UNIVERSITY OF QUEENSLAND
Accepted for the award of
on ICCILI !SC<

1Development of a Methodology and Theoretical Framework
for Melodic Discrimination
Ross W. Gayler, B.Sc. (Hons)
Being a dissertation submitted as a partial requirement
for the Degree of Doctor of Philosophy
within the University of Queensland, Department of Psychology
August, 1987.

Sources Statement
The present thesis describes original research undertaken in the Department of
Psychology, University of Queensland. Any theories and techniques not my own have been
acknowledged in the text. The theoretical contributions in this thesis are my own original
work and have not been submitted for any other degree.
Signed

iii
Abstract
The psychology of music has the potential to make great contributions to
knowledge of cognition in general because musical stimuli come from a natural and highly
structured domain, (as do the linguistic stimuli normally used in cognitive research), and yet
they lack the referential meaning of linguistic stimuli. This lack of reference by musical
stimuli to entities outside the musical domain should make it easier to elucidate the cognitive
mechanisms by which structured and patterned stimuli are manipulated than is the case with
linguistic stimuli. Yet there is not a single result from the psychology of music that is
generally regarded as illuminating basic cognitive mechanisms.
The ability to discriminate two melodies as differing or identical is arguably the
most basic musical task. I have concentrated on that task in this research. Modern research
on melody discrimination dates from 1960 and yet the literature reporting that research is
quite small with only a limited number of investigators. The effects and theoretical models
reported have been specific to the musical domain with almost no appeal to any general
cognitive mechanisms. I believe that because of this the field is seen as peripheral to the
advance of cognition, very few researchers are attracted to it, and hence the rate of progress
is low.
In order to unlock the potential of the psychology of music this area of research
must be tied back to general cognition. In my review of previous research I have identified
the lack of a sophisticated theoretical framework and adequate experimental and data
analytic methodologies as the key factors preventing rapid progress in this field. Therefore,
the aim of my research has been threefold: to develop an adequate theoretical framework
that will serve as a bridge from musical phenomena to concepts from general cognition; to
develop sophisticated methods of data analysis that allow much more fine-grained analyses

iv
of data than are currently possible in order to investigate the proposed framework; and to
conduct empirical investigations in order to explore the consequences of the framework, test
the new data analyses, and to discover new, more subtle effects than those previously
reported, to serve as the starting points for further investigation.
The framework that I have proposed is based on the distinction between
attributes describing a melody and the units in which those attributes are organised. This
distinction is commonly acknowledged in models of cognitive representations and yet it has
not been made at all in previous melody discrimination research. That research appears to
have identified the attribute with the units, as exemplified by the assertion that "well-known
melodies must be stored as sequences of pitch intervals between successive notes" (Dowling,
1978, p. 346). My framework makes it clear that the issue of what information is stored
(attributes) can be investigated independently of the issue of how that information is
organised in the representation (units).
Another point which is made clear by my framework is the need for some
mechanism to ensure that corresponding units are compared in the process of comparing the
representations of two melodies. In my fourth experiment I discovered a pair of melodies in
which non-corresponding units were compared. This problem of matching corresponding
units for comparison is likely to exist in all cognitive domains. Thus this is an area in which
the psychology of music could elucidate a general cognitive mechanism.
In my review of the methodology used in melody discrimination research I
found that there were characteristics of the melodic domain that made traditional means of
analysis particularly inappropriate. There are marked differences in the psychological
characteristics of individual melodies and there are also idiosyncratic interactions of subjects
with melodies. Another previously unrecognised problem is that it is literally impossible to

Vgenerate musical stimuli in such a way as to avoid confounding. I refer to this characteristic
as obligatory confounding. These characteristics reduce the utility of traditional analyses
which aggregate data over melodies and analyse them in terms of fixed orthogonal factors.
However, the major problem with previous analyses is that they are carried out
at the level of groups of melody pairs rather than at the single pair level. That is, measures of
discriminability could not be derived for single pairs of melodies. Thus the
discriminabilities could only be analysed and explained in terms of the summary properties
of groups of melody pairs rather than the properties of individual melodies involved in
individual judgments.
I have developed an extension to signal detection analysis that allows the
discriminability of individual melody pairs to be calculated. These discriminabilities can
then be analysed and interpreted in terms of the characteristics of the particular melodies
involved. Thus, I have developed a technique to allow melody discrimination phenomena to
be examined at a far finer level of resolution than was previously possible. Using this
technique I have demonstrated several previously unknown effects and the number of effects
found appears to have been limited primarily by the quantity of data collected.
In my first experiment I was attempting to find clues to the existence of
previously unreported effects for further investigation in the subsequent experiments. The
effect which I found and chose to pursue was the increased saliency of changes occurring at a
contour reversal. This experiment also demonstrated effects related to the overall contour
shape, a particular pitch transition, the pitch range, and cadence.
The second and third experiments further investigated the contour reversal
effect. This effect was convincingly demonstrated in these experiments while I developed
my methods of data analysis. The third experiment also demonstrated effects associated with

vi
the repetition of a note across a contour reversal and with rhythmic stress.
In my fourth experiment I used the methodology that I had developed to attack
directly the question of the relative importance of interval-based and note-based attributes.
This experiment demonstrated that simple measures of the number of notes and interval
changed are inadequate to account for melody discrimination performance. I found effects
related to repetition across a contour reversal, the tonic, the major triad, the unusuality of
particular pitch transitions, and the process of matching of corresponding units. These
effects were more naturally described in terms of note-based attributes than interval-based
attributes.
Thus, the research reported here has accomplished my original aims of
developing a framework, developing a methodology, and demonstrating novel effects with
that framework and methodology. However, the most important aspect of this work is that it
provides a significant break from previous work and acts as a starting point from which to
develop the area of melody discrimination research in the manner which it deserves.

vii
Acknowledgements
I commenced working on the research reported here in 1980 as a full-time
student and converted to part-time status in 1981. Since 1982 I have worked off campus in a
job having no connection with this research. This arrangement has absolutely nothing to
recommend it as a way of conducting doctoral research except for ensuring that the mortgage
repayments are met.
For most of my candidacy I have been isolated from the intellectual stimulation
in which full-time students are immersed. I have been frustrated by having more odd
moments travelling to and from work in which to come up with bright ideas and less
available time in which to implement and test them. I have also had more opportunity for the
occurrence of significant life-events, not all of them welcome. In particular, I am saddenned
by the deaths during the course of this research of my friends, Dr. Henry Law and Dr. Bill
From.
As a consequence of the conditions of my candidacy, I have been something of a
burden to my supervisors, colleagues, friends, and family during this period and I am deeply
grateful for the assistance, support, tolerance, and love which they have given so freely.
I cannot adequately express my thanks to my supervisors, Dr. Cathy Brown and
Dr. John Bain. This work would not have been possible without their enthusiasm,
scholarship, and ability to harass me into action when I fell behind.
Special thanks are due to those who participated as subjects in my experiments.
Their tasks were difficult, long, and boring. Many of the subjects can still remember some of
the stimuli after up to seven years, and none of them have carried out their threatened legal
actions. Lisa Carley deserves special mention as the only subject to serve in two
experiments, and for claiming that they were more interesting than her job.

