A new illusion in the perception of relative pitch intervals

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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

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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.

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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.

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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

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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).

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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

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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.

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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. However, this is not the case for Mandarin speakers, for example. They must pay attention to absolute pitch to make sense of the words. Several studies showed that even though people do not know the exact size of the relative pitch intervals, they do make use of such information. A famous and one of the best-known theories about relative interval perception is the gap-fill theory of Meyer (1973). According to his theory, two elements form the basis of the gap-fill melody: the interval that creates a gap, and an interval that fills that gap. It is mostly the case that the larger the gap, the

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more strongly a conjunct fill is implied (Meyer, 1973; Rosner & Meyer, 1986). Thus, a large interval is followed by notes that fall in between the interval, and in that way fill in the gap that it created. “.... incompleteness gives rise to expectations of

completeness”, according to Meyer. Figure 5 shows an example taken from

Geminiani’s Concerto Grosso in E. Minor, Op. 3N No. 3 illustrates a gap-fill melody. The lower graph (a) shows that the gap consists of an octave from a low to a high E and is followed by motion in the opposite direction to fill the gap through a harmonic minor scale down to the tonic E (Deutsch, 1982).

Figure 5: Geminiani’s Concerto Grosso in E. Minor, Op. 3N No. 3, mm 1-4. Lower graph shows gap-fill process. Retrieved from Deutsch (1982).

Another study about pitch interval perception is the study of Huron (2001). It studies the size of pitch intervals. Huron noticed that the smaller the size of pitch interval the easier it is to identify the size of the interval. He explained that melodies most often contains small intervals, and besides that also sound more coherent when comprising a sequence of small intervals. Examining the interval preferences of listeners, Dowling (1986) found that melodies containing small intervals are favoured over melodies containing larger intervals. Furthermore, small intervals are processed more accurately and easily (Deutsch, 1978). A reason for this could be that small intervals are more common in melodies and perhaps listeners are conditioned to

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expect typically sized intervals (Dowling & Horwood, 1986). Across cultures this predominance of small intervals in music is consistent with the idea that this pitch-proximity principle is a musical universal phenomenon (Schellenberg, 1997). These studies suggest that the size of intervals have an effect on the expectancy of the listeners. Not only is it easier to identify smaller intervals, we also seem to prefer melodies build up from small interval and this might be a universal phenomenon. However Carlsen (1981) did found difference in preference of intervals between musicians from different cultures. He showed that listeners have expectancy for pitch contours with intervals of small sizes. He played a sequence of tones and asked musicians from three different countries (Hungary, Germany and The United States) what an appropriate continuation would be. Carlsen found significant

differences between the three groups, indicating that cultural background has an effect on the expectations of a listener. However his method relies on the fact that the

participants were comfortable with improvising and singing the melodies. The results could have had something to do with the singing constraints of the musicians. Huron (2006) further clarifies this effect of singing constraints on the melodic expectancy. He explains that if the given melody is low in pitch compared to the vocal range of the singer, than there will be a natural tendency for the singer to come up with a continuation that rises in pitch. On the contrary if the given melody is high in pitch compared to the singer’s vocal range, then there will be a natural tendency to come up with a continuation that falls in pitch. In other words, the melodic contour will be a reflection of the vocal range of the participant, rather than a universal trend as Carlsen suggests. Bergman (1990) also suggests that our preference for small intervals in melodies could be attributed to vocal limitations. Large intervals are more difficult

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to sing accurately than small intervals, this possibly exemplifies why small intervals are processed more easily than large intervals.

Russo & Thompson (2005a) also studied the influence of different interval sizes on listeners by letting them estimate the size of different intervals. Each interval was formed by two pitches that differed between one half of a semitone and two octaves. Not only were they presented in a high or low pitch, but also in ascending or

descending direction, to find out if this influenced the participants’ estimation. The estimations were larger for intervals in the higher register than for the intervals in the lower register. The descending intervals were also estimated as larger than the ascending intervals. But when ascending intervals were presented in a high pitch register they were estimated as larger than descending intervals and when descending intervals were presented in a low pitch register they were perceived as larger than ascending intervals. Musically trained listeners had the same amount of difficulty differentiating intervals larger than an octave than the untrained listeners. But, for intervals up to an octave differentiation of intervals was greater for trained listeners. Russo & Thompson presumed that trained listeners are sensitive to differences

between intervals up to an octave because of their experience with these intervals. The resemblance in the results for the trained and untrained listeners insinuates that the effects of musical training are not observed for the intervals larger than an octave, maybe because intervals larger than an octave are rare in Western melodies.

Moreover, several studies have shown that it takes longer to process and discriminate intervals larger than an octave (Deutsch, 1969; Deutsch 1972; Deutsch & Boulanger, 1984; Deutsch, 1978).

Narmour also discussed that certain melodies or intervals imply a certain expectation of the listener. The Implication-Realization model (I-R) is a modern

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theory about this melodic expectation. It provides clarification of why certain melody structures provoke these expectations. It was developed by Eugene Narmour and is seen as an alternative to the Schenkarian analysis. A Schenkarian analysis shows hierarchical relationships among pitches in a given certain melody (Beach, 1983). The model of Narmour (1989) focuses more on cognitive aspects of expectation instead of the Schenkarian musical based analysis. Narmour states that melodies often create conscious and unconscious expectations among listeners, as opposed to what is the most probable continuation. For the analyses of the results of this study the

Implication-Realization model plays an important role. That is why (after explaining the research question) in subsection1.3 the Implication-Realization model of Narmour will be further clarified.

