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The effects of timbre on aural skills: An exploration of the attributes of timbre and spectral parsing for sounds used in aural training
Lochstampfor, Mark Lewis, Ph.D.
The Ohio State University, 1990
Copyright ©1990 by Lochstampfor, Mark Lewis. All rights reserved.
UMI 300 N. Zeeb Rd. Ann Arbor, MI 48106
THE EFFECTS OF TIMBRE ON AURAL SKILLS:
AN EXPLORATION OF THE ATTRIBUTES OF TIMBRE AND
SPECTRAL PARSING FOR SOUNDS USED IN AURAL TRAINING
A Dissertation
Presented in Partial Fulfillment of the Requirements for
the degree Doctor of Philosophy in the
Graduate School of The Ohio State University
by
Mark Lewis Lochstampfor, A. A., B. M., M. A.
O O O 0 o
The Ohio State University
1990
Dissertation Committee
David Butler Approved ^ Lora L. Gingerich Mari Riess Jones L,'Adviser School of Music Copyright by
Mark Lewis Lochstampfor
© 1990 To
Ann L, Lochstampfor for her patience and encouragement
through this endeavor
u ACKNOWLEDGMENTS
So many people influence our lives. Their contributions that affect our success surpass our opportunities to adequately credit and thank each one; to those people in my life—my colleagues, friends in the community, and especially my friends at Parkview
Church—I express my appreciation for your support and friendship. I acknowledge the graciousness of Albert Bregman and Stephen McAdams in furnishing unpublished documents that were helpful in the initial preparations for this study. Acknowledgment also goes to Thomas Wells for providing access to additional electronic sound equipment necessary for preparing the experimental stimuli. Sincere thanks go to the members of my dissertation committee for their assistance in this research effort I express my appreciation to Mari Jones for assistance in designing the experimental research and advice in interpreting the data, and to Lora Gingerich for editorial suggestions beneficial toward obtaining a clearer communication of this work. My most earnest gratitude is extended to David Butler, whose steady counsel and words of encouragement provided me with the countenance necessary for this accomplishment Finally, to my wife, Ann, and my children, Erin and Adam, to whom I am indebted for their relentless patience, understanding, and support through this time-consuming venture, I express my most heartfelt appreciation.
ui VITA
January 22, 1956 ...... Bom - Portsmouth, Virginia
1975 ...... A. A., Lakeland Community College, Mentor, Ohio
1978 ...... B. M., Ohio University, Athens, Ohio
1978-1980 ...... Entertainer, Joe Gadd and Associates, Inc., Aurora, Ohio
1980-1985 ...... Instructor of Piano and Music Theory, Conservatory of Piano, Columbus, Ohio
1985 ...... Consultant/Instructor of Music Theory Encore Music Studios, Westerville, Ohio
1980-Present ...... Music Director, Parkview Presbyterian Church, Reynoldsburg, Ohio
1985-1990 ...... Graduate Teaching Associate, The Ohio State University, Columbus, Ohio
1986 ...... M. A., The Ohio State University, Columbus, Ohio
1990- ...... Adjunct Professor of Music, University of Rio Grande, Rio Grande, Ohio
IV FIELDS OF STUDY
Major Field: Music
Music Perception and Cognition, Acoustics ...... David Butler Schenkerian and Post-Schenkerian Theories ...... Gregory Proctor Music Theory Pedagogy, and CAI progranuning ...... Ann Blorabach Electronic Music ...... Thomas Wells Set Theory ...... Lora Gingerich History of Music Theory ...... Burdette Green Gregorian Chant ...... Gertrude Kuehefuhs Counterpoint ...... Gertrude Kuehefuhs, Marshall Barnes, and Gregory Proctor TABLE OF CONTENTS
DEDICATION...... ü
ACKNOWLEDGMENTS ...... üi
VITA ...... iv
LIST OF TABLES ...... vüi
LIST OF FIGURES ...... ix
CHAPTER PAGE
I. STATEMENT OF PURPOSE ...... 1
Introduction ...... 1 Purpose of the Study ...... 2 Need for tlie Study ...... 3 Presumptions ...... 5 Limitations of the Study ...... 7
n. REVIEW OF THE LITERATURE ...... 9
Introduction ...... 9 Studies of the effects of timbrai variation on pitch identification ...... 1 0 Killam...... 10 Bales and Foltz ...... 12 Other perceptual studies of timbre ...... 14 Sergeant ...... 14 Blatter...... 15 Elliott ...... 16 Grey ...... 16 Howell ...... 17 Kubovy and Jordon ...... 19 Wapnick and Freeman ...... 19 Charbonneau ...... 20 Goldman ...... 20 McAdams ...... 21 Weaver ...... 22 Crowder ...... 23 Miyazaki...... 24 Yost and Sheft ...... 24
VI Auditory streaming ...... 25 Summary of the literature ...... 26 Hypotheses ...... 27
m. METHODOLOGY...... 29
Introduction ...... 29 The timbre of the stimuli ...... 30 The pitch-interval stimuli ...... 31 The experimental design ...... :...... 33 Preparation of the stimuli ...... 37 Subjects ...... 38 Administering the tests ...... 38
IV. RESULTS ...... 40
Pretest and posttest observations ...... 40 Data analysis ...... 41 Sawtooth vs. square waveform ...... 49 Synthesized tones vs. traditional instmmental tones ...... 55 Steady-state tones vs. amplitude- and frequency-modulated tones ...... 58 Spectral content ...... 63 Pitch-interval stimulus type ...... 65 Interactions among the variables ...... 6 8
V. CONCLUSIONS ...... 69
Suggestions for future research ...... 70
APPENDICES A. Pitch-interval and timbrai stimuli ...... 75 B . Examples of answer sheets ...... 101 C. Test scores ...... 105 D. Data for subjects who scored below chance levels (S 24) ...... 112 E. Number of correct responses ...... 118 F. Example of data averaged across trial blocks ...... 125 G. Scores for ANOVA ...... 127 H. Analysis of variance data ...... 140 I. D ata...... 142
LIST OF REFERENCES ...... 153
vu LIST OF TABLES
TABLE PAGE
1. Counterbalance design of the trial blocks ...... 34
2. Tested stimulus types ...... 35
3. Principle instruments represented in the population sample ...... 38
4. Conversion of responses to scores ...... 41
vui LIST OF FIGURES
HGURE PAGE
1. Mean scores for each test condition across all 12 timbres for Group S 1 2 . 44
2. Mean scores for each test condition across all 12 timbres for Group S 3 6 . 45
3. Correct responses (%) for each test condition for Group S 1 2 ...... 47
4. Correct responses (%) for each test condition for Group S 3 6 ...... 48
5. Mean scores, Group S 12: sawtooth vs. square waveforms ...... 51
6 . Mean scores, Group Sgg: sawtooth vs. square waveforms ...... 52
7. Correct responses (%), Group S 12: sawtooth vs. square waveforms ... 53
8 . Correct responses (%), Group S 12: sawtooth vs. square waveforms ... 54
9. Mean scores. Group S 12: synthesized vs. natural instrumental tones ... 55
10. Mean scores. Group 8 3 0 : synthesized vs. natural instrumental tones ... 56
11. Correct responses (%), Group S 12: synthesized vs. natural instrumental tones ...... 5 7
12. Correct responses (%), Group 8 3 5 : synthesized vs. natural instrumental tones ...... 5 7
13. Mean scores. Group 8 1 2 : steady-state vs. AM-&FM-modulated tones . 59
14. Mean scores. Group 8 3 5 : steady-state vs. AM- & FM-modulated tones . 60
15. Correct responses (%), Group 8 1 2 : steady-state vs. AM- & FM-modulated tones ...... 61
16. Correct responses (%), Group 8 3 5 : steady-state vs. AM- & FM-modulated tones ...... 62
17. Mean scores. Group 8 1 2 : spectral content ...... 63
18. Mean scores. Group 8 3 5 : spectral content ...... 64
19. Correct responses (%), Group 8 1 2 : spectral content ...... 64
20. Correct responses (%), Group 8 3 g: spectral content ...... 65
ix 21. Mean scores, Group S 12: pitch-interval stimulus effects ...... 6 6
22. Mean scores, Group S 3 6 : pitch-interval stimulus effects ...... 6 6
23. Correct responses (%), Group S 12: pitch-interval stimulus effects . 67
24. Correct responses (%), Group 8 3 5 : pitch-interval stimulus effects . 67 Chapter I
Statement of purpose
Introduction
Musicians’ aural skills include the abilities to perceive pitches of tones accurately
in temporal sequence (melodic aural skills), and within simultaneous patterns (harmonic
aural skills) such as harmonic intervals and chords. These skills affect the abilities of
music students to comprehend more complex musical concepts, theories, and academic
musical coursework, their abilities to perform music as competent soloists and ensemble
members, and ultimately affect their abilities to function well as future performing artists
and music educators. The development of strong atu-al skills is an essential element in
the education of college music students.
We all should be familiar with the “elements of sound”—pitch, duration, timbre,
and loudness—introduced to us in our early studies of music. Two of these elements of
sound, pitch and duration, form the primary bases for aural training.
One of the complaints students frequently raise about aural training is the ambiguity of pitch in the sounds used for aural training exercises. A second commonly voiced criticism is that it is difficult to separate tones in harmonic stimuli such as harmonic interval, chord quality, and harmonic dictation drills. If pitch and duration are the fundamental constituents of aural training exercises, then we should consider what effects are influenced by other characteristics of sound. One such consideration for music theory instructors who teach aural training courses, should be the effect of timbre on the accurate pitch perception of these students.
1 Piano is the instrument traditionaily used in college classrooms for the
development of aural skills. Students’ practice of aural skills outside the classroom is
often accomplished through the use of audio tapes of prerecorded drills, or by use of
computer-assisted instruction (CAI) software. Many music educators who have used
CAI as additional drill for aural skills training have probably heard the common students’
complaint that the pitches of computer-generated tones are difficult to recognize. This
raises the question of whether computer-generated tones, or any other electronically
synthesized tones, succeed or fail to support the development of aural skills. This
concomitantly poses a related question: are piano tones, with their characteristic rapid
decay, the best timbre to choose for developing aural skills?
Purpose of the study
It is reasonable to assume that there are two attributes of sound, belonging within
the broad category of “timbre,” that are critically important to aural skills. These two
characteristics are that: ( 1) sounds used for aural training must provide good pitch
identifiability, and ( 2) perceptual separation of tonal stimuli, rather than perceptual fusion
of tones, is desirable for aural training exercises, particularly for harmonic dictation.
This study examines the correlations between various timbres and higher or
lower accuracy levels of students’ performances of typical aural skills exercises.
Attributes of timbre will be identified and explored as properties of sound, effective for
enriching the pitch identifiability of tones, and enhancing the separation of tones in
sounds used for aural training. This objective will be realized by exploring the effects of
timbre on college musicians’ abilities to recognize and identify intervals, triads and
seventh chords within both melodic and harmonic constructs. This study is designed as the author’s initial survey of the relationship between timbre and aural skills. Need for the study
Timbre is defined in the dictionary American National Standard Psychoacoustical
Terminology (1973, p. 56) as “that attribute of auditory sensation in terms of which a subject can judge that two sounds similarly presented and having the same loudness and pitch are dissimilar.” This is indeed a very general definition. The multidimensional nature of timbre is a complex attribute of sound that is woven into the very fabric containing all other sound attributes. More than a century has passed since Helmholtz
(1863/1954) recorded his theories on the building of timbre. It has been only during the past two to three decades, however, that technology has provided the means for many acoustical and psychological advancements in understanding timbre. McAdams (1980;
1982a; 1982b; 1984a; 1984b) has shown that the spectral fusion, a perceptual process of grouping the spectral components of a tone into a single auditory image, is influenced by various physical attributes of the components. These physical attributes include the coherent application of low-frequency amplitude modulation (AM) and fiequency modulation (FM) on the components, and the coherence of phase of the components resulting firom their synchronous onset. AM may be defined for purposes of this discussion as the alteration of a tone’s characteristics by the amplitude of another
“modulating” tone. FM, by the same reasoning, is the alteration of a tone’s characteristics by the frequency of a modulating tone. The perceptual separation of tones into multiple auditory images can be evoked or enhanced by using asynchronous onsets of the tones, or by imposing different modulation frequencies for AM and FM on those tones. Although phase differences greater than 40° can also be used to support multiple images with short tones (Kubovy & Jordon, 1979), the perceptual significance of phase lies in the phase-locking of tone partials elicited by onset synchronicity (Yost & Sheft,
1989). The psychoacoustic literature on the formation of auditory images (viz. McAdams, 1982b; 1984a; 1984b) supports current theories of the perceptual processing
of aural stimuli into categories of either successive groupings or simultaneous groupings
of stimuli (Bregman, McAdams & Halpem, 1979; Bregman & Pinker, 1978; McAdams,
1985; McAdams & Saariaho, 1985).
Timbre appears to affect absolute pitch judgments (Goldman, 1984; Miyazaki,
1989) and our perception of flamess or sharpness of pitch (Wapnick & Freeman, 1980),
but does it also affect categorical pitch perception? More specifically, does it influence musicians’ recognition of intervals or chords? Categorical perception is a process of grouping the perceived features of physical stimuli along a perceptual continuum into discrete categories even though the attributes of the stimuli may not accurately represent the specific characteristics of those categories. Bums (1977), and Siegal and Siegal
(1977), have shown that the identification of pitch intervals employs systematic judgments and categorizations of the pitch differences between the tones forming the pitch intervals. Categorical pitch perception as examined in these studies, and in the context of traditional Western music, is defined as a twelve-tone to the octave system.
Thus far, variations of timbre have not been found to have a significant effect on aural skills. The studies reviewed, however, have principally focused on intervals, and have used a limited range of timbres for comparisons. None of the pedagogical studies
(Howell, 1976; Killam 1982; Bales & Foltz 1987; Weaver, 1987) has explored the possible effects evoked by specific attributes of timbre such as low-frequency AM and
FM, size of the spectral content, spectral waveform, or the difference within and between traditional instrumental timbres and synthesized timbres.
Application of the findings from psychoacoustic research to the study of sound sources for aural training could prove beneficial. Such a study should focus on the perceptual phenomena of pitch identification, and the fusion and separation of timbres. Attention must also be given to the physical properties of the sounds, most notably, their
spectral content, harmonicity, and the coherence of low-ffequency AM and FM. These
sounds should be examined within the contexts of melodic and harmonic dictation, and
within two-, three-, and four-tone contexts to test for robustness of the timbrai effects.
Presumptions
Sounds used for aural training should allow clear perception of pitch for both
melodic and harmonic presentations. If students can easily identify pitch in a dictation
exercise, improved aural skills should be reflected by increased accuracy levels.
There are at least four properties of sound that may support clearer pitch
perception and elicit higher achievement scores. First, sawtooth and sawtooth-like
waveforms should promote better pitch recognition than squarewave, squ^ewave-like,
or sinusoidal waveforms, for reasons to be discussed later. The waveform of a tone may
be considered to be the general characteristic shape formed by the spectral content of the
tone. Sawtooth waveforms are composed of odd and even numbered partials in a
harmonic relationship to the fundamental frequency, while square waveforms comprise
the odd numbered partials only. The relative amplitudes of the partials for both
waveforms diminish from the amplitude of the fundamental component at a rate that is
inversely proportional to the harmonic number of the partial (Wells, 1981). While
sawtooth and squarewave waveforms may be produced electronically, traditional musical
instruments do not produce such steady-state waveforms. The term spectral envelope is
more useful for referring to graphic shapes formed by the transient and unique spectral
characteristics of traditional instrumental tones. These unique characteristics are in part
due to differences in the relative amplitudes of the tone’s partials. The amplitudes of
some of the partials may be strengthened to form broad resonant amplitude regions called formants. Formants result from a frequency filtering effect, which in turn results from the resonating environment around the source of the tone. Most of our current
understanding of formants is the result of research, conducted in the speech sciences, on
vowel formation and perception. Traditional instruments, however, do produce
waveforms that resemble defined waveforms. These similar waveforms wiU be
designated for the puiposes of this study, as sawtooth-like and squarewave-like
waveforms.
Harmonicity of the spectral content of a tone greatly contributes to perceptibility
of pitch (Slaymaker, 1970; de Boer, 1976; Cohen, 1980; Mathews & Pierce, 1980).
The number of harmonic components may influence pitch perception in aural skills
(Plomp, 1967; Smoorenburg, 1970a, 1970b; Moore, Glasberg, & Shailer, 1984;
Radocy & Boyle, 1988). The presence of only the odd-numbered partials may also
affect pitch perception (Sergeant, 1973; Howell, 1976). Sawtooth-like tones appear to
evoke clearer pitch perception and timbre identification than do squarewave-like tones
(Blatter, 1975; Grey, 1975; Goldman, 1984). This phenomenon may result from the
different inter-relationships between the frequencies of the partials in the two dissimilar
waveforms. The perception of pitch in complex tones is believed to be affected by the rate of repetition of the tone partials above the fundamental pitch (Ritsma, 1962;
Schouten, Ritsma, & Cordoza, 1962; Ritsma, 1963; Schouten, 1970; Terhardt, 1970; de
Boer, 1976). Aural stimuli are spectrally analyzed along a dominant stimulation region of the basilar membrane in the ear (Ritsma, 1970). The pitch resulting from this phenomenon is called the residue or periodicity pitch (Schouten, 1938). Recognition of pitch is also believed to be dependent on comparisons of the stimuli with perceptual models of the basic patterns or features of harmonic spectra called harmonic spectral templates (Goldstein, 1973; Wightman, 1973; Terhardt, Stoll, & Seewann, 1982a,
1982b). A second property of sound that may improve pitch perception is an increase in
the number of partials. It is reasonable to believe that tones with rich spectral content
may elicit better pitch judgments than tones with sparse specttal content. The increased
frequency information from richer spectra may induce better response patterns on the
basilar membrane.
Third, tonal stimuli containing unique low-frequency AM and FM should provide
improved tonal separation for aural training, especially for harmonic dictation tasks
(McAdams, 1984a; 1984b). Separation of tonal stimuli for aural training is dependent
upon clear perception of multiple auditory images, or a single, but complex auditory
image, enhanced by imposition of different AM and FM rates on individual stimulus
tones.
Fourth, tones from traditional musical instnunents should support more-accurate
pitch perception as compared to steady-state tones. Because natural tones do not
conform to the characteristics of ideally defined waveforms, the term spectral envelope is
more accurate for referring to the collective features of a tone’s spectrum. The spectral
envelopes of traditional music instruments include the features of harmonicity, onset
synchrony and phase-locking of the components, coherent low-frequency AM and FM,
and moderately rich spectral content when played at moderate to loud volume levels.
Hence, they should elicit higher accuracy levels on aural skills tasks than synthesized tones, that may contain few to none of these characteristics.
Limitations of the study
This study focuses on the recognition of pitch-interval patterns—intervals, triads, and seventh chords—within both melodic and harmonic contexts. Subjects will be asked to identify pitch-intervals. This study explores timbrai effects on categorical pitch perception, not absolute or intonational pitch judgments. Subjects will not be asked to identify specific pitches (i.e., make absolute pitch judgments), or to make judgments regarding the flatness or sharpness of pitches. No other intonation systems beyond the twelve-tone equal tempered system (A = 440 Hz) will be examined.
Consideration will be given to sounds that may be used in the classroom environment as well as those used in CAI. Attention will be focused on the spectral content of the sounds’ waveforms, and the effects of low-frequency AM and FM, and phase on the tones’ spectra. The spectral content and harmonicity of the components will be examined in relation to pitch identifiability. Testing the effects of low-frequency AM and FM, and phase, will be examined in relation to improvement of tone separation.
These results may show that sound sources for aural skills training may be improved through use of synthesized tones with the properties of unique coherent low-frequency
AM and FM for each tone used in dictation exercises.
Subjects will be limited to college music majors enrolled at The Ohio State
University, who have completed a minimum of one year of formal aural traiiting.
There will be no attempts to correlate the effects of timbre on aural skills with other musical abilities using standardized tests or measures of musicality. Possible correlations between the timbrai effects on aural skills and subjects’ principal instruments, the pitch ranges of those instruments, or the categories of instruments, will not be examined. No attempts will be made to correlate the experimental results with any other factor (e.g. gender, race, age, etc.).
There will be no consideration of effects of inharmonic spectra, or of varying attack transients on accuracy levels of pitch judgments, nor will the effects of phase on tonal stimuli be examined, aside from its attribution to AM and FM effects. Chapter H
Review of the literature
Introduction
The relative scarcity of literature regarding the relationship between timbre and aural skills suggests that there has been little formal research addressing this concern.
Much of the available literature regarding aural training is concerned with such pedagogical matters as the accurate identification of intervals using both piano and computer-generated tones, while the literature on timbre addresses the acoustical and psychoacoustical nature of this highly complex and little understood perceptual issue.
Studies from each of the areas that are relevant to this research will be reviewed later in this chapter.
The experimental study of timbrai perception is increasingly addressed in the psychological literature, but not in the context of aural training. Timbre is a multidimensional property of sound. The many attributes of sound that contribute to, or affect, timbre complicate research regarding timbre perception. These attributes include the number and relative strength of spectral components of a tone, the harmonic or inharmonic relationships of these components, the degree of synchronicity among the onsets of the components, and among changes of their individual amplitude envelopes, amplitude modulation and frequency modulation (defined below) of the spectrum, frequency range of the components, attack transients, and loudness. Attempting to focus on only one or a few timbrai dimensions requires careful consideration because of the interdependencies among these dimensions. Such attempts can reduce the reliability and 10
validity of the results. When the focus of a study is very narrow and uses little musical
or classroom context, these results lose ecological validity and, hence, provide little
information applicable for improving music education techitiques or musicianship.
While much of the pedagogical research has included timbre as an aspect of
broader research topics (e.g. Haack, 1975; Liesch, 1980; Ely, 1988), timbre is most
often considered within the context of the identification of traditional instruments (Elliott,
1975; Grey, 1975), or within timbre’s relationship to various aspects of pitch, including
intonational pitch (Wapnick & Freeman, 1980), categorical pitch (Sergeant, 1973;
Blatter, 1974; Howell, 1976), and absolute pitch (Goldman, 1984; Miyazaki, 1989).
Only two studies (Killam, 1982; Bales & Foltz, 1987) have been found that
directly addressed the effect of timbre employed in the teaching of aural skills using
pitches in melodic and harmonic contexts. The principal focus of both studies was the
difference in subjects’ accuracy levels on aural skills tasks employing different
synthesized tones, or synthesized and natural instrumental tones.
Studies of the effects of timbrai variation on pitch identification
Killam. Killam (1982) examined students’ abilities to identify chords, intervals, and
harmonic cadences, using three different synthesized timbres. Killam does not describe
the perceptual qualities of the three timbres. The three synthesized timbres were
generated by (1) an Apple II computer interfaced with two ALF sound generation circuit-
boards, (2) a Micromusic synthesizer, and (3) the North Texas State University (NTSU)
CAI system using AMUS sound generating software and hardware. The thirty-six
subjects employed in this study were undergraduate music majors at NTSU.
Examination of chord qualities in this study was limited to major and minor triads; all chordal inversions were used. The experiment did not actually test subjects’ 11
abilities to identify chord qualities, but in fact tested their abilities to identify which chord
tones were present in the bass and soprano voices. Eighteen chordal stimuli were tested,
using all nine possible bass and soprano voicing combinations for each of the major and
minor chord qualities.
Killam’s examination of melodic intervals tested twenty-four different intervallic
stimuli. Each interval, from minor second through the perfect octave, was used once in
each the ascending and descending directions. Six types of harmonic cadences were
examined: perfect and imperfect authentic, perfect and imperfect plagal, and “authentic”
and “plagal” half cadences. The “authentic half’ cadence, usually referred to as the half cadence, is characterized by a harmonic arrival on the dominant, while the “plagal half’ cadence, found infrequently in music of the common practice period, is characterized by the progression of tonic to an arrival on the subdominant.
Killam observed no significant effects of the different sound sources on subjects’ abilities to perform the aural skills tasks. This led to the conclusion that timbre probably does not affect aural skills. Killam observed, however, that students show preferences for different sound sources, and that these “preferences correlate most closely with [the students’] achievement^ on a given curriculum area, rather than with the sound itself’
(1982, p. 10). These observations should be generalized with caution, because the subjects were informed before the experiment that they were participating in a survey to find the most satisfactory sound source for CAI learning, and that they would be asked for a personal evaluation of the sounds at the conclusion of the testing.