Colleagues, friends, and relatives who have helped in various ways by providing
coffee, companionship, computing, consultation, conversation, and much more, are (in
alphabetical order): Joanne Ballantyne, Dr. Tony Barnes, Dr. David Chant, Robert
Enchelmaier, Darryl Godfrey, Mike Hill, Jill Jeffery, Lewis Jeffery, Dr. Luke Jones, Ian
Maurer, Lynne Maurer, Barbara Morton, Graeme Morton, Murray Maybery, Vince Murdoch,
Peter Pamment, Robert dal Santo, Dr. Wes Snyder, Rick Stevenson, and Dr. Leigh Ward.
Lastly, I owe an enormous debt of gratitude to my wife Sallyanne for her love,
support, and tolerance during the seven years this thesis was in preparation and in the years
as a full-time student which preceded it. Without her, this work would not only have been
impossible, it would have been pointless. Our two older children Madeleine and Katherine
will no longer have to bid me farewell every night and our new-born son, John, will not have
to acquire that habit. They also helped. Thankyou children. All I can say by way of
atonement is that it seemed like a good idea at the time, and if anybody ever asks me again
whether I would like to commence doctoral research my answer will be a firm 'no'.

xi
Tables
Table 5.1. Analysis of discriminability (d * ). 118
Table 5.2. Mean discriminability as a function of transposition.
118
Table 5.3. Mean discriminability as a function of change position.
118
Table 5.4. Analysis of logit-transformed false-alarm rates.
120
Table 5.5. Mean transformed false-alarm rate as a function of transposition.
120
Table 5.6. Mean transformed false-alarm rate as a function of change position.
120
Table 6.1. Conventional signal detection by regression.
133
Table 6.2. Signal detection by regression with multiple signals and one noise.
136
Table 6.3. Signal detection by regression with multiple noises and one signal.
138
Table 6.4. Signal detection by regression with multiple signals and multiple noises.
139
Table 6.5. Mapping of experimental elements onto regression predictors.
141
Table 6.6. Identification of signal and noise with trial type.
143
Table 6.7. Identification of final signal detection model.
145
Table 7.1. Discriminability as a function of distance from the contour reversal.
160
Table 7.2. Discriminability as a function of change serial position.

161
Table 7.3. Discriminability as a function of subject.

162
Table 7.4. Discriminability advantage of 4/4 over 3/4 rhythm as a function of change position. 163
Table 8.1. Final selection of prototype pairs. 175
Table 8.2. Trial structure. 176
Table 8.3. Preliminary models. 182
Table 8.4. Contrasts of preliminary models. 182

xii
Table 8.5. Simple models. 185
Table 8.6. Contrasts of simple models. 185
Table 8.7. Simple model (M 6) regression parameters. 185
Table 8.8. Final models. 187
Table 8.9. Examples of the calculation of IC . 189
Table 8.10. Final model (M 9) regression parameters. 193
Table 8.11. Discriminability of melody pairs minimal on 176,up and lice& . 197

31.1.2 Melodic identity
An operational definition of the identity of each physical melody is required in
order to investigate the relationship between physical melody and psychological melody. I
have taken the identity of a physical melody to be defined by the sequence of intervals
between successively played single notes. This definition excludes rhythm, harmony, and
many other factors which probably influence the mapping from physical melody to
psychological melody. This extreme limitation of area is adopted purely for empirical
tractability.
The definition of the identity of a physical melody can be applied to any
sequence of notes irrespective of how musical that sequence may be. I In fact some
researchers have used stimuli that were almost totally unmusical. However, their ultimate
intent was to shed light on the processing of musical stimuli.
The most frequently used methods for investigating the representation of melody
involve the comparison of melodies. For some of these methods it is necessary to know
whether the two physical melodies presented to the listener had the same identity. I have
defined two melodies to have the same identity if they both have the same sequence of
intervals and the corresponding notes of the two melodies are played with identical timing
and identical stress. That is, the note strings must be exact transpositions of each other;
explicit harmony is excluded by using single notes and other factors, chiefly rhythm, are
controlled for by requiring them to be identical in the two melodies.
It is most important to be aware that the definitions I have chosen for calculating
the identity of stimuli have no implications for the way in which melody is represented
1. From this point I will cease making explicit the distinction between psychological melody and physical
melody as the meaning should be clear from the context.

5various attributes. Attributes that do contribute to melodic identity but do not effectively
discriminate the set of possible melodies in the experiment will have a decreased weight in
the calculation of similarity.
The similarity rating task is preferred to the melody naming task because it can
be used with novel melodies and because the process underlying the similarity rating task is
simpler.
1.1.3.2 Looking for differences amongst many similarities
If the stimulus set is homogeneous there will be many similarities between the
melodies and the relationship between the melodic identities of any two melodies can be
most parsimoniously described in terms of the points of difference. Melody discrimination
tasks are suited to comparison of melodies that are only slightly different. If it were possible
to generate pairs of melodies differing on only one attribute then these tasks could be used to
investigate whether that attribute was relevant to melodic identity while the effect of the
similar attributes was held constant.
In the same/different melody discrimination task two melodies are presented and
the subject is required to judge whether they are the same or whether they differ. That is, the
subject is asked to detect any difference at all between the melodies. I have taken this task to
be the canonical means for measuring melody discrimination.
A common variant of the melody discrimination task is to use a two-alternative
forced-choice procedure. In this task the standard melody is followed by two comparison
melodies. One comparison will have the same identity as the standard and the other
comparison will have a different melodic identity. The subject is required to indicate which
of the comparison melodies is identical to the standard.
The two-alternative forced-choice task places greater demands on the subject's

heuristic devices for informing experimental design. However, because so little is known, all
theoretical models will be false and hence there is little point in attempting to generate
conclusive tests. By concentrating on the demonstration of novel effects and rapidly
increasing the number of known effects the theoretical possibilities will become more
constrained to the point where testing of theories becomes more fruitful. Therefore, a major
focus of my research has been the demonstration of new effects.
In the research that has been reported previously the types of effects that can be
demonstrated and the theoretical models that can be adequately investigated are drastically
restricted by the research methodology. Therefore, a major portion of my own research has
involved methodological development to support a much more fine-grained level of analysis
and modelling than has been possible before. Because of the prominence of methodological
problems and developments in my work I have devoted two chapters to them (Chapters 3 and
6).
As I carried out this research I developed a theoretical model (more properly a
framework) that accounts for the results reported by others and the new effects that I have
found. However, the framework is more complex than any previously proposed model and
incapable of being adequately assessed in a single research programme. I have used this
framework as a heuristic device to aid me in the design and interpretation of my experiments,
but I have not attempted to test it as I regard that as totally inappropriate given the state of
development of this field.

11
the melody, whereas parameters, such as musicality, modify the effectiveness of the cues.
The distinction between cues and parameters is important to the interpretation of the stimulus
effects. However, because consideration of the interpretations is postponed until a later
section, the distinction between cues and parameters will not be drawn here.
2.1.1 Individual melodies
There are individual differences between melodies in the characteristics that
determine the discriminability of those melodies from other melodies. This effect is
demonstrated as an interaction between, the identity of individual melodies and the changes
in discriminability induced by other stimulus effects. It has been demonstrated most
frequently in studies involving familiar melodies such as nursery rhymes, because
experimenters carrying out such studies have occasionally analysed their data individually
for each melody. In contrast, experimenters using novel melodies composed for the
experiment have usually aggregated their data over melodies before analysis, thus precluding
examination for individual differences between melodies.
An early study that reported differences in the identifiability of melodies is that
of White (1960). The main effect of melody identity accounted for approximately one third
of the total variance in a two way analysis of variance of the number of subjects correctly
identifying 10 melodies under 13 transformations. The main effect of transformation
accounted for approximately two thirds of the variance and the melody by transformation
interaction accounted for less than one twentieth of the variance. It is interesting that the
variance due to the experimental manipulations was only twice that due to melody
differences.
Main effects of individual melodies and interactions with other factors have also
been reported in the naming of familiar melodies by Dowling and Hollombe (1977), Idson

12
and Massaro (1978), Kallman and Massaro (1979), Kallman (1982), and Dowling (1984).
These experimenters often remarked that no consistent patterns could be discerned in the
main effect and interactions of individual melody differences.
Two studies using novel melodies also report individual differences between
melodies. Cuddy and Cohen (1976) reported statistically significant differences in the
detectability of transition errors across individual three-note melodies, and individual
differences between melodies were reported by Cuddy, Cohen, and Miller (1979). They
discovered an anomalous pair of melodies in their set of stimuli which were consistently and
replicably discriminable at no better than the chance level.
Differences between individual melodies were demonstrated in all my
experiments. The first experiment used a similarity rating task with all the pairs of 20
melodies. The melodies in this experiment were all distinguishable. In my second, third,
and fourth experiments the presence of individual differences between the melodies is best
demonstrated by examining the response rates to trials in which the comparison melody is
the same as the standard. In these three experiments there were significant differences across
melodies in these types of trials.
In my third and fourth experiments the data were analysed in terms of the
attributes of the individual melodies in each trial pair. The reasons for this style of analysis
and the technique by which it is accomplished are given in Chapters 3 and 6. Using these
analyses I was able to demonstrate variation in discriminability at the single trial level and
account for it in terms of the attributes of individual melodies. I also modelled the effect that
individual melodies had on the propensity to judge the standard and comparison as different
independently of the actual presence of difference.