To outline the above-mentioned studies, it can be said that people are extremely sensitive to relative pitch and this sensitivity seems to increase due to the amount of received musical training. Thus, this increase in sensibility might explain that in some of these studies there is a difference found in how trained and untrained listeners perceive relative pitch intervals. Nonetheless there are other components that appear to have an effect on the perceived distance of intervals or on the expected continuation of a melody. Pitch size, registral direction (ascending or descending intervals), pitch contour, vocal range and the height of the tones all seem to have an effect on our melodic expectations. These expectancies show to be the same for untrained and trained listeners and this confirms the idea of Narmour’s “genetic code”: “There is no reason not to think that all melodies written and ever to be written conform to a “genetic code” of perception, just as human evolution is partly controlled by DNA”. He continues by saying that scaling reflects an inborn, inherent ability in the physiological mechanism of the brain. Scaling of stimuli is an inherent

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part of human cognition and memory (Narmour, 1989). Smith, Nelson, Grohskopf, & Aplleton (1994), agree with this “genetic code”, as they state that untrained listeners possess implicit knowledge of interval categories. Similarly, Russo & Thompson agree with this statement. According to them interval size perception may come from early stages of processing and pitch analysis arising from later stages. Musical training can enhance better computations and decrease the influences of timbre on pitch-related tasks. Bergman confirms by saying that expectancies are typically considered to represent learned schemas, however perceptual grouping, based on proximity, is considered as innate or primitive.

1.2 Research question

All theory discussed how much we use relative pitch in daily life and when performing musical activities and tasks. However, not many studies directly assessed one’s ability to compare pitch intervals. There is one study by Sadakata & Ohgushi’s (2000) and it examined how well people could judge relative pitch intervals, with the expectation that musicians would perform better than non-musicians. Participants had to listen to two relative pitch intervals and indicate whether the second interval was similar in size, smaller or larger than the first interval. There were four different conditions: UpUp, UpDown, DownUp, DownDown (further explained in 2.2, see figure 6). It is called underestimation when the participants thought the distance of the second interval was smaller than it actually was and it is called overestimation when the participants thought the distance of the second interval was larger than it actually was.

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Figure 6: Four different conditions used in Sadakata & Ohgushi (2000). This figure illustrates the conditions UpUp, UpDown, DownUp, and DownDown. The two intervals in each condition are of the same size.

Contrary to their expectation, there was little to no difference in the ability to estimate the relative pitch interval between musicians and non-musicians. However,

interestingly, the study found that the direction and size of a relative interval affected the perceived distance of the interval. In the UpUp and DownDown conditions (when the direction of the first tone to the second tone was the same as the first tone to the third tone) the participants overestimated the size of the second interval significantly, and in the UpDown and DownUp condition (when the direction of the first tone to the second tone was different from the first tone to the third tone) there was a slight underestimation. Along with these findings they found that participants tended to over- or underestimate the second interval more, when the intervals were larger in size. The tendency to over- or underestimate was not as significant for intervals with a

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smaller size. Furthermore, this study showed that the smaller the interval, the easier it was to determine the size of the interval.

Although the results of the study of Sadakata & Ohgushi are interesting, it remains unclear what causes this tendency to over- or underestimate certain pitch intervals. The aim of this study is to get a better understanding in the perception of relative pitch intervals, by replicating the study of Sadakata & Ohgushi. Does the perception of relative pitch intervals depend on the direction and size of the intervals? Furthermore, will there be a difference in performance between musically trained and untrained listeners. Literature suggests that the sensitivity to relative pitch is something every human being develops, but it can develop more strongly if the listener is

musically trained. If the results of this study show that the same tendency to over- or underestimate is found for trained and untrained listeners, this will back up the idea of a “genetic code” of perception. Also, the usage of musical and non-musical intervals (will be further explained in subsection 1.4) will be a manner to find out if people have developed a higher sensibility for known musical intervals. And to make sure the starting note does not have an effect on the results, two different starting notes were used.

1.3 The Implication-Realization model

In this study the Implication-Realization model of Narmour is used frequently for the analyses of the results. This section will provide for an explanation of this model. Narmour describes his model as follows: “The implication realization model hypothesizes that intervallic continuation, registral direction, and specific pitch (when mode is known) are all separately subject to cognitive prediction and thus dependent on laws of implication and expectancy” (Narmour, 1989). According to Schellenberg

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(1996) his model can be divided into five main principles that form the core of the melodic implications: registral direction, interevallic difference, registral return, proximity and closure. These principles are expressed in terms of pitch direction (upward, downward, or lateral) and interval size.

1. Registral direction

The first principle implies that small intervals imply melodic continuation in the same direction, although large intervals imply a change of direction. Narmour hypothesizes that as a bottom up constant all intervals of a perfect fourth or smaller imply a continuation of registral direction in the original mode.

