by pressing the "3", "4", and "5" keys, making their choice by combining that number with the SHIFT key.

The emphasis cases were presented in two possible orders over the three trials (randomly assigned between participants). In the first ordering, trial 1 emphasized the lower pitch and trials 2-3 emphasized the higher; in the second ordering, the emphases were switched such that trial 1 emphasized the higher pitch, and 2-3 emphasized the lower. In both orderings, the emphasis case changed between trials 1 and 2 but not between 2 and 3, allowing us to analyze whether a change in emphasis affected participant response. We hypothesized that participants would gravitate toward harmonizations in which the emphasized note was more consonant, such that G7 and B-flat 7 would be chosen more frequently when D was emphasized and F7 would be chosen more frequently when C was emphasized, with a hypothesized effect of 80%. The null hypothesis was that the emphasized note would not effect which choice was made by participants such that the two possible emphases within each harmonization choice could be accounted for by a 50% binomial distribution. (Given that the number of emphasis cases would be randomly generated and harmonizations would be chosen by the participants, confidence intervals would be calculated during the analysis stage.) Since our experimental and null hypotheses involve categorical responses (the choice between three harmonizations) to categorical variables (emphasized note), a chi-square test was used, and Cramer's V was used to quantify the resulting effect size.