13
2.12 Contour
Contour refers to the rise and fall of pitch over the length of a melody
irrespective of the size of the pitch movement. It is usually defined as the sequence of
directions of pitch change between adjacent notes.
Most experimenters have treated contour as a global property of the melody.
That is, they have ignored any internal structure of the contour and treated it as a uniform
whole. Only one study has examined the local features of contour. The difference between
local and global contour lies in the way that contour is used as a predictor in data analysis
0
and in the way that stimuli are constructed.
If contour is being treated as a global function of the melody the contour effect
predictor has only two values indicating whether the contours of the standard and
comparison melodies are identical. When the data are to be analysed this way the stimuli are
constructed with no control over the way in which the contours differ.
If contour is being treated as a local function of the melody the contour effect
predictor takes on multiple values indicating the way in which the contours are different. In
this case much more care is put into construction of the stimuli to ensure that the contours
differ in the stated manner.
2.12.1 Global contour
The global contour effect is probably one of the strongest and most consistent
reported in this literature. In melody discrimination, melodies differing in contour are rarely
confused as being identical (Dowling 1971; Deutsch 1979; Watkins 1985) whereas melodies
that are not identical but do have the same contour are far more often confused and are
sometimes virtually indistinguishable (Dowling & Fujitani 1971; Dowling 1978; Bartlett &
Dowling 1980). However, the contour effect is not always the strongest in an experiment. It

20
were much easier to detect when scale membership information was available.
The confounding of scale membership with pitch recognition and musicality was
overcome in a later study (Cuddy, Cohen, & Miller, 1979). In this study the standard
melodies were tonal and the comparisons differed by one note that was either within or
without the scale of the transposed comparison. Once again it was found that changes were
more easily detected when they introduced a note from outside the established scale.
A different approach was used by Dowling (1978) and Bartlett and Dowling
(1980). In these studies the standards were tonal melodies but instead of altering a single
note in the comparison melody more than one note was altered. "Same" comparisons were
transpositions of the standard melodies. "Different" comparison melodies were of two types,
both of which retained the contour of the standard melody. "Tonal lure" comparisons
remained wholly within the untransposed scale of the standard while being shifted in pitch
from the standard. Atonal comparisons were also shifted in pitch relative to the standard, but
contained a set of pitches inconsistent with any single key.
Both these studies found that atonal comparisons were easily distinguished from
transpositions of the standard. It was also found that "tonal lures" were very difficult to
distinguish from exact transpositions of the standard.
2.14.2 Chroma
Chroma is the property of notes such that all notes separated by an octave in
pitch have the same chroma value. The abstraction of octave equivalence was a component
of the neural model of music perception proposed by Deutsch (1969).
Dowling (1984) investigated the effect of chroma by using comparison melodies
in which the notes of the standard had been displaced by multiples of an octave. The task of
the subject was to discriminate such a comparison from one which was produced by octave

22
standard melody was either presented once, or presented once and followed by six (possibly
modified) repetitions. The repetitions were either exact copies of the standard, or were
transposed in their entirety to the octaves above and below the standard, or were transposed
on an alternating note-by-note basis to the octaves above and below the standard.
Deutsch found that intact, octave-displaced repetition produced an increase in
discrimination relative to no repetition. Note-by-note octave-displaced repetitions (which
altered the contour of the standard) produced relatively poorer discrimination than no
repetitions. Thus she claimed to have demonstrated a chroma effect. However, it should be
noted that the comparison melodies were always transposed up four semitones from the
standards. Therefore, although chroma could have been effective in the repetition of the
standard it could not have carried across to the comparison. The original conception of
chroma does not allow for this and it is not at all clear whether Deutsch's demonstration
should be regarded as a chroma effect.
2.1.43 Scalar degree
The scalar degree of a note is its position in the scale relative to the tonic or key
note. The scalar degree of any note is determined by its pitch and the currently operative
scale. That is, the scalar degree of any note is dependent on the the listener's interpretation
of the current scale.
Dowling (1986) manipulated the scalar degree of the notes of the comparison
melodies while leaving the notes unchanged. He used melodies consisting of six notes
embedded in a chordal context. He was able to alter the scalar degrees of the test core by
altering the chordal context. Thus there were four types of comparison melodies created
from the combination of same or different contexts in the standard and comparison with the
comparison test core being identical to, or different from, the standard test core.

23
He found that moderately experienced listeners were able to discriminate
identical from changed test cores when the standard and comparison chordal contexts were
the same, but that discrimination performance dropped almost to chance when the chordal
contexts of the standard and comparison differed.
I did not manipulate scalar degree in any of my experiments but it did emerge as
a predictor of discriminability in the fourth experiment. I found that the discriminability of
the melodies was higher when the difference between the standard and comparison melodies
involved the tonic of the scale.
2.1S Interval-related characteristics
The effects discussed in the previous section were associated with manipulation
of the characteristics of single notes. The effects discussed in this section were discovered in
attempts to manipulate global attributes such as contour. In these experiments there was
found to be a residual element of discriminability that was associated with the precise
sequence of intervals.
2.15.1 Interval magnitude
The interval magnitude effect is typically demonstrated by altering at least one
of the intervals of a melody and showing that the altered melody can be discriminated from
the original. As melodic`identity was defined in terms of interval magnitudes it follows that
any alteration of the intervals necessarily alters melodic identity and any other attributes that
are functions of melodic identity. I argue in Chapter 3 that the interval magnitude effect is
guaranteed to occur by virtue of the definition of melodic identity. This guarantee makes it
impossible to decide whether the interval magnitude effect should be interpreted as evidence
for a psychological process or as an artifact.
Interval magnitude effects have been demonstrated as the discriminability of

25
that were undistorted or modified in such a way that contour and relative interval magnitude,
or contour only, were preserved. Identification performance was highest for the undistorted
melodies, lowest for the contour only melodies, and had an intermediate value for the
melodies that preserved relative interval magnitude. This effect was demonstrated by White
(1960), Dowling and Fujitani (1971), Idson and Massaro (1978), and Moore and Rosen
(1979).
2.1.53 Configuration
Cuddy and Cohen (1976) found that the ability to detect changes in three-note
melodies was greater than the ability to detect changes in the component two-note intervals,
and that discrimination of the melodies was not predictable from the performance on the
component intervals. From this they concluded that a melody could not be treated as a string
of successive intervals and that the overall configuration of intervals was important to the
determination of melodic identity.
All the experiments which I have performed have supported the contention that
melodies are represented as more than uniform sequences of intervals. Each of my
experiments has demonstrated patterns of melodic discriminability correlated with attributes
of individual notes or patterns of notes.
2.2 Procedural effects
In this section, effects will be discussed that arise from manipulations which do
not alter the musical character of the stimuli. These manipulations are discussed under three
categories: stimulus characteristics; subject characteristics; and task characteristics. I also
indicate the choices for these procedural attributes which I have made in my experiments.

27
Bartlett (1981) that, at a short retention interval, comparison melodies were easily confused
with the standard melody when they had the same contour and were in the same key as the
standard. When the retention interval between presentation of the standard and comparison
melodies was increased the confusability of the comparison melodies dropped. DeWitt and
Crowder replicated this effect but also found that when the melody length was reduced from
seven notes to five, the confusability of the same-contour, same-key melodies did not
decrease with an increased retention interval.
Overall, it appears as though the discriminability of novel tonal melodies is
slightly increased with greater length. However, the really interesting finding is the
decreased magnitude of the contour effect relative to other effects with increased melody
length.
I have not manipulated length as an experimental variable in my experiments. In
my first, second, and third experiments melody length was constant at seven notes and in the
fourth experiment the melodies were nine notes long. These lengths were chosen so that the
note strings would be long enough to be musical (five notes seems too short) and to allow
enough degrees of freedom to be able to choose melodies with the appropriate
characteristics, but not so long as to make perception in terms of phrases inevitable or to
overwhelm the complete enumeration procedures that I used for stimulus generation and
selection.
22.1.2 Familiarity
Familiarity of the melodies has been shown to alter their discriminability. A
distinction which has not been made in the literature is that between familiarity due to the
use of pre-existing melodies which are well known in the subject's culture, and familiarity
brought about by repeated exposure to a previously unknown melody. In this section I will