The results of Killam’s study could have been strengthened by retaining equality of the tasks required of the subjects across the three experiments. Killam does not clearly describe the subjects’ response tasks. Responses could have been made in a variety of ways. Though Killam states that the experimental tasks were similar to the 12
NTSU CAI format, she never describes what that format is. The chord quality test
required subjects to “enter” the bass note of the chord and then the soprano note of the
chord using the numbers 1 [chord root], 3 [third of the chord], or 5 [fifth of the chord].
Eighteen stimuli, with nine possible combinations of bass and soprano voices, were
tested. While the term “enter” may be assumed to refer to computer-entiy response
tasks, it is not known whether or not the subjects were able to consult a list of response
options (i, e,, recognition). Twenty-four melodic intervals were to be identified as
intervals, minor second through perfect octave, without regard to direction; twelve
answers were possible. The harmonic cadences test contained twenty-four stimuli
representing only six possible choices. While these tasks are realistic objectives for
classroom instruction or CAI, they were not controlled for similarity of response task,
nor for equality of response choices.
There is no evidence that Killam controlled for pitch range in this study. While it
may be that timbres of synthesized tones do not vary across pitch range as much as
traditional instrumental timbres, some variance can occur. The strength of the results
from this study is weakened because of the unknown pitch range used for the stimuli,
and the amount of variance that may have occurred with these three synthesized timbres.
Although Killam's test design may have served its purpose, the uncontrolled variables (pitch range, dissimilarity of response tasks, and unequal numbers of possible responses for each task), reduces the usefulness of the results, and the conclusions regarding the effects of the independent variables, the three synthesized timbres. Most importantly, since Killam’s study was concerned with only synthesized sound sources, it provides no data generalizable to the effects of natural instrumental timbres.
Bales and Foltz, Apparently the only study that has considered the effects of both synthesized and traditional instrumental timbres on aural skills was performed by Bales 13
and Foltz (1987) at the University of Nebraska. Bales and Foltz used two aural skills classes randomly assigned to four groups in a Randomized Solomon Four-Group Design
(Campbell & Stanley, 1966). The experiment was administered to sixty-one subjects over two regular semesters. A control group (N=31) received both classroom instruction and outside-of-class drill, using piano as the sound source. The outside drill was administered in small groups of five or fewer, with an instructor playing the musical examples. An experimental group (N=30) used Apple II computers, equipped with digital synthesis boards, for drill outside the classroom. Subjects in this group received classroom instruction using an amplified Yamaha DX7 synthesizer, programmed with a timbre that the researchers judged to be similar to the timbre used in the CAI portion of the study. A standardized curriculum, and a rotation of classroom instructors every two weeks, were used to promote uniform instruction.
Regulation of the outside-of-class drill could have been more uniform. The data are biased because outside-of-class drills for the experimental group vs. the control group represent dissimilar practice environments; the experimental group received individualized CAI drill, while the control group was divided into small subgroups and drilled by an instructor. Similarity of the drill task could have been ensured if the CAI software had been programmed for use with a musical instrument digital interface (MIDI) device. This would permit use of a digital sampler and acoustic piano tone samples to be driven by the CAI software for the control group drill sessions. It should be noted, however, that at the time their study was initiated, MIDI controlled digital audio samplers were just beginning to enter an affordable price range.
Results of the Bales and Foltz study showed little difference between learning achievements of subjects instructed with synthesized tones and subjects taught with traditional piano tones. Bales and Foltz recognized that their results were subject to a 14
high level of error due to potential maturation effects. These maturation effects were possible because the skill development was nurtured over a two semester period of time.
Their statistical analysis and concluding comments reflect their awareness of this problem. They caution against overgeneralization of their results and encourage continued research by others.
Other perceptual studies of timbre
Sergeant. Sergeant (1973) performed three experiments examining pitch recognition.
In the first, using a forty item, two alternative forced choice (2AFC) test, in which subjects (N=20) were asked to judge if the second tone of each pair was higher or lower, he measured the effects of variations in acoustical environments (an open room, a closed sound booth, and headphones) on pitch discrimination of pure tones. Results showed significant differences among three testing environments. Subjects exhibited higher judgment levels under closed environments and individual testing than when tested in open field and group environments. Sergeant measured the sound intensity levels of the stimuli at various locations in the open field environment and found that the levels varied.
He concluded that pure tones are unsuitable sounds for pitch recognition in group-tests because of the unequal distribution of sound intensity, and unsuitable “for measuring musical perceptual skills where learning factors are present” (1973, p. 19). Sergeant’s results support findings of several earlier studies (Shower & Biddulph, 1931; Fletcher &
Munson, 1933; Stevens, 1935; Snow, 1936; Cohen, 1961) regarding the relationship of intensity to pitch of pure tones.
Sergeant used a 2AFC test similar to the first experiment to examine the effects of pure tones versus square-wave tones on subjects’ pitch discrimination. Two subject groups were used to examine the affect on pitch judgments of both musicians (N=25), 15
and non-musicians (N=21). Accuracy levels of pitch judgments were compared for each
timbre between the two groups of subjects. Musicians performed the tasks with higher
accuracy than did the non-musicians. The differences in accuracy levels between the two
groups with pure and square-wave tones varied greatly. Results for the differences in
accuracy levels for judgments with pure tones proved significant at the .05 level (t=2.5,
d/=44), while differences for judgments with square-wave tones proved significant near
the .001 level (t=3.25, d/=44). Sergeant concluded that these results were evidence of a
learning effect on pitch judgments for musicians.
In the third experiment, using a similar 2AFC test, Sergeant measured subjects’
ability to recognize pitch using pairs of synthesized square-wave tones and pairs of piano
tones. It was hypothesized that the richer spectra of the piano tones would elicit higher
accuracy levels than the square-wave tones. Results showed no significant influence of
the two timbres on the subjects’ judgments. Sergeant concluded that superior judgments
evoked by complex tones are primarily influenced by the learning environment and not
an improved basilar response to the presence of richer spectra.
Blatter. Examining the pitch matching abilities of college musicians. Blatter (1974) found that complex tones elicited more accurate pitch judgments than did pure tones.
Subjects (N=18) participating in this study were asked to tune a second tone to be in unison with a fixed tone. Using sine, square, and sawtooth waveforms, he showed that the complex waveforms evoked greater tuning accuracy than did the sine tone, and that the sawtooth tones elicited better tuning precision than did the square-wave tones.
Blatter’s findings regarding square-wave tones are in complete opposition to Sergeant’s results. 16
Elliott. Numerous studies have examined the effects of different attributes of timbre on the recognition and identification of traditional musical instruments. EUiott (1975) investigated the effects of attack and release transients on college music students’ ability to identify acciuately the nine musical instmments that produced the tones. Flute, clarinet, oboe, bassoon, saxophone, tmmpet, trombone, violin, and cello tones at a pitch of E4 were recorded to tape.i The original tones had seven-second durations, and were randomized and prepared with eight-second sUent intervals between each tone.
Duplicates of the original tones were altered to remove the attack and release transients by deleting the first and last half-seconds of the tones. The altered tones were six seconds in duration and organized similarly to the set of original tones. Original and altered tones were presented as separate parts of the test Subjects were asked to identify the source of the tones from a list of the nine instruments at the top of the test answer sheet.
Apparently, there was no rotation of subtest order. Elliott’s findings show that transient attributes of tones contain important information for the accurate identification of instmmental tones. His findings concur with those of earlier studies by Saldanha and
Corso (1964) and Berger (1964).
Grey. Grey (1975) performed a series of eight experiments investigating the perception of timbre. He used sixteen instrumental tones that represented twelve different traditional instmments: oboe, English horn, bassoon, Eb clarinet, bass clarinet, flute, Eb alto saxophone, Bb soprano saxophone, tmmpet, French horn, muted trombone, and violoncello.^ Grey used computers to analyze the numerous time-variant
^ Elliott docs not clarify the details of the instruments used. E sed on the pitch of the stimulus tones, E4, we are left to assume that he used the more common members of those instrumental families: soprano flute, Bb soprano clarinet, Eb alto saxophone, and Bb trumpet ^ Grey does not clarify what type of trumpet was used. Based on his selection of instruments (pp. 31- 32), we might assume it was a Bb trumpet. 17
amplitude and frequency functions of the instrumental tone samples taken at the pitch
Eb 4 , 311 Hz. The computer analyses provided data that allowed him to resynthesize
these tones and alter specific attributes of the time-variant functions. The most
significant results and conclusions in Grey’s study came from the last four experiments,
that explored the perceptual continuity of timbrai transitions. In these experiments he
combined tones to create stimuli that transformed from one instrumental tone to another
across a steadily changing interpolation. Grey’s summary of the four experiments
suggested that there is little evidence for categorical perception for timbrai discrimination,
but strong evidence for timbrai discrimination that follows a perceptual continuum.
Howell. Howell (1976) surveyed the effect of timbre on the ability of college
musicians to identify harmonic intervals. Subjects (N=80) participating in this study
were marching band instrumentalists and piartists at the University of Oklahoma at
Norman. Subjects were asked to identify seventy-five pitch intervals. The stimulus
timbres tested were pure tones, clarinet, trumpet, piano, and a mix of flute and horn
tones.3 Howell is unclear in his use of the term “mixed,” but in his concluding chapter he alludes to the use of flute and horn for the individual tones of the interval. There is no discussion of comparative loudness levels of the two instrumental tones if the flute and horn were used in this manner. If the loudness of each instrument is not carefully controlled, this “mixed” stimulus timbre risks a problem with one of instrumental tones masking the other tone. Given the date of Howell’s research, it is doubtful that he used the term to mean fusion of the flute and hom tones into a new fused timbre. Under carefully controlled acoustical conditions, however, timbrai fusion may occur perceptually without electronic manipulations of the tones (Smoot, 1986).
^ Howell does not specify what type of clarinet and trumpet were used. The stimuli and context of the experiment suggest that we may assume that he used a Bb soprano clarinet and a Bb trumpet 18
Howell organized the stimuli into five subtests, one for each timbre examined in the study. Each subtest contained fifteen randomized intervallic patterns: one of each of the twelve possible intervals from the minor second to tlie perfect octave, and three repeated intervals that were randomly selected. Four hundred one students were given a test of interval identification. Eighty subjects were randomly selected firom those students, and assigned to four test groups (N=20) classified as clarinetists, trumpeters, pianists, and other instnunentalists. Presentations of the five subtests were rotated according to a Latin Squares Rotation Design. Subjects were informed which of the timbres was going to be tested at the beginning of each subtest. His study could have been strengthened, however, if he had randomized the timbrai treatment across trial blocks, rather than presenting subtests organized by timbre. Howell’s design did not sufficiently control for possible learning effects that may have occurred from hearing successive stimuli with a single timbre. Informing the subjects of the timbre before each subtest also weakens the validity of his results.
Results showed that pianists scored significantly higher than other instrumentalists. It is interesting to note that this is the only study to yield data reflecting higher accuracy levels for clarinet tones than for piano or trumpet tones.
Howell concluded that the undergraduate musicians’ abilities to identify intervals was partially due to the experience acquired through their primary performance medium.
Subjects did not perform identification tasks with greater accuracy for stimuli employing timbres of their own primary performance medium than for other stimulus timbres.
Howell appears to have overlooked the greater amount of musical experience and individualized instruction encountered by most undergraduate pianists, as opposed to their marching band peers. Neitiier did he account for the significantly greater experience with harmonic intervals acquired by pianists than by most marching band 19
instrumentalists. The limitations of his subject pool (viz. the lack of vocalists and
orchestral instrumentalists, such as string and double reed players), hinder Howell’s
findings firom being generalizable to college instrumentalists in particular, and college
musicians in general.
Kubovy and Jordon. When the phases of a modulating waveform are also applied
coherently to the components, spectral fusion is strengthened. Kubovy and Jordon
(1979) investigated the effect of phase on the fusion of sinusoidal components of twelve-
component harmonic complexes. In a series of four experiments, they explored various
degrees of phase shifts of single sinusoids within the harmonic complex. Results
showed that pitch information about the prominent low pitch of a complex tone (usually
the fundamental) was perceptually retained, and that out-of-phase sinusoids were
consistently separated from the tone complex for shifts of 40° or greater.
Wapnick and Freeman. Wapnick and Freeman (1980) examined the effects of
variations in the relative amplitudes of the partials in clarinet tones on the perception of
“flatness and sharpness” of pitch.'* Two tones, A 3 and A 5 , were recorded on tape, and
the relative amplitudes of their partials were altered by frequency regions using a seven
band graphic audio equalizer. A variable speed tape recorder was modified to have the
playback speed controlled by a sine wave oscillator. This permitted accurate control of
the pitch of the tones during playback. The tones were altered 12 cents above and below
the originally recorded frequencies. The test stimuli were prepared by pairing according
to four timbrai categories: dark-dark, dark-bright, bright-bright, and bright-dark.
Subjects (N=50) were tested in small groups of twelve to fifteen, in a classroom-like
'* Although Wapnick and Frcemaii do not clarify which type of clarinet was used, we might assume that it was a Bb soprano clarinet based on common usage of that instrument and the pitches of the stimulus tones. 20
environment. The subjects were required to indicate if the second tone in each pair was
sharp or flat in comparison to the first tone. Results showed that tones with relatively
strong lower partials and weak upper partials were perceived as being flat, while tones
with relatively weak lower partials and strong upper partials were perceived as being
sharp.
Charbonneau. Charbonneau (1981) explored the effects of data reduction techniques
on the digital resynthesizing of tones to determine what techniques resulted in the least
audible difference in timbrai discrimination. He discovered that replacing the incoherent
FM fluctuations on the individual components with a single modulation function
improved the perception of similarity of the resynthesized tone to the original one.
Goldman. Goldman (1984), using two experiments, examined the effects of both
original and electronically altered instrument tones on absolute pitch judgments. In the
first experiment, twelve differently pitched tones from each of three musical
instruments—oboe, clarinet, and French hom^—were recorded with three second
durations. The use of absolute judgments necessitated a wide pitch range, A 2 to Ebg.
The tones were checked for accuracy of tuning with a StroboConn tuner, and the maximum deviation from “in-tuneness” was eleven cents. The organization of the tones were randomized for testing. Subjects (N=28), undergraduate and graduate music students and music faculty, were asked to identify the tones by pitch name. In the second experiment, the instrumental tones were altered three ways: ( 1) tones were passed through a filter and given a resonance peak at 1(X)0 Hz; ( 2) harmonic distortion was added to the tones by clipping the peaks of the waveform and the strengths of the lower
^ Goldman does not specify which type of clarinet was used. Based on comments in the text, and the given pitch range of the clarinet tones used as stimuli, F#3 - BbS (p. 35), we might assume it was a Bb soprano clarinet 21
partials were reduced by means of a high pass filter, and (3) the attack transients and final
decay were removed. The altered tones were randomized for the stimulus trials. Again,
the subjects (N=21) were asked to identify the pitches of the tones. These alterations
were shown to have no significant effect on absolute pitch judgments. Oboe tones
evoked the greatest accuracy in pitch judgments for both the original and altered tone
stimuli. Clarinet tones elicited the fewest correct responses.
McAdams. McAdams’ (1984b) work has contributed greatly to our understanding of
the perceptual process of grouping of simultaneous components of complex tones, and
the physical attributes of sound that contribute to this process. His work focuses on the
spectral and transient characteristics of sound. The grouping process, or spectral fusion,
is described as a psychological model of any sound entity that exhibits a coherence.
These models are referred to as source images, or auditory images (1984a). The
extraction of pitch fix)m these images may depend upon the existence of harmonic
spectral templates, and periodicity detectors (see Chapter 1, p. 6 ). McAdams (1984b)
outlined six perceptual cues that contribute to the formation or separation of these
simultaneous images. These perceptual cues are:
1. spatial location 2 . pitch separation as defined by a. degree of spectral overlap b. harmonic coincidence 3. harmonicity of the spectral content 4. coherence of frequency modulation (FM) 5. coherence of amplitude modulation (AM) 6 . stable resonance structure(s) forming the amplitude of the spectrum
Harmonic coincidence is the amount of concurrence of the frequency components
firom different sound sources.
Coherence of modulation is defined as the use of modulation synchronously imposed on aU spectral components of the tone complex. McAdams found that regions 22
of stable resonance, known zs formants in the speech sciences, interact with the coherent
FM on the individual spectral components. This interaction causes amplitude
fluctuations in the individual components because the individual amplitudes conform to
the spectral envelope that is shaped by these resonance regions.
McAdams (1984b) has concentrated much of his research on the effects of
coherence of FM and AM on tone complexes in regard to spectral fusion. He has
identified two significant attributes affecting the fusion of tone complexes, that he calls
vibrato and jitter. Vibrato is defined by McAdams as periodic fluctuations of frequency
(FM) imposed upon a tone complex. Jitter is defined as aperiodic, sub-audio (< 20 Hz)
AM and/or FM fluctuations imposed upon a tone complex. McAdams (1982b) once
defined random FM as shimmer^ but in all subsequent studies, he uses the term “jitter” to
mean both FM and AM fluctuations. McAdams showed that spectral fusion is enhanced
when vibrato and jitter are coherently imposed upon a harmonic complex. M cAdams and
Rodet (1988) found that vibrato also improves discrimination of the timbres of complex
spectral stimuli containing as few as eight components. Their study showed that
recognition of timbres with similar spectral envelopes is improved when vibrato is
imposed on the tones.
Weaver. Weaver (1987) investigated the relationship between subjects’ preferences for
natural and synthesized timbres. Weaver (1985) designed a Timbre Preference Test
(TFT) to examine subjects’ preferences among nine natural instrumental timbres—flute,
clarinet, oboe, bassoon, alto saxophone, trumpet, French hom, trombone, and tuba.^
Weaver’s TFT was designed to be similar to Gordon’s (1984) Instrument Timbre
^ Weaver does not specify the details of the instruments used. Based upon the information regarding the stimuli and general comments in the dissertation, we may assume the most commonly used members of the instrument families, for example Bb soprano clarinet, Bb trumpet, etc. 23
Preference Test (H PT) for seven synthesized timbres—flute, oboe, clarinet, alto
saxophone/French hom, trumpet, trombone/baritone, French hom, and tuba. A melody
was recorded using each of the nine instruments. Each instrumental timbre was paired
twice with each of the other timbres to form a seventy-two item test. The subjects, 246
children in grades four through six, were required to indicate the timbre they preferred
from each pairing. Weaver found that subjects preferred the flute and oboe timbres, and
expressed dislike for the tuba timbre. These findings were shown to correlate closely
with the results of Gordon’s study with synthesized timbres (1986). These results
indicate that students have biases towards timbres, biases that may carry over to college
students, and possibly affect attitudes toward leaming.
Accurate recognition of pitch is an essential attribute of aural skills. Several
studies have contributed important secondary evidence of the effects of timbre on pitch recognition; however, the results reported in the literature are not always consistent
Crowder. Crowder (1989) employed guitar, flute, and trumpet tones to examine pitch recognition.^ Three tones, F 4 , G4 , and A 4 (USA Std.), were digitally sampled from each instrument for this study. Tones were paired into tone sequences, and the sequences randomized into six blocks of thirty-six trials each. Subjects (N=12) were asked to judge if two tones played in sequence were, or were not the same pitch. He found that subjects’ responses were quicker when the timbres of both tones were the same.
^ Crowder does not clarify the type of guitar or wind instruments used. While it might be assumed that the wind instruments were soprano flute and Bb trumpet, we can not be sure of the guitar. Even if we assume that Crowder used a hollow-body “acoustic” guitar, as opposed to an acoustically amplified “electric” guitar, we still do not know whether the strings were nylon or steel. These two types of strings evoke significantly different timbres, and this is without regard for the different kinds of steel strings (e.g. flat-wound, round-wound, etc.). 24
Miyazaki. Miyazaki (1989) explored the effects of timbre and pitch height on absolute
pitch identifications using sine tones, piano tones, and FM digital synthesis piano tones.
Subjects (N=10) were asked to identify the pitches by depressing keys on a keyboard.
Results showed that 91.6% of the piano tones were accurately identified, while
synthesized piano and sine tones evoked only 80.4% and 74.4% accuracy respectively.
He concluded that timbre has a significant effect on absolute pitch recognition.
The different results reported by Goldman and Miyazaki may be due largely to
the different timbrai attributes the two studies explore, as well as the different
experimental tasks and controls employed by the experimenters. It is important to note
that Miyazaki’s study was biased fiom its onset. He could readily expect to find
significantly different results between the piano and sine tones based on earlier studies
comparing sine tones and complex tones (viz. Plomp, 1967; Henning & Grosberg,
1968); complex tones are defined as those containing two or more sine components.
Summarizing the findings in this area of research over the past few decades, Radocy and
Boyle (1988) state that “Pure tones, being of one frequency, actually are less clear in pitch than complex tones.”
Yost and Sheft. Yost and Sheft (1989) examined effects in the processing of low- frequency AM that occur across ffequency-channels on the basilar membrane. The stimuli comprised two sets of paired sinusoids that were amplitude-modulated. One pair of sinusoids used a common modulator sinusoid, while the other pair used individual modulators of the same modulation rate, but different modulation phases. The stimuli were presented diotically to the subjects. The subjects (N=3) were asked to identify if the stimuli presented to each ear were the same or different. Results showed that 25
listeners can discriminate modulated tones of different phases when the variance of phase
is 50° to 70° or greater.
Auditory streaming
Auditory streaming has been defined by Dannenbring and Bregman as “a
phenomenon in which a rapid sequence of high and low tones splits into two separate
perceptual streams, one consisting of the high tones and the other of the low tones”
(1976a, p. 987). The interest in this phenomenon has stimulated research regarding the
perceptual separation of tone complexes into their sinusoidal components, and the
extraction of the source of pitch firom tone complexes. Investigation of auditory
streaming has helped impart to us some understanding of the perceptual processes
employed to parse complex auditory stimuli into sensible information (e.g. Bregman,
1976; Dannenbring & Bregman, 1976b; Dannenbring & Bregman, 1978; McAdams &
Bregman, 1979; Tougas & Bregman, 1985; Wright & Bregman, 1987). Much of this research opened the door to other explorations of the fusion of sinusoids into a single complex tone. Bregman and Pinker (1978) first noted that two perceptual processes
seem to be at work in organizing auditory input: they called these “sequential grouping” and “simultaneous grouping.” Bregman, McAdams & Halpem (1979) explained that sequential grouping occurs when a sequence of “acoustic components” originates across time fiom the same source, and that simultaneous grouping occurs when a set of
“spectral components” arrives at the ear at a single instant so that they must be parsed
“into the contributions of the individual sources.”
De Boer (1976) has shown that the most consistent and unmistakable sense of pitch is evoked by harmonic complexes. Sinusoidal components fuse much more readily for harmonic tones than inharmonic tones under similar conditions of regular, predictable transformations of a spectral pattern (Slaymaker, 1970; Mathews & Pierce, 1980). 26
McAdams (1984b) believes this phenomenon is due partly to the phase locking of partials of harmonic complexes; partials of inharmonic complexes are not phase locked.
Sound waves are regarded as being “in phase” when they reach the same portion of their wave cycles simultaneously. Because the spectral components of a single tone share a synchronous onset, these sinusoids begin “in phase.” The partials of harmonic complexes will simultaneously complete their wave cycles at a regular rate, or period.
The harmonic relationship of the jBrequencies of the partials ensures periodicity of all these partials and results in their being phase locked.
Bregman and Pinker (1978), and Dannenbring and Bregman (1978) found that synchronicity of the onsets of tones is a principal factor in the fusion of two-tone and three-tone complexes respectively, where tire individual sinusoids are of roughly the same intensity. Cohen (1980) showed that inharmonic complexes can be successfully fused when an amplitude envelope is synchronously applied to tire onset of aU the components.
Summary of the literature
The research reported in the literature reviewed in the last section has greatly contributed to our understanding of the perceptual nature of timbre. It is clear that pure tones are not good sources of pitch information. Among the synthesized complex tones, sawtooth waves evoke better pitch-tuning accuracies than squarewaves. Studies on absolute pitch judgments have shown that natural instrumental tones elicit better pitch judgments than do synthesized tones. Of the natural instrumental tones examined, oboe tones have been found to produce the best pitch judgments, while clarinet tones produce the poorest pitch judgments. Varying the strengths of different partials of a tone also appear to affect absolute pitch judgments. 27
Studies on categorical pitch judgments do not report the same results as absolute pitch studies, nor do their findings agree among themselves. Clarinet tones have been reported to elicit better pitch judgments than either piano or trumpet tones. Some studies report no significant effects of timbre on categorical pitch judgments among various synthesized timbres, or between synthesized and piano tones. There is evidence that subjects exhibit timbrai preferences. These preferences appear to be for timbres of instruments with higher pitch ranges, viz. flute and oboe.
Harmorticity of the components in a tone’s spectrum contributes to both clear pitch perception and the fusion of the components into a single auditory image. This spectral fusion is also dependent upon the synchronous onset and phase-locking of a tone’s components, and the application of coherent modulation rates of botli vibrato and jitter on these components.