2. Intervallic difference

The second principle discusses the sizes of implicative and realized intervals. According to this principle small intervals imply similarly sized intervals, however large intervals imply smaller intervals. The exact size of a similar interval is

determined by the registral direction. If the registral direction stays the same, similarly sized intervals means the same size plus or minus three semitones; if the registral direction changes similarly sized intervals means the same size plus or minus two semitones. When listeners hear a large interval (perfect fifth or greater), they expect (if all other things are equal), a change in registral direction and a differentiation of interval. Change of registral direction is defined as ascending/descending, ascending/lateral, descending/ascending or descending/lateral. Reversal is the intervallic and registral opposite of process. Thus, small intervals imply continuation and large intervals imply reversal. Important to note is that the threshold takes place

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at the triton (A4/d5). Augmented fourth implies continuation and the diminished fifth reversal (Schellenberg, 1996).

3. Registral return

This third principle discusses the cases where the second tone of the realized interval changes pitch direction (ascending – descending or descending – ascending) and when it is within two semitones of the first tone of the implicative interval. This principle refers to patterns that are symmetrical (ABA) and approximately

symmetrical (ABA’).

4. Proximity

The fourth principle is based on a general preference for smaller intervals, because of this preference; these small-realized intervals are more implied than larger intervals. Moreover, implications are stronger for smaller sized intervals.

5. Closure

Both pitch direction and interval size contributes to the element of closure and explains how listeners divide a melody. This is when implicative and realized intervals are different in direction and when a larger implicative interval is followed by a smaller realized interval.

These principles are based on perceptual processes that are of importance in audition and vision (Schellenberg, 1996). Furthermore, this model seems to apply to listeners from different cultures and with different musical backgrounds, experience

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and training. Nonetheless, musical training or exposure to specific musical styles might have an effect on melodic expectations.

1.4 Hypothesis and expected outcome

The Implication-Realization model of Narmour is not constructed to be used when the stimuli consists of two intervals. Narmour explains his model using three tones, in which the tone after an interval is looked at. The stimuli of Sadakata & Ohgushi contain four tones (two intervals), but the I-R model could be used if the stimuli are seen as a melodic contour instead of two separate intervals. Additionally, Narmour solely explains what listeners expect to hear; over- or underestimation is not taken into consideration. Nevertheless, taken a closer look at the tendency to over- or underestimate depending on melodic expectancy could be a valuable addition to his model.

The I-R model can help to explain the results in the study of Sadakata & Ohgushi. Participants overestimated the second interval when there was a violation in registral direction and they slightly underestimated the second interval when there was a violation in intervallic difference. The created stimuli in the study of Sadakata & Ohgushi were in violation with the principles of the registral direction and intervallic difference. As explained in figure 7 there was a violation in registral direction in the UpUp and DownDown condition. The third note in these conditions is not in violation with the expectancy of the listener, but according to Narmour listeners do not expect another ascending note

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Figure 7: Violation registral direction in the UpUp and DownDown condition. “Expectation” shows an example of what listeners were expecting to hear.

.

Figure 8: Violation in intervallic difference in the UpDown and DownUp condition. “Expectation” shows an example of what listeners were expecting to hear.

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after the third note. Therefore the distance between the third and fourth note is in violation with the principle of registral direction. Listeners would expect a note in the same direction as the third note, and in that way getting closer to the first note (filling the gap). Moreover, in the UpDown and DownUp condition there was a violation in intervallic difference. The third note is in the right direction, acoording to Narmours model, but listeners do not expect a large interval in a different direction. Thus in case of the UpDown and DownUp condition the third note is in violation with the

intervallic difference principle. Listeners expect the note to change direction after the first interval, but they expect a smaller note to follow up that interval (figure 8). Accordingly it seems that the perception of relative pitch intervals depend on the direction and size of the intervals. When the condition was UpDown or DownUp listeners tended to underestimate the second interval slightly. After the first interval, listeners do not expect a big leap in the opposite direction. According to Narmour and Meyer a tone that will fill the gap is expected, but in the case of UpDown and

DownUp there is a huge leap between the second and third tone, which seems to change listeners perception of the interval. This results in the following hypotheses: 1) Even though two large intervals follow each other up, if there is a violation of

intervallic difference, listeners underestimate the second interval slightly (in the UpDown and DownUp condition). 2) But, when two intervals follow each other up violating the principle of registral direction, listeners overestimate the second interval (in the UpUp and DownDown condition).

Literature suggests that smaller intervals are not only easier and more accurately to process, they also sound more coherent and are favoured over larger intervals. As aforementioned, this might be caused by vocal limitations or because

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melodies consist mostly out of smaller intervals (Huron, 2000; Dowling, 1976;

Deutsch, 1978; Dowling & Horwood, 1986; Schellenberg, 1997; Carlsen, 1981). This is why it is hypothesized that 3) the smaller the interval the easier to determine the size of the interval (the easier the task) and 4) the larger the interval the bigger the over- or underestimation. Figure 9 shows the expected outcome for hypothesis 1, 2 and 4. On the x-axis are the four different conditions (DownDown, DownUp, UpDown and UpUp) and the three different intervals (minor third, augmented fourth and minor seventh). The y-axis shows the amount of over- or underestimation. It is expected that the participants overestimate in the UpUp and DownDown condition and

underestimate slightly in the UpDown and DownUp condition.