28
refer to the former type of familiarity simply as familiarity and I will refer to the latter as
repetition familiarity.
Discrimination performance was found to be higher with familiar melodies by
Bartlett and Dowling (1980) and Dowling and Fujitani (1971). Discrimination performance
was also found to be higher with melodies made familiar by repetion by Deutsch (1979) and
Dyson and Watkins (1984). Dyson and Watkins also found that the relative salience of
contour reversals was decreased by repetition. This point is relevant to a difference between
the findings of my third and fourth experiments. In my third experiment there was no
repetition of melodies within trials and I found a decrease in the discriminability of melodies
with increasing distance of the change from a contour reversal. In my fourth experiment the
standard melody was repeated within each trial and there was no evidence for a
discriminability gradient. These findings are consistent with the observation of Dyson and
Watkins.
Familiarity was not manipulated in any of my experiments which all used
unfamiliar melodies because the use of well-known melodies would not have allowed me to
choose melodies satisfying my constraints on attributes such as contour or location of
difference. There was, however, scope for repetition familiarity. Melodies were repeated in
all four experiments. In the first and second experiments melodies were repeated across
trials but trials were not repeated. In the third and fourth experiments melodies were
repeated across trials and trials were repeated in order to satisfy the requirements of the data
analysis procedure. In the fourth experiment the standard melody was presented three times
before the presentation of the comparison because pilot testing had indicated that the task
was too difficult without such repetition.

29
22.1.3 Presentation rate
Dowling (1972) presented stimuli at the rates of five and two notes per second.
He found that melody discrimination was better at the slower rate. The same effect was also
found by Dyson and Watkins (1984) with presentation rates of ten, four and three notes per
second.
Bartlett and Dowling (1980) found that the false alarm rate (the tendency to
respond 'same' to comparison stimuli differing from the standard) was reduced at the lower
presentation rate of one note per second compared to the false alarm rate at six notes per
second. However, the presentation rate did not alter the discriminability of their stimuli.
Presentation;ate was not manipulated as ,
an experimental variable in any of my
experiments. The presentation rate in all my experiments was in the range 3.5 to 4 notes per
second. These rates of presentation were chosen during pilot testing for a balance between
performance level and total session duration.
22.14 Sound source
The acoustic characteristics of the sound source have been manipulated in some
studies but for various reasons.
Cuddy, Cohen, and Miller (1979) used a piano and an oscillator as sound sources
for their stimuli. They performed this manipulation to see whether apparent musicality of
the sound would alter their results. They found no effect for this manipulation.
Moore and Rosen (1979) used sound sources intended to mimic differing
degrees of hearing impairment. They used pulse trains high-pass filtered at 2 kHz and 4 kHz.
These sound sources appeared to evoke a sense of musical pitch but differences in pitch were
much harder to discriminate than usual. Moore and Rosen found that the more extreme
distortion of the sound source was accompanied by reduced melody naming performance.

30
Dyson and Watkins (1984) used pulse train and square wave sound sources for
their stimuli. They had found a greater salience of upper contour reversals compared to
lower contour reversals in an experiment using pulse trains. Unfortunately, the volume level
of the pulse train sounds increased with pitch. As the upper contour reversals generally
occurred at higher pitches they were worried that the higher relative salience might have
been due to the confounded greater volume level. The square wave source was used to
investigate this confound. No effect of sound source characteristics was found.
Sound source was not manipulated as an experimental variable in any of my
experiments. The sounds used for the stimuli were chosen to be pleasant in order to
minimise the stress on the subjects.
22.1.5 Test transposition
A stimulus attribute that has been fairly frequently manipulated is the
transposition between the standard and comparison melodies. Initially this transposition was
introduced purely to prevent subjects from being able to use simple pitch information in their
judgements. Later the transposition effect became an object of study in its own right.
Dowling and Fujitani (1971) manipulated the presence of transposition while
investigating the effect of contour on the discriminability of five-note, atonal, random note
sequences. The standard melodies all started at a fixed pitch. The comparison melodies
were either untransposed or started on a pitch chosen at random from the 14 notes of the
chromatic scale, one to seven semitones above or below the untransposed starting pitch.
Dowling and Fujitani found that discriminability was increased in the untransposed
condition.
Dyson and Watkins (1984) also investigated the effect of the presence of
transposition. However, the conditions of their study differed markedly from those of

35
melody. Dowling found that inexperienced subjects were unaffected by the context
manipulation and displayed a moderately low level of discrimination. Professional
musicians were also unaffected by the context manipulation and produced consistently high
discrimination scores. Subjects of moderate musical experience were able to discriminate
the melodies as well as the professional musicians when the contexts were the same.
However, when the contexts differed their level of performance fell to below that of the
inexperienced listeners.
Musical experience was not an experimental variable in any of my experiments.
My interest was in establishing the existence of effects rather than describing the abilities of
the general population, and I therefore used the most experienced subjects available. When I
could, I used choristers from good a capella choirs because unaccompanied choral
performance requires a well developed sense of melody and particularly of tonality. Tan
(1979) has reported that vocalists rely more on tonal strategies than other musicians.
223 Task characteristics
Several task characteristics have been manipulated, but only the retention
interval between presentation of the standard and comparison melodies has been studied
repeatedly. The other manipulations such as the rehearsal method and type of concurrent
task, if any, have only been used in single studies (Davies & Yelland, 1977; DeWitt &
Crowder, 1986). These one-off manipulations have been either to examine some specific
procedural issue raised in the study or have been peripheral variations introduced by the
experimenter.
Dewar, Cuddy, and Mewhort (1977), Dowling and Bartlett (1981) and DeWitt
and Crowder (1986) manipulated retention interval within their studies and found that
discrimination was better at shorter delays. Dewar et al. (1977) used unfilled delays of half

36
and four seconds in order to investigate the use of concurrently presented information.
Dowling and Bartlett, and DeWitt and Crowder were attempting to simulate the
difference between short and long term memory with their manipulations of retention
interval. They used unfilled short delays of 1 and 5 seconds and long, filled delays of 31 and
25 seconds. They found that although overall performance was better at short delays, tonal
answers were relatively better discriminated at long delays.
Short, unfilled retention intervals were used in all my experiments in order to
minimise the length of the sessions.
23 Melody discrimination models
In this section I will discuss the models that have been proposed to account for
the findings in the field of melody discrimination. I will not discuss the interpretation of the
results from specific studies but will concentrate only on those models that have been
assumed to be generally applicable. I present these models in terms of historical
development within broad families of concepts.
23.1 Deutsch's neuratmodel
Deutsch (1969) proposed a neural model of music recognition. which assumed
two channels. One channel represented the sequence of a melody as a string of signed
intervals. That is, intervals of differing sizes were represented by distinct neurons, and
ascending intervals were distinct from descending intervals. The second channel represented
pitch in terms of chroma. A second stage of this channel used the chroma information to
map all the inversions of a chord onto a single representation for that chord. There was no
provision in the second channel for encoding the sequential nature of melodies.
Deutsch expressed the process (channel) differences in terms of a neural model,
which she described in the following way:

37
[It] consists of two parallel channels each of which has two stages.... In the first stage
of transformation on Channel A, primary neurons feed in twos and threes on to
second-order neurons [which] respond to specific intervals and chords. In the second
stage of transformation second-order neurons are linked to third-order neurons in
such a way that ... the third-order neurons respond to abstracted intervals and chords.
The second-order neurons on Channel A which respond to combinations
of two tones fall into three categories. Those belonging to the first category ... would
be sensitive to simultaneous intervals. Neurons belonging to the second and third
categories ... will produce an output only when a successive interval occurs. ...
[One] will respond only to the ascending successive interval and the other only to the
descending successive interval....
In the first stage of transformation on Channel B, the primary
frequency-specific neurons are linked in such a way that all neurons separated by
octaves are joined to the same second-order neuron. In the second stage of
transformation these second-order neurons are joined in groups of three to third-order
neurons. However there is no linking of combinations of two here. Thus inversion
of three-note chords is produced, but intervals and tunes are not inverted. (Deutsch,
1969, pp. 303-304)
The virtues of her model were that it was explicit and precise making the derivation of
predictions comparatively easy. This is not the case for later models.
Because of the historical primacy of Deutsch's model, other models have been
developed from it or in contradiction to it. Most researchers have avoided any neural
interpretation of their models, although some have taken Deutsch's process specification
while remaining neutral about the way in which it is implemented.
23.2 Octave equivalence models
One path of development from Deutsch's proposal has involved investigation of
the chroma component. This component is comparatively easier to investigate than the
interval component because the appropriate experimental manipulation is octave
randomisation, whereas the appropriate manipulation for interval representations is unclear.
Because of this comparative simplicity chroma was investigated fairly early and interest in it
has now waned.
All the studies that have investigated chroma models have demonstrated a