H ypotheses
None of the studies reviewed in this chapter has explored the influence of timbre on the perception of pitch in the manner as designed for this study.
In Chapter 1 (p. 2), two intrinsic properties of sound were proposed as necessary to aural skills. These properties are:
1. sounds used for aural training must provide good pitch identifiability
2 . separation of tonal stimuli, rather than fusion of tones, is desirable for aural training exercises, particularly for harmonic dictation
This study will investigate the effect that varying timbres might have on the perception of pitch. Response tasks commonly used in aural training will be employed.
These tasks include the recognition and identification of intervals, triads, and seventh chords for contexts of both melodic and harmonic dictation. Six experiments will be used to test the effects of twelve timbres on the subjects’ abilities to identify the stimuli 28
selected for this study. Each experiment will pursue a different type of stimulus pattern—interval, triad, or seventh chord—within either a melodic or harmonic context.
The twelve timbres chosen for this investigation represent attributes of sound that are suspected to influence the perceptibility of pitch for the dictation tasks employed in this study. These attributes of sound are:
1 . waveform 2 . the number of components contained in the harmonic spectrum 3. effects of vibrato and jitter modulations 4. the use of synthesized and traditional instmmental tones
Four hypotheses are proposed, based on the results of the experimental research reviewed earlier. These hypotheses are:
1. sawtooth and sawtooth-like waveforms should support better pitch recognition than square-wave or squarewave-like waveforms;
2 . tones containing a rich harmonic spectmm should enhance pitch recognition when compared to tones contaiiting a sparse harmonic spectrum;
3. tones containing distinct vibrato and jitter should enhance the separation of tones for harmonic stimuli when compared to steady-state tones; and
4. traditional instmmental tones should promote more-accurate pitch perception than steady-state synthesized tones. Chapter HI
Methodology
Introduction
This study comprised a series of six experiments testing several timbrai conditions of tonal stimuli under two principal testing conditions, namely, melodic dictation and harmonic dictation. Melodic dictation will be defined, for the purposes of this study, as stenographic transcription of stimuli composed of single successive tones, while harmonic dictation will be defined as the transcription of stimuli composed of simultaneous tones. The pitch-interval stimulus conditions were as follows:
1. melodic musical constructs a. single melodic intervals, ascending and descending b. arpeggiated triads, ascending direction only c. arpeggiated seventh chords, ascending direction only
2 . harmonic musical constructs a. harmonic intervals b. block triads c. block seventh chords
The dependent variable for each of these six experiments was the subjects’ accuracy in identifying pitch intervals. The independent variable was defined as the timbrai variations of the tones. The various melodic and harmonic stimulus conditions also constituted levels of an independent variable, but were not the main focus of this study.
The effect being examined was the effect of the timbrai variations on the accuracy levels in the identification of various kinds of pitch-intervals when the tones were presented either successively or simultaneously.
29 30
The timbre of the tone stimuli
Twelve timbres were selected for this study. These timbres were:
1. sawtooth 1, no modulations, 4 to 6 partials 2. sawtooth 2, with AM & FM, 4 to 6 partials 3. sawtooth 3, no modulations, 20+ partials 4. sawtooth 4, with AM & FM, 20+ partials 5. square 1, no modulations, 4 to 6 partials 6 . square 2, with AM & FM, 4 to 6 partials 7. square 3, no modulations, 20+ partials 8 . square 4, with AM & FM, 20+ partials 9. Bb trumpet 10. Bb soprano clarinet 1 1 . oboe 1 2 . piano
The twelve timbres listed above can be grouped into eight sensible categories, which in turn form the basis of four comparisons. The attributes were investigated within four comparisons, which were:
1. sampled instrumental sounds vs. synthesized sounds 2 . sawtooth waveform vs. square waveform 3. rich spectral content vs. sparee spectral content 4. steady-state sounds vs. amplitude- and frequency-modulated sounds
Four instrumental timbres—piano, oboe, Bb soprano clarinet, and Bb tmmpet—were chosen for this study. Piano tones were selected because they are the instmmental tones most frequently used for the instmction of aural skills. Oboe, clarinet, and tmmpet tones were selected for two reasons. First, oboe and tmmpet tones somewhat resemble sawtooth waveforms, and clarinet tones somewhat resemble square waveforms, at least within the pitch range used for this study. (The pitch range of the stimuli was limited in this study to one octave, C 4 to C 5 USA Std.) Second, these instmmental timbres have been used to explore timbre in earlier studies (see Chapter 2). A survey of the spectral content of selected timbrai samples showed that the oboe tones contain upwards of twenty-four partials, and the tmmpet tones upwards of twenty-six. The clarinet tones 31
contained ten partials, five that are quite strong. The spectral content of the piano tones fluctuates drastically, because of the rapid decay of the tones’ envelopes. The piano tones sampled for this study contained more than twenty partials at the attack onset, given the moderate loudness of stimuli used during the testing. The synthesized tones used in this study included examples of both sawtooth and square waveforms. The synthesized tones with low spectral content—sawtooth waves 1 and 2 , and square waves
1 and 2 —contained four to six partials, and tones with high spectral content—sawtooth waves 3 and 4, and square waves 3 and 4— contained more than twenty partials.
It is important to note that because performers inevitably induce vibrato and jitter into instrumental tones, it was necessary to generate synthesized sounds both with and without vibrato and jitter in order to observe the effects of those transient characteristics.
The synthesized tones containing vibrato and jitter modulations are sawtooth waves 2 and 4, and square waves 2 and 4, while the steady-state tones are sawtooth waves 1 and
3, and square waves 1 and 3.
The pitch-interval stimuli
The four melodic intervals chosen for the stimuli were the ascending and descending minor sixth (m 6 ) and the ascending and descending minor seventh (m 7 ).
The harmonic intervals examined were the tritone ( IT), minor sixth (m 6 ), minor seventh
(m7), and major seventh (M7). The principal criterion for choosing these pitch-intervals was the high level of difficulty for recognizing and identifying them (Killam, Lorton, and
Schubert, 1975). This choice was necessary to avoid ceiling effects in the data. A ceiling effect is the accumulation of scores at the maximum level of the score range. This skewing of the data will not accurately reflect any variance in the data. The triads selected for this study were major first inversion (M®), minor second inversion (m®), diminished first inversion (d®), and augmented (A). The augmented 32
triad, because of its symmetrical division of the octave, is typically perceived in root position when not in a musical context. Arpeggiated triads were presented in ascending form only.
The seventh chords selected were major-minor (dominant) seventh, third inversion (Yg); minor seventh, second inversion (m 3 ); half-diminished seventh, first inversion (^|); and fully diminished seventh, root position (°^). The fully diminished seventh chord, as with the augmented triad, is a symmetrical division of the octave, and is generally perceived to be in root position when not in a musical context Arpeggiated seventh chords were presented in ascending form only.
None of the studies discussed earlier provided data indicating that chords are most difficult to recognize. Selections for the study of triads and seventh chords were made on other criteria. Triads included one representative firom each of the four triadic qualities: augmented, major, minor, and diminished.
Seventh chords, having seven possible qualities in the diatonic major-minor tonal system, could not each be represented while retaining a balanced test design. It was first decided to consider only the five more commonly used seventh chords (major-major, major-minor, minor-minor, diminished-minor, and diminished-diminished). It was then decided to omit the major-major seventh chord from the testing because of its unique structure containing the M7/m2 interval class. This narrowed the choices of seventh chord to four, balancing the number of choices in each of the other pitch-interval categories, intervals and triads.
The criterion for choosing chord inversions was to maintain a high level of difficulty in recognizing and identifying the chord, while retaining a balance of confusion among the choices of seventh chords. This latter criterion is necessary for retaining validity of the experiment. Experimental validity requires unbiased presentations of 33
stimuli, and choices of stimuli. Hence, each pitch-interval chosen for this study, along with all the possible pitch-interval choices presented on the answer sheets, must present a relatively equal amount of possible confusion and difficulty of recognition. The selection of chord inversions was determined by the author’s observations of students’ difficulties in aural skills classes over five years as an instructor, and on the basis of the results of a pilot study.
The experimental design
The experimental design of this study was three-factor (2 X 3 X 12) repeated measures with factors of the melodic vs. harmonic condition, the pitch-interval (interval, triads, seventh chords), and the timbre (twelve variations). This choice was necessitated by the multiple timbrai variables and the multiple pitch-interval stimuli examined under conditions of both melodic and harmonic dictation.
Each test condition (melodic and harmonic intervals, arpeggiated triads and seventh chords, and block triad and seventh chords) was designed with the stimuli organized into six equal blocks. Each trial block contained the same forty-eight testable stimuli and ten “red herring’’ stimuli, for a total of fifty-eight stimuli per block. The twelve timbrai conditions were treated equally across all testable pitch-intervals.
Consideration was given to all pitch combinations possible within the octave range limit for each pitch-interval. The stimuli were randomized within each trial block in regard to the order of pitch-intervals, timbre, and pitch assignments to the stimuli. The order of pitch-intervals and timbre within the six different trial blocks was retained across each of the six test conditions. This was necessary to ensure equal presentation of all possible combinations of stimuli within the ranges of experimental control. The order of trial blocks was randomized for presentation to subject groups. All six testing conditions 34
were administered in a counterbalanced design to avoid order effects. This
counterbalance design is shown in Table 1.
Table 1. Counterbalance design of the trial blocks.
Experimental sub-groups: I, II, HI, IV, V, VI, VII, VUI, IX, X, XI, XII Trial blocks: 1,2, 3, 4, 5, 6 Test conditions: MI - melodic intervals HI - harmonic intervals MT - arpeggiated triads HT - block triads MS - arpeggiated seventh chords HS - block seventh chords
Test First Second Third Fourth Fifth Sixth
I MI HI MT HT MS HS 123456 321654 142536 563412 635241 236145 n MI HT HI MS MT HS 214365 321654 142536 563412 643152 654321 m HI MI HT MT HS MS 123456 321654 142536 563412 643152 236145 IV HI HS MI MT HT MS 214365 321654 142536 635241 643152 654321 V MT HI MI HS MS HT 123456 351642 351642 563412 643152 236145 VI MT MS MI HS HI HT 214365 351642 251346 635241 643152 654321 v n HT HI HS MI MS MT 123456 251346 142536 563412 426153 236145 v m HT MS HS MI HI MT 214365 351642 251346 635241 426153 654321 IX MS HT MT MI HS HI 123456 321645 321654 643152 426153 236145 X MS HS MT HT MI HI 214365 321654 251346 635241 426153 654321 XI HS MT MS HI HT MI 123456 351642 251346 563412 426153 236145 XII HS MS HT MT HI MI 214365 142536 251346 426153 635241 654321 35
The six trial blocks yielded six repetitions of each stimulus for a total of 288
stimuli. Table 2 lists all the pitch-intervals used in this study. All stimuli are illustrated
in Appendix A (p. 75).
Table 2. Tested stimulus types.
Pitch-interval type Stimuli “Red herring” stimuli
melodic intervals minor sixth ascending perfect fourth minor sixth descending tritone minor seventh ascending major sixth minor seventh major seventh descending (both ascending and descending directions for each)
harmonic intervals tritone perfect fourth minor sixth major sixth minor seventh major seventh
triads au^ented minor, first inversion (melodic & harmonic) major, first inversion diminished, root position minor, second inversion diminished, first inversion
seventh chords dominant seventh, dominant seventh, (melodic & harmonic) third inversion first inversion minor seventh, half-diminished, second inversion third inversion half-diminished seventh, first inversion fully diminished seventh
Selection of the additional pitch-intervals used as “red herring” stimuli was based
on two criteria: ( 1) a high level of difficulty in recognition and identifiability was necessary for the same reasons as discussed earlier for the pitch-intervals chosen to be examined in this study; and ( 2) the possible confusion patterns among the choices of pitch-intervals must be balanced for each testing condition. 36
The pitch range of the stimuli, from C 4 to C 5 , was limited for two reasons.
First, this octave lies within the ranges of all four instruments chosen for this study.
Second, it is a pitch range commonly used in aural training activities.
Each stimulus pattern had a duration of one second. Every example began with a verbal cue (1 sec.) presenting the item number of the example to be heard. The verbal cue was followed by a brief pause (’/z sec.) and then the stimulus was heard. Another pause (4Vz sec.) following the stimulus, serving as the subjects’ response interval for that example. The total duration for each example was 7 seconds. Each example was heard only once.
Each test employed the same response task; using an answer sheet, the subjects were asked to select an answer &om a group of six choices, and then rate the certainty of their choice on a scale of 1 (very sure) to 5 (very unsure). These two answers produce data for an analysis of variance ( ANOVA). The same answer sheet was used for melodic and harmonic constructs; e.g. melodic and harmonic intervals, aipeggiated and block triads, and arpeggiated and block seventh chords. Examples of the three answer sheet formats are shown in Appendix B (p. 101).
A pretest and posttest, each containing ten stimuli, were included within each experiment The ten stimuli consisted of two each of the four pitch-intervals selected for examination within each experiment, and two “red herring” stimuli. Piano tones, being the timbre most commonly employed in aural skills class environments, served as the timbre for the pretest and posttest stimuli. The pretest was intended to verify the subjects’ abilities to identify the musical constructs within a typical classroom environment. The posttest was used to detect learning effects that would be reflected by significantly higher posttest scores, and for fatigue effects as reflected by significantly lower posttest scores. 37
The six trial blocks, the pretest, and posttest totaled 368 stimuli per experiment
Since each trial required seven seconds, the testing duration of each experiment amounted to roughly 45 minutes. Subjects participated in all six tests.
Preparation of the stimuli
The synthesized tones were initially generated with FM synthesis using a Yamaha
DX7 synthesizer. Tones composed of sawtooth waveforms and square waveforms were generated with and without jitter, and with both low and high spectral content. These tones were digitized at a 30 kHz sampling rate, and stored to disk using a Roland S-330 digital sampler.
Low firequency vibrato was applied to the already-amplitude-modulated tones— sawtooth 2, sawtooth 4, square 2, and square 4 tones—using a low frequency oscillator
(LFO). The vibrato was applied so that each tone in a stimulus would be given a unique rate of vibrato. The contrast between rates of vibrato of adjacent semitones was enhanced by applying alternating 180° phase polarities of the LFO at the onset of the tones. It was expected that this contrast would aid tone separation during harmonic dictation tasks.
The natural instrumental tones were also digitized at a 30 kHz sampling rate and stored to disk.
Trial blocks were sequenced with a Macintosh SE computer using Opcode’s
“Vision” sequencing software. The software enabled accurate temporal control of the stimulus tones, vocal announcements, and response intervals. Using the computer to control two digital samplers via MIDI, the trial blocks were digitally recorded on Sony digital audio tapes (DAT) at a 48 kHz sampling rate via a Sony PCM 2500 DAT recorder. The outputs from the digital samplers were mixed to a monophonic signal through a NEV 5305. 38
Subjects
Thirty-six volunteers from The Ohio State University School of Music were used
as subjects. All subjects were music majors, and had completed a minimum of one year of college-level aural training prior to participation in the study. This training prerequisite was used to avoid confounding variables that might have resulted from learning new aural skills during the testing. Subjects were randomly assigned to twelve groups of three to insure equivalent experimental groups.
The thirty-six subjects who completed the study form a reasonable representation of the college music student population. This is reflected by their grades, and by the diversity of their performance mediums. A survey of these subjects’ grades fiom their first quarter of aural training shows a grade range fi-om A to D+, and a mean grade point of 3.38 using the 4.0 grade point system. The standard deviation for these grade points is 0.72. Table 3 shows the distribution of principal instruments represented by this population sample.
Table 3. Principal instruments represented in the population sample.
1 2 voice (8 F, 4 M) 1 violin 3 trumpet 2 violoncello 4 French horn 1 string bass 1 euphonium 1 guitar 1 tuba 1 electric bass 2 flute 4 piano 1 bassoon 3 percussion
Administering the tests
All testing was administered in a classroom in one of the music buildings at The
Ohio State University. A classroom environment was deemed necessary to retain ecological validity in this study. No testing booths were used to reduce the typical 39
ambient noise that students are subjected to during classroom instruction. This is
particularly relevant at The Ohio State University where aural skills students must not
only contend with common distractions by other students outside on the campus, and by
nearby automobile traffic on one of the city’s primary streets, but must also contend with
the incessant distraction of air traffic resulting from being directly beneath the primary
approach-departure route of an intemational airport.
The test stimuli were played firom the DAT recordings on a Sony PCM 2500
DAT recorder through a Sony MX-P21 mixer. Carver PM 175 amplifier, and EV Sentry
lOOA studio monitors set to a flat frequency response. A moderate volume level, judged
to be typical for a classroom environment, was used. A uniform set of instructions was presented orally to the subjects at the beginning of each testing session. Chapter IV
R esults
Pretest and posttest observations
Results from the pretests and posttests provide no significant information regarding effects of learning or fatigue. Observation of the individual block scores, in the order that the blocks were administered to the subjects, proves to be more informative. Appendix C (p. 105) shows the individual block scores in succession order, as well as the mean score and standard deviations for each test, for each subject.
To protect confidentiality, test participants are identified by alphabetical letters in this report. Learning effects are reflected by high deviation from the mean and by increasing scores across the score succession; e.g., arpeggiated triad scores for subject D show a learning effect. Fatigue scores are reflected by high deviation from the mean and decreasing scores across the score succession; e.g., block triad scores for subject C show a strong fatigue effect Combinations of these effects also appear to have occurred. Several subjects exhibited a learning effect followed by fatigue; for example, subject T’s scores for the melodic interval test increase dramatically over the first four trial blocks, and then decrease over the last two blocks. The opposite pattern is also found, such as in BB’s scores for melodic intervals that drop for the third trial block, then slowly increase through the sixth block. These patterns should not be mistaken for random variations. Subjects’ scores that demonstrate random accuracy patterns are also found in the data; for example, subject M’s scores exhibit erratic patterns for all the experiments.
40 41
Examination of these scores shows that twenty-four of the thirty-six subjects
scored at or below the chance level for at least one of the trial blocks across the six
experiments. The wide range and inconsistency of these twenty-four subjects’ scores
distorts the data, and necessitates a separate examination of the data for the other twelve
subjects. The scores from the twelve subjects (Group S 12) who scored consistently
better than chance provide the most reliable measurements of the treatment variables.
Data for all thirty-six subjects (Group 8 3 0 ) and for the Group S 12 will be examined for possible correlation, and to obtain information that might be useful for future research and pedagogy. Such examination of the data considers the accuracy levels of the entire
subject group while retaining observations that are valid and can be generalized to the population. Readers interested in the data for the subjects who scored below chance levels (Group 8 2 4 ) can find them in Appendix D (p. 112).
Data analysis
The data were analyzed using ANOVA statistics. The ANOVA was made possible by converting to scores the two-part responses from the subjects’ answer sheets. This method of conversion is illustrated in Table 4.
Table 4. Conversion of responses to scores.
pitch-interval rating of sco re response certainty
incorrect 1 1 incorrect 2 2 incorrect 3 3 incorrect 4 4 incorrect 5 5 correct 5 6 correct 4 7 correct 3 8 correct 2 9 correct 1 1 0 42
The rating of certainty employs a five-level system to indicate the confidence in a
subject’s choice fi-om a rating of 1, very sure, to 5, very unsure. The rating of certainty
is combined with the correctness of the pitch-interval choice to produce a combined score
that lies between 1 and 10. These combined scores are not ordinal measurements of the
subjects’ proficiencies; they are measurements of perceptual judgments combining
confidence ratings with accuracy. A score of 10, for example, is not better than a 9.
Both scores represent correct answers; however, the 10 represents greater confidence in
a subject’s perceptual judgment than a score of 9. A mean score of 6.0 used in an
ANOVA could represent 100% correct answers with very little certainty of choice (e.g.
6,6,6,6,6,6), or it could represent 50% correct answers with a variance in certainty of
choice (e.g. 7, 5,9, 8,4, 3). Hence, in addition to the ANOVA, the data is viewed from
two perspectives, the means of the raw scores averaged across subjects, and the
percentages of correct responses. The data for correct responses by each subject are
shown in Appendix E (p. 118).
Scores are averaged across the six trial blocks to yield a single mean score for
each timbre, and for each test condition. These mean scores provide good means of
exploring the timbrai effects on pitch-interval stimulus types rather than examining an
individual pitch-interval stimulus; for instance, examining harmonic intervals in general
rather than a harmonic tritone specifically. An example of these data fiom one subject’s
responses for a single test condition is shown in Appendix F (p. 125). These averaged
scores serve as the test scores for the ANOVA. Scores for all tests are shown in
Appendix G (p. 127).
