A new illusion in the perception of relative pitch intervals by Maartje Koning A thesis submitted to the Faculty of Humanities of the University of Amsterdam in partial fulfilment of the requirements for the degree of Master of Arts Department of Musicology 2015 Dr. M. Sadakata University of Amsterdam Dr. J.A. Burgoyne University of Amsterdam 2 Abstract This study is about the perception of relative pitch intervals. An earlier study of Sadakata & Ohgushi ‘Comparative judgments pitch intervals and an illusion’ (2000) showed that when when people listened to two tone intervals, their perception of relative pitch distance between the two tones depended on the direction and size of the intervals. In this follow-up study the participants had to listen to two tone intervals and indicate whether the size of the second interval was smaller, the same or larger than the first. The conditions were the same as in the study of Sadakata & Ohgushi. These four different conditions were illustrating the relationship between those two intervals. There were ascending and descending intervals and the starting tone of the second interval differed with respect to the starting tone of the first interval. The study made use of small and large intervals and hypothesized that the starting tone of the second interval with respect to the starting tone of the first interval had an effect on the melodic expectancy of the listener and because of that they over- or underestimate the size of the second tone interval. Furthermore, it was predicted that this tendency would be stronger for larger tone intervals compared to smaller tone intervals and that there would be no difference found between musicians and non-musicians. The findings were in line with the study of Sadakata & Ohgushi and were the strongest for the ascending intervals. Furthermore, the participants over- or underestimated the size of the second interval more with larger intervals. Moreover, musical training and better hearing can help when discriminating smaller intervals. 3 Acknowledgments I would like to thank Makiko Sadakata very much for her guidance throughout the whole process of writing this thesis. Not only was she there to help and advise me, her enthusiasm was contagious and inspiring. Furthermore, I would like to thank Teun Koning, for all his advice and assistance with the analysis of the results and Marit Bohnenn for her guidance during the writing process. Finally, I would like to thank Ashley Burgoyne for his time and effort for being the second reader of my thesis. 4 Contents ABSTRACT 2 PREFACE 5 1. INTRODUCTION 9 1.1 Importance of relative pitch perception 9 1.2 Research question 14 1.3 The Implication-Realization model 16 1.4 Hypothesis and expected outcome 19 2. METHODS 24 2.1. Participants 24 2.2 Materials and experimental design 24 2.3 Procedure 27 3. RESULTS AND DISCUSSION 29 3.1 Pitch discrimination test 29 3.2 The self-report questionnaire from Goldsmith University of London 29 3.3 Perception of relative pitch interval, main experiment 30 3.3.1 Results correct response rate 30 3.3.2 Results error type 33 3.3.3 Correlation 37 3.4 Discussion 39 4. GENERAL DISCUSSION 42 4.1 General finding 42 4.2 Future research 42 REFERENCES 44 APPENDIX A 47 APPENDIX B 49 APPENDIX C 50 5 Preface The human ear is extremely sensitive to pitch relations and sequences of occurring pitches. Sensitivity to pitch relations, often called relative pitch, refers to the ability to produce, recognize, or identify pitch relations (Thompson, 2009). It is the ability of the listener to identify and compare given notes to a reference note. This sensitivity to relative pitch can be seen as fundamental to the perception and cognition of tonal music and is a foundation for psychological models of tonal music (Thompson, 2009; Russo & Thompson, 2005a). Intervals are an important aspect in the discussion about relative pitch perception. An interval is the distance between two tones and is either formed when two tones are sounded simultaneously or sequentially. Musically trained listeners associate these intervals with certain labels. For example, in Western music intervals are traditionally labelled with quality (perfect, major, minor, augmented and diminished) and number (unison, second, third, fourth, etc.). The size of the interval depends on the number (the bigger the number, the larger the interval). Another element that is central to Western tonal music is musical key. The establishment of a key begins with a collection of tones that have a hierarchical function in which some pitches are more stable than others. For Western music the most common tuning system is the equal temperament tuning. It is a collection of a set of tones acquired by dividing the octave into 12 equal logarithmic steps. The smallest interval, 1/12 of an octave, is called a semitone. In a chromatic scale