The finding from the Sadakata & Ohgushi paper, that musicians and non-musicians showed the same tendency, is in line with Narmour’s idea of a “genetic code”. Untrained listeners indeed seem to possess this implicit knowledge of interval categories and when evaluating the distance of pitches they seem to process the information the same as musicians. But musical training can enhance better computations (Narmour, 1989; Smith et al, 1994; Russo & Thompson, 2009; Bregman, 1990). Thus, 5) musicians might perform better, but they will show the same tendency in over- or underestimation as non-musicians.

Firstly, the participants did an online pitch discrimination test, to find out how well they could discriminate pitches from each other. Thereafter the main experiment began, in which they had to listen to two intervals and indicate whether the second interval was smaller, the same or larger than the first heard interval. They ended the test by filling in a self-report questionnaire from the University of Goldsmith. This questionnaire contained music related questions that determined their self-reported level of musicality.

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Figure 9: Expected outcome. The expected over- or underestimation for the four different conditions and different intervals.

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2. Methods

2.1. Participants

Twenty-seven students (15 female and 12 male), 21 – 59 years old (mean = 26 years), volunteered to participate in the experiment. All were assigned to the same experimental task. In this experiment, informed consent was obtained from all participants. They all declared to not have hearing difficulties.

2.2 Materials and experimental design

Prior to the experiment, the participants read the information brochure (appendix A) and signed the informed consent form (appendix B), to make sure they knew their rights and what was expected of them. After signing the consent form, the individual took part in a pitch discrimination test to determine how well they could discriminate pitch differences. For this the online pitch discrimination test was used (Music and neuroimaging laboratory at beth israel deaconess & harvard medical school, 2015). In the main experiment the participants listened to two pairs of tone intervals and indicated whether the second tone interval was larger, smaller or the same, in comparison to the first pair. These musical intervals, referred to as “M”, differed in length: small, medium and large. Therefore the following musical intervals were used: minor third, augmented fourth and minor seventh, respectively referred to as “m3”, “A4”, and “m7”. For the non-musical intervals, referred to as “NM”, the same intervals were used, only 50 cents (quartertone) below the original interval (Table 1). These non-musical intervals were used for the non-musical condition. Non-musical and musical notes were not mixed.

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The intervals were built up from two different starting notes: 440 Hertz (musical starting note) and 380 Hertz (non-musical starting note). For the ascending intervals, increasing the pitch of the notes, the first note of the second interval is a tritone above the first note of the first interval. In case of the descending intervals, the first note of the second interval is a tritone under the first note of the first interval. For an overview of all the stimuli that were created see Appendix C.

1st_interval ₂nd_interval

Interval type Same Smaller Larger

Small (Musical, minor third +300 +300 +200 +400

Small (Non-musical, minor third +250 +250 +150 +350

Medium (Musical, Augmented fourth) +700 +700 +600 +800

Medium (Non-musical, Augmented

fourth

+650 +650 +550 +750

Large (Musical, minor seventh) +1000 +1000 +900 +1100

Large (Non-musical, minor seventh) +950 +950 +850 +1050

Table 1: The different interval types and the distance in cents between the first note and the second note of the interval (for the first and second interval). The second interval could have the same distance, or was smaller or larger than the first interval.

The tones were created using Praat. Each single tone was created separately and combined afterwards. The cosign filter was applied to each tone. The duration of each tone was 500 ms and the pause between the first and second interval lasted one second. In total, 144 stimuli were created. After analyzing the results three of the stimuli were removed (Musical interval, minor seventh, UpUp, same, smaller and large), as the pitch relationship of the stimuli was not correct. The listening

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experiment was made with Psychopy. At the end of the experiment, the participants filled in the self-report questionnaire that was compiled for the BBC’s Lab UK ‘How Musical Are You?’ program, by the Goldsmith University of London. The purpose of this self-report questionnaire is to calculate the amount of musical activity and to record the self possessed level of several musical skills (Mullensiefen et al, 2013).

The main experiment was conducted on a Macbook Pro (13 inch, Mid 2009) with high quality Sennheiser headphones in a sound proof room.

As mentioned before, there were four different conditions: UpUp, UpDown, DownDown and DownUp. These conditions are the same as the previous study done by Sadakata & Ohgushi, 2000 (figure 1). The first part of the condition (UpUp

DownDown) refers to the direction of the intervals. That is, if it is “Up”, pitch heights from 1 to 2 and 3 to 4: ascending. If it is “Down”, pitch heights from 1 to 2 and 3 to 4: descending. The second part of the condition (UpUp DownDown) refers to the

distance between the first note of the first interval and the first note of the second interval (tone 1 and 3). If it is “Up”, tone 3 was a tritone higher than tone 1. If it is “Down”, tone 3 was a tritone lower than tone 1.

To summarize, there were four different conditions (UpUp, UpDown, DownUp, DownDown), six different intervals (“m3”, “A4”, “m7” in the musical condition (M) and the slightly lower “m3”, “A4”, and “m7 “in the non-musical condition (NM)) and the musical and non-musical intervals both had two optional starting notes (“M1” or “M2” and “NM1” or “NM2”). In the excel sheet, included in the appendix, all these different tones in the different conditions are set out.