The principal finding of this study is that timbrai variations do not have a
substantial effect on listeners’ accuracy at pitch judgments of intervals or chords in either melodic or harmonic contexts. The ANOVA shows that there were no significant effects 43
of timbre on the subjects’ abilities to perform the various aural skills tasks. Calculation of the within treatment variable, timbre, results in F (11,792) = 0.13, p<.05, for Group
S 12, and F (11,2520) = 0.24, p Figures 1 and 2 show the mean scores for all six test conditions for the Groups Si2 and Sgg, respectively. All twelve timbres are represented in these figures. Characteristics of the synthesized tones can be reviewed in Chapter 3 (p. 30). Appendix I (p. 142) shows the scores represented in these figures, and in all other figures discussed below. svl sw2 sw3 sw4 sql sq2 sq3 sq4 cl ob pno S m t D h t E m s B h s Figure 1. Mean scores for each test condition across all 12 timbres for Group S 12. s v l SV2 sv3 sv4 sql sq2 sq3 sq4 cl ob pno IMI I HI SmT DHT 0MS SHS Figure 2. Mean scores for each test condition across all 12 timbres for Group Sgg. 46 Examination of the mean scores for each test condition across all twelve timbres shows little variation among the scores for each test condition; for example, the largest deviation for Group S 12 occurs among the harmonic interval scores, that range from 7.56 for the clarinet timbre, to 8 .11 for the sawtooth 4 timbre. The responses appear less consistent when viewed as percentages of correct answers rather than as raw scores (Figures 3 & 4). The greatest variance in response accuracy occurs in the block triad data for both Groups S 12 and 8 3 5 ; the ranges of difference in the mean percentages of correct answers for these groups are 10.42% and 8.22% respectively. Deviations of this size would appear to be significant if patterns can be found to correlate with them. Closer examination reveals an association between the accuracy of responses and the spectral waveform of the stimulus tones. The fewest correct responses were evoked by square-wave or squarewave-like timbres, while the most correct responses generally were evoked by sawtooth waves or sawtooth-like timbres. This tendency appears to be consistent for the intervallic and triadic data, but an opposite trend occurs for the seventh chords, where synthesized square-wave tones evoked the more correct responses than synthesized sawtooth wave tones. 100 % c 0 r r e c X 3Vl sv2 sv3 sv4 sql sq2 sq3 sq4 cl ob pno ^ M T D h t 0 M S S h s Figure 3. Correct responses (%) for each test condition for Group S 12. s v l sv2 sv3 sw4 sql sq2 sq3 sq4 cl ob pno S m t []HT 0MS B h s Figure 4. Correct responses (%) for each test condition for Group Sgg. 00 49 Sawtooth vs. square waveform An overview of the data regarding waveform shows higher levels of response accuracy with sawtooth and sawtooth-like waveforms than with square-wave and squarewave-like waveforms. Separate examination of the synthesized waveforms from the natural instrumental waveforms reveals two patterns of response accuracy. Discussion of one of these patterns will benefit from the establishment of an order of difficulty for the six different types of pitch-intervals. It seems reasonable to consider that the more tones contained in a stimulus, the more difficult it should be to identify. Harmonic stimuli are generally considered more difficult to recognize than melodic stimuli. These criteria might be used to establish the following order of difficulty, from simplest to most complex, for these six different types of pitch-intervals used in this study. The easiest would be melodic intervals, followed by harmonic intervals, aipeggiated triads, block triads, arpeggiated seventh chords, and block seventh chords, respectively. The response accuracy for synthesized waveforms is higher for sawtooth waves than square-waves for the simpler response tasks, MI, HI, and MT. The opposite is true for the more difficult seventh chord tasks, MS, and HS. The block triad tasks, HT, is a pivoting point in this pattern. Viewing the accuracy levels as mean scores, square-waves elicit higher response levels, while viewing the responses as percentages of correct answers shows improved accuracy with sawtooth waves. This pattern is consistent for both subject groups examined. Sawtooth-like waveforms induced better accuracy than squarewave-like waveforms. This tendency is steadily reflected by the scores. Only the response scores for MT in the S 12 group differed from this pattern, showing a slightly higher response mean (+.14) and percentage (1.31%) of correct answers for squarewave-like than 50 sawtooth-like waveforms. Examination of the differences in percentages of correct responses between sawtooth-like and squarewave-like waveforms shows greater variances for harmonic stimuli than for melodic stimuli. These variances, that range from 4.29% to 6.34% for S 12 and from 2.55% to 4.39% for S 3 6 , are the largest variances found among any of the comparisons examined among these data, but do not prove to be statistically significant. Figures 5 through 8 show response accuracy means for the small and large subject groups, separated by waveform category. Ml HI MT HI MS HS Mel Her All E sevtooA; synth □ square; synth only B savtooOi-like I squarewave-like only Figure 5. Mean scores, Group S 12: sawtooth vs. square waveforms. Ml HI MT HT MS HS Mel Her All 0 savtooth; synth □ sq.uare; synth only E savtooth-like I squarevavB-like only Figure 6 , Mean scores, Group Sgg: sawtooth vs. square waveforms. Ml HI MT HT MS HS Mel H er All I savtooth; synth □ square; synth only B savtooth-like I square vave-lihe orûy Figure 7. Correct responses (%), Group S 12: sawtooth vs. square waveforms. : || i Ml HI MT HT MS HS Mel H er All I sawtooth; synth □ square; synth only B sawtooth-like I squarewave-like only Figure 8 . Correct responses (%), Group Sgg: sawtooth vs. square waveforms. 55 Synthesized tones vs. traditional instrumental tones This analysis compares the responses to synthesized tones with responses to traditional instrumental tones. Although the previous discussion regarding the observation of responses to waveform considered the separation of synthesized tones from traditional instrumental tones, this analysis differs in that data for piano tones are included, and that it examines only the response differences between the two categories, synthesized tones and traditional instrumental tones, without any regard to waveform. Traditional instrumental tones elicited only slightly higher mean scores for both Groups Si 2 and Sgg across all stimulus conditions, except arpeggiated seventh chords. The differences between these scores are not sufficient to indicate an effect on the response tasks. Figures 9 and 10 illustrate the mean scores for synthesized and traditional instrumental tones. 1 0 9 8 7 s % c 6 o 5 r 4 e 3 * 2 1 0 mm Ml HI MT HT MS HS Mel Her All B synthesized □ natural instruments Figure 9. Mean scores, Group S 12: synthesized vs. natural instrumental tones. 56 1 0 9 8 7 s c 6 o 5 r 4 e 3 2 # 1 0 J Ml HI MT HT MS HS Mel Har All I synthesized □ natural instruments Figure 10. Mean scores, Group 8 3 5 : synthesized vs. natural instrumental tones. The variance between the number of correct responses for synthesized tones and instrumental tones is small, and shows no effect on the subjects’ accuracy levels. Traditional instrumental tones elicited slightly more correct answers than synthesized tones for all test stimulus conditions for Group 8 1 2 . Responses for Group 8 3 5 , however, are not as consistent While natural instrumental tones evoked the most correct responses for most pitch-interval conditions, synthesized tones prompted more correct responses for aipeggiated triads and block seventh chords. Figures 11 and 12 show the percentage of correct responses for synthesized and traditional instrumental tones. 57 1 00 90 % 80 70 c o 60 r 50 r 40 e 30 c a * t 20 M 1 0 î 0 __ {la™ Ml HI MT HT MS HS MEL HAR ALL H synthesized □ natural instruments Figure 11. Correct responses (%), Group S 12: synthesized vs. natural instrumental tones. 100 90 % 80 c 70 o 6 0 r 50 ^ 40 : 30 t 20 Ml HI MT HT MS HS Mel Har Ail B synthesized □ natural instruments Figure 12. Correct responses (%), Group 8 3 5 : synthesized vs. natural instrumental tones. 58 Steady-state tones vs. amplitude- and frequency-modulated tones Sounds used in this study are divided into four categories of steady-state, and amplitude- and frequency-modulated tones; (1) steady-state tones, (2) amplitude- and frequency-modulated synthesized tones, (3) modulated tones and wind instmments, and (4) modulated tones, wind instruments, and piano. This categorization is necessary to avoid misinterpretation of data regarding the effects of amplitude- and frequency- modulation. Data for the steady-state tones could be compared with all non-steady-state data. This comparison, however, might not lead to an accurate conclusion of experimental results for two important reasons, reasons that illustrate the need for the other two categories. First, piano tones do not contain a recognizable vibrato induced by the performer or incorporated in a sound synthesis program; hence the other modulated tones should be compared with steady-state tones excluding the piano data. Second, the steady-state tones should be compared with modulated tones that are alike in all regards other than amplitude- and frequency-modulations, to ensure valid conclusions pertaining to the effects of this modulation. Scores thus grouped show no significant differences among the six pitch-interval conditions for either Groups S 12 or Sgg. The variance in mean scores is negligible across the four categories, as illustrated in Figures 13 and 14. This indicates that there are no effects of amplitude- and frequency-modulation. Examining the number of correct responses (Figures 15 and 16) confirms the findings of the mean score analysis; there are no significant effects resulting from amplitude- and frequency modulations on the subjects’ performances of the experimental tasks. Ml Hi MT HT MS HS Mel H ar All S steady-st&te □ modulated E mod. synth. & I mod. synth., synthesis vinds ■brands, & piano Figure 13. Mean scores, Group S 12: steady-state vs. AM- & FM-modulated tones. 10 9 8 7 s c 6 • 0 5 - r 4 e 3 -] 2 1 0 Ml H! MT HT MS HS Mel H ar Ail B steady-state □ modulated Bmod. synth. & ! mod. synth., synthesis tmids winds, & piano Figure 14. Mean scores, 835 ; steady-state vs. AM- & FM-modulated tones. o c 0 r r e c t Ml HI MT HT MS HS Mel Her All B steady-state □ modtilated Omod. synth. & I mod. synth., synthesis winds winds, & piano Figure 15. Correct responses (%), Group S 12: steady-state vs. AM- & FM-modulated tones. o\ % c 0 r r e c t Ml H! MT HT MS HS Mel H ar All H steady-state □ modulated E mod. synth. & B mod. synth., synthesis winds winds, & piano Figure 16. Correct responses (%), Group 8 3 5 : steady-state vs. AM- & FM-modulated tones. S 63 Spectral content Examination of the spectral content of the tones used in this study involves the comparison of tones composed of four to six harmonic partials (low spectral content), and tones composed of greater than twenty harmonic partials (high spectral content). The data show small variances within the scores and within the number of correct responses. No systematic effect on response accuracy levels in identifying the various categories of pitch-intervals is apparent These data are illustrated in Figures 17 through 20. s c o r e HI MT HT MS HS Mel Har H low spectral content □ high spectral content Figure 17. Mean scores, Group S 12: spectral content. 64 1 0 9 8 7 s c 6 o 5 r 4 e I 3 - ; 2 1 ' I f'S iâ » I 0 Ml HI MT HT MS HS Mel Har Ail 5 low spectral content □ high spectral content Figure 18. Mean scores, Group Sgg: spectral content. 1 00 90 % 80 c 70 0 60 r 50 C r 40 e 30 I c t 20 1 0 0 HI MT HT MS HS Mel Har Ail B low spectral content □ high spectral content Figure 19. Correct responses (%), Group S 12: spectral content. 65 100 90 % 80 70 c o 60 r 50 a r 40 e 30 c ! t 20 ■■ j 1 0 . 0 __ ï'û' Ml HI MT HT MS HS Mel Har Ail U low spectral content □ high spectral content Figure 20. Correct responses (%), Group 8 3 5 : spectral content. Pitch-interva! stimulus type Although it was not among the purposes of this study to compare responses to different categories of intervallic combinations, examination of these data clearly shows that these various types of stimuli significantly influence the accuracy and confidence levels of responses. This influence seems to be principally associated with the pitch- interval category (interval, triad, and seventh chord), and not so much with the melodic versus harmonic structure of the stimulus. Examining the effects of pitch-interval stimulus categories was not the intent of this study; however, the congruity and strength of the effect across all six experiments is an observation too strong to be dismissed. An ANOVA performed on the pitch-interval categories resulted in F (2,792) = 62.22, p < .05, for Group S 12, and F (2,2520) = 187.98, p < .05, for Group Sgg. These results are significant, indicating an effect by pitch-interval categories on accuracy and confidence levels. Surveying all the data discussed above, it is apparent that responses to triads consistently produce lower scores than responses to intervals, and 66 that responses to seventh chords generated even lower scores. Figures 21 through 24 show mean scores for responses by pitch-interval categories. 1 0 9 7.74 8 7.24 7 6.11 s 6 c o 5 r 4 e 3 2 1 0 intervals triads seventh chords Figure 21. Mean scores. Group S 12: pitch-interval stimulus effects. 1 0 9 + 8 -■ 7 6.39 6.19 s 6 -- c 4.99 o 5 r 4 e 3 " • 2 1 • - 0 + 4- interval triads seventh chords Figure 22. Mean scores. Group 8 3 5 : pitch-interval stimulus effects. 67 1 00 90 74.49 % 70 66.03 o 6 ° 51.04 r 50 e C 30 ^ 20 intervals triads seventh chords Figiure 23. Correct responses (%), Group S 12: pitch-interval stimulus effects. 100 T 90 80 -■ % 70 c 60 56.98 o 50.99 r 50 r 40 e 31.15 c 30 t 20 1 0 ______j 0 intervals triads seventh chords Figure 24. Correct responses (%), Group Sgg: pitch-interval stimulus effects. 6 8 Interactions among the variables The ANOVA shows no effects of interactions between the timbrai variables and either of the other two variables (pitch intervals, and melodic vs. harmonic) for the S 12 group. Calculation of the interaction between the timbre and pitch interval variables resulted in F(22,242) = 0.16, p<.05. The F statistic for interaction between timbre and the melodic-harmonic variables is F(11,121) = 1.6, p>.05. Results of the calculation of the interaction between timbre and the pitch interval variables for the 8 3 5 group, F(22,690) = 0.17, p<.05, are consistent with the results for the S 12 group. Results for the interaction between the timbre and melodic-harmonic variables for the 8 3 5 group are significant, F(11,345) = 4.66, p<.05. This suggests that some effect of timbre on melodic and harmonic stimuli exists for the subjects ( 8 2 4 ) with poorly developed aural skills, and that this effect was obscured by the interaction between the timbre and melodic-harmonic variables. Chapter V Conclusions This study investigated the effect that varying timbres might have on the perception of pitch, employing tasks commonly used in aural training. These tasks involved the recognition and identification of intervals, triads, and seventh chords for both melodic and harmonic dictation. Six experiments were used to test the effects of twelve timbres on the subjects’ abilities to identify the pitch-intervals selected for this study. Each experiment tested a different type of pitch-interval within either a melodic or harmonic context The twelve timbres chosen for this survey represented several important attributes of sound. These attributes were suspected to influence the perceptibility of pitch for the dictation tasks used in this study. The attributes of sound examined in this study were waveform, richness of the harmonic spectrum of the sounds’ waveforms, effects of vibrato and jitter, and the use of synthesized and traditional instrumental tones. Four principal hypotheses were proposed, based on the results of previous experimental research: (1) sawtooth and sawtooth-like waveforms would promote better pitch recognition than square-wave or squarewave-like waveforms; (2) tones composed of rich harmonic spectral content would enhance pitch recognition when compared to tones composed of sparse harmonic spectral content; (3) tones containing distinct vibrato and jitter would evoke improved separation of tones for harmonic stimuli when compared to steady-state tones; and (4) traditional instrumental tones would foster more- accurate pitch perception than steady-state synthesized tones. The results of this study do not support these hypotheses. 