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Participants showed learning of directed interval listeners may have attuned to intervals in some of the pairs, but not intervals possibly due to the more tonal above experiments to complete the tasks. For example, nature of interval successions within familiarization. In the subsequent trial phase, participants heard transformations P, I, R, RI of the two rows and were asked to categorize each transformation as 1 or 2. Experiment 3 was similar to Experiment in a number of diverse ways, by espousing 2, except the rows were presented in a variety of rhythms several views: 1 that it is based on group-theoretical and tempi.

In both experiments, participants correctly principles Babbitt, , ; Forte, , 2 that it categorized rows at above-chance levels.

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DOI: Listeners had a mean Participants in other studies on twelve-tone percep- age of Bigand et al. They reported to have stud- first presented participants with a familiarization ied their instrument for an average of The canons contained transformations of a single theory.

In ory and aural skills classes. They were paid for their each forced-choice trial, listeners heard two canons and participation. The Participants were randomly divided into two groups. Both musicians and non- an average of They may have done so by 0. This At the end of the experiment, all participants were initial interval was exposed due to the nature of the administered a questionnaire about their background imitative canons, providing participants with a success- and music training, along with a short item pitch- ful strategy for choosing correctly during the trial phase.

Six of the 20 participants had AP. Responses between AP and non-AP possessors were After finding that the same learning processes underlie compared, and no main effect for AP was found. The experiment took place in a small room. Participants The present study builds upon these earlier experi- were tested individually, and responded to prompts on ments by further exploring the perception of intervals in an iMac computer while hearing the music stimuli twelve-tone music.

Specifically, Experiments 1 and 2 through headphones. Responses were collected using Experiment Cre- a question not asked in the empirical literature to date. Therefore, the familiarization phases ated by the Sibelius notation software program ver- herein consisted of a single, monophonic twelve-tone sion 6 and exported as.

All stimuli were row followed by its 48 transformations, where each played by the same piano sound sample from the pitch was heard the same number of times as any other. Sibelius Sounds Essentials bank that came standard It was hypothesized that the repetitive pitch intervals with the program. Each note was heard individually embedded in the familiarized row would be learned. A The row used as source material for Familiarization Phase 1 heard in Experiment 1 , showing the pitch intervals between adjacent notes.

B The row used as source material for Familiarization Phase 2 heard in Experiment 2.

Just Intonation in Renaissance Theory and Practice

PROCEDURE a twelve-tone composition to use all 48 of its row trans- The experiment contained five different phases: formations, all were presented to ensure that no trans- 1. As in Saffran tion is whether listeners brought to the experiment any et al. There were no pauses between any of the notes therefore ratings of short melodies were obtained prior for the entirety of the familiarization phase.

Notes ran- to familiarization. Group 1a rated 24 two-note melodies ged from F3 to F 5. The author composed the row to highlight repetitive Throughout, I refer to the distance between pitch in intervals and directed interval pairs.


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Figure 1a illustrates semitones. Group 1b rated the row, with intervals 1 and 3 being most frequent. Melodies ranged from C4 to C5. It was Both groups rated the short melodies on how often hypothesized that the frequency of these intervals would they occurred in music heard throughout their lifetime be learned. It was also hypothesized that listeners would scale, where 1 was never and 7 was very often. Participants This stems from the fact that Familiarization Phase 1 could take as long as they wanted to rate each melody, consisted of transformations of a derived row, built and trials were ordered randomly for each participant.

They were not given any learning studies e. However, the additional information.

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Listeners Familiarization Phase 1 was made up of the row were asked to learn the motive as a series of rules: the shown in Figure 1a, heard in its 48 transformations. While it is uncommon for descend , and the motive started on any note. Examples of partmotives in Familiarization Phase 1. In Saffran et al. The motive versus a partmotive 6 trials. This While the motive was heard as many combinations of condition tested whether listeners could recognize notes, what remained constant were its directed pitch the often-occurring motive over less frequent intervals.

A partmotive spans a motive bound- 3. In any row, forced-choice test.

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Each trial contained two three-note there are six possible within-row partmotives. A partmotive versus a nonmotive 4 trials. These there was no time constraint on making the decision in comparisons were foils, inserted randomly so that each trial. After participants made their selection, the listeners were less likely to notice that the motive next trial began. The three-note melodies heard during always appeared as one of the two forced-choice the test phase started on a variety of notes and ranged options in the above conditions.

Nonmotives were from C4 to C5. There were three types of comparisons: would have appeared different from the motive. A one-sample t-test comparing chance.

Music Theory: Intervals as Ratios (Just Intonation)

The motive versus a nonmotive 11 trials. This mean performance in this condition was not condition tested whether listeners could recognize significant.


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  • Motives were tri- identical to the first familiarization phase and lasted for chords that could start on any note and contained These lures were prompt asked listeners to rate how often the short mel- chosen because they contained pitch intervals less ody occurred in familiarization scale, 7 being very than 7 mimicking the small size of intervals heard often.

    Trials were again randomized differently for each during familiarization , and were heard in a variety participant. It was hypoth- Contour is, of course, an important aspect of melody esized that Group 1b would rate motives higher than perception Deutsch, ; Dowling, ; Quinn, partmotives and nonmotives, because motives occurred Nevertheless, listeners chose motives over nonmo- more often during familiarization. In this test, the main research tion some occurred infrequently when one row question was whether listeners would rate common connected to another.

    Results mean ratings between repeated trials did not differ suggest that Group 1a learned the within-row intervals significantly. These means Post-exposure forced-choice test. Further- groups: Group 1a rated melodic intervals, and Group more, ratings for common within-row intervals intervals 1b rated melodic trichords. For example, some nonmotives in the motive vs. A two- combined for the two groups in the forced-choice test. There was no significant difference in mean performance between these two types of trials: a mean significantly higher than chance.

    A Two-alternative forced-choice test in Experiment 1. B Mean post-exposure ratings of trichords in Experiment 1. C Two-alternative forced-choice test in Experiment 2. D Mean post-exposure ratings of trichords in Experiment 2. In 3a and 3c, asterisks indicate the mean is significantly different from chance 0. D-scores of motives for intervals heard on a daily basis. Post-expo- motive and other nonmotives did not.

    Motives were rated significantly higher motive. Experiment 2 It is possible that listeners learned the intervals in Experiment 1 due to the nature of the particular inter- vals heard during Familiarization Phase 1 it was pre- dominated with intervals 1 and 3. A The bar graph shows the distribution of pitch intervals nearly identical to Experiment 1, except that a new heard in Familiarization Phase 1 and the line illustrates mean post- group of participants heard a different row that empha- exposure ratings of intervals in Experiment 1.

    B The bar graph shows sized intervals 2 and 5 in the familiarization phase. Another set of listeners from the Eastman School of Music participated in Experiment 2. Listeners 12 to the familiarization phase. Listeners were volunteers and were paid for Experiment 1 suggests that listeners implicitly learned their participation. Like in Experiment 1, they had no the intervals and directed interval pairs from formal theory training in nontonal music. An AP test familiarization: administered after the experiment found that two of the subjects possessed AP as determined by the same Post-exposure forced-choice test.