The experiment used a within-subject design: all participants were exposed to the same set of stimuli.

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2.3 Procedure

The aim of the experiment was explained to the participants and there was time to ask questions if anything was unclear. They started with the pitch discrimination test designed by Musicianbrain (Musicianbrain.com, 2015). This test is designed to compute the participants’ pitch discrimination abilities. Two tones are presented to them sequentially and they have to indicate whether the second tone is higher or lower than the first. The distance between these two tones will become smaller and smaller, subtracting the point where the participant still hears a difference.To acquire the results of the pitch test an email address was required, for which

koningmaartje@gmail.com was used. The participants were informed that it is common to feel as if they were guessing and that they should continue despite this uncertainty. According to their answer the distance between the notes changed, to find out which pitch differences (Hz) the participant could still hear.

For the main experiment, the first instruction explained the concept of intervals and their task as follows:

“Thank you for your participation. This experiment is about tone interval perception. A tone interval is the distance between two tones. You have to listen to two intervals and indicate, whether the second interval had the same distance or if it was smaller or larger. After each two intervals you have the option to choose if the second interval was 'smaller', 'same', 'larger'. First, there are some illustrations to clarify the concept of intervals and this experiment. You don't have to memorize this. Always press the space bar to proceed.”

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This was followed by the illustrations to clarify the concept of the ascending interval with the second interval being larger than the first (UpUp, figure 10). There were six examples in total, three ascending intervals with the second interval of the same length, larger than the first and smaller than the first. Similar illustrations were given for the descending intervals. These examples were not accompanied by sounds, to prevent the influence of training.

Figure 10: Illustration used for the instruction. Second interval is larger than the first.

The last instruction was given as follows:

“Throughout the experiment, please try to concentrate on the sounds. Again, your task is to indicate whether the second interval was smaller, the same, or larger. If you have any questions, please ask them before you start the session. Ready to start the first listening session? If so, press the space bar.”

The stimuli were presented to them in random order and they could respond using three categories: ‘smaller’, ‘same’, and ‘larger’.

After finishing the main experiment, the participants had to fill in the self-report questionnaire. In total, the whole experiment took about 30 minutes per participant.

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3. Results and discussion

Before analysing the results of the main experiment, the pitch discrimination test and the self-report questionnaire are examined. What follows is a discussion about the findings, separated by the results of the correct response rate and the results of the “error types”. Following are the correlations between the results and musicality (pitch test and self-report questionnaire). Finishing with a discussion about the findings.

3.1 Pitch discrimination test

We found that the participants in our experiment could reliably hear pitch differences At 500 Hertz was 6,8 Hertz on average (σ = 25,4). The percentage represents ones score of the pitch test compared to the average of all respondents.

3.2 The self-report questionnaire from Goldsmith University of London

This test contained 50 questions in total. Questions 1 to 31 could be answered on a scale from 1 to 7. Questions 32 to 38 had different scales depending on the question (lowest 0, highest 11). Questions 38 to 50 were asking for demographic information. The questions were divided into five groups: active engagement,

perceptual abilities, musical training, emotion, and singing abilities. Analysing the self-report questionnaire, two aspects seemed to be of importance: perceptual abilities (question 5, 6, 11, 12, 13, 18, 22, 23, 26) and musical training (question 14, 27, 32, 33, 35, 36, 37). “Perceptual abilities” refers to the accuracy of musical listening skills and “musical training” to the received amount of musical training. A high score indicated a higher accuracy or a higher amount of received musical training. The average of these questions were taken into account. The mean of the total score was 4.52, with a

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standard deviation of 1.07. Among all questionnaires, participants tended to agree more on their perceptual abilities (μ = 5.16, σ = 0.73) while there was a larger variation in how participants answered the musical training related questions (μ = 3.20, σ = 2.02). More variation was found in the amount of received musical training than in the accuracy of musical listening skills.

3.3 Perception of relative pitch interval, main experiment

In this subchapter the results of the main test are analysed and it is divided by the results of the average correct response rate and the average of type of error.

The overall correct response rate of perception of relative pitch interval test was 39% on average. Paired t-test confirmed no significant difference of correct response rates between two starting notes, 440 hertz and 380 hertz (t(26)=0.05, n.s.), therefore the results of two starting notes were averaged. Interestingly, no significant difference of correct response rates between musical and non-musical intervals was confirmed (t(26)=0.27, n.s.). Therefore, the results of Musical and Non-musical intervals were also averaged.

3.3.1 Results correct response rate

Taking a closer look at the correct response rate, the smallest interval had a slightly higher correct response rate than the larger ones (figure 11). This is in line with our predictions; the larger the interval, the more difficult it is to distinguish. However, an repeated measure ANOVA comparing three interval sizes confirmed that this difference was not statistically significant (F(2, 25)=2.08, n.s.).

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Figure 11: Results different intervals, mean correct answers for the minor third, augmented fourth and minor seventh with standard error.