69 70 Analysis of variance shows that timbre had no significant effect on the accuracy levels of the subjects’ responses to the aural skills tasks in this study. The other two methods of analysis used—examination of the response scores, and observation of the number of correct responses—converge with the results of the ANOVA, Although there was no intention to compare responses to the various categories of intervallic combinations, the ANOVA provided strong evidence of effects on the accuracy and confidence levels of the responses associated with the category of pitch- interval used for the stimuli. This should not be surprising, since the values of the scores correlate with the number of tones in the pitch-intervals; as the number of tones in the stimuli increase from two to four, the response scores decrease. It is reasonable to expect that the more tones that are contained in a stimulus pattern, the more demanding the identification task will be. The greater challenge in identifying more-complex pitch- interval structures is probably due in part to the fact that most music students are vocalists or performers of instruments that produce only one tone at a time. These students have little experience with identifying chord structures, because they have had little or no relevant formal musical training prior to college, in contrast to most instrumentalists who play keyboard or bowed string instruments. Suggestions for future research The study was intended to serve as a basis for further research on the effects of timbre on aural skills. This study may be subject to a high degree of error because the study explores a broad range of attributes of sound within various musical contexts, and because the duration of the testing in regard to both the number of tests and the length of each test, places great physical and aural demands on the subjects. Therefore, it is advisable to be cautious in generalizing the results obtained here without further study. 71 Others are encouraged to repeat this study. Beneficial modifications of this study might include focusing subjects’ attention on fewer stimulus patterns for both melodic and harmonic dictation. The possible choices within a particular category of pitch- interval should be expanded while narrowing the focus of the timbrai effects examined; for example, it would be worthwhile to examine six or seven different harmonic intervals for effects of amplitude- and ffequency-modulations. Future studies might also use test designs that demand shorter testing times. Test sessions designed for a maximum of twenty to twenty-five minutes may prove to be more suitable, because subjects may be able to concentrate throughout the experiment The forty-five minute test sessions composed of stimuli presented every seven seconds demands a high level of endurance and concentration that are atypical of the demands placed on students in the classroom. Subjects’ concentration may have declined because there were six experimental sessions, each with a duration of 45 minutes. This may explain the two unusual score patterns that were observed. Subjects showing steady or slightly rising scores across three or four trial blocks, followed by descending scores, may have exhausted their abilities to concentrate late in the test session. The opposite trend, showing low scores in the middle trial blocks surrounded by higher scores in the outer trial blocks, may indicate that these subjects lost their concentration earlier in the test session and regained concentration when nearing the end of the session. This second pattern is similar to the “eleventh-hour-worker” syndrome. While there is no evidence that these tendencies distorted the data in this study, such patterns can bias the results. While Group S 12 was generally more consistent in its response patterns, some subjects in that group do exhibit the first pattern, with scores dropping after the fourth trial block; for instance, in the melodic interval experiment, consider the accuracy levels of responses by subjects F, J, HH, and II (see Appendix D, p. 112). Although the 72 responses of the remaining twenty-four subjects generally reflect less consistent patterns of scores than did the responses of Group S 12, it is these twenty-four subjects who represent the students who most need assistance in developing stronger aural skills. Experiments of shorter duration, that put less demand on the subjects’ endurance, may produce data revealing clearer patterns of eirors that would help us gain a better idea of what timbres might help these students. The suspicion that students may perform better with sounds that are most familiar to them has been voiced in conclusions by Killam (1982), and by Bales and Foltz (1987). This study was not intended to explore such a conjee tine, nor is there any evidence from the results of this study to support it. It is reasonable, however, that the familiarity of the timbre from a student’s principal performance instrument may elicit quicker and stronger development of aural skills, especially at early levels of aural training. Students who have well developed aural skills will probably perform well despite the timbre, but again, these are not the students who need the help; for example, the accuracy levels for the responses from subjects N and Q are consistently very high (see Appendix D, p. 112), indicating that these two subjects already possess well developed aural skills. Studies examining the correlation of the familiarity of the timbres of subjects’ principal instruments, with the subjects’ accuracy levels of responses to aural tasks, might prove beneficial to our understanding of students’ pedagogical needs. Results from current research, however, suggest that timbre does not affect abihties to accurately recognize the pitch of tones. The limitations of this study prohibited examination of other attributes of sound that need to be explored with respect to aural skills. The onset asynchrony of tone partials and transients are two such attributes. Although studies examining onset asynchrony are found in the experimental literature (e.g., Bregman & Pinker, 1978; 73 Dannenbring & Bregman, 1978; McAdams, 1982b; McAdams, 1984b), there have been no studies examining the effects of onset asynchrony of spectra on pitch-intervals in harmonic contexts. Studies exploring the effects of attack transients are also found in the literature (e.g., Saldanha & Corso, 1964; Grey, 1975; Elliott, 1975; Kendall, 1986), but again, not in regard to effects on the identification of pitch-interval structures. Results firom such examinations could be useful to the pedagogical and psychoacoustic community. While no statistical evidence has shown that timbre significantly affects college musicians’ accuracy levels in identifying pitch-intervals, it would be difficult to convince many musicians that timbre does not effect the accuracy of their judgments. More research examining the effects of the niunerous attributes of sounds used for aural skills training should be encouraged. A greater variety of instruments should be examined. The programming of harmonic dictation drills for CAI software may be improved by the study of the effect of onset synchronicity for tone partials within harmonic stimuli. We need to explore ways to improve effectiveness in teaching aural skills. Current cornputer and sound synthesis technology provides us with the means to utilize a vast resource of sound choices. Digital sampling of traditional instrument sounds is a practical tool for CAI either via MIDI or by direct storage of sound data on hard disks. The cost of mass data storage and digital sampling technology has decreased significantly during the past two years. This helps to make these technologies plausible alternatives for improving computer-assisted instruction of aural skills. College music curriculums are joined with other academic disciplines in being overwhelmed by the age of mass infomiation. As curriculums grow, standard courses are abbreviated to make room for new program requirements. Our attempts to update these programs with progressive subject materials, while retaining traditional studies taught within a standard four-year curriculum, can be a 74 colossal task for the faculty, and the amount of information overwhelming for the students. Although we may need to reconsider the structures of our curriculums, it is clear that we must also become more efficient in teaching these most basic of music skills. Appendix A Pitch-interval and timbrai stimuli 75 76 This appendix shows the randomized sequences of pitch-interval stimuli organized by trial blocks. The stimuli are delineated by barlines. The number above each stimulus represents the timbre used for that stimulus according to the following legend: 1. sawtooth 1, no vibrato, 4 to 6 partials 2. sawtooth 2, with vibrato, 4 to 6 partials 3. sawtooth 3, no vibrato, 20+ partials 4. sawtooth 4, with vibrato, 20+ partials 5. square 1, no vibrato, 4 to 6 partials 6 . square 2, with vibrato, 4 to 6 partials 7. square 3, no vibrato, 20+ partials 8 . square 4, with vibrato, 20+ partials 9. Bb trumpet 10. Bb soprano clarinet 1 1 . oboe 1 2 . piano 77 Melodic intervals - block 1 A 4 12 11 ®r- BT- 1 2 -3P- W 1 1 12 Sjr- W -Sjr- 10 8 10 W" — — .1 CT PC>— ■' ------'' O 1 ------1 1 2 SSr- Z w ■■■ .... 78 Melodic intervals - block 2 7 12 5 6 2 10 2 f d? - ' 4V "W g3 8 4 8 12 3 , —, ■ 12 "W" — ' " ‘ 11 10 11 —*y- 8 7 12 ------cr- 6 9 10 11 - s y - 10 10 4y aT ■& . .. .2 5 2 11 8 1 2 AI ^ qS> -... - 1 "- ' —ay- . av...------— 79 Melodic intervals - block 3 « 9 12 — ...... 1 0 1 212 4V" 1 0 8 11 1 ------43» 5 P — - S j r - 11 9 3 5 W- 10 11 1------jor------ 10 8 12 4 IT------ 11 5 4 r«y- 80 Melodic intervals - block 4 a 7 2 ------ 12 5 10 11 '4LV ‘ AV ------^ ---- 1 0 10 -Æ9- ------ST" 11 9 -4»- -sy- fe "'ff—".7.-' 1= ^ -----~t~ -.. 11 —zy- 5 12 11 -%y- 12 TST" ?3»“ 81 Melodic intervals - block 5 « 1 1 12 8 11 10 11 1 0 —Ix ------ 9 4 12 11 10 11 rsy- -zyr- fll 2 7 5 3 6 7 ^ —:------ 12 1 2 zszz "39------s r - -5S3T- 8 3 10 2 ."ktf'.,—^ .... 1 L—"^y...... 1 12 82 Melodic intervals - block 6 4 1 3 ®r- g 7 9 11 5 4 12 & ------Inre— ------eT <23 * ------—|gy- . 8 10 1 6 4 1 W5>---- I».. ^ • <3> h . 2 3 1 5 7 11 e) ^ ^ H -<0> 10 8 1 5 ■& —ggy—J 8 1 0 12 10 [------a ST"------ 2 6 12 -3y- 12 - Harmonie intervals - block 1 A 4 12 2 3 7 11 4 6 fo ------^ ------...... -1 1 2 11 I —I 4V '—tW . 1 1 1 0 3 1 2 2 1 9 4 — ------h® — J .... " |- T ^ ----- — ------.1. ..I __ «4 1 3 7 1 0 8 1 0 1 | l _ 2 ------— 9 I k 10 6 11 10 5 12 %?- “©r* -53pn 2 1 3 2 ror- -%y- 84 Harmonie intervals - block 2 — ^ — /O ...... «5----- ,8 4 8 12 3 4 12 7 6 -37- T s r *asr- — 1 W""" '4 L-4^ ■*------fm "Aji — 11------J______ ^ ------3 T P ------. ... .1 : - g g . " " : 11 6 10 1 10 - |w 5 11 8 12 1 1 n -----=T------^------1 85 Harmonie intervals - block 3 . 9 12 4 2 6 3 12 ' or- . L1.. ,11 11 2 9 3 5 -W ■531 "" jty «CV "tr or- 8 10 3 7 11 7 5 1 3 -®r- ,2 1 4 6 7 10 8 12 4 1 -i— -— «P “T*®----- 11 9 bT---^ ------1[—^ ----- i——----- u 86 Harmonic intervals - block 4 . 7 2 3 8 1 2 9 12 5 10 11 4 6 10 7 ” -03- 1 10 8 10 7 3 1 "W" XSr- 9 6 2 8 11 9 -or 4V * ^ 8 7 4 12 3 nsT" # *50» g 1 0 11 11 9 8 1 5 6 5 -.4X ""— ' ' ...... 3 •& -& Ç 4 ^ ..... tnu> ‘ 8 ^ . 1 2 6 4 11 7 3 2 12 4 or 87 Harmonie intervals - block 5 ...... I...... rht—^ 1 ^ kit------1—ga—■ 1-4™------ _JUs----- 1 0 8 5 9 4 s z z ^ ^ 6 4 9 12 7 8 9 SP------fw 11 10 11 1 7 5 inp> ---—— z r %p- 6 7 12 4 3 1 2 8 4 -sp- -[ray- 8 3 2 10 2 6 5 12 7 -çjr- I k # 88 Harmonie intervals - block 6 ^2 3 1 5 7 11 7 3 — 4 k = r ^ 10 8 1 3 9 2 11 - V t y - ---- ■J—J3»----- aT 8 ^ ■o ■& 11 7 8 10 8 10 Q ^ 12 — btzr-::; ~ —J—— Æ — 5 — —F---- _j------tv tv 7 jH" •<3> I k 89 Triads (arpeggiated & blocked) - block 1 « 4 12 2 3 7 11 1 2 11 11 9 11 8 2 6 9 3 4 1 6 4 11 1 0 5 1 2 5 9 90 Triads (arpeggiated & blocked) - block 2 ^ 7 12 5 6 10 4 8 1 2 12 ' — ■ ■ I T O 11 10 11 12 jfe :l |#g I g— 10 11 1 0 5 4 -%y- 10 2 11 8 12 1 -Iw — 91 Triads (arpeggiated & blocked) - block 3 A 9 12 4 2 12 - 10 12 8 10 8 11 1 11 9 3 10 11 I 10 8 %7- 12 11 9 8 6 9 .. ^ 7 ^ 92 Triads (arpeggiated & blocked) - block 4 „ 7 2 3 8 tS r :g : Î 9 6 8 11 9 Sjr- 2 12 3 10 11 ■ST---- S—.. 11 5 6 1 2 | g i'i,g 4 11 12 -W {t'S? 93 Triads (arpeggiated & blocked) - block 5 1 1 12 8 11 2 5 10 5 2 10 11 10 Æ"'"" ^ - ! « ■ - - — '" g ------r g ------£T kr rW9 ^ —54” i-SB»------—(no»------L_<îj------= F S ig"'" — 1 - 8 -- 8 6 5 4 3 ■©r- 12___ 7 8 11 10 11 12 -(>< # 12 8 1 0 =S^iS= -%y 12 94 Triads (arpeggiated & blocked) - block 6 4 1 3 5 9 11 1 2 8 10 M g : ri>-"' 1 Iw»1§—— — ^ § = : : :l - L j l i — 5 3 9 2 11 1 11 7 8 - 10 8 12 10 12 6 l ^g— I s - I % 12 95 Seventh chords (arpeggiated & blocked) - block 1 12 2 3 7 11 4 — kWf------L t L g x r r i 4 ^ = r ^ -." — I:: i ^ ^ = l . 6 12 ! 6 5 1 8 # — ri7-T=------4»-^^ 1 j = f e ^ ~ l ~ f •! g 9 11 11 10 3 12 2 -----H-Wp------ 9 11 Ü 1 ^ 4 ^ 8 ■ - t #------^ g = U f—âjty---- g 8 2 6 9 3 4 1 1 t^y r ^ ^ = r - \ = E p = y — 7 10 Î 10 1 6 Ü ^ iff------L. r ~ ^ ~: ' : 1# - — 1: - f s ------ 10 4 11 1 0 12 ►3^ 1 8 3 ÎS: 96 Seventh chords (arpeggiated & blocked) - block 2 « 7 1 2 S 6 2 1 0 :? - 1 1 b t-lrx? ----- 8 4 8 112 3 4 TT r,r^ .— ----- ^ ——L|^ . 12 7 6 3 5 7 2 — «Sr——H ----: AH— CT i.^ r 1 -y 11 1 0 11 1 9 8 -t-l»a5>------»... ^ e = LJ t ^ = k =^FEF=^ 12 9 4 6 9 3 ---r.^«sr— T ^-j] r - L ^ " - 1 9 5 6 8 1 10 é = = rt-W ' ' ' "-" w #W !■~ f^ ~ ... g 11 6 10 1 2 5 4 ^ '• 1 = # = ± f S = fl 10 2 5 2 11 8 1 2 • 1 1 97 Seventh chords (arpeggiated & blocked) - block 3 =4 = 9 12 4 2 L, I 1 1,1-^ OJ 3Z 93 5 1 8 10 3 1 4 ^ 11 9 7 3 5 9 ~ ----- — J— — g 2 8 6 9 5 Î 1 /1 —rl------= ^ = L 4^ — ^ — L|4»-§5>—L 98 Seventh chords (arpeggiated & blocked) - block 4 7 2 3 8 12 10 11 m .§> ..I |'’j , ..I 10 1 10 %;0 »- 10 ^ j)!»' 11 12 T3P^ 4n 11 11 9 jfl 1 If <3^ —1------—rtrrsn»----- —htran f S z z z — ...-1 M A 3 2 12 4 3 Z: T3pr 3 2 = 99 Seventh chords ( arpeggiated & blocked) - bl ock5 1 12 8 11 2 5 fi ^ ----- r f c :------J = S ê : ^ z p g c z J —p — ------j 2 10 I 5 ) 1 10 — 1------l^-.:' =1 t p p i J 11 10 1 ^ 8 6 5 9 AV— ^y., .P # = - # t = k e = &!&, = Î 9 6 4 9 12 — M-Wp ------j f e = — ^ 7 8 9 1 11 10 11 1 Lÿ|lg^- -1.^ 12 s ^ ~ 12 8 p F - jF - 10 12 ^SS3»" 100 Seventh chords (arpeggiated & blocked) - block 6 2 9 4 5 3 7 9 11 12 10 ----- A O 4 X c o X 3 “ ■W» ” r f e — — ------# # : ^"1 ------11 10 11 1 11 d i,l ^ := i gt^: SI 10 12 10 j'^g" :l ip I S' 12 12 Appendix B Examples of answer sheets 101 102 Interval Answers Format. Subject, certainty of choice certainty of choice interval very very very very sure unsure interval sure unsure 1. P4 TT m b M6 m7 M7 1 2 3 4 5 31. P4 TT m6 M6 m7 M7 1 2 3 4 5 2. P4 TT m6 M6 m7 M7 1 2 3 4 5 32, P4 TT m6 M6 m7 M7 1 2 3 4 5 3. P4 TT mb Mb m7 M7 1 2 3 4 5 33. P4 TT m6 M6 m7 M7 1 2 3 4 5 4. P4 TT m b M6 m7 M7 1 2 3 4 5 34. P4 TT m6 M6 m7 M7 1 2 3 4 5 5. P4 TT m6 M6 m7 M7 1 2 3 4 5 35. P4 TT m6 M6 m7 M7 1 2 3 4 5 6. P4 TT m b M6 m7 M7 1 2 3 4 5 36. P4 TT m6 M6 m7 M7 1 2 3 4 5 7. P4 TT m6 M6 m7 M7 1 2 3 4 5 37. P4 TT m6 M6 m7 M7 1 2 3 4 5 8. P4 TT m6 M6 m7 M7 1 2 3 4 5 38. P4 TT m6 M6 m7 M7 1 2 3 4 5 9. P4 TT m6 M6 m7 M7 1 2 3 4 5 39. P4 TT m6 M6 m7 M7 1 2 3 4 5 10. P4 TT m6 M6 m7 M7 1 2 3 4 5 40. P4 TT m6 M6 m7 M7 1 2 3 4 5 11. P4 TT m& M6 m7 M7 1 2 3 4 5 41. P4 TT m6 M6 m7 M7 1 2 3 4 5 12. P4 TT m6 M6 m7 M7 1 2 3 4 5 42. P4 TT m6 M6 m7 M7 1 2 3 4 5 13. P4 TT m6 M6 m7 M7 1 2 3 4 5 43. P4 TT m6 M6 m7 M7 1 2 3 4 5 14. P4 TT m6 M6 m7 M7 1 2 3 4 5 44. P4 TT m6 M6 m7 M7 1 2 3 4 5 15. P4 TT m b M6 m7 M7 1 2 3 4 5 45. P4 TT m6 M6 m7 M7 1 2 3 4 5 16. P4 TT m6 M6 m7 M7 1 2 3 4 5 46. P4 TT m6 M6 m7 M7 1 2 3 4 5 17. P4 TT m6 M6 m7 M7 1 2 3 4 5 47. P4 TT m6 M6 m7 M7 1 2 3 4 5 18. P4 TT m6 M6 m7 M7 1 2 3 4 5 48. P4 TT m6 M6 m l M l 1 2 3 4 5 19. P4 TT m6 M6 m7 M7 1 2 3 4 5 49. P4 TT m6 M6 m7 M7 1 2 3 4 5 20. P4 TT m6 M6 m7 M7 1 2 3 4 5 50. P4 TT m b M6 m l M7 1 2 3 4 5 21. P4 TT m6 M6 m7 M7 1 2 3 4 5 51. P4 TT m6 M6 m7 M7 1 2 3 4 5 22. P4 TT m6 M6 m7 M7 1 2 3 4 5 52. P4 TT m6 M6 m l M7 1 2 3 4 5 23. P4 TT m6 M6 m7 M7 1 2 3 4 5 53. P4 TT m6 M6 m7 M7 1 2 3 4 5 24. P4 TT m6 M6 m7 M7 1 2 3 4 5 54. P4 TT m6 M6 m l M l 1 2 3 4 5 25. P4 TT m6 M6 m7 M7 1 2 3 4 5 55. P4 TT m6 M6 m7 M7 1 2 3 4 5 26. P4 TT m6 M6 m7 M7 1 2 3 4 5 56. P4 TT m6 M6 m7 M7 1 2 3 4 5 27. P4 TT m6 M6 m7 M7 1 2 3 4 5 57. P4 TT m6 M6 m l M l 1 2 3 4 5 28. P4 TT m6 M6 m7 M7 1 2 3 4 5 58. P4 TT m6 M6 m7 M7 1 2 3 4 5 29. P4 TT m6 M6 m7 M7 1 2 3 4 5 30. P4 TT m6 M6 m7 M7 1 2 3 4 5 w N i N) N) N) Ni N i N i N i Ni N i l-k l-k l-k l-k l-k l-k l-k l-k l-k o 03 p* CJl W N i #-k O 00 N p p l fk Gi N i l-k p p co p ai AW N i > > > > > > > > > > > > > > > > > > > > > > > > > > > > > a t s s s K s ^ S S S S S S S S S s s s s §: S S S S S S S g S - > 9^ ov Cl 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 3 g l % %. %. %! % l l l l l % % l l 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 33333 3 3 3 3 3 3 3 3 3 ^01 4k^ ^0% ^9> ^ 9 ^ 9 ^ 9 •k'9 ^ 9 ^9 *9 *9 ^9 *9 *9 99 HJk *-k »-k >-k N-k *-k Mk #-k wk $-k l-k l-k l-k l-k l-k l-k l-k l-k l-k l-k l-k l-k l-k l-k A l-k A A N> N i N) N i N i Ni N i N i N i N i Ni N i N i Ni Ni N) N i N i Ni Ni Ni N i N i N i N i N i Ni N i N i : w | ( WWW W w Oi w Ck) Cki Cki Cki C*i C i C*i Cii Gi Gi c*i C*i Cii Gi co co c*i Gi Gi co co CO f * fh Æk •A Æk ipk fk iCk fk fk fk fk Jk iPk 1^ iPk 1 0 Ipk iCk •& •Ck Ipk AAAAA A CJl Ol Ol CJl CJl CJl CJlCJl CJl CJlCJl CJlCJl CJl CJl CJl CJl CJl CJl CJl CJlCJl CJl CJl CJl CJl CJl CJl:pî CJl CJ] CJl cg CJl CJl CJlCJl CJl fk A fk fk fk fk l> •Ck •pi iCk Gi Gi C*i Gi CO co co CO 03 Ch ÇJl fk w N i »-k p o 03 74p» p i ÿk Gi l-k 0p GO p en A w N i > > > > > > > > > > > > > > > > > > > > > > > > > > > S s s s m: S K s s s s S S 2 : z S 2: 2: 2: 2: 2: 2: 2: 2: 2: 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 g 3 3 3 3 l %. % 9 l %. 