39
bidimensional concept of pitch. A note of a given pitch gave rise to two pitch attributes:
tone height (congruent with the simple pitch) and chroma. They proposed that the pitch
height was processed to yield a contour and other unspecified attributes. The chroma was
transformed to yield unsigned intervals, that is, intervals represented so that an ascending
interval is indistinguishable from a descending interval of the same size. Massaro and his
co-workers did not specify the process by which these attributes were to be used in making
judgements. However, it seems likely that they intended that each melody be represented as
a sequence of the available attributes and that the representations of standard and comparison
melodies would be matched rather than only used for confirmation.
233 Interval models
The octave equivalence studies pursued the chroma component of Deutsch's
1969 two channel model. Other studies have pursued the interval component. Deutsch's
model represented melodic identity as a sequence of signed intervals. Several models have
been proposed (mostly by Dowling) which are extensions and modifications of Deutsch's
model. The constant component of these models has been the representation of well-known
melodies as sequences ofintervals.
Dowling's models will be discussed later and their evolution over time will be
followed. However, in the immediately following section I will deal with studies that have
dissented from the view that melodies are represented as intervals.
233.1 Dissenting models
Over the period 1971 to 1981, Dowling (the most prolific researcher in this
field), based his models on interval representations. During this same period other
researchers consistently , voiced the opinion that interval based models were inadequate.
Since 1981 Dowling has modified his models away from total reliance on interval

40
representations. Simultaneously, the dissenting researchers have ceased publication in this
area.
Because the dissenting researchers were reacting against interval based models
their work concentrated more on finding evidence to support their contentions that interval
based models were inadequate, rather than advancing specific alternative models. They have
proposed other attributes to explain melody discrimination, but their models have not been
defined as specifically as the interval based models. In part this lack of specificity can be
attributed to the inability of the current methodology to adequately investigate the types of
attributes they were proposing. This point is taken further in the chapter on methodological
problems (Chapter 3). Another probable reason for the lack of specificity is that a fully
developed model based on other attributes would be more complex than an interval based
model.
Cuddy and Cohen (1976) obtained results which they interpreted as showing that
melodies were represented as more than simple sequences of intervals. They concluded that,
[Recognition] depends not merely on the intervals contained in the sequence but upon
the interval configuration. ... The abstraction of structure may occur either in
addition to, or as alternative to, interval abstraction and synthesis. ... [It] may be
suggested that interval abstraction and synthesis play a role in melody recognition,
but that there are severe limitations to interval processing. (Cuddy & Cohen, 1976, p.
269)
Davies and Jennings (1977) and Davies and Yelland (1977) conducted
experiments using production tasks rather than recognition tasks. They proposed that
melodies are represented in terms of relative pitch within a tonal system. They also pointed
out that the production of effects by manipulating contour and interval sizes does not
necessarily imply that these attributes are abstracted from melodies. They stated that,
It is apparent ... that interval information is not coded in terms of absolute or relative
magnitude, in any literal sense. ... [Subjects] perform interval tasks by matching
tones to one of a set of learned internal standards. Once the tonality (key) of a piece

41
is established (either internally or externally), a series of internal standards is
spontaneously produced. (Davies & Jennings, 1977, p.539)
[It] appears that the presence of a stored tonal representation is the critical variable in
memory for tunes. In recognition experiments, the fact that manipulating variables
like interval or contour (which are abstractions from tonal sequences) affects
recognition does not mean that these variables are important or necessary in subjects'
internal representation. (Davies & Yelland, 1977, p. 8)
Davies (1979) argues that melodies are not represented in terms of intervals but
rather in terms of whatever more configurational attributes it is within the subject's capacity
to perceive.
[Melody] is a psychological event and not a physical one. Melody is not a property
of tones, but a function of the listener's ability to organise or chunk tones into
meaningful perceptual patterns and forms. (Davies, 1979, p. 205)
He questions the importance which had been attached to the 'transposition problem' by other
researchers.
In real-life situations ... there is no initial sequence. A person hears a tune, and
merely recognises it, as it were, out of the blue. ... [People] recognise a transposed
version in exactly the same way as they recognise an untransposed version, i.e. in
terms of features and configurations which are independent of any particular
frequency, rather than by using information about abstracted frequency ratios.
(Davies, 1979, pp. 208-209)
Davies also identified and criticised an error in the interpretation of results, commonly made
by researchers proposing interval based representations.
The error comes about because it is assumed that, since it was intervals which were
manipulated in the stimulus material, it must be the intervals which were recognised
or not recognised. In fact, when intervals were manipulated, it was the tune which
was either recognised or not recognised. (Davies, 1979, p. 207)
Davies aimed his argument specifically at interval based representations because he not only
believed that the interpretation was unnecessary, but that it was also wrong given the results
of his research. The argument applies to any interpretation that links as a necessity the
manipulation with the representation. In Chapters 3 and 6 I argue against the manipulation
of melodic stimuli and develop a method of data analysis that makes such manipulation

42
unnecessary.
The dissenting research cited so far has been vague with respect to specific
attributes which might be used other than to describe them as higher level configurations and
tonal encoding. This is repeated (with some improvement) in other studies of this type.
Dewar, Cuddy, and Mewhort (1977) suggested that melodies were encoded "in
terms of relational cues, that is, the tone pattern" (p. 66). Cuddy, Cohen, and Miller (1979)
are somewhat more specific when they appear to be proposing that the relative pitch of notes
is represented by scalar degree. Although Cuddy, Cohen, and Mewhort (1981) do not
explicitly state a model for the representation of melodies it appears that they would propose
encoding in terms of scalar degrees, harmonic progressions and cadences.
233.2 Dowling's models
In this section I will pursue the development of the interval based models.
These models have been primarily developed by Dowling. Of all the researchers in this field
he has been publishing for the longest period. Over this period Dowling has been modifying
his models to accommodate new effects, especially those discovered by the dissenting
researchers. Therefore, in this section I will follow the evolution of Dowling's models over
time.
233.2.1 Dowling,1971
Dowling (1971) initially proposed that melodies are represented in terms of
contour and unsigned intervals. He stated that,
.., melodic contour and the set of interval sizes in a melody are separable features or
dimensions of the melodic pattern. ... [The results suggest] that intervals of the
same size can be processed as equivalent, regardless of direction. (Dowling, 1971, p.
349)
This model differs from Deutsch's of 1969. In her model intervals were represented as
signed magnitudes whereas in Dowling's model these have been broken into two

44
situation ... where he hears a test item and must decide if it matches any one of 18
previously presented melodies. Here, the process of reminding is crucial. If a cue
does not provide access to the appropriate trace, the listener is unable to detect any
type of similarity between the test cue and the appropriate input item. ... [It] is easy
to imagine why a same-contour-different-interval cue might be ineffective. First, it is
certain that many songs in long-term memory contain the same or similar contours,
especially if we restrict attention to seven-note segments. Moreover, even within the
context of an 18-item list ... many melodies have identical contours up to the third
or fourth note. Thus, contour information by itself might be of little use in memory
retrieval simply because it is not very discriminating. Interval information might be
much better in this regard. While many songs share segments of contours, fewer
share precise patterns of intervals for several notes in succession. Hence, subjects
might be forced to use interval information in the retrieval process. (Dowling &
Bartlett, 1981, pp. 47-48)
233.24 Dowling, 1984
The next step in the extension of this model by Dowling (1984) was to allow for
octave equivalence effects. He did this by specifying the matching process in more detail.
Dowling proposed that the comparison melody accesses long term memory to retrieve an
internal representation. This retrieved representation is then combined with the key of the
comparison melody to generate the absolute chromas of the notes of the retrieved melody
within the key of the comparison melody. These chromas are then compared on a note by
note basis with the chromas of the comparison melody.
Dowling continued to retain his concern for differential retrieval processes. He
stated his model in the following way.
[In] tasks like those used here listeners generate tone chromas from tonal scale-step
or interval representations in memory in order to evaluate chroma-only test stimuli.
Such memory representations cannot easily be accessed given only chroma
information in a stimulus. Rather, retrieval from memory seems to require additional
melodic contour and/or rhythmic contour information. Retrieval of a relevant
memory representation via contour does not seem sufficient for the listener to report
remembering the stimulus. The information from memory must be verified against
the chromas in the stimulus. Only then does the listener recognise the test melody.
This is true not only of octave-scrambled melodies in the present study, but also of ...
string quartet fragments presented with musical context. (Dowling, 1984, p. 30)
This model is no longer an entirely interval based model. The long term