each step represents a semitone interval (figure 1), while the major scale is made out of seven tones. The sequence of intervals between the notes of a major scale is: whole note, whole note, half note, whole note, whole note, whole note, half note. Figure 2 shows the sequence of 6 intervals based on the key Major C. Based on their interval pattern; scales can be put into categories like the diatonic, chromatic, major and minor scale. Figure 1: Ascending and descending chromatic scale. Retrieved from http://www.rpmseattle.com/of_note/west-meets-east-notation-playback-of-quarter-tone-music-using- sibelius/ Figure 2: An example of C Major, with the sequence of intervals (whole, whole, half, whole, whole, whole, half). Retrieved from https://en.wikipedia.org/wiki/Scale_(music) Intervals smaller than a semitone are called microtones and microtonal music can refer to any music containing microtones. Before the use of the word microtone, the word “quarter tone” was used, but this was causing some confusion because it could refer to intervals half the size of a semitone, but also for all intervals smaller than a semitone. The quartertone scale is considered to be a theoretical construct in Arabic music. The easiest way to describe quartertones is a pitch that falls halfway between a semitone (half tone) in the traditional Western chromatic scale. Instead of dividing an octave into 12 steps, they can be divided into 24 steps (figure 3). 7 Figure 3: An octave divided by 24 quartertones. Retrieved from http://www.rpmseattle.com/of_note/west- meets-east-notation-playback-of-quarter-tone-music-using-sibelius/. Listeners also appear to be sensitive to relation among keys. To represent the relationship between diatonic scales the circle of fifth is often used (figure 4). The note names on the cycle represent the tonic notes of the 12 major or minor keys. The numbers on the inside of the cycle show how many sharps or flats the key of the scale has. For example C is closely related to its neighbours G and F, and most distant from the key of F#. The number of tones shared between keys decreases as the distance in steps between keys increases (Thompson, 2009). People are also exceptionally sensitive to pitch relations; this sensitivity is often called relative pitch. It refers to the ability to produce, recognize and identify pitch relations. Because of this sensitivity to pitch relations, people can recognize a melody even if it is sung in a different voice or performed on different instruments. On the contrary, people are less sensitive to isolated tones. When they hear a familiar song they do not recognize it because of the 8 individual pitches, but because of the relationships between those pitches. They can quite easily tell if a tone is high or low, but to identify the exact pitch is for most Figure 4: Circle of fifths showing major and minor scales. Retrieved from https://en.wikipedia.org/wiki/Circle_of_fifths. people too difficult. This identification or recognising of individual pitches is called absolute pitch. Absolute pitch is rare, whereas most listeners are sensitive to relative pitch. This sensitivity to relative pitch is fundamental to our understanding of music. The current thesis aims at investigating whether the perception of distance between intervals depends on the direction and size of the intervals. In the introduction I will first touch upon the theoretical background, thereafter the research question is explained. To explain the expected outcome there will be touched upon the Implication-Realization model of Narmour, ending the introduction with the hypothesis. 9 1. Introduction 1.1 Importance of relative pitch perception As explained earlier, sensitivity to relative pitch is an important skill when listening to music. Nonetheless absolute pitch seems to be innate, but this skill usually disappears when it is not repeatedly trained. Those who do not get musical training at an early age seem to shift from sensitivity for absolute pitch to sensitivity for relative pitch (Deutsch, 1972). In a study with 8-year-olds Saffran and Griepentrog (2001) found out that babies recognize and remember absolute pitch while the adults focus on the relationships between the notes. This finding suggest that at some point babies stopped noticing the absolute pitches, probably because they offer little valuable information. “Somewhere along the line, we stop paying attention to absolute pitch,” states Saffran (Saffran & Griepentrog, 2001). A reason for this shift could have something to do with speech. In English language, it is more important to be sensitive to relative pitch. A rising tone at the end of a sentence indicates that someone asks a question, and a child knows if it gets punished or loved by the tone of voice of the mother. Thus, relative pitch is more important than recognizing separate pitches.