A repeated one-way ANOVA on the mean of correct answers comparing the four conditions (UpUp, UpDown, DownUp and DownDown) indicated a significant main effect of condition (F3,24)=4.18, p<.05). Further analysis indicated that correct response rate of UpUp was significantly higher than UpDown and DownUp (p<.05). (figure 12).

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Figure 12: Results different conditions, mean correct answer for the “DownDown’, DownUp, UpDown, and UpUp condition with standard error.

For analyzing the results for the correct answers a two-way repeated measure ANOVA was used, with intervals “m3”, “A4”, and “m7” and conditions UpUp, UpDown, DownUp and DownDown as within subject factors. The main effect of intervals was marginally not significant (F(2, 52) = 3.0, p = .057, Eta square = .105), but the main effect of conditions was significant (F(3, 78) = 5.8, p <.001, Eta square =.182). There was no significant interaction between conditions and intervals, so the main effect can be interpreted independently (F(6, 156)=1.1, p < .37, Eta square = .04). Using a multiple comparison, the intervals showed no significant difference p>0.05, but there was significant difference found between the conditions. The mean correct answer for the UpUp condition was significantly higher than for the UpDown and DownUp condition (p<.05, figure 13).

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Figure 13: Main result for the different conditions and intervals. The mean correct answer for the intervals “m3”, “A4”, and “m7” in the four different conditions DownDown, DownUp, UpDown, and UpUp.

3.3.2 Results error type

Another way of analysing the results is by looking at the different mistakes the listeners made (referred as the “errortypes” hereafter). Five different “errortypes” are considered: the minus “errortypes” representing the cases when listeners thought the interval was smaller than it actually was, called underestimation, and the plus

“errortypes” representing the cases when listeners thought the interval was larger than it actually was, this is called overestimation. Minus 2 points are given when the second interval was larger than the first, but the participant answered “smaller”, -1 points are

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given when the correct answer was larger, but the participant answered “same” or when the correct answer was same and the participant answered “smaller, 0 points are given when they gave the right answer, +1 points are given when the correct answer was smaller, but the participant answered “same” or when the correct answer was same, but the participant answered “larger”, +2 points are given when the correct answer was smaller, but the participant answered “larger” (summarized in table 2).

Table 2: Five different “errortypes”, depending on the response of the participants and the correct answer.

As table 2 shows, the participants made different types of errors for the three different intervals. A repeated measure ANOVA confirmed that three conditions significantly differ with regard to the “errortypes” (F(2,25)=7.3, p<.01). Further analysis indicated that the mean “errortypes” between m3 and m7 as well as m3 and A4 were significantly different (p < .05). The difference of the mean “errortypes” between A4 and m7 was not significant (figure 14).

Error type Error type Correct answer Response

Underestimation -2 Larger Smaller -1 Larger Same Same Smaller 0 Correct answer Overestimation +1 Smaller Same Same Larger +2 Smaller Large

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Figure 13: Results different intervals, mean “errortypes for the minor third, augmented fourth and minor seventh with standard error.

The analyses of the correct response rate indicated that, in the UpUp and DownDown conditions, participants performed better than in the UpDown and DownUp conditions. Now we turn to the “errortype” analysis. Overall, participants tended to overestimate the second interval in the UpUp condition and underestimate it in the UpDown condition. A repeated measure one-way ANOVA on “errortypes” indicated strong main effect of four conditions (F(3,24)=35.2, p<.0001). Further analyses indicated that all differences between conditions were statistically significant (p<.01), except for DownUp and DownDown (figure 15).

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Figure 15: Results different conditions, mean “errortypes” for the DownDown, DownUp, UpDown, and UpUp condition.

For analyzing the results for the different “errortypes” a two-way repeated measure ANOVA was used, with intervals “m3”, “A4”, and “m7” and conditions UpUp, UpDown, DownUp and DownDown as within subjects factors. The main effect of intervals was significant (F(2, 50) = 12.5 < p < .001, Eta square = .33), as well as the main effect of conditions (F(3, 75) = 32.9, p <.001, Eta square =.57). There was a significant interaction between conditions and intervals, so they can not be looked at separately (F(6, 150)=8.6, p < .001, Eta square = .26). Simple effect analysis indicated that, in general, the UpDown condition was significantly more underestimated than the other three conditions (p<.05). The UpUp was significantly more overestimated than the other three (p<.05, except for “m3”). This tendency was stronger for larger intervals (“A4” and “m7” than for “m3”). We expected the DownDown condition to show a trend of overestimation, and the participants have seem to overestimate the

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second interval in this condition, but not as strong as in the UpUp dondition. The analysis indicated that participants overestimated in the “A4” and “m7” conditions more than the “m3” condition (p<.05, figure 16).

Figure 16: Main result for the different conditions and intervals. The mean “Errortype” for the intervals “m3”, “A4”, and “m7” in the four different conditions DownDown, DownUp, UpDown, and UpUp.

3.3.3 Correlation

Is there any significant correlation between perception of relative pitch intervals and the performance of pitch discrimination, musical listening skills (perceptual abilities), musical training and the total score of the self-report

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questionnaire?