45
memory representation is still interval based (tonal scale-steps or intervals) but the retrieval
is based on a combination of chroma (note based) and contour (interval based) and the final
judgement is made on note by note matching of chroma.
233.25 Dowling, 1986
The most recent model (Dowling, 1986) is an extension of the previous model to
allow for differences in experience level of the subjects. Dowling manipulated the harmonic
context of the standard and comparison melodies so that they were either the same or
different. In this way he was able to assign different scalar degrees to the notes of melodies
that were identical in interval pattern. He found that inexperienced listeners had a
moderately low level of performance irrespective of the context, professional musicians had
a high level of performance irrespective of the context, and moderately experienced listeners
had a level of performance equal to the professional musicians when the standard and
comparison contexts were the same, and a level of performance only slightly above chance
when the contexts differed.
Dowling did not propose any new components for the model. Instead he
proposed that subjects with differing levels of experience performed in accord with different
previously proposed models. He stated his proposal in the following way.
[Different] processes, best described by different theories, characterise performance at
different levels of experience. The inexperienced listeners appear to have been
relying on a process that was heavily dependent on something like Deutsch's (1969,
1982) interval abstracting channel - a process that was well suited to transposition
recognition and that was independent of context. Moderately experienced listeners
appeared to behave in a way closer to that characterised by Dowling's (1978)
contour-plus-tonal-framework model. And professionals were able to use even more
sophisticated strategies that probably included components of both the preceding
schemes. (Dowling, 1986, p. 294)

46
2.4 Conjectured framework
I have arrived at my own framework for melody discrimination that defines a
family of melody discrimination models which can be regarded as being in the tradition of
the models of the dissenting researchers, but much more specific than their proposals.
Despite being more specific this framework is far from a complete specification of the
memory representation and judgment process. The framework specifies some of the major
characteristics which I expect to be possessed by the representation and process, but leaves
most of the details unspecified.
This conjectured framework is not a necessary consequence of any of my
research nor of any of the research reported in the melody discrimination literature. I am
reporting it here in order, to provide a starting point for further research and to give the reader
an insight into the framework which guided the conception and conduct of my research.
The effects reported in the literature and demonstrated in my experiments are
consistent with my framework. As my conjectured representation is more complex than
those considered in the literature it is not surprising that it can explain results capable of
being explained by simpler models. On the other hand, because of my methodological
developments, the results of my experiments are at a more detailed level than has been
previously possible and they would be more difficult to explain with the simple models
proposed in the literature.
I believe that my framework is best regarded as a heuristic to guide the conduct
of research and interpretation and that there is no value in attempting to specify the
framework too precisely. From my framework it is possible to generate many plausible,
tightly constrained models of the exact details of representation and the judgment process.
Unfortunately, the predictions of these tightly specified instances of my framework are

49
difference. That is, when corresponding units are found to have different values on the same
attribute the melodies are judged to be different. Although the correspondence between units
is defined in terms of serial position, the process of establishing correspondence is probably
partially dependent on matching the attributes of the units. In some cases the correspondence
between the units of the two melodies could become mis-aligned due to similarities between
non-corresponding units of the melodies. For example, in my fourth experiment there were
two melodies containing the note strings OD E F' G') and (C D E F') which both contain the
string OD E F'), but at non-corresponding locations. The discriminability of this pair of
melodies was lower than predicted, suggesting that the presence of the shifted note string
caused the units corresponding to the notes of the common string to be spuriously regarded
as corresponding.
24.1 Interpretation of stimulus effects
In this section I will interpret the stimulus effects reported in the literature in
terms of my framework. The results of my experiments are interpreted in terms of this
framework in Chapters 7 and 8.
The first effect to be interpreted is the individual melodies effect. In my
framework each melody is represented as a complex multi-unit entity in which the attributes
that are encoded vary from unit to unit depending on the conditions at encoding. Therefore it
is not at all surprising that some melodies are inherently more easily recognised than others,
that the effect of various !transformations on recognisability varies across melodies, and that
the recognisability of melodies varies idiosyncratically across subjects. This follows from
the fact that under my framework melodies are not describable in terms of a fixed set of
attributes in a fixed form. Some units of a melody, such as a single note outside the key of
the melody, may possess a particular attribute which contributes strongly to the

52
the existing representation either lacks appropriate encoding in terms other than intervals or
else the expectations raised by the remainder of the melody run counter to the note which is
actually required.
2.4.2 Interpretation of procedural effects
In this section I will interpret the procedural effects reported in the literature in
terms of my framework. Melody length would affect discriminability because longer
melodies that conform to musical norms would provide more opportunities for the use of
higher level units and hence provide a more detailed and elaborated representation and thus
more opportunities to detect differences. It is also the case that it would take some short time
for the higher level attributes to be established; for example, the key of a melody may not be
apparent until after the first few notes. Therefore the first few note units of a melody would
have fewer encoded attributes and thus contribute less to discriminability. The
discriminabilty of short melodies would be more dominated by the first few notes than the
discriminability of longer, melodies.
The effect of familiarity can be easily explained as due to the presence of pre-
existing representations of the melodies that are more detailed and elaborated than the
representations that can be abstracted from a novel melody on the first hearing. When the
same novel melody is listened to several times in rapid succession there is the opportunity to
abstract successively more detail on each hearing, leading eventually to the level of
performance that would be expected with a familiar melody. This accounts for the repetition
familiarity effect. °
The presentation rate effect can easily be accounted for in terms of the time
available for encoding each melody. When the presentation rate is too high the number of
units and attributes that can be abstracted drops and the discriminability of the melody

53
declines.
As all the attributes which support the discriminability of melodies ultimately
depend on the pitch of the notes, it seems reasonable to expect that any sound source will
be adequate provided that it gives rise to a clear sensation of pitch.
When there is transposition of the comparison melody relative to the standard
melody the pitch attributes of the note units are automatically different and their use in the
melody discrimination judgment is precluded. This means that the choice of attributes to be
used in the comparison must be under some degree of control by the listener. The
availability of pitch information in an untransposed test trial should lead to a higher
discriminability, as has been reported. However, when the standard melody is presented
repeatedly, as was done by Dyson and Watkins (1984), there are more opportunities for the
encoding of attributes other than pitch, and the relative importance of pitch should drop, as
was reported.
When the comparison melody is transposed to one of several keys relative to the
standard, the difficulty of resetting the encoding process to the new key must be taken into
account. Any difficulty in establishing the key of encoding would result in the first notes
lacking scalar degree attributes and, as the melodies used in this research are relatively short,
a significant proportion of the attributes supporting discriminability would be lost. Sudden
transpositions to musically distant keys are uncommon in normal music and therefore it is
reasonable to expect that the ability of subjects to ascertain the new key, and engage it in
their encoding process, will drop with increasing musical distance from the key of the
standard.
If more context is available in the comparison melody, then more units and
attributes can be abstracted resulting in greater discriminability. The inclusion of the notes