9 l 9 % l 3 3 3 3 3 3 3 3 3 3 3 3 33333 3 3 3 3 3 3 3 3 3 ^ 9 ^ 9 ^ 9 Ë , "»9 ^ 9 ^ 9 <^9 «k9 ^ 9 ^ 9 ^ 9 N) r o Ni N i N i N i N i N i N i N i Ni Ni Ni N i N i N i N i N) N i N i N i Ni N i Ni N i N i N i GJ w Ck) c*i Cki Cki Cki Cki Ck) Cki Cki CO Gi Cji Cji Gi Gi C*i CO c*> Gi co Gi CO CO co CO *p> ipk ■pk iP> tPk iPk fk iPk iPk fk ipk A iPk iPk fk iPk tCk ipk lA lA AA A AA A CJl Ul CJl Seventh Chord Answer Format Subject_ seventh chords certainty of choice seventh chords certainty of choice v e r y very v e r y v e r y sure unsure sure unsure /TG l.Y l mt 'I '3 2 4 5 31. Y# Y3 m3 5 2 1 2 3 4 5 /f6 <7 2. YI Y| m 3 2 5 5 1 2 3 4 5 <7 3. Y | YÎ mj 2 5 33. Y | Y3 m3 5 1 2 3 4 5 ^6 ■7 4. Y | Y3 m3 'I '3 2 5 34. Y | Y3 m3 5 ^3 1 2 3 4 5 t s \ 0 7 Û4 «7 5. Y | Y3 m 3 5 2 2 5 5 2 1 2 3 4 5 if6 Û4 -7 6. Y | Y3 m3 ^3 2 5 5 2 1 2 3 4 5 jtfs Jtf4 «7 <7 7. Y | Y3 m3 5 2 2 5 5 ^3 1 2 3 4 5 i^G <7 8. Y | Y3 m3 “% '3 2 5 5 ^3 1 2 3 4 5 jtf6 ^6 «7 9. Y | Y3 m3 5 2 2 5 5 ^3 1 2 3 4 5 10. Y | Y3 m3 Jtf65 J@4 2 «7 2 5 40. Y | Y3 m3 ^3 <7 1 2 3 4 5 A «7 its <7 11. Y | 23 m3 5 ^*2 1 2 3 4 5 41. Yi Y t m i 5 ^3 1 2 3 4 5 jfffi «7 as <7 12. Y| 23 m3 5 ^3 1 2 3 4 5 42. Yi 2 i m | s ^3 1 2 3 4 5 <7 13. Y | 23 m3 ^3 ®7 1 2 3 4 5 43. Yi 25 m i ^3 1 2 3 4 5 Jfi «7 as «7 14. Y | 23 m3 5 2 1 2 3 4 5 44. Yi 2 i m i s 1 2 3 4 5 Jf6 <7 as <7 15. Y| 23 m3 5 ^3 1 2 3 4 5 45. Yi 2 i m i 5^3 1 2 3 4 5 jgA «7 as itf4 <7 16. Y| 23 m3 5 2 1 2 3 4 5 46. Yi 2 i m i 5 2 1 2 3 4 5 <7 as «7 17. Y| 23 m3 ^3 1 2 3 4 5 47. Yi 2 i m | 5^3 1 2 3 4 5 «7 ÜT6 «7 18. Y | 23 m3 5 ^3 1 2 3 4 5 48. Yi 2 i m | 5 ^3 1 2 3 4 5 /f6 <7 as <7 19. Y| 23 5 ^3 1 2 3 4 5 49. Yi 2 i m | s ^3 1 2 3 4 5 J^6 <7 <7 20. Y| 23 m3 5 ^3 1 2 3 4 5 50. Y| 2J m i 5 ^3 1 2 3 4 5 Jff6 <7 as <7 21. Yg 23 m3 5 ^3 I 2 3 4 5 51. Yi 2 i m i 5^3 1 2 3 4 5 J^6 «7 /rs <7 22. Y| 23 m3 S ^3 1 2 3 4 5 52. Yi 2 i m i 5 ^3 1 2 3 4 5 /f6 <7 Jtf6 <7 23. Y| 23 m3 S ^3 1 2 3 4 5 53. Yi 2 | m i S ^3 1 2 3 4 5 Jg4 <7 iï5 ■7 24. Y| 23 m3 S 2 1 2 3 4 5 54. Yi 2$ m i 5 2 1 2 3 4 5 J^6 <7 4^6 <7 25. Yi 23 m3 S 1 2 3 4 5 55. Yi 2 i m i 5 ^3 1 2 3 4 5 <7 as «7 26. Y | 23 m3 S ^3 1 2 3 4 5 56. Yi 2 i m i s ^3 1 2 3 4 5 «7 i^fi <7 27. Y| 23 m3 5 ^3 1 2 3 4 5 57. Yi 23 m i s ^3 1 2 3 4 5 jgfô ^4 «7 <7 28. Yi 23 m3 5 2 1 2 3 4 5 58. Yi 23 m i 2 1 2 3 4 5 If6 <7 29. Yi Y3 m3 5 ^3 1 2 3 4 5 30. Yi 23 m3 '1 4T4 <7 1 2 3 4 5 Appendix C Test scores 105 106 Melodic interval scores Ascending and descending m6 & m7; maximum score = 48. Subject test 1 test 2 test 3 test 4 test 5 test 6 X <7 A 41 46 44 47 46 48 45.33 2.503 B 31 31 30 36 37 26 31.83 4.07 C 31 35 40 38 39 42 37.5 3.937 D 21 19 22 27 17 21 21.17 3.371 E 16 18 20 25 26 26 21.83 4.401 F 15 23 19 19 12 15 17.17 3.92 G 29 24 26 30 24 25 26.33 2.582 H 38 41 41 32 38 38 38 3.286 I 12 8 14 19 12 17 13.67 3.933 J 39 38 43 42 43 36 40.17 2.927 K 31 30 33 33 38 37 33.67 3.204 L 46 43 46 48 48 48 46.5 1.975 M 8 6 11 7 10 14 9.333 2.944 N 46 48 48 48 48 48 47.67 0.816 O 14 15 13 16 16 14 14.67 1.211 P 22 24 25 29 34 32 27.67 4.761 Q 44 44 46 48 47 48 46.17 1.835 R 18 18 18 25 22 28 21.5 4.278 S 28 26 34 41 36 37 33.67 5.68 T 0 11 18 19 17 14 13.17 7.083 U 23 16 15 20 15 17 17.67 3.204 V 8 11 12 9 11 10 10.17 1.472 W 7 4 3 8 5 1 4.667 2.582 X 30 33 32 32 35 32 32.33 1.633 Y 29 28 33 35 36 34 32.5 3.271 Z 19 18 19 19 15 16 17.67 1.751 AA 29 39 44 40 38 47 39.5 6.156 BB 19 20 16 17 18 23 18.83 2.483 CC 33 40 38 37 34 37 36.5 2.588 37 38 39 41 42 47 40.67 3.615 EE 48 48 48 48 48 48 48 0 FF 40 36 36 34 37 37 36.67 1.966 GO 22 22 23 22 21 24 22.33 1.033 HH 19 15 22 28 23 20 21.17 4.355 n 9 14 12 22 15 13 14.17 4.355 JJ 29 36 30 36 29 31 31.83 3.312 107 Harmonie interval scores TT, m6, m7, M7; maximum score = 48, Subject test 1 test 2 test 3 test 4 test 5 test 6 X <7 A 38 41 44 41 44 47 42.5 3.146 B 36 37 36 32 35 36 35.33 1.751 C 14 15 15 20 21 18 17.17 2.927 D 7 8 11 11 8 11 9.333 1.862 E 11 23 16 16 14 16 16 3.95 F 22 17 26 22 15 23 20.83 4.07 G 15 16 25 21 21 30 21.33 5.61 H 23 19 31 34 35 35 29.5 6.863 I 19 14 17 14 21 19 17.33 2.875 J 25 31 31 32 42 38 33.17 5.981 K 28 27 43 39 38 37 35.33 6.408 L 47 48 47 47 48 48 47.5 0.548 M 6 6 6 9 5 10 7 2 N 47 48 48 48 48 48 47.83 0.408 0 4 9 11 8 15 13 10 3.899 P 36 40 40 37 41 37 38.5 2.074 Q 44 46 47 46 48 46 46.17 1.329 R 22 21 21 21 22 22 21.5 0.548 S 24 18 24 23 23 18 21.67 2.875 T 7 15 8 15 14 13 12 3.578 U 21 28 26 28 30 29 27 3.225 V 14 10 9 7 12 13 10.83 2.639 w 8 12 14 11 12 10 11.17 2.041 X 17 10 14 17 13 18 14.83 3.061 Y 33 38 44 36 43 42 39.33 4.367 Z 15 23 20 18 19 15 18.33 3.077 AA 44 47 47 48 47 47 46.67 1.366 BB 21 16 24 22 16 19 19.67 3.266 CC 20 24 25 23 30 31 25.5 4.231 IX> 42 39 45 43 42 39 41.67 2.338 EE 47 48 48 48 46 48 47.5 0.837 FF 23 24 18 12 24 21 20.33 4.676 0 0 21 18 23 19 20 24 20.83 2.317 HH 14 14 15 13 10 12 13 1.789 n 16 17 20 22 21 18 19 2.366 JJ 42 45 46 44 46 45 44.67 1.506 108 Aipeggiated triad scores A, M®, m®, d®; maximum score = 48. Subject test 1 test 2 test 3 test 4 test 5 test 6 X A 33 36 32 33 36 38 34.67 2.338 B 12 18 18 14 13 9 14 3.521 C 17 25 31 26 25 33 26.17 5.601 D 16 15 28 27 25 28 23.17 6.047 E 18 22 24 23 18 23 21.33 2.658 F 17 14 13 17 14 24 16.5 4.037 G 20 29 36 27 31 27 28.33 5.279 H 24 31 36 27 33 35 31 4.69 I 20 14 9 19 24 13 16.5 5.468 J 15 18 23 16 18 30 20 5.621 K 18 31 40 26 38 40 32.17 8.909 L 23 37 33 31 31 40 32.5 5.857 M 8 8 5 5 4 6 6 1.673 N 45 47 45 42 45 48 45.33 2.066 0 8 7 7 12 14 10 9.667 2.875 P 32 36 36 39 43 39 37.5 3.728 Q 42 46 48 46 47 44 45.5 2.168 R 16 21 23 21 21 15 19.5 3.209 S 18 17 14 19 16 17 16.83 1.722 T 17 26 27 21 15 21 21.17 4.75 U 7 9 11 11 10 11 9.833 1.602 V 16 17 16 17 24 17 17.83 3.061 W 15 18 17 17 19 23 18.17 2.714 X 29 33 32 32 33 29 31.33 1.862 Y 36 30 36 34 33 36 34.17 2.401 Z 9 15 12 11 8 10 10.83 2.483 AA 41 42 42 42 43 45 42.5 1.378 BB 21 18 20 18 20 19 19.33 1.211 CC 19 22 15 17 14 21 18 3.225 EO 39 35 40 41 40 39 39 2.098 EE 46 47 46 45 48 47 46.5 1.049 FF 14 24 17 22 25 21 20.5 4.231 GO 24 25 20 22 23 16 21.67 3.266 HH 14 20 17 17 10 10 14.67 4.082 n 14 21 23 31 27 24 23.33 5.75 JJ 22 25 28 32 33 33 28.83 4.622 109 Block triad scores A, M^, m l, d^; maximum score = 48. Subject test 1 test 2 test 3 test 4 test 5 test 6 X 0 A 27 30 35 40 28 33 32.17 4.875 B 18 16 20 13 15 21 17.17 3.061 C 27 21 24 25 12 8 19.5 7.714 D 21 25 26 25 31 25 25.5 3.209 E 24 26 19 24 19 23 22.5 2.881 F 14 12 13 15 13 14 13.5 1.049 G 20 23 21 22 23 23 22 1.265 H 39 41 35 37 39 36 37.83 2.229 I 23 17 16 9 20 27 18.67 6.218 J 19 17 21 14 16 23 18.33 3.327 K 34 31 34 35 30 30 32.33 2.251 L 32 35 36 37 38 38 36 2.28 M 12 17 6 14 13 15 12.83 3.764 N 42 45 45 46 44 41 43.83 1.941 0 13 10 14 13 13 14 12.83 1.472 P 27 28 32 32 29 33 30.17 2.483 Q 42 45 48 48 44 47 45.67 2.422 R 13 20 19 16 8 18 15.67 4.502 S 19 21 22 19 9 6 16 6.753 T 17 17 22 30 30 22 23 5.865 U 16 17 13 10 12 13 13.5 2.588 V 16 15 15 12 10 14 13.67 2.251 W 18 20 16 20 18 18 18.33 1.506 X 31 26 26 29 28 25 27.5 2.258 Y 23 20 28 29 30 27 26.17 3.869 Z 11 8 11 12 12 15 11.5 2.258 AA 31 46 39 41 40 40 39.5 4.848 BB 15 24 18 18 20 18 18.83 2.994 CC 20 18 23 22 19 20 20.33 1.862 IX) 30 27 24 26 27 25 26.5 2.074 EE 39 44 46 48 48 47 45.33 3.445 FF 23 23 24 24 27 26 24.5 1.643 GO 20 24 19 24 21 27 22.5 3.017 HH 18 21 24 24 22 20 21.5 2.345 n 21 27 15 18 16 18 19.17 4.355 JJ 23 30 30 20 22 20 24.17 4.665 110 Arpeggiated seventh chord scores 2 . m 3 , ^5 , maximum score = 48. Subject test 1 test 2 test 3 test 4 test 5 test 6 X <7 A 16 18 17 11 1 0 15 14.5 3.271 B 9 9 16 1 0 1 0 6 1 0 3.286 C 13 8 8 15 13 1 2 11.5 2.881 D 6 8 3 7 7 6 6.167 1.722 E 5 6 6 0 2 8 4.5 2.95 F 17 1 0 11 15 1 0 14 12.83 2.927 G 1 2 17 1 0 17 16 1 0 13.67 3.386 H 14 1 2 1 2 1 2 13 2 1 14 3.521 I 1 2 16 8 17 13 15 13.5 3.271 J 13 17 18 23 26 31 21.33 6.593 K 6 8 8 1 0 9 7 8 1.414 L 2 0 37 40 38 45 46 37.67 9.395 M 6 9 1 0 3 8 4 6.667 2.805 N 38 41 47 45 45 47 43.83 3.601 0 4 1 2 7 11 7 9 8.333 2.944 P 1 2 11 13 1 2 1 0 14 1 2 1.414 Q 36 38 44 46 47 46 42.83 4.665 R 11 8 7 7 8 9 8.333 1.506 S 8 17 14 16 14 9 13 3.688 T 6 6 8 9 6 4 6.5 1.761 U 14 14 1 2 16 19 19 15.67 2.875 V 1 0 13 8 1 0 7 1 0 9.667 2.066 W 1 2 4 11 8 6 8 8.167 2.994 X 13 8 8 4 9 1 2 9 3.225 Y 2 2 23 25 28 27 27 25.33 2.422 Z 8 8 1 0 9 15 8 9.667 2.733 AA 2 0 29 43 40 46 47 37.5 10.75 BB 11 3 4 9 7 8 7 3.033 CC 1 2 8 8 7 8 8 8.5 1.761 EO 18 29 26 28 28 28 26.17 4.119 EE 23 35 38 37 40 43 36 6.928 FF 7 6 7 13 9 7 8.167 2.563 GO 14 8 9 8 6 1 0 9.167 2.714 HH 11 14 13 9 11 1 2 11.67 1.751 n 17 23 18 1 2 1 2 11 15.5 4.68 JJ 7 7 7 1 0 11 5 7.833 2.229 I ll Block seventh chord scores Y z, m 3 , ^|, maximum score = 48. Subject test 1 test 2 test 3 test 4 test 5 test 6 X <7 A 17 16 11 14 17 9 13.83 3.656 B 8 7 9 9 9 10 8.667 1.033 C 7 11 8 7 15 14 10.33 3.559 D 8 5 10 6 7 8 7.333 1.751 E 9 6 6 6 7 5 6.5 1.378 F 12 18 16 13 8 15 13.67 3.502 G 10 12 6 7 13 15 10.5 3.507 H 11 13 7 6 18 15 11.67 4.633 I 17 14 6 14 15 15 13.5 3.834 J 9 20 19 21 18 15 17 4.427 K 19 20 19 20 19 29 21 3.95 L 5 7 9 9 4 8 7 2.098 M 10 8 10 5 9 3 7.5 2.881 N 38 40 38 39 41 41 39.5 1.378 0 14 11 4 11 13 11 10.67 3.502 P 15 26 25 15 24 24 21.5 5.089 Q 38 45 46 45 47 47 44.67 3.386 R 10 14 8 11 11 14 11.33 2.338 S 11 8 9 13 12 9 10.33 1.966 T 12 11 12 10 6 12 10.5 2.345 U 16 15 12 13 9 13 13 2.449 V 8 10 9 16 12 6 10.17 3.488 w 9 10 8 8 8 7 8.333 1.033 X 14 17 18 14 16 13 15.33 1.966 Y .2 4 23 27 24 32 27 26.17 3.312 Z 10 12 9 11 7 8 9.5 1.871 AA 26 28 32 31 26 32 29.17 2.858 BB 17 19 20 18 9 14 16.17 4.07 CC 3 7 6 4 6 3 4.833 1.722 ED 29 34 36 34 33 29 32.5 2.881 EE 20 20 14 19 18 22 18.83 2.714 FF 14 20 16 24 18 20 18.67 3.502 GO 18 18 24 25 27 26 23 4 HH 17 13 10 18 14 17 14.83 3.061 n 23 18 9 17 11 23 16.83 5.879 JJ 17 5 6 11 8 7 9 4.427 Appendix D Data for subjects who scored below chance levels (S 24) 112 113 Mean scores for each test condition across all 12 timbres for Group S 24. Maximum score = 10. MI HI MT HT MSHS sw l 5.98 5.4 5.85 6.07 4.36 4.53 sw2 6.14 5.38 5.55 5.73 4.51 4.61 sw3 6.02 5.6 5.51 5.61 4.21 4.34 sw4 5.92 5.51 5.35 5.53 4.24 ' 4.65 sql 5.96 5.38 5.83 5.85 4.41 4.49 sq2 5.82 5.33 5.63 5.61 4.4 4.51 sq3 5.98 5.55 5.42 5.83 4.2 4.64 sq4 5.83 5.52 5.61 5.73 4.27 4.66 tr 5.86 5.68 5.57 5.79 4.38 4.62 cl 5.87 5.45 5.47 5.56 4.26 4.4 ob 6.16 5.41 5.58 5.88 4.35 4.42 pno 6.07 5.51 5.56 5.81 4.33 4.6 rcent correct responses for each test condition for Group S 24 . MI HI MT HT MS HS swl 51.91 43.92 49.31 48.96 20.31 21.53 sw2 54.69 42.53 44.27 44.27 22.4 25.69 sw3 51.39 46.7 41.49 42.71 17.53 20.49 sw4 51.22 45.49 39.93 40.45 17.01 25.69 sql 50.69 42.88 44.27 44.97 20.66 22.57 sq2 48.96 40.97 42.36 41.67 18.58 22.22 sq3 51.39 47.74 41.84 41.84 19.1 24.83 sq4 48.78 45.83 42.88 43.75 17.36 25.35 tr 50.17 48.26 41.67 44.44 19.97 25 cl 49.13 45.31 40.63 40.97 18.23 19.79 ob 55.73 44.1 42.36 46.7 18.4 22.05 pno 52.95 46.53 44.97 46.7 19.97 24.13 114 Mean scores, Group S 2 4 : sawtooth vs. square waveforms. Maximum score = 10. sawtooth; square; synth. sawtooth-like squarewave synth. only only MI 6 .0 2 5.9 6 .0 1 5.87 HI 5.47 5.45 5.54 5.45 MT 5.56 5.62 5.57 5.47 HT 5.74 5.75 5.83 5.56 MS 4.33 4.32 4.36 4.26 HS 4.53 4.58 4.52 4.4 Mel 5.3 5.28 5.31 5.2 Har 5.25 5.26 5.3 5.14 M 5.27 5.27 5.31 5.17 Percent correct responses, Group S 2 4 : sawtooth vs. square waveforms. sawtooth; square; synth. sawtooth-like squarewave synth. only only MI 52.3 49.96 57.98 49.13 HE 44.66 44.36 50.57 45.31 MT 43.75 42.84 46.01 40.63 HT 44.1 43.06 49.9 40.97 MS 19.31 18.92 2 1 .0 1 18.23 HS 23.35 23.74 25.76 19.79 Mel 38.45 37.24 41.67 36.0 Har 37.37 37.05 42.08 35.36 All 37.91 37.15 41.87 35.68 115 Mean scores, Group S 2 4 : synthesized vs. natural instrumental tones. Maximum score =10. synthesized natural instruments MI 5.96 5.99 HI 5.46 5.51 MT 5.59 5.54 HT 5.75 5.76 MS 4.32 4.33 HS 4.55 4.51 Mel 5.29 5.29 Har 5.18 5.26 AU 5.23 5.27 Percent coirect responses, Group S 2 4 : synthesized vs. natural instrumental tones. synthesized natural instruments MI 51.13 52.0 HI 44.51 46.05 MT 43.29 42.4 HT 43.58 44.7 MS 19.12 19.14 HS 23.55 22.74 Mel 37.85 37.85 Har 37.21 37.83 AU 37.53 37.84 116 Mean scores, Group S 2 4 : steady-state vs. AM & FM modulated tones. Maximum score = 10. steady-state modulated mod. synth. & mod. synth. , synthesis winds winds, & piano MI 5.99 5.93 5.94 5.96 HI 5.48 5.44 5.47 5.47 MT 5.65 5.54 5.54 5.54 HT 5.84 5.65 5.69 5.71 MS 4.29 4.36 4.34 4.34 HS 4.5 4.61 4.55 4.56 5.31 5.27 5.27 5.28 Har 5.27 5.23 5.24 5.25 AU 5.29 5.25 5.26 5.26 :nt correct responses, Group S 24 : steady-state vs. AM & FM modulated tones. steady-state modulated mod. synth. & mod. synth., synthesis winds winds, & piano MI 51.35 50.91 51.24 51.45 HI 45.32 43.71 44.64 44.88 MT 44.23 42.36 42.01 42.38 HT 44.62 42.53 43.18 43.62 MS 19.4 18.84 18.85 18.99 HS 22.35 24.74 23.69 23.74 Mel 38.32 37.37 37.37 37.61 Har 37.43 36.99 37.17 37.41 AU 37.88 37.18 37.27 37.51 117 Mean scores, Group S 2 4 : spectral content. Maximum score =10. low spectral high spectral content content MI 5.98 5.94 HI 5.37 5.55 MT 5.72 5.47 HT 5.81 5.68 MS 4.42 4.23 HS 4.54 4.57 Mel 5.37 5.21 Har 5.24 5.26 AU 5.31 5.24 Percent correct responses. Group S 2 4 : spectral content. low spectral high spectral content content MI 51.35 50.91 HI 45.31 43.71 MT 44.23 42.36 HT 39.67 42.53 MS 19.4 18.84 HS 22.35 24.74 Mel 38.32 37.37 Har 35.78 36.99 AU 37.05 37.18 Appendix E Number of correct responses 118 119 Melodic intervals: subjects in bold type are members of Group S 12. Maximum correct responses per block = 24. A B C DE FGH I J K L sawtooth 1 24 18 19 10 12 10 15 23 5 22 22 23 sawtooth 2 22 18 21 13 11 8 17 20 7 19 17 23 sawtooth 3 23 16 17 12 11 7 17 19 5 20 17 24 sawtooth 4 23 11 19 9 11 6 12 19 7 22 17 23 square 1 23 18 15 11 10 10 20 18 8 17 19 21 square 2 23 14 15 9 14 5 11 19 8 17 20 24 square 3 23 19 21 12 9 4 10 18 6 20 15 23 square 4 22 14 20 12 10 14 8 19 6 21 16 24 trumpet 23 14 21 9 10 11 14 19 8 19 13 23 clarinet 22 16 20 11 10 8 10 16 6 20 12 24 oboe 23 18 19 11 14 13 10 21 10 21 18 23 piano 22 14 18 10 9 9 11 17 9 22 16 24 MN 0 P Q RSTUVW X sawtooth 1 7 24 5 15 24 6 19 6 9 6 3 16 sawtooth 2 6 24 8 14 24 15 16 7 6 6 1 16 sawtooth 3 3 24 5 12 23 12 16 10 8 5 0 13 sawtooth 4 7 24 7 16 23 6 16 7 12 7 3 15 square 1 2 24 10 11 23 9 19 7 11 6 1 17 square 2 5 24 6 12 24 12 14 9 9 3 4 13 square 3 6 24 8 12 23 13 16 8 8 5 3 13 square 4 6 24 8 14 22 9 17 7 6 6 0 13 trumpet 2 24 6 14 24 13 17 3 8 4 2 17 clarinet 1 23 9 18 23 11 16 5 9 1 3 16 oboe 7 23 6 16 22 13 18 4 10 6 6 16 piano 6 24 11 11 24 14 19 8 8 8 4 17 Y Z AA BB CC DDEEFF GG HHII JJ sawtooth 1 16 12 20 5 15 22 24 19 11 9 5 13 sawtooth 2 18 9 19 14 19 23 24 18 13 11 5 14 sawtooth 3 18 11 19 12 21 20 24 15 11 14 11 16 sawtooth 4 18 12 19 6 19 22 24 18 15 14 8 17 square 1 15 9 22 6 17 19 24 14 6 8 8 18 square 2 13 5 19 11 17 20 24 15 10 12 7 15 square 3 17 6 17 10 19 17 24 19 10 10 8 19 square 4 17 9 18 10 17 20 24 18 13 10 4 13 trumpet 16 10 21 11 17 20 24 21 8 9 9 19 clarinet 15 6 19 12 19 21 24 19 15 8 6 16 oboe 16 11 22 11 17 19 24 22 13 12 7 17 piano 18 8 21 8 21 21 24 21 9 10 8 15 120 Harmonic intervals Maximum correct responses per block = 24. A B CD EF G HI J KL sawtooth 1 22 18 10 4 10 11 8 15 10 16 21 23 sawtooth 2 23 17 8 3 10 8 8 15 6 16 19 23 sawtooth 3 22 20 8 4 11 11 11 14 6 15 16 24 sawtooth 4 20 14 9 6 8 11 13 14 11 18 17 24 square 1 20 20 9 4 8 11 9 13 10 17 18 24 square 2 22 15 6 4 8 9 9 16 8 17 17 24 square 3 21 18 8 8 8 12 8 13 8 17 19 24 square 4 21 14 10 5 9 9 16 16 11 18 18 24 trumpet 21 23 11 2 7 15 14 17 11 17 17 24 clarinet 23 18 6 5 5 14 8 17 8 15 18 24 oboe 20 19 10 5 13 13 13 11 10 17 14 24 piano 19 17 12 5 2 7 17 19 6 18 18 23 M N 0 P Q R S TUV WX sawtooth 1 1 24 3 21 23 13 6 7 14 2 6 11 sawtooth 2 2 24 3 18 20 9 11 5 14 2 5 10 sawtooth 3 2 24 8 22 24 9 11 8 16 8 1 9 sawtooth 4 3 23 5 20 24 12 14 7 14 8 3 8 square 1 5 24 3 21 23 9 10 3 13 4 9 12 square 2 4 24 2 18 24 8 10 7 11 4 3 6 square 3 8 24 9 19 24 15 12 7 10 2 7 6 square 4 4 24 8 18 23 10 10 5 13 6 6 5 trumpet 2 24 10 17 23 11 11 6 19 4 8 6 clarinet 3 24 1 11 21 14 14 9 13 10 2 7 oboe 2 24 0 19 24 10 11 8 