Table 3 shows the correlations of the mean correct answers and table 4 shows the correlations of the mean “errortypes”. The mean of correct answers and the mean “errortypes” did not have a significant correlation with musical listening skills. The mean correct answers for the minor third in the DownUp and UpUp condition did show significant correlation with the total score of the self-report questionnaire,

musical training and the pitchtest (p<.05). There was also significant correlation found in the UpDown condition between the minor seventh and musical training. There was no significant correlations between the mean “errortypes” and musical training, listening skills and the total score of the self-report questionnaire (p>.05). Only in the UpDown condition there was a significant correlation between pitch discrimination and all the interval types in the UpDown condition.

DownDown DownUp UpDown UpUp

m3 Pitchtest Musical training Total Score GS 0,213 0,252 0,202 0,594** 0,619** 0,422* 0,329 0,342 0,182 0,472* 0,510** 0,414* A4 Pitchtest Musical training Total Score GS 0,244 0,286 0,264 0,287 0,029 0,076 0,285 0,366 0,255 0,18 0,046 -0,033 m7 Pitchtest Musical training Total Score GS 0,127 -0,153 -0,276 -0,085 0,162 0,145 0,233 0,507** 0,355 0,196 0,063 0,053

Table 3: Pearson correlation between mean correct answer for each interval + condition and Pitchtest, Musical training and Total score of the self-report questionnaire. (*) p = marginally significant, * p=.01, ** p=.001.

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DownDown DownUp UpDown UpUp

m3 Pitchtest Musical training Total Score GS -0,186 -0,104 -0,098 -0,051 -0,153 -0,149 0,388* 0,161 0,123 -0,304 0,074 0,084 a4 Pitchtest Musical training Total Score GS -0,064 -0,059 -0,042 0,076 -0,127 -0,256 0,544** 0,137 0,106 -0,09 0,251 0,222 m7 Pitchtest Musical training Total Score GS -0,164 -0,082 0,002 0,364 -0,015 0,012 0,468* 0,267 0,311 -0,175 -0,172 -0,159 Table 4: Pearson correlation between mean “errortype” for each interval + condition and Pitchtest. (*) p = marginally significant, * p=.01, ** p=.001.

3.4 Discussion

Overall, the low correct response rate (less than 39% on average) indicates that the task was difficult. It is surprising because relative pitch perception is vital in our cognition of musical melodies. Musical and non-musical intervals were used as a way to check if listeners are more sensitive to intervals as we know them in Western

notation. Two different starting notes were chosen (a musical and non-musical starting note), to tackle the influence a starting note might have on the results. Both the

musical and non-musical intervals and different starting notes showed the same tendency and they did not seem to interfere with the results. This might indicate that, when estimating the size of intervals we are as sensitive to our learned musical

intervals as to less used, less “musical” intervals.

While it was hypothesized that smaller intervals would be easier and more accurately processed, although found, this tendency was not telling. Listeners tended

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to underestimate the smallest interval more than larger intervals (m3 vs. A4 and m7). Interesting to note is that according to Narmour there should be a threshold at the A4, but this interval shows the same tendency as the other intervals.

The findings of the different conditions suggested that the size of the second interval in the UpUp condition was easier to estimate than in the other conditions. But if the listeners did not give the right answer, they overestimated the second interval in the UpUp condition and underestimated in the UpDown condition. In the DownDown and DownUp there is a slight overestimation, but this overestimation was not considerable. It was expected that in the DownDown condition the listeners would show somewhat the same overestimation as in the UpUp condition. A slight overestimation is confirmed in the DownDown condition, however not as strong as in the UpUp condition. Furthermore, in the DownUp condition it was expected to see a slight underestimation, instead there is a slight overestimation. Maybe the tones in the ascending intervals were too low, making it too difficult to judge the size of the

intervals. But leaving the DownUp condition out of consideration, the main results are in line with the hypothesis. If there is a violation in intervallic difference, listeners underestimated the second interval (in the UpDown condition). But when there was a violation in registral direction, listeners overestimated the second interval (in the UpUp and DownDown condition). Moreover, if the interval was larger, the tendency to under- or overestimate the second interval was stronger.

As in the study of Sadakata & Ohgushi, it was expected that musicians and non-musicians showed the same tendency. Nevertheless, the results show that participants with more accurate hearing (higher score on the pitchtest) and more musical training (higher score for the self-report questionnaire) scored better than the other respondents when estimating the second interval in the DownUp and UpUp

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condition for the minor third. Apparently, musical training and better hearing can help when discriminating smaller intervals: small intervals are common in melodies, listeners could learn to expect typically sized intervals (Schellenberg, 1997). But when the more unusual large intervals are being evaluated, the participants seem to find it evenly difficult. Participants with a high pitch test score tended to underestimate the second interval less in the DownUp condition. These results suggest that expectancies are presumed to result from a combination of innate and learned factors

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4. General discussion

4.1 General finding

The current study confirmed the idea that the perception of distance between intervals depends on the direction and size of the intervals. The I-R model of

Narmour showed to be an accurate model to explain the found tendency to over- or underestimate certain intervals. When there were two intervals of the same size, violating the principle of registral direction, listeners seemed to overestimate the size of the second pitch interval. Although when a violation in intervallic difference occurred, listeners seemed to underestimate the second interval. This shows that certain melody structures provoke certain expectations. Melodies create conscious and unconscious expectations among the listener to what is the most probable

continuation. These expectations are derived from innate and learned factors. It seems that listeners with musical training can judge small intervals more accurately than listeners with little or no musical training. Moreover, listeners with musical training overestimated less than listeners with little or no musical training, when there was a big leap in a different direction. Both trained and untrained listeners indeed seem to possess implicit knowledge of interval categories, nevertheless, musical training can enhance better computations.