54
prior to the changed note would allow a better reconstruction of the encoding environment of
that note than would be possible if only the notes after the changed note were included. Thus
discriminability should be better if full context is provided in the comparison melody and
preceding context should lead to better discriminability than following context, as has been
reported.
In general, listeners with more musical experience would be able to encode
melodies more easily and would have more elaborate and detailed representations so that
they should have better discrimination performance. Very experienced listeners probably
have some degree of control over the encoding that they use. This mechanism can be used to
explain the result of Dowling (1986) who reported that professional musicians were not
affected by the chordal context in which a test melody was embedded. Dowling suggested
that the professional musicians had available a number of encoding strategies, without being
specific as to what the strategies might be or how they are used. The professional musicians
were aware that the scalar degrees of the test melodies would change if interpreted in
different chordal contexts, and that they were to ignore these and judge the melodies only in
terms of the pattern of intervals. The results could be accounted for in several ways. The
scalar degree of the notes might be excluded from the judgment just as the pitch attribute is
excluded from the judgment of transposed melodies. An alternative is that the subjects do
not encode scalar degree, at all. The final possibility is that the subjects do encode scalar
degree but encode it with respect to a scale other than the one established by the chordal
context, that is, the chordal context is ignored. The ability to ignore aspects of music is
important to musicians. For example, in an unaccompanied choir singing a piece of
contemporary music, it is sometimes the case that the members of one part sing in a key
distant from the keys of the other parts. To accomplish this the choristers need to be able to

55
listen to the pitch of crucial notes sung by the other parts in order to ensure that they stay in
tune while simultaneously ignoring the difference in key.
Retention interval effects can be explained by the melodic representations
being ephemeral and having different components decaying at different rates. As time passes
after the encoding of the standard melody, various attribute values become unavailable for
the discrimination judgment, resulting in lower discriminability. If the pitch information
decays fairly rapidly then the relative contribution of more configurational attributes to
discriminability will increase with time. Loss of the pitch of the tonic note at a long delay
would allow the key of the comparison melody to be determined afresh without interference
from the key of the standard. This would account for the effects reported by Dowling and
Bartlett (1981) and DeWitt and Crowder (1986) who found that tonal answers were relatively
better discriminated from the standard at longer delays.
Although the findings of my experiments differ in detail from the effects
reported in the literature; with one exception they fall within the categories set out above
(section 2.1). In my third experiment I introduced rhythm as a factor in order to remove its
effect from the results. This experiment demonstrated an increase in discriminability
associated with changes occurring at a position of rhythmic stress. This can be accounted for
within my framework by assuming that rhythmic stress can be marked in a manner analogous
to contour reversal, that is, as an attribute of a note or as a separate unit that is linked to the
stressed note.

57
CHAPTER 3
METHODOLOGICAL PROBLEMS
The ability of researchers to investigate new phenomena in melody
discrimination is severely limited by several methodological problems. In this chapter I
examine these problems and show how I have solved them in my own work. Some of these
problems derive from characteristics of melody discrimination, others from inappropriate
methodology imported into the field. The net effect of these problems is to restrict research
to a very coarse level of analysis. My methodological developments allow the design and
analysis of melody discrimination experiments at a much finer-grained and more appropriate
level of detail, as well as supporting detailed post-hoc examination of alternative hypotheses.
Subject by melody interactions and obligatory confounding are content area
characteristics that underlie some of the methodological problems. I argue that subject by
melody interaction effects are ubiquitous in the phenomena under study and are likely to be
major sources of variance in any experiment. I also argue that confounding is obligatory;
that by the nature of melodic stimuli it is literally impossible to generate stimuli such that the
desired attributes are mutually uncorrelated and free from confounding by other attributes.
Both of these difficulties have implications for the methodology that should be used.
Other problems have arisen from the methodology that was imported into this
field from other areas of research without adequate examination of its assumptions. These
methodological problems arise in relation to experimental design, measures of
discriminability, methods of analysis, and transformation based techniques.
The final methodological problem concerns the interpretation of results. The
interval model of representation was proposed very early in the history of this field. This
resulted in many results being interpreted in terms of the interval model to the exclusion of

59
melodies or repetitions. Very few experiments have included repetitions (Cuddy & Cohen,
1976; Idson & Massaro, 1978) so the proportions have usually been formed by collapsing
over melodies and sometimes over both subjects and melodies.
If a table of three (or more) dimensions is collapsed across one dimension the
relationship of the two remaining variables may be completely different from the relationship
between the same two variables measured at any level of the varAable over which the table
was collapsed (Simpson's Paradox). This effect arises from interactions between the
marginal variables of the sub-tables and the variable over which the sub-tables are collapsed.
Because melody discrimination data are usually collapsed over melodies and there probably
are subject by melody interactions, it is very likely that effects attributable to Simpson's
paradox have been reported in the literature. Although Simpson's paradox is possible no
matter which dimension is collapsed, it seems reasonable that repetition would be the least
interactive and hence least likely to introduce artifact when collapsed. The importance of
Simpson's paradox to the study of memory has been pointed out by Hintzman (1980).
Strong individual differences between subjects and between melodies have been
found since the earliest studies. The early investigators such as White (1960) and Cuddy and
Cohen (1976) remarked upon these individual differences, although later investigators have
not commented on them.
None of the studies reported in the literature have demonstrated subject by
melody interactions directly. However, the existence of interactions can be inferred from
experimental results which show interactions between conditions defined by groups of
melodies and levels of subject experience (Cuddy & Cohen, 1976; Dowling, 1986).
Researchers have not commented on subject by melody interactions because they have been
prevented from observing them by methodological problems.

60
Subject by melody interactions can only be demonstrated directly if there are
repeated presentations of identical trials. This is an uncommon procedure, as is explained
further in section 3.2.1. The generation of stimuli and interpretation of results in terms of
transformations of melodies led to focusing on the transformations and consequent lack of
attention to the individual melodies. The use of analysis of variance to investigate the effects
of aggregate factors such as experience level and transformation type resulted in the subject
by melody interaction being included in the error term and removed from theoretical
attention. This is discussed in section 3.4.
Subject by melody interactions have been directly demonstrated in my first,
third, and fourth experiments. These interactions were not able to be accounted for in terms
of interactions between experimental factors. That is, they were essentially idiosyncratic in
nature.
I was able to demonstrate these interaction effects because my experimental
designs differed significantly from those commonly used. I did not use a transform approach
to generate the stimuli or to interpret the results, preferring instead to concentrate on the
properties of individual melodies. Individual melodies in these experiments were used in
multiple combinations giving rise to replications of melodies across trials. In addition, entire
trials were repeated in the third and fourth experiments. This replication allowed the data to
be collapsed across repetitions thus preserving the subject by melody interactions for
examination. I also avoided the use of analysis of variance by using regression techniques
with the predictors being properties of individual melodies. The third and fourth
experiments were analysed using predictors supplied by me whereas the first experiment was
analysed using an exploratory technique that attempted to derive good predictors from the
patterns of subjects' responses. It is important to note that my experiments have been

68
The remainder of my experiments avoided this particular effect by only testing
pairs of melodies having the same contour. The second and fourth experiments used the
same contour for all the melodies of each experiment. The apparent homogeneity of the
stimuli used in these experiments was quite high. In the fourth experiment there were 34
different melodies. After completing the experiment, subjects were asked to estimate the
number of melodies that had been used. Most subjects thought that around five melodies had
been used, with the highest estimate being eight.
33 Measures of discriminability
The choice of dependent variable for these studies is important. The behaviour
of theoretical interest is the discriminability of melodies, hence a response variable is
required which actually measures discriminability rather than some other function.
33.1 Proportion correct is inappropriate
Historically, two types of response measures have been used: proportion correct
and signal detection measures. Proportion correct was used by White (1960) and also by
Dowling and Fujitani (1971) in their second experiment with familiar folk-tunes. It is still in
use, for example Cuddy, Cohen and Mewhort (1981), although perhaps a little less frequently
than previously. Unfortunately, proportion correct does not measure discriminability. It
confounds the ability to detect a difference with any bias in the response process (McNicol,
1972).
Signal detection analyses derive measures of discriminability that are unaffected
by response bias. I. used signal detection measures of discriminability in my second, third,
and fourth experiments. In these studies discriminabilities were derived from the raw data
and then analysed further using other techniques to model the variation of discriminability as
a function of attributes of the melodies being compared.