12 4 9 4 piano 5 24 6 24 24 9 10 2 13 9 8 8 Y Z AA BB CC DDEE FF GG HHII JJ sawtooth 1 21 9 23 7 11 23 24 12 10 9 12 22 sawtooth 2 19 10 23 8 12 22 24 11 13 5 11 21 sawtooth 3 18 10 23 11 15 22 23 12 12 11 11 23 sawtooth 4 22 7 24 12 17 22 23 8 6 10 13 22 square 1 19 11 23 11 9 22 24 6 7 1 5 20 square 2 21 11 24 9 15 17 24 10 8 0 5 21 square 3 20 12 23 14 15 18 24 10 10 11 7 24 square 4 17 8 24 10 12 17 24 7 13 7 6 24 trumpet 20 12 24 6 13 22 24 13 9 7 8 22 clarinet 22 10 23 12 11 19 24 12 11 3 7 23 oboe 17 7 23 9 14 23 23 10 12 7 14 23 piano 20 8 23 10 10 24 24 15 13 8 15 23 121 Arpeggiated triads Maximum correct responses per block = 24. A B CD EFG H I J K L sawtooth 1 19 10 11 16 12 6 16 17 11 13 17 17 sawtooth 2 18 9 13 13 10 10 13 16 8 9 16 18 sawtooth 3 18 8 16 10 11 9 13 14 5 8 16 20 sawtooth 4 19 6 13 8 8 8 13 17 7 12 18 18 square 1 15 7 13 12 14 8 15 14 9 9 15 14 square 2 15 6 13 11 10 5 15 17 9 12 18 16 square 3 15 6 11 10 14 10 15 12 10 7 18 15 square 4 16 7 15 15 12 7 12 16 10 9 15 14 trumpet 20 6 16 11 13 6 14 11 6 7 15 15 clarinet 19 6 11 11 6 9 14 16 7 10 14 18 oboe 16 8 13 11 8 10 12 19 10 12 19 15 piano 18 6 11 12 10 11 18 16 8 11 16 16 M N 0 P Q R S TUVWX sawtooth 1 5 23 1 18 22 10 7 14 7 13 11 19 sawtooth 2 5 24 5 20 23 9 10 11 3 7 13 15 sawtooth 3 0 22 2 21 23 8 7 11 6 9 7 14 sawtooth 4 4 23 6 19 24 11 7 11 2 7 6 14 square 1 6 20 3 19 21 14 13 9 6 11 9 19 square 2 4 20 6 17 23 12 7 14 1 8 7 15 square 3 1 23 7 18 23 7 8 9 7 10 7 13 square 4 2 23 4 21 22 9 9 9 7 8 11 16 trumpet 2 23 5 17 24 9 9 11 5 8 8 16 clarinet 5 24 8 18 23 11 7 9 3 7 9 16 oboe 1 23 2 18 21 10 6 8 6 12 10 11 piano 1 24 9 20 23 9 10 11 6 10 9 18 YZ AA BB CCDD EEFF GG HH IIJJ sawtooth 1 17 6 23 15 12 21 23 10 11 11 11 16 sawtooth 2 16 6 22 11 8 20 24 13 10 4 11 13 sawtooth 3 16 7 22 8 10 2 0 23 12 10 7 13 15 sawtooth 4 18 4 22 8 9 22 23 9 12 6 15 12 square 1 15 2 19 8 9 19 21 10 10 9 9 13 square 2 19 5 22 7 11 20 24 9 9 9 11 14 square 3 17 8 20 6 11 17 23 9 12 7 10 15 square 4 20 3 19 10 9 17 23 10 9 6 11 15 trumpet 17 6 20 10 7 18 23 12 10 7 12 15 clarinet 17 5 22 10 6 17 24 8 11 8 13 16 oboe 17 6 22 11 9 20 24 12 12 11 13 13 piano 15 6 21 12 8 22 24 11 12 5 12 14 122 Block triads Maximum correct responses per block = 24. A B CD E F G H I J K L sawtooth 1 17 13 14 13 14 6 15 21 9 13 15 20 sawtooth 2 14 7 12 13 10 9 10 18 10 10 14 19 sawtooth 3 17 8 11 10 13 7 7 17 9 10 15 16 sawtooth 4 14 7 7 13 9 6 11 21 10 8 19 17 square 1 17 9 10 18 12 5 12 15 10 6 16 17 square 2 20 9 7 14 8 8 11 19 9 9 16 17 squares 13 8 10 7 13 7 12 17 9 8 15 18 square 4 13 8 6 10 9 7 12 18 9 11 17 20 trumpet 16 8 9 15 9 3 9 20 8 9 16 17 clarinet 14 7 10 13 11 8 8 20 7 5 17 19 oboe 17 11 11 15 15 8 12 20 11 8 14 18 piano 19 8 10 13 13 8 13 21 10 9 19 20 MNOP Q RS TUVWX sawtooth 1 4 20 6 15 22 11 10 10 9 8 11 16 sawtooth 2 9 19 8 15 22 9 4 13 6 8 10 16 sawtooth 3 8 24 9 20 24 6 9 8 8 7 8 17 sawtooth 4 9 22 7 14 22 8 6 7 7 6 7 15 square 1 6 21 3 17 23 8 7 15 5 7 9 16 square 2 5 22 4 20 24 7 8 16 4 3 6 12 square 3 5 21 6 13 21 8 7 12 5 9 7 16 square 4 6 24 9 14 22 9 7 9 9 6 12 12 trumpet 7 22 7 11 24 8 9 10 10 10 7 12 clarinet 4 22 6 15 24 6 8 13 3 6 12 12 oboe 6 23 5 14 24 7 9 13 9 7 10 13 piano 6 23 6 15 22 8 12 12 7 5 9 11 YZAA BB CCDDEEFF GG HH II JJ sawtooth 1 15 6 20 10 10 12 24 12 12 16 12 13 sawtooth 2 13 5 18 9 10 14 21 11 11 10 6 13 sawtooth 3 10 9 17 7 9 13 22 12 10 12 12 13 sawtooth 4 14 7 21 6 7 16 22 10 8 11 10 9 square 1 14 4 19 11 10 13 23 14 11 14 8 14 square 2 12 5 2 0 13 12 15 23 10 14 12 6 11 square 3 14 5 18 8 8 12 20 13 12 8 7 11 square 4 16 4 19 11 11 11 21 15 12 10 11 11 trumpet 12 6 21 11 7 12 24 14 12 12 10 15 clarinet 11 5 22 10 10 10 24 12 8 8 8 9 oboe 15 9 20 8 11 17 24 11 11 11 8 13 piano 12 4 20 9 14 14 24 14 14 7 15 11 123 Arpeggiated seventh chords Maximum correct responses per block = 24. ABC D EF GH I J K L sawtooth 1 6 4 5 0 1 10 11 9 5 12 4 3 sawtooth 2 8 8 6 6 5 5 6 13 6 10 7 5 sawtooth 3 5 2 6 4 2 5 8 4 6 10 4 1 sawtooth 4 8 8 6 • 3 0 4 10 4 8 10 3 4 square 1 8 7 8 3 2 9 4 6 7 12 7 4 square 2 7 2 5 5 2 7 5 10 4 10 5 4 square 3 12 4 2 3 0 3 10 5 7 9 4 5 square 4 5 4 6 3 2 11 6 3 8 9 2 6 trumpet 6 3 8 3 3 4 7 10 7 10 5 3 clarinet 5 6 7 3 2 5 4 5 10 12 1 3 oboe 10 3 6 2 3 5 7 5 5 13 3 6 piano 7 6 2 2 1 9 7 9 8 11 3 6 M NO P Q RS TU VWX sawtooth 1 2 20 4 5 21 6 7 6 9 8 5 5 sawtooth 2 7 21 8 8 21 6 3 4 6 5 4 4 sawtooth 3 1 23 5 8 20 8 7 2 5 4 1 5 sawtooth 4 5 21 4 5 22 2 4 1 8 2 3 3 square 1 3 23 6 9 24 5 4 2 8 2 4 6 square 2 1 23 4 6 22 3 7 4 9 5 6 3 square 3 2 23 3 6 22 1 10 6 8 5 5 6 square 4 4 21 2 4 19 2 9 3 6 4 6 6 trumpet 4 22 1 5 22 3 5 3 9 8 4 7 clarinet 2 22 6 2 22 3 4 3 8 3 4 3 oboe 2 21 3 7 23 6 8 3 6 4 3 4 piano 4 23 4 7 20 4 6 5 8 6 4 3 YZAABBCC DDEEFF GG HHII JJ sawtooth 1 10 6 2 0 5 1 16 17 1 5 6 7 5 sawtooth 2 14 5 18 3 5 9 16 2 3 5 5 2 sawtooth 3 14 7 19 3 5 12 19 4 3 3 8 4 sawtooth 4 15 3 16 2 6 15 18 3 3 5 8 3 square 1 11 6 2 0 3 4 10 18 5 7 6 6 6 square 2 15 2 20 6 4 18 20 4 6 5 11 1 square 3 13 6 19 4 3 15 16 3 4 6 4 4 square 4 11 4 21 3 4 11 19 0 5 8 10 2 trumpet 11 6 19 1 5 13 18 4 2 7 7 4 clarinet 13 1 19 6 7 13 20 8 3 6 7 3 oboe 12 6 16 1 5 14 19 6 4 5 13 5 piano 13 6 19 4 3 13 14 3 9 8 9 2 124 Block seventh chords Maximum correct responses per block = 24. AB C DEFG HI J K L sawtooth 1 5 6 3 4 1 6 3 3 9 9 11 1 sawtooth 2 7 5 7 8 6 7 3 4 8 7 11 3 sawtooth 3 7 2 6 6 4 4 8 2 5 8 9 3 sawtooth 4 9 6 6 6 4 5 7 5 7 6 7 4 square 1 9 3 6 4 4 7 4 4 9 5 8 3 square 2 9 4 4 2 2 7 3 8 6 11 8 3 square 3 6 3 6 1 2 10 7 7 6 14 12 4 square 4 8 6 8 3 2 10 5 6 5 10 13 2 trumpet 10 4 6 5 5 4 5 8 7 12 11 3 clarinet 2 3 1 1 3 9 5 3 6 7 12 4 oboe 5 4 6 1 2 12 5 1 4 8 13 6 piano 8 5 3 3 2 5 9 8 5 5 10 1 M N 0 P Q RS T UVW X sawtooth 1 4 20 7 12 22 6 3 5 6 5 4 10 sawtooth 2 6 20 5 13 22 7 7 6 5 2 4 7 sawtooth 3 3 19 3 9 22 2 4 4 . 3 5 2 9 sawtooth 4 6 19 8 12 22 8 4 5 7 7 3 5 square 1 1 22 5 8 22 4 5 7 6 3 6 8 square 2 4 19 7 10 23 5 5 4 6 5 5 6 square 3 3 20 5 14 22 5 4 5 8 8 4 11 square 4 5 17 5 11 23 5 6 6 7 10 4 7 trumpet 3 21 5 14 22 8 7 5 8 4 3 8 clarinet 3 20 4 7 22 6 7 3 4 5 4 6 oboe 4 17 5 7 23 6 3 7 5 1 7 5 piano 1 22 5 13 23 6 7 5 10 5 3 11 Y Z AA BB CC DDEEFF GG HH IIJJ sawtooth 1 11 1 14 7 1 14 6 9 11 8 6 4 sawtooth 2 12 3 13 13 3 18 7 10 11 4 10 4 sawtooth 3 13 7 15 4 2 16 8 10 11 11 7 4 sawtooth 4 IS 7 15 7 3 16 8 8 14 6 7 4 square 1 13 5 18 8 1 17 9 11 10 10 6 5 square 2 14 5 13 9 5 12 8 9 11 3 5 2 square 3 12 4 16 11 2 17 13 8 12 8 9 5 square 4 15 5 15 8 2 17 6 10 9 8 8 7 trumpet 13 4 13 8 1 16 8 8 12 8 9 6 clarinet 14 6 14 7 1 15 10 9 8 7 9 3 oboe 15 6 15 6 4 19 12 8 13 7 12 5 piano 13 3 14 8 2 16 10 8 14 8 11 5 Appendix F Example of data averaged across trial blocks 125 126 Subject: AA stimulus timbre B lk l B lk 2 BlkS B lk4 B lk 5 B lk 6 X total X correct tt sawtooth 1 10 10 10 10 8 10 9.67 23 9.083 tt sawtooth 2 10 10 10 10 10 10 10 23 9.25 tt sawtooth 3 10 10 10 10 10 8 9.67 23 9.292 TT sawtooth 4 10 10 10 9 10 9 9.67 9.125 tt square 1 10 10 10 10 10 9 9.83 23 9 tt square 2 10 9 10 10 10 10 9.83 24 9.458 tt squares 10 10 10 8 10 10 9.67 23 9.375 TT square 4 10 10 10 10 10 9 9.83 24 9.417 tt trumpet 10 10 10 8 10 10 9.67 24 9.375 tt clarinet 10 10 10 10 10 9 9.83 23 9.375 tt oboe 10 10 10 10 10 10 10 23 8.958 tt piano 10 10 10 10 9 9 9.67 23 9.167 nrô sawtooth 1 10 8 10 10 9 5 8.67 m6 sawtooth 2 10 10 9 9 9 3 8.33 n)6 sawtooth 3 5 10 10 10 9 9 8.83 nJ6 sawtooth 4 10 10 9 10 9 8 9.33 w6 square 1 10 10 10 10 9 3 8.67 m6 square 2 10 10 9 10 10 9 9.67 m6 squares 10 9 9 10 8 9 9.17 square 4 6 10 10 10 10 7 8.83 m6 tnimpet 10 10 9 9 10 9 9.5 m6 clarinet 10 10 10 10 9 9 9.67 m6 oboe 10 9 7 9 9 10 9 m6 piaiK) 9 10 10 10 9 9 9.5 m7 sawtooth 1 7 10 8 9 6 8 8 m l sawtooth 2 10 9 8 8 9 9 8.83 m l sawtooth 3 9 10 8 8 9 8 8.67 m7 sawtooth 4 6 7 10 7 6 9 7.5 tn7 square 1 6 9 6 6 9 9 7.5 m l square 2 10 10 8 7 8 7 8.33 m7 squares 10 5 10 10 8 9 8.67 m7 square 4 10 8 9 9 8 10 9 m l trumpet 10 7 8 10 6 9 8.33 m7 clariibt 9 9 8 9 9 5 8.17 m l oboe 7 7 6 8 5 8 6.83 m7 piano 7 9 8 4 10 7 7.5 M7 sawtooth 1 10 10 10 10 10 10 10 M7 sawtooth 2 10 10 10 10 9 10 9.83 M7 sawtooth 3 10 10 10 10 10 10 10 M7 sawtooth 4 10 10 10 10 10 10 10 M7 square 1 10 10 10 10 10 10 10 M7 square 2 10 10 10 10 10 10 10 M7 squares 10 10 10 10 10 10 10 M7 square 4 10 10 10 10 10 10 10 M7 trumpet 10 10 10 10 10 10 10 M7 clarinet 10 10 10 10 10 9 9.83 M7 oboe 10 10 10 10 10 10 10 M7 piano 10 10 10 10 10 10 10 Appendix G Scores for ANOVA 127 128 Melodic interval scores: subjects in bold type are members of Group S 12- Responses converted to scores for ANOVA; maximum score = 10. ABC DEFGHI sawtooth 1 10 8.17 7.21 5.54 5.62 5 .2 1 6.21 8.17 4.52 sawtooth 2 9.37 7.58 7.75 5.71 5.54 4.83 6.42 7.67 5.5 sawtooth 3 9.71 7.17 6.62 5.62 5.62 4 .2 9 6.54 7.63 4.42 sawtooth 4 9 .6 3 6 7.29 5.29 5.33 4 .2 5 5.42 7.29 4.71 square 1 9.71 7.25 6.71 5.75 5.08 5.17 6.58 7.29 5.08 square 2 9.71 6.92 6.17 5.67 6.21 4 5.42 7.38 5.08 square 3 9.67 7.46 7.67 6.21 5 3 .4 6 5.5 7.21 4.46 square 4 9 .3 3 6.37 7.42 5.58 5.08 5.75 5.08 7.58 5.04 trumpet 9 .2 5 6.54 7.79 5.58 5 5 .0 8 5.96 7.54 4.96 clarinet 9.42 7.08 7.58 5.83 5 4.79 5.46 6.71 4.25 oboe 9 .6 3 7.5 7.25 5.62 5.92 5 .6 2 5.71 8.04 4.96 piano 9 .4 2 7.08 7 5.04 5 4.96 5.63 7.21 5.46 J KLMN OP Q R sawtooth 1 9.46 8.92 9.54 4.42 9 .9 6 4.67 6 .6 3 10 4.58 sawtooth 2 8 .2 1 7.17 9.54 4.54 9.96 5.04 6.04 10 6.13 sawtooth 3 8.67 7.38 9.92 4.5 10 4.88 5.63 9.63 5.96 sawtooth 4 9 7.67 9.58 4.54 9 .9 2 5.04 6 .6 7 9 .6 3 4.58 square 1 7.75 8.13 9.04 4.17 9 .9 6 5.25 5.79 9.63 5.13 square 2 7.71 7.96 9.79 4.67 9 .9 2 4.46 5 .5 8 10 5.79 square 3 8 .3 8 6.67 9.71 4.63 9 .9 2 5.04 5 .9 2 9 .6 3 5.88 square 4 8 .7 1 7 10 4.54 9 .8 8 5.54 6 .0 8 9 .6 1 5.25 trumpet 8 .5 6.63 9.58 4 9 .9 6 4.61 5 .8 8 10 5.75 clarinet 8 .4 6 5.54 9.92 4 9.63 5.17 6.92 9.63 5.79 oboe 8.75 7.29 9.71 4.91 9 .6 7 4.79 6.75 9.25 5.71 piano 9 .1 7 6.79 10 4.63 9 .9 2 5.67 5.38 10 6.21 129 Melodic interval scores, continued S T U VW XYZAA sawtooth 1 7 4.25 4.75 3.75 4.25 6.13 7 .2 5 5.5 7 .7 5 sawtooth 2 6.67 4.46 4.17 3.96 3.96 6.58 7 .6 3 5 7 .4 6 sawtooth 3 6.71 5.08 4.71 4.09 3.88 5.88 7.79 5.29 7 .5 4 sawtooth 4 6.38 4.46 5.63 3.92 4.08 6.17 7.58 5.58 7.75 square 1 7.21 4.46 5.33 4.29 4.08 6.63 6 .6 7 4.87 8 .2 9 square 2 6.04 4.88 4.42 3.25 4.58 5.71 6 .3 4 7 .3 8 square 3 6.54 4.67 4.79 3.96 4.25 5.54 7 .3 3 4.42 7 .2 1 square 4 6.83 4.46 3.88 4.36 3.54 5.79 7 .7 9 4.7 7 .2 5 trumpet 6.79 3.63 4.58 3.33 4 6.58 6.88 5.13 8 clarinet 6.29 4.04 5.04 3.5 3.83 6.33 7 .3 8 4.08 7 .5 oboe 7 3.83 5.13 3.91 4.29 6.42 6.88 5.33 8.25 piano 7.21 4.74 4.67 4.38 4.71 6.67 7.92 4.67 8 .0 8 BB CC DD EE FF GG HHII JJ sawtooth 1 4 6.63 7 .6 7 10 8.04 5.5 4 .7 5 4 .7 1 6.21 sawtooth 2 5.79 7.58 7 .7 9 10 7.75 5.96 5 .1 3 4 .6 7 6.92 sawtooth 3 5.33 7.67 7 .3 3 10 7.17 5.58 5 .8 8 5 .5 6.92 sawtooth 4 4.75 7.33 7 .7 5 10 8 6.29 5 .9 2 5 .0 4 6.83 square 1 4.88 6.92 7 .0 8 10 6.87 4.48 5 .1 3 4 .9 6 7.65 square 2 5.29 7.04 7 .1 7 10 6.91 5.29 5.33 4.83 6.87 square 3 5.25 7.5 6.71 10 8.21 5.29 4.75 5.04 7.75 square 4 5 6.87 7 .4 2 10 7.96 5.75 5 4 .5 4 6.25 trumpet 4.88 6.71 7 .3 8 10 8.83 4.5 4 .7 1 5 .1 3 7.63 clarinet 5.67 7.38 7 .5 8 10 8.58 6.42 4.42 4 .8 8 7.38 oboe 5.08 7.08 7 .1 3 10 9.08 5.79 5.58 4.92 7.54 piano 5 7.5 7 .4 6 10 8.96 5.25 4.83 5 .2 1 6.29 130 Harmonie interval scores A B C DE F G H I sawtooth 1 8 .9 2 7.42 4.71 3.21 4.92 5 .1 7 5.09 6.46 4.88 sawtooth 2 9 .3 3 7.29 4.54 2.96 4.71 4.88 4.87 6.71 4.5 sawtooth 3 8 .5 8 7.96 4.58 3.29 5.17 5 .3 8 5.43 6.13 4.17 sawtooth 4 8 .5 2 6.71 4.92 3.79 3.92 5 .4 6 6.04 6.42 5 square 1 8 .1 3 7.46 5.13 3.54 4.25 5.83 5.42 6.25 5.04 square 2 8 .8 8 6.58 3.88 3.38 4.29 5.08 5.21 6.83 4.96 square 3 8 .4 2 7.25 4.75 3.58 4.25 5 .4 6 5 5.83 4.17 square 4 8.5 6.46 5.25 3.88 4.63 5 .2 1 6.61 6.75 4.83 trumpet 8 .5 8 8.21 5.04 2.83 4.04 6.38 5.92 7.04 5.21 clarinet 9 .0 4 6.88 3.92 3.5 3.25 5.75 4.87 6.5 5 oboe 8.33 7.25 4.71 3.71 5.38 5.58 5.78 5.75 5 piano 7 .8 8 7.46 5.58 3.54 2.75 4.83 6.58 7.42 4.3 J K LMN O P Q R sawtooth 1 7 .2 5 8.29 9.67 3.38 9.83 3.71 8.63 9 .7 9 5.75 sawtooth 2 7 .3 8 7.75 9.63 3.42 9.96 3.71 7 .8 3 9 .1 7 5 sawtooth 3 6 .8 8 6.92 9.96 3.55 9.75 5.17 8.5 10 5.04 sawtooth 4 7.71 '7.25 10 3.71 9 .6 3 4.25 8.33 9.83 5.63 square 1 7 .3 3 7.42 10 3.92 9.75 4.04 8 .2 5 9 .7 9 4.71 square 2 7 .4 6 7.71 9.96 4.09 9 .7 9 3.46 7.83 9.83 5.08 squares 7.58 7.88 10 4.92 9 .9 2 5.58 8 .2 1 10 6.33 square 4 7.63 7.67 9.92 3.63 9 .9 2 5.08 7.67 9.46 5.04 trumpet 7 .7 1 7.46 10 3.75 9.88 5.13 7 .5 8 9 .6 3 5.79 clarinet 7 .2 5 8 9.92 3.57 9.92 3.5 5.92 8 .7 1 6 oboe 7 .5 6.79 10 3.5 9.83 3.83 7.96 10 5.08 piano 7 .6 7 7.71 9.71 3.46 10 4.25 9 .1 7 10 4.83 131 Harmonie interval scores, continued S TU V W XYZAA sawtooth 1 5.33 3.92 6.33 2.36 4.33 4.96 8.71 5.17 9.08 sawtooth 2 5.67 3.75 6.58 3.55 4.08 4.83 8.17 5.25 9.25 sawtooth 3 5.42 4.21 6.67 4.39 3.83 4.54 7.79 5.58 9.29 sawtooth 4 6 4.17 6.08 4.65 3.83 4.38 9 .2 1 5.17 9 .1 3 square 1 5.92 3.42 6.04 3.83 4.5 5.33 8 .2 9 5.5 9 square 2 5.71 4.29 5.54 4.23 3.83 3.96 9.08 5.5 9 .4 6 square 3 5.75 4.17 5.29 3.5 4.17 3.96 8.46 5.42 9 .3 8 square 4 5.83 3.67 6.17 4.08 4.29 3.54 8 .0 4 5.25 9 .4 2 trumpet 5.71 3.67 8.08 4.08 4.42 4.04 8 .5 4 5.29 9 .3 8 clarinet 5.92 4.54 6.33 5.33 3.67 3.75 8.75 5.5 9.38 oboe 5.79 4.46 5.88 3.54 4.46 3.38 7 .5 4 5.21 8 .9 6 piano 5.63 2.96 5.88 5.13 4.58 4.17 8 .2 5 5 9 .1 7 BB CC DD EE FF GG HH IIJJ sawtooth 1 4.54 5.58 8 .7 9 1 0 5.67 5.38 5 .0 4 5 .5 8 8.54 sawtooth 2 5 5.79 8 .5 4 1 0 5.25 5.67 4 5 .7 1 8.58 sawtooth 3 5.04 6.54 8 .7 1 9 .6 3 6.17 5.5 5 .3 8 5 .4 2 9.04 sawtooth 4 5.54 6.83 8 .6 3 9 .6 3 4.63 4.5 5 .2 5 6 .0 4 8 .8 8 square 1 5.17 5.25 8 .3 8 1 0 3.67 5.08 3 .2 1 4 .7 9 8.29 square 2 4.88 6.29 7 .0 4 9 .9 2 5.17 4.96 3.25 4 .8 8 8.25 square 3 5.63 6.71 7 .5 8 1 0 4.79 5.13 5 .3 3 5 .2 5 9.21 square 4 4.83 5.79 7 .1 7 1 0 4.22 5.79 4 .6 7 4 .9 2 9.29 trumpet 4.13 6.46 8 .8 3 1 0 6.13 5.21 4 .5 8 5 .2 5 8.71 clarinet 5.29 5.5 7 .5 4 9 .9 2 5.67 5.25 3 .5 8 4 .9 6 9.04 oboe 4.75 6.38 8 .9 2 9.63 5.33 5.29 4.39 6.04 8.58 piano 4.83 5.46 9 .1 3 1 0 6.33 5.83 4 .5 8 6 .2 5 8.79 132 Arpeggiated triad scores A BC D EFGH I sawtooth 1 8 . 2 1 5.17 5.67 6.83 5.79 4 .4 6 6.38 6 .8 8 5.71 sawtooth 2 7 .6 7 5.21 6.42 5.63 5.38 5 .0 8 5.92 6.58 5.18 sawtooth 3 7 .7 9 5 6.63 5.58 5.63 4 .7 5 6.17 6.29 4.33 sawtooth 4 7 .9 6 4.71 6.25 5 5.13 4 .7 1 5.92 6 .8 8 4.63 square 1 7 .2 7 4.32 6 .6 8 6 6.41 4.68 6.73 6.73 5.68 square 2 7 .0 8 4.42 6.46 5.63 5.5 3 .9 2 6.54 6.92 5.46 square 3 7 .0 4 4.29 5.88 5.25 6.17 4.96 6.25 5.71 5.83 square 4 7.61 4.33 6.67 6.71 6.09 4.33 5.71 7.08 5.92 trumpet 8 . 2 1 4.42 6.92 5.33 5.88 4 .0 4 6.26 5.63 4.75 clarinet 8 .1 3 4.46 5.83 5.79 4.58 5 .3 6.46 6.67 5.33 oboe 7 .3 3 4.79 6.04 5.96 5.04 5.13 6.04 7.63 5.5 piano 7 .7 9 4.33 5.71 5.67 5.54 5 .1 3 6.75 6.92 5.04 J K LM N O P Q R sawtooth 1 6 . 2 1 7.58 7.5 4.46 9 .5 4 4 7 .7 5 9 .2 5 5.63 sawtooth 2 5 .4 2 7.29 7.42 4.46 9.88 4.38 8 .3 3 9 .6 3 5.33 sawtooth 3 5 .2 5 7.08 8 .2 1 3.96 9 .3 3 4.08 8 .7 5 9 .7 9 4.79 sawtooth 4 6.13 7.71 7.42 4.54 9.75 4.88 8.33 9 .8 3 5.46 square 1 5.68 7 7.27 4.59 9 .4 1 4.5 8 .2 7 9 .4 1 6.41 square 2 6.13 8.25 7.75 4.67 8.75 4.79 7.29 9 .7 9 5.79 square 3 4.88 7.54 6.96 4 9.46 4.88 7.96 9 .2 9 4.295 square 4 5.5 7.21 6.71 4.17 9.63 4.88 8 .6 7 8 .9 2 5.17 trumpet 4 .5 8 7.38 7.38 3.88 9 .6 7 5 7 .2 9 9 .8 3 5.5 clarinet 5 .5 4 6.74 7.96 4.54 9 .8 8 4.88 7 .6 7 9 .4 6 5.71 oboe 6 .1 7 7.71 7.25 4.08 9.54 4.38 7.46 8 . 8 8 5.79 piano 5 .7 1 7.21 7 3.96 9.92 5.08 8.46 9 .6 3 5.42 133 Arpeggiated triad scores, continued S TUV WX YZAA sawtooth 1 4.83 5.63 4.46 5.92 5.42 7.75 7.79 3.96 9.46 sawtooth 2 5.58 5.21 3.54 4.5 5.67 6.58 7 .4 6 4.08 9 .0 8 sawtooth 3 4.83 5.13 4.29 5.22 4.67 6.58 7 .2 1 4.58 9 .1 7 sawtooth 4 5.04 4.96 3 4.38 4.58 6.5 7 .7 9 3.79 8 . 8 8 square 1 6.09 5.09 4.23 5.82 5.17 8.09 7 .0 9 3.5 8 .5 square 2 5.35 5.96 3 5.04 4.88 6.63 7.83 4.25 8 . 8 8 square 3 5.21 4.63 4.88 5.17 4.67 5.79 7.79 4.75 8.38 square 4 5.21 4.71 4.5 4.71 5.5 7.08 8 .2 5 3.83 8 .2 5 trumpet 5.58 5.21 3.88 5.04 4.92 6.67 7 .4 6 4.17 8 .3 3 clarinet 4.96 4.83 3.17 4.46 4.92 7.13 . 