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4.2 Future research

In a potential follow-up experiment, the experimental design could be expanded. It seems that the third note (or contour) had a big influence on the perception of the size of the second interval. In the main experiment the third note was a tritone higher or a tritone lower than the first note, creating a violation with registral direction or intervallic difference, resulting in over- or underestimation. In theory there should be a threshold in the middle, this is when the third note is the same as the first note, at this point there should be no tremendous over- or

underestimation. This would confirm the hypothesis that if a violation in intervallic difference takes place, listeners underestimate the second interval, and when there is a violation in registral direction, listeners overestimate the second interval. However, this only seems to be the case when using two intervals of the same size. It would be interesting to see the effect of using intervals of different sizes. By doing so, we hopefully gain a better understanding in the way people perceive and judge relative intervals.

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References

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Carlsen, J.C. (1981). Some factors which influence melodic

expectancy. Psychomusicology: A Journal of Research in Music Cognition, 1(1), 12-29. Deutsch, D. (1978). Delayed pitch comparisons and the principle of

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Deutsch, D. (1982). The Psychology of Music. (3rd edition ed.). California: Academic

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Deutsch, D., & Boulanger, R. C. (1984). Octave equivalence and the immediate recall of pitch sequences. Music Perception, 2, 40-51.

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Huron, D. (2001). Tone and Voice: A Derivation of the Rules of Voice-Leading from Perceptual Principles. Music Perception: An Interdisciplinary Journal, 19(1), 1-64. Huron, D.B. (2006). Sweet Anticipation: Music and the Psychology of Expectation. (2nd ed.). MIT Press.

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Meyer, L.B. (1973). Explaining music: Essays and exploration. California: University of California Press.

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Appendix A

Information Brochure for research project “A new illusion in the perception of relative pitch intervals”

Dear participant,

You will participate in a study on pitch perception. Before the experiment starts, it is important that you take note of the procedure to be followed. Please read the

following information carefully. Aim of the experiment

The experiment is about pitch perception. Who can participate in this research

For this study, it is important that you do not have hearing difficulties. You cannot participate in this study if you have a hearing impairment or severe hearing damage. Instruction

You will be asked to sit in front of a laptop and put the headphones on. Before the experiment starts, there will be a short test to see how well you can discriminate pitch. After that the main experiment starts, there are instructions before you start. If you don't understand the instructions, please feel free to ask questions. You can ask as many questions as you like, some of them can be answered only at the end of the experiment. After the main experiment there will be some questions about your musicality.

Voluntariness

If you decide to quit the experiment, or decide to refrain from participating, this will not affect you in any way. Additionally, within 24 hours after the experiment you may withdraw your data. You are free to stop the experiment at any time, without giving reasons. If you discontinue your participation, or withdraw consent within 24 hours, your data will be removed from our files and destroyed.

Confidentiality of the results

The results of this experiment will be documented and used in publications in the academic field. However, your personal details will never be published, so your anonymity is guaranteed.

Safety and insurance

Experiences from earlier experiments show that this type of experiment does not pose any health or safety threat to participants. Therefore, no additional insurance was taken out to perform this experiment.

Further information

If you would like to have more information about this research project, you can contact Maartje Koning (phone number: 00316-17996509, e-mail:

koningmaartje@gmail.com). Any complaints about this experiment can be sent to the Secretary of the Ethics Committee of the Faculty of Humanities of the University of

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Amsterdam: e-mail: commissie-ethiek-fgw@uva.nl, phone number: 003120-525 2543, address: Spuistraat 210, 1012 VT Amsterdam).”

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Appendix B

Informed consent form used for research project “A new illusion in the perception of relative pitch intervals”

“Hereby I declare that I have been informed elaborately about the content and methods of this experiment, as described in the information brochure “Information brochure for the research project “Perception of Intervals”. My questions were answered satisfactorily.

My participation in this experiment is fully voluntary. I may quit at any moment and without further explanation. If the results of the experiment will be used in a

publication or disclosed in any other way, my anonymity will be guaranteed. My personal details will not be shown without my permission to others than the research team.

If I would like to have more information about this research project, I can contact Maartje Koning (phone number: 00316-17996509, e-mail:

koningmaartje@gmail.com).

Any complaints about this experiment can be sent to the Secretary of the Ethics Committee of the Faculty of Humanities of the University of Amsterdam: e-mail: commissie-ethiek-fgw@uva.nl, phone number: 003120-525 2543, address: Spuistraat 210, 1012 VT Amsterdam).”

As signed twice in Amsterdam:

………. ……….

Name participant Signature

“I declare that I have given a clear explanation of my research. Whenever there will be questions from a participant about this project, I will try to answer these questions as good as possible.“

………. ……….

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A new illusion in the perception of relative pitch intervals