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3 32 Measures from the theory of signal detection
This section examines problems in the use of measures of discriminability
derived from the theory of signal detection. In Chapter 6 I develop extensions of the
standard methods of analysis that overcome some of these problems. In order to discuss
these problems it is necessary to present the model underlying the theory of signal detection.
The theory of signal detection was originally applied to simple perceptual tasks
such as the detection of a tone in a background noise. In this situation a trial consists of a
background sound (referred to as the 'noise') possibly containing an embedded tone (referred
to as the 'signal'). The subject is required to judge on each trial whether the tone is present.
The signal and noise are constant across the experiment.
The model assumed to underlie the subject's performance requires that the
percept arising from each trial should be mapped onto a unidimensional decision axis. That
is, for the purpose of judging the presence of the signal the perceptual evidence is
summarised into a single quantity representing the degree to which the signal appears to be
present.
Furthermore, there is assumed to be some uncertainty in the mapping from the
percept to the decision axis. That is, repeated presentation of the same physical stimulus
does not always lead to the same value on the decision axis. Instead, repeated presentation of
the same stimulus gives rise to a distribution of values on the decision axis. The two
different trial types give rise to two overlapping distributions on the decision axis, one
corresponding to noise trials and the other to signal plus noise trials.
So far the model specifies how the trials are mapped into the internal
representation, the next component specifies how this information is used. The subject is
assumed to have a criterion point on the decision axis. The presence of the signal on any

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components of their running memory span task and memory model. Each subject was shown
a list of words, one at a time, and was required to judge whether each word had been
presented previously in the list. A noise trial consisted of the presentation of a new word
whereas a signal plus noise trial consisted of the presentation of a previously presented word.
The decision axis was identified with the familiarity elicited by the presented word. The
distribution of familiarities generated by the items not on the preceding list was identified
with the noise distribution and the distribution of familiarities generated by the items that
were in the preceding list was identified with the signal plus noise distribution.
Dowling and Fujitani (1971) were the first researchers to use signal detection
measures in the study of melody discrimination and they cited Norman and Wickelgren
(1965) as the source of their procedure. Dowling and Fujitani used a melody discrimination
task in which a standard melody was presented followed by a comparison melody. The
subject's task was to judge whether the comparison was an exact transposition of the
standard.
Dowling and Fujitani did not make explicit the way in which they had mapped
their task into that of Norman and Wickelgren. Their only explicit statement was to identify
exact transposition with the signal and other comparisons with noise. Although Dowling and
Fujitani's discrimination' task differs from that of Norman and Wickelgren, it can be
analogically mapped into the running memory span task by regarding each comparison as an
entire list of the running memory span task. That is, the lists are always two melodies long
and there are no intervening items between the presentation of a melody and its probe. Test
trials consist of the comparison melody only; the standard melody is an entity external to the
signal detection trial that modifies the state of the listener's memory.
Using this mapping a comparison melody that is an exact transposition of the

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332.14 Pooling over melodies
Dowling does not analyse his results at the single melody level because of the
lack of repeated trials and the inability to associate signal and noise trials at the single trial
level. Because of this he is necessarily pooling raw responses over melodies. McNicol
(1972) warns against pooling raw data over subjects and the same argument applies to
pooling over any variable. McNicol advised that the data should be transformed before
pooling. Unfortunately this option is not open to anyone using Dowling's identification
system.
The data analysis method which I have used in my third and fourth experiments
deals with the discriminability component of the data at the single trial level, thereby
avoiding the problem of pooling. The part of the analysis which estimates the response rates
to the noise trials does involve pooling across trial types but this operates on transformed
data and hence adheres to McNicol's advice.
3322 Use of proportions as propensities
Another problem derives from the way in which signal detection measures are
calculated. They are usually calculated by taking the experimentally observed proportions
and substituting them directly into formulae for discriminability. That is, the empirical
proportions directly determine the parameters of the signal detection model. However, the
parameters of the signal detection model determine the probability of the subject's responses,
and these probabilities will not generally be equal to the observed proportions. The
empirical proportions are binomially distributed about the probabilities, which must be
estimated from the empirical proportions. Use of the proportions as probabilities will bias
the results and also invalidate the significance tests of the discriminability measures. This is
a problem which has not been recognised in melody discrimination research.

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attribute of the interval sequence necessarily involves changes in other attributes, and hence
gives rise to obligatory confounding.
When combined with ANOVA technology, this problem of using manipulations
that cause obligatory confounding has serious consequences. Traditionally, ANOVA
manipulations are able to be applied independently, and hence the treatment factors are
orthogonal. In melody discrimination there is a finite universe of melodies satisfying the
constraints of a given experiment. The researcher does not manipulate these melodies, but
instead searches for melodies that have the attribute values implied by the 'manipulations'.
The combinations of attribute values implied by combinations of 'manipulations' may not be
equally frequent in the universe of melodies; in fact some combinations may be logically
impossible. Consequently, when the design variables of an analysis of variance are
orthogonalised, this is done by selecting or generating melodies, some of which may be very
unusual. This leads to a problem of ecological validity.
More importantly, however, when the design variables are orthogonalised they
are confounded with other variables not included in the study, because of the presence of
obligatory confounding. Potential confounding variables cannot be used as covariates
because this begs the question of which variables, the design variables or the covariates, are
more important to the phenomena under investigation. It is also not possible to include all
the potential confounding variables as design variables, because this would rapidly make the
orthogonalisation requirement impossible to satisfy, and the set of stimuli unworkably large.
Also, as with the manipulations free from obligatory confounding, there is an
abiding tendency to ignore individual melodies in the analytic process and concentrate on
models that derive parameters for groups of melodies. This is particularly inappropriate with
the more recent conception of the transformation approach, where the choice of transformed

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using the regression-based technique described in Chapter 6. These analyses derived the
discrhninability of individual pairs of melodies and then modelled these discriminabilities in
terms of the attributes of individual melodies.
With the exception of rhythm and transposition (manipulations which do not
alter the sequence of intervals), I have not attempted to orthogonalise the analytic variables,
although I did try to avoid full colinearity. In my first experiment, the manipulation
consisted of forming all possible pairs of melodies from the stimulus set with no other
constraints. The second and third experiments required the manipulation of transposition and
rhythm factors. As these manipulations do not affect the interval sequence they can be
dropped from consideration. The second experiment required the manipulation of the
position of the altered note. Thus, it was a single (obligatory confounding) factor design and
did not require the orthogonalisation of obligatory confounding factors. Similarly, the third
experiment was essentially a single factor design. The fourth experiment required
manipulation of the number of altered notes and intervals, which are obligatory confounding
factors. Orthogonality of these variables is impossible to achieve over a reasonable range of
levels of both factors. In this experiment no attempt was made to orthogonalise the factors,
although I did ensure thati.they were not colinear.
34.3 Inference of representations from effects
A problem that is applicable to both classes of independent variable mentioned
above (sections 3.4.1 and 3.4.2) is the incorrect assumption that if a variable affects
performance it must be directly incorporated into the representation. In fact, some variables
may not be represented at all. For example, severe degradation of a melody by white noise
will alter the representation of the melody, but the white noise is unlikely to be directly
represented. Other independent variables, such as interval size, which are much more central

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3.53 Data interpreted as support for processes
The same arguments apply even more strongly to interpretations which claim to
support particular processes. Dowling (1986) claims that his data support the notion that
scalar degrees are generated at the time of recall rather than being encoded when the melody
is heard. That is, he is claiming that his data support a particular representation and a
particular process. Although the data may be compatible with his claim, other
representations and processes may be equally compatible with the data.
When consideration is given to the nature of cognitive models and the
constraints that exist on observability it can be seen that processes cannot be directly
observed. Knowledge of a process must be inferred from knowledge of the input and output
representations that are linked by that process. But it has already been argued that
representations cannot be unambiguously supported by experimental data. Therefore
interpretations supporting particular processes are based on more tenuous inferences from the
data and should be regarded as mostly conjectural. This should not be taken as a criticism of
the proposal and use of models which specify representations and processes. The difficulty
arises out of interpreting .
experimental results as strong support for theoretical models.
I have dealt with these problems in my research in a number of ways. I have not
used the interval abstraction model nor allowed it to dominate the design of my experiments.
Experiment four was the only experiment to address the question of whether intervals are
abstracted and it did this using a method totally different from any reported in the literature.
I also have raised the issue of the distinction between attributes and units. In my
research I have made no attempt to investigate the question of the units of representation. I
have concentrated entirely on investigating the attributes encoded in the representation.
Even in my fourth experiment, in which I examined the salience of interval and note