7.63 4.33 8.96 oboe 4.71 4.42 4.04 5.67 4.96 5.71 7 .3 8 4.21 8 .9 6 piano 5.17 5.21 4.25 5.17 4.88 7.58 7 4.17 8 .7 5 BB CC DD EE FF GG HH IIJJ sawtooth 1 6.79 5.63 7.83 9.58 5.67 5.57 5 .5 4 5 .9 2 7.13 sawtooth 2 5.5 5.08 7.58 9.92 6.38 5.29 4 5 .8 8 6.7 sawtooth 3 5.25 5.5 7 .7 1 9 .7 5 6.17 5.26 4 .9 2 6 .0 4 6.92 sawtooth 4 4.92 5.21 7 .7 9 9 .6 3 5.13 5.79 4 .7 5 6 .2 5 6.55 square 1 5.23 5.41 7.73 9.55 6.41 5.64 5 .1 4 5 .5 9 6.95 square 2 4.88 5.25 7 .5 8 1 0 5.67 5.33 5 .1 7 5 .6 7 6.79 square 3 4.58 5.71 6.92 9.63 5.26 5.79 4 .8 8 5 .7 9 6.5 square 4 5.46 5.42 7 .1 7 9 .7 1 5.83 4.96 4.46 6.04 6.92 trumpet 6 5.04 7.04 9.58 6.58 5.33 4 .8 3 6 .1 3 6 .8 8 clarinet 5.63 4.88 6 .8 3 1 0 5.08 5.54 5 .0 4 5 .7 9 7.29 oboe 5.88 5.67 7 .5 1 0 6.25 5.75 5 .6 7 6 .0 8 6.55 piano 5.92 4.96 8 .1 3 1 0 5.54 5.58 4 .5 6 .1 3 6.42 134 Block triad scores A B C DEFGHI sawtooth 1 7 .2 9 6.17 6.42 6.79 6.25 4.25 6.83 8.17 5.65 sawtooth 2 6 .8 3 4.96 6.13 6.54 5.42 5 .1 3 5.67 7.42 6.3 sawtooth 3 7.17 5.13 5.75 6.17 6.17 4 .5 8 5.17 7.04 5.29 sawtooth 4 6.42 4.67 4.67 6.33 5.5 4 .8 8 5.96 7.88 5.96 square 1 7.52 5.26 5.83 7.78 5.78 4 .5 2 6.17 6.57 5.91 square 2 7 .9 6 5.17 5.17 6.96 5.08 5 5.83 7.54 5.59 square 3 6.45 5.55 5.63 5.14 6.36 5 6.23 7.5 6.14 square 4 6 .3 3 5.17 4.58 6.5 5.21 4 .7 1 6 7.04 6 .2 1 trumpet 7 .0 8 5.17 5.21 7.04 5.46 4 .0 4 5.63 7.88 5.75 clarinet 6.46 5.17 5.33 6.5 5.46 4 .9 2 5.29 7.5 5.3 oboe 7 .2 1 6.08 5.71 6.71 6.42 4 .5 4 6.04 7.71 6.04 piano 7 .5 4 5.04 5.17 6.67 6.04 5 .0 8 6 7.79 6.13 J K L M NO P Q R sawtooth 1 6 .6 3 7.38 8.25 5.13 8 .4 2 4.46 6 .9 2 9 .4 2 5.5 sawtooth 2 6 7.17 8.04 5.29 8 .0 4 5.25 6 .6 7 9 .2 5 5.08 sawtooth 3 5 .5 4 7.17 7.46 5.54 9.58 5.33 6.92 9 .8 3 4.25 sawtooth 4 5.38 7.83 7.71 5.33 9 .0 4 4.96 6 .5 4 9 .2 5 4.71 square 1 4 .8 3 7.52 7.57 5.04 9 .0 4 4.13 7 .2 2 1 0 4.78 square 2 5 .0 8 7.5 7.58 4.83 9 4.67 7.17 1 0 4.5 square 3 5.77 7.64 8.09 4.68 9 .3 2 5.23 6 . 8 6 9 .5 9 4.86 square 4 5 .9 2 7.58 7.88 5 9.25 5,58 6 .8 3 9 .5 8 5.29 trumpet 5 .5 8 7.46 7.42 5.17 9 .1 3 5.17 6 . 2 1 9 .8 3 4.83 clarinet 4 .5 4 7.71 8.13 4.75 8 .9 2 4.67 6.79 9.83 4.54 oboe 5 .4 2 7.13 8 5 9 .2 9 4.46 6 .7 9 9 .8 3 4.38 piano 5 .5 8 8.13 8.43 5.61 9 .1 3 4.46 6.46 9.42 5.04 135 Block triad scores, continued S T U VW XYZ AA sawtooth 1 5.63 5.08 5 5.7 5.88 6.96 6.96 4.46 8 . 2 1 sawtooth 2 4.29 5.71 4.08 5.04 5.87 6.92 6 4.29 7 .7 1 sawtooth 3 5.25 4.67 4.54 4.54 4.83 7.08 5 .5 4 5.17 7 .3 3 sawtooth 4 4.96 4.46 4.17 5.3 5.42 6.5 6 .6 3 4.88 8 .3 3 square 1 4.87 6.26 4.22 4.65 5.3 7.04 6.87 3.87 8 .5 square 2 5.42 6.33 4 3.73 4.74 6.13 6 .2 5 4.08 8 . 2 1 square 3 5.04 5.5 4.32 5.52 5.05 7.32 6 .9 5 4.21 8 .5 square 4 4.58 4.88 5.5 4.3 6 .2 1 6 6.96 4.08 7.96 trumpet 5.08 5.08 5.48 6.17 5.04 5.88 6 .4 6 4.54 8 .2 9 clarinet 4.96 5.71 3.71 4.71 5.92 6.08 6 .0 4 4.17 9 .0 4 oboe 5.33 5.71 5.21 4.88 5.5 6.13 7 .0 4 5.13 8 .2 5 piano 5.46 5.5 4.46 3.91 5.71 5.54 6 .2 5 3.96 8 .2 9 BB CC DD EE FF GG HH II JJ sawtooth 1 6.04 5.58 6.13 9.54 6.08 6.08 6 .9 6 5 .8 8 6.25 sawtooth 2 5.38 5.42 6.38 8.67 5.42 5.58 5 .4 2 4 .8 8 6.35 sawtooth 3 5.42 5.13 6 .3 3 9 .2 1 5.71 5.38 5 .7 9 5 .9 2 6.42 sawtooth 4 5.13 5 7 9 .1 7 5.38 5.04 5.71 5 .5 8 5.08 square 1 6.09 5.82 6 .7 8 9 .5 2 6.96 5.91 6 .3 9 5 .2 6 6.95 square 2 6.17 5.92 6 .7 5 9 .2 5 5.25 6.38 5 .6 7 4 .5 6.04 square 3 5.74 5.32 6 .3 2 9 .1 8 6.73 6.18 5 .4 5 5 .2 7 6.05 square 4 5.96 5.96 5.92 8.63 6.78 5.67 5.5 5.88 5.58 trumpet 6.25 4.71 6.33 9.5 6.42 5.79 5 .7 9 5 .5 4 6.25 clarinet 5.88 5.67 5 .8 3 9 .5 6.25 4.92 5 .1 3 5 .2 1 5.22 oboe 5.46 5.88 7.17 9.83 5.92 5.79 5.71 5.42 6.48 piano 5.67 6.3 6.54 9.38 6.42 6.29 4 .8 3 6 .5 8 5.75 136 Aipeggiated seventh chord scores A B C DE F G H I sawtooth I 3 .9 6 4.29 4.42 3.42 2 .8 8 5 .6 3 5.5 5.13 4.83 sawtooth 2 4.46 5.08 4.75 4.08 3.67 4 4.92 6.29 5.29 sawtooth 3 3.67 4.17 4.58 3.79 3.46 4.67 5.33 3.67 5.38 sawtooth 4 4 .5 8 4.58 4.79 3.58 2.83 4 .0 8 5.46 3.92 5.54 square 2 4 .1 7 4.38 4.83 4.33 2.92 4 .7 5 5.08 5.29 5.25 square 3 5 .2 1 4.5 3.63 3.63 2.63 4 .0 8 5.38 4.42 5.17 square 4 3.88 4.42 4.75 3.38 3 5 .5 8 5.04 3.96 5.33 trumpet 4 .3 3 4.13 5.29 3.83 3.21 3 .8 8 5.13 5.33 5.39 clarinet 3 .8 8 4.42 5 3.58 3.04 4.17 4.88 4.21 5.57 oboe 5 .0 4 4.21 4.92 3.5 3.42 4 .2 9 5.25 3.88 5.08 piano 4 .2 9 5.04 4.21 3.54 3 5 4.96 4.96 5.48 J K L MN OP Q R sawtooth 1 5 .8 3 4.29 3.08 4.67 8 .5 4 4.67 5.21 9.04 4.46 sawtooth 2 5 .0 8 4.71 3.5 4.79 8 .9 2 5.04 5 .3 3 8 . 8 8 4.67 sawtooth 3 5.58 4.21 2.65 4.17 9 .3 8 4.83 5 .3 3 8 .5 4.83 sawtooth 4 5 .2 1 4 3.25 4.67 8 .7 5 4.54 5 .2 1 9 .0 8 3.75 square 1 5 .6 3 4.5 3.04 4.5 9 .3 8 4.88 5 .3 8 9 .5 4.46 square 2 5 .1 7 4.58 3.46 4.46 9 .5 4.67 5 .2 5 9 .2 5 3.88 square 3 5 .2 9 3.83 3.92 4.25 9.33 4.7 5.25 9.08 3.38 square 4 5 .2 9 4.29 4 4.75 8 .9 6 4.54 5 .1 7 8 .4 6 3.42 trumpet 5 .4 6 4.42 3.04 4.46 9 .2 9 4.42 5 .2 1 9 .0 8 3.58 clarinet 6 .0 4 3.88 3.33 4.33 9 .1 3 4.67 5 .0 8 9 .0 8 3.5 oboe 6 . 2 1 4.21 3.75 4.38 8 .8 3 4.54 5 .2 9 9 .1 3 4.25 piano 5 .3 8 4.21 4.13 4.67 9 .5 4 4.08 5 .2 9 8 .5 3.96 137 Arpeggiated seventh chord scores, continued S TUV W XY ZAA sawtooth 1 5.17 4.96 4.63 5.21 4.17 3.96 5 .3 3 4.75 7 .7 9 sawtooth 2 4.75 4.78 4.13 4.21 4.21 3.71 6 .4 2 4.67 7 .5 sawtooth 3 5.25 4.79 3.29 3.65 3.75 3.92 6 .5 4.79 7 .6 7 sawtooth 4 4.83 4.58 4.58 3.71 4.17 3.42 6 .7 5 4.58 6 .8 3 square 1 4.88 4.54 4.25 3.83 4.33 4.21 5 .6 7 4.71 8 .1 7 square 2 5.25 4.71 4.67 4.25 4.33 3.63 6 .8 3 4.21 8 .1 3 square 3 5.21 5.13 4.71 4.08 4.29 4.08 6 .0 4 4.46 7 .7 1 squared 5.33 4.96 3.71 4.29 4.92 4.04 5.75 4.5 7.88 trumpet 4.91 4.71 4.54 4.92 4.08 4.42 5 .4 2 4.75 7 .3 3 clarinet 5.04 4.71 4.71 4 4.21 3.5 6.08 3.96 7 .4 2 oboe 5.25 4.83 4.04 4.25 4 3.71 6 4.79 7 .1 3 piano 5.04 5.17 4.5 4.46 4.5 3.58 6 .1 7 4.57 7 .5 8 BB CC DD EE FF GG HH IIJJ sawtooth 1 4.63 4.21 6.13 7 .4 6 2.43 4.67 4 .7 9 5 .1 3 4.13 sawtooth 2 3.83 6.5 5.33 7.25 3.05 4.13 4 .6 7 4 .8 8 3.54 sawtooth 3 4.25 4.83 5 .5 4 8 .3 8 3.04 4.46 4 .3 3 5 3.83 sawtooth 4 4 5 6 7.71 3.42 4.42 4.75 5 .3 3 4.04 square 1 4.46 4.79 5 .9 6 8 .7 5 3.74 4.83 4 .5 8 5 .3 8 3.67 square 3 4 4.54 6 .0 8 7 .2 5 3.05 4.42 4 .7 9 4 .8 3 3.46 squared 4 4.75 5.88 8.13 3.08 4.79 5 5 .2 1 3.29 trumpet 3.83 4.92 5 .7 5 8 .1 3 3.54 4.21 4 .9 2 4 .9 6 3.96 clarinet 4.08 4.96 5 .6 3 8 .4 2 4.43 4.46 4.96 5.21 3.83 oboe 3.79 5 5 .9 2 8 4.61 4.42 4 .7 1 5 .6 7 4.22 piano 4.29 4.58 5.71 6.54 2.92 5.13 5 5 .2 5 2.96 138 Block seventh chord scores A B C DE F G H I sawtooth 1 3 .9 2 4.79 4 3.71 3.54 4.38 4.63 3.88 5.46 sawtooth 2 4 .2 5 4.13 4.92 4.92 4.54 4.63 4.58 4.25 5.46 sawtooth 3 4.17 4.46 4.67 4 3.96 3 .9 2 5.25 3.96 4.67 sawtooth 4 4.79 4.96 4.58 4.08 4.29 4 .0 8 4.75 4.33 5.45 square 1 4 .7 9 4.25 4.58 3.96 4 4 .7 1 4.83 4.25 5.21 square 2 4 .5 8 4.54 4.25 3.46 3.79 4.71 4.88 5.08 5.13 square 3 3.92 4.42 4.57 2.79 3.88 5 .2 1 5.04 4.88 5.08 square 4 4 .5 4 4.83 4.96 3.21 3.67 5 .0 8 4.88 4.54 4.83 trumpet 4.83 4.75 4.63 4.09 4.29 3 .9 2 4.92 4.42 5.17 clarinet 3 .0 4 4.46 4.04 3.04 3.92 4.83 4.96 4.5 4.79 oboe 3 .6 7 4.29 4.75 2.75 3.67 5.75 4.88 3.67 4.74 piano 4 .3 3 5.08 4.17 3.42 3.96 4 .2 1 5.25 4.54 4.91 J KLMN 0 P Q R sawtooth 1 5 .2 1 6 4.08 4.83 8 .4 6 4.33 5.88 8.92 4.54 sawtooth 2 4 .3 8 5.79 4.38 4.96 S .33 4.17 5 .8 3 9 .0 8 4.54 sawtooth 3 4 .8 3 5.46 4.21 4.42 8 .1 7 3.67 5.46 8.58 3.79 sawtooth 4 4.83 5.08 4.25 5 7.75 4.75 5.75 9 .2 5 4.79 square 1 4 .6 7 5.5 4.04 4.38 8 .8 3 3.92 5 .3 3 9 .2 5 4 square 2 5.42 5.04 4.25 4.88 8 .0 4 4.63 5 .7 1 9 .4 6 4.33 square 3 6 .3 8 6.42 4.13 4.5 8 .5 4.38 6.04 8.92 4.42 square 4 5.17 6.43 4.29 4.96 7.83 4.35 5 .6 7 9 .7 9 4.21 trumpet 5 .3 8 5.92 4.5 4.58 8 .5 3.96 6 . 2 1 9 .4 2 4.83 clarinet 4.67 5.96 4.46 4.5 8 .3 3 4.17 5 .5 4 8 .9 2 4.46 oboe 4 .7 5 6.3 4.63 4.46 7.67 4.46 5 .6 7 9 .4 6 4.58 piano 4 .3 3 5.92 4.22 4.46 8 .6 3 3.75 5.83 9.63 4.58 139 Block seventh chord scores, continued S TUV W X YZ AA sawtooth 1 4.54 4.54 4.63 4.42 3.92 4.71 4 .9 2 5.67 4 sawtooth 2 5.08 4.75 4.18 2.63 4 4.38 5 .7 1 4.38 6 .0 4 sawtooth 3 4.71 4.5 3.33 3.42 3.58 4.5 6 .1 7 4.83 6 .6 3 square 1 4.75 4.88 4.38 3.17 4.63 4.58 6 .0 4 4.29 7 .1 3 square 2 4.75 4.5 4.25 3.42 4.38 4.08 6.08 4.46 6.25 square 3 4.71 4.63 4.83 4.46 4.5 5.29 5.71 4.79 6.79 squared 4.92 4.75 5 4.96 3.92 4.29 6 .3 8 4.63 6 .4 2 trumpet 5.25 4.63 4.67 3.46 4.04 4.67 5 .8 8 4.38 6 .0 4 clarinet 5.08 4.38 3.71 3.33 4.04 4.08 6 . 2 1 4.67 6 .4 2 oboe 4.5 4.88 4.13 2.79 4.63 3.79 6 .6 3 4.88 6 .6 3 piano 5.17 4.63 5.54 3.25 3.96 5.13 5 .9 6 4.21 6 .1 7 BB CC DD EE FF GG HH II JJ sawtooth 1 5.04 4.21 6 5 .1 3 4.96 5.63 5 4 .9 6 4 sawtooth 2 5.79 4.46 6 .5 4 4 .9 1 5.13 5.33 4 .2 9 5 .5 4 4 sawtooth 3 4.54 4.46 6 .3 3 5 .3 9 5.25 5.22 5.38 5.04 3.42 sawtooth 4 5.13 4.54 6 .6 3 5 .4 3 5.22 6.33 4 .7 5 4 .9 2 4 square 1 5 4.33 6 .2 9 5 .3 9 5.21 5.29 5 .2 1 4 .8 3 4.29 square 2 5.29 4.75 6 .0 4 5 .3 9 5.42 5.46 4 .2 5 4 .8 3 3.29 square 3 5.33 4.25 6.5 6 .7 8 4.67 5.58 5 5 .3 3 3.96 squared 4.96 4.54 6 .5 5 .0 9 5.17 5.04 4 .9 2 5 .2 5 4.46 trumpet 4.75 4.38 6.33 5 4.96 5.67 5 5 .0 8 4 clarinet 4.83 4.33 6 . 2 1 5 .2 6 5.29 5.04 4 .7 9 5 .1 7 3.58 oboe 5 4.38 6 .9 2 6.35 4.7 5.42 4 .8 8 5 .5 8 3.75 piano 5.29 4.25 6.63 5.78 4.75 6.17 4 .8 8 5 .5 4 3.79 Appendix H Analysis of variance data 140 141 N = number of scores G = grand total of the scores = sum of the squared scores n = number of subjects a, b, c = the number of variables within the independent variables A = timbrai variable B = melodic vs. harmonic variable C = pitch interval variable ANOVA for Group S 12 N = 864 SStotal = 3012.5 G= 6073.77 SSwithin = 2566.64 2X2= 45710.1 SSbetween — 445.86 n = 12 S S a = 4.5 a (timbre) = 12 SSb = 4.31 b (melodic/harmonic) = 2 SSc = 403.25 C (pitch-interval) = 3 M Sa = 0.41 riftotal “ 863 MSb = 4.31 r if within “ 792 M Sc = 201.63 d/bctween ~ 71 MSwithin “ 3.24 d/A= 11 F a (11,792) = 0.13 d/B= 1 Fb (1,792) = 1.33 rife = 2 F c (2,792) = 62.22 ri/A B = 11 Fab (11,121) = 1.6 r i/A C = 22 F a c (22,242) = 0.16 ri/A B C = 22 FabC (22,242) = 0.14 ANOVA for Group 835 N; 2592 SStotal — 7697.35 G 15185.5 SSwithin = 6664.01 96663.3 SSbetween = 1033.34 n = 36 SSa = 6.97 a (timbre) = 12 SSb = 3.22 b (melodic/harmonic) = 2 SSc = 994.22 C (pitch-interval) = 3 M Sa = 0.63 r if total : 2591 MSb = 3.22 r if within : 2520 MSc = 497.11 ri/between = 71 MSwithin ~ 2.64 ri/A = 11 Fa (11,2520) = 0.24 ri/B : 1 Fb (1,2520) = 1.22 r i/c = 2 Fc (2,2520) = 187.98 ri/AB = 11 Fab (11,345) = 4.66 ri/AC = 22 F a c (22,690) = 0.17 ri/ABC= 22 FABC (22,690) = 0.15 Appendix I Data 142 143 Mean scores for each test condition across all 12 timbres for Group S 12. Maximum score = 10. MI m MT HT MS HS sw l 7.78 8.07 7.63 7.22 6.24 5.81 sw2 7.59 7.85 7.49 6.75 6.06 5.8 sw3 7.66 7.94 7.54 6.98 6.21 5.84 sw4 7.76 8.11 7.65 6.99 6.19 5.95 sql 7.51 7.73 7.36 7.21 6.4 6.04 sq2 7.33 7.71 7.34 7.07 6.48 5.9 sq3 7.33 7.97 7.25 7.06 6.25 6.26 sq4 7.61 7.72 7.38 6.96 6.26 6.05 tr 7.56 8.03 7.25 6.98 6.15 5.97 cl 7.55 7.56 7.52 6.85 6.26 5.78 ob 7.7 7.89 7.51 7.21 6.35 6.16 pno 7.69 8.08 7.59 7.09 6.19 5.99 Mean scores for each test condition across all 12 timbres for Group S 36. Maximum score = 10. MI HIMT HT MS HS sw l 6.58 6.29 6.44 6.45 4.98 4.96 sw2 6.62 6.2 6.2 6.07 5.03 5.01 sw3 6.57 6.38 6.18 6.06 4.87 4.84 sw4 6.54 6.38 6.11 6.02 4.89 5.08 sql 6.48 6.16 6.34 6.3 5.08 5.01 sq2 6.33 6.13 6.2 6.1 5.09 4.97 sq3 6.43 6.36 6.03 6.24 4.88 5.18 sq4 6.42 6.25 6.2 6.14 4.94 5.12 tr 6.42 6.46 6.13 6.18 4.97 5.07 cl 6.43 6.15 6.15 5.99 4.93 4.86 ob 6.68 6.24 6.22 6.32 5.01 5.0 pno 6.61 6.36 6.24 6.24 4.95 5.06 144 Percent correct responses for each test condition for Group S 12. MI HI MT HT MS HS sw l 74.65 79.51 71.88 66.67 52.08 46.18 sw2 73.26 73.96 69.79 59.38 48.61 48.61 sw3 74.65 78.47 70.14 65.28 50.69 48.26 sw4 76.04 79.86 73.26 62.5 51.04 48.61 sql 70.83 72.92 63.89 62.5 54.17 50.69 sq2 69.44 71.18 68.4 66.32 56.94 46.53 sq3 69.1 76.39 65.97 56.25 51.39 55.9 sq4 72.92 72.22 67.36 62.15 51.74 51.39 tr 74.31 77.08 67.36 61.11 50 52.08 cl 71.88 71.53 70.83 59.38 50.69 47.22 ob 75.69 77.78 71.88 65.63 54.86 52.78 pno 74.31 79.86 71.53 65.28 53.13 51.39 rcent correct responses for each test condition for Group 8 36 - MI HI MT HT MS HS sw l 59.49 55.79 56.83 54.86 30.9 29.75 sw2 60.88 53.01 52.78 49.31 31.13 33.33 sw3 59.14 57.29 51.04 50.23 28.59 29.75 sw4 59.49 56.94 51.04 47.8 28.36 33.33 sql 57.41 52.89 50.81 50.81 31.83 31.94 sq2 55.79 51.04 51.04 49.88 31.37 30.32 sq3 57.29 57.29 49.88 46.64 29.86 35.19 sq4 56.83 54.63 51.04 49.88 28.82 34.03 tr 58.22 57.87 50.23 50 29.98 34.03 cl 56.71 54.05 50.69 47.11 29.05 28.94 ob 62.38 55.32 52.2 53.01 30.56 32.29 pno 60.07 57.64 53.82 52.89 31.02 33.22 145 Mean scores. Group S 12: sawtooth vs. square waveforms. Maximum score = 10. sawtooth; square; synth. sawtooth-like squarewave synth. only only MI 7.7 7.45 7.63 7.55 HI 7.99 7.78 7.96 7.56 MT 7.58 7.33 7.38 7.52 HT 6.98 7.07 7.1 6.85 MS 6.17 6.35 6.25 6.26 HS 5.85 6.06 6.06 5.78 Mel 7.15 7.04 7.09 7.11 Har 6.94 6.97 7.04 6.73 All 7.05 7.01 7.06 6.92 Mean scores, Group Sgg: sawtooth vs. square waveforms. Maximum score =10. sawtooth; square; synth. sawtooth-like squarewave synth. only only MI 6.58 6.42 6.55 6.43 HI 6.31 6.22 6.35 6.15 MT 6.23 6.19 6.18 6.15 HT 6.15 6.19 6.25 5.99 MS 4.94 5 4.99 4.93 HS 4.97 5.07 5.03 4.86 Mel 5.92 5.87 5.91 5.84 Har 5.81 5.83 5.88 5.67 All 5.87 5.85 5.89 5.75 146 Percent correct responses, Group S 12: sawtooth vs. square waveforms. sawtooth; square; synth. sawtooth-like squarewave synth. only only MI 80.22 75.84 80.6 77.24 m 83.77 78.64 83.21 76.87 MT 76.59 71.36 74.81 76.12 HT 68.19 66.42 68.1 63.81 MS 54.38 57.56 56.34 54.48 HS 51.49 54.94 56.34 50.75 Nfel 70.4 68.25 70.58 69.28 Har 67.82 66.67 69.22 63.81 AU 69.11 67.46 67.79 66.54 Percent correct responses, Group Sgg: sawtooth vs. square waveforms. sawtooth; square; synth. sawtooth-like squarewave synth. only only MI 59.75 56.83 60.3 56.71 m 55.76 53.96 56.6 54.05 MT 52.92 50.69 51.22 50.69 HT 50.55 49.31 51.5 47.11 MS 29.75 30.47 30.27 29.05 HS 31.54 32.87 33.16 28.94 Mel 47.47 46 47.26 45.49 Har 45.95 45.38 47.09 43.36 AU 46.71 45.69 47.17 44.43 147 Mean scores. Group S 12: synthesized vs. natural instrumental tones. Maximum score = 10. synthesized natural instruments MI 7.57 7.63 HI 7.89 7.89 MT 7.45 7.47 HT 7.03 7.03 MS 6.26 6.24 HS 5.95 5.98 Mel 7.1 7.11 Har 6.96 6.99 All 7.03 7.04 Mean scores, Group Sgg: synthesized vs. natural instrumental tones. Maximum score = 10. synthesized natural instruments MI 6.5 6.54 HI 6.27 6.3 MT 6 .2 1 6.19 HT 6.17 6.18 MS 4.97 4.96 HS 5.02 5 Mel 5.89 5.89 Har 5.8 5.83 All 5.85 5.86 148 Percent correct responses. Group S 12: synthesized vs. natural instrumental tones. synthesized natural instruments MI 72.61 74.05 m 75.56 76.57 MT 68.84 70.4 HT 62.63 62.85 MS 52.08 52.17 HS 49.52 50.87 Mel 64.51 65.54 Har 62.57 63.43 All 63.54 64.48 Percent correct responses, Group 8 35 : synthesized vs. natural instrumental tones. synthesized natural instruments MI 58.29 59.35 HI 54.86 56.22 MT 51.81 51.74 HT 49.93 50.75 MS 30.11 30.15 HS 32.2 32.12 Mel 46.73 47.08 Har 45.66 46.36 AU 46.2 46.72 149 Mean scores. Group S 12: steady-state vs. AM & FM modulated tones. Maximum score = 10. steady state modulated mod. synth. & mod. synth., synthesis winds winds & piano MI 7.57 7.57 7.59 7.6 m 7.93 7.85 7.84 7.87 MT 7.44 7.46 7.45 7.47 HT 7.11 6.94 6.97 6.99 MS 6.27 6.25 6.25 6.24 HS 5.98 5.92 5.94 5.95 Mel 7.1 7.1 7.09 7.1 Har 7.01 6.9 6.92 6.93 AU 7.05 7 7.01 7.02 Mean scores, Group 835 : steady-state vs. AM & FM modulated tones. Maximum score = 10. steady state modulated mod. synth. & mod. synth., synthesis winds winds & piano MI 6.52 6.48 6.49 6.51 m 6.3 6.24 6.26 6.27 MT 6.25 6.18 6.17 6.18 HT 6.26 6.08 6 .1 2 6.13 MS 4.95 4.99 4.98 4.98 HS 5 5.05 5.02 5.02 hfcl 5.91 5.88 5.88 5.89 Har 5.85 5.79 5.78 5.81 AU 5.88 5.84 5.84 5.85 150 Percent correct responses, Group S 12: steady-state vs. AM & FM modulated tones. steady state modulated mod. synth. & mod. synth., synthesis winds winds & piano MI 72.31 72.92 73.36 73.48 m 76.82 74.31 74.8 75.43 MT 67.97 69.7 69.84 70.05 HT 62.67 62.59 62.35 62.72 MS 52.08 52.08 51.98 52.13 HS 50.26 48.78 49.6 49.83 Mel 64.12 64.9 65.06 65.22 Har 63.25 61.89 62.25 62.66 All 63.69 63.4 63.71 63.94 Percent correct responses, Group Sgg: steady-state vs. AM & FM modulated tones. steady state modulated mod. synth. & mod. synth., synthesis winds winds & piano MI 58.33 58.25 58.61 58.8 HI 55.82 53.91 54.7 55.06 MT 52.14 51.48 51.29 51.61 HT 50.64 49.22 49.57 49.99 MS 30.3 29.92 29.89 30.03 HS 31.66 32.76 32.32 32.44 Mel 46.92 46.55 46.6 46.81 Har 46.04 45.29 45.53 45.83 All 46.48 45.92 46.06 46.32 151 Mean scores, Group S 12: spectral content. Maximum score = 10. low spectral high spectral content content MI 7.55 7.59 HI 7.84 7.93 MT 7.45 7.45 HT 7.06 7 MS 6.29 6.23 HS 5.88 6 .0 2 Mel 7.1 7.09 Har 6.93 6.98 All 7.01 7.04 Mean scores, Group 8 3 0 : spectral content. Maximum score = 10. low spectral high spectral content content MI 6.5 6.49 HI 6 .2 6.34 MT 6.3 6.13 HT 6.23 6 .1 2 MS 5.04 4.9 HS 4.99 5.06 Mel 5.95 5.84 Har 5.8 5.84 All 5.88 5.84 152 Percent correct responses, Group S 12: spectral content. low spectral high spectral content content MI 72.31 72.92 HI 76.82 74.31 MT 67.97 69.7 HT 62.67 62.59 MS 52.08 52.08 HS 50.26 48.78 Mel 64.12 64.9 Har 63.25 61.89 AU 63.69 63.4 Percent coirect responses, Group Sgg: spectral content. low spectral high spectral content content MI 58.33 58.25 HI 55.82 53.91 MT 52.14 51.48 HT 47.05 49.22 MS 30.3 29.92 HS 31.66 32.75 Mel 46.92 46.55 Har 44.84 45.29 AU 45.88 45.92 List of References Acoustical Society of America. (1973). American National Standard Psychoacoustical Terminology. 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