Learning Novel Musical Grammars

Familiarity,
Expectation, and Preference

The present chapter
demonstrates the human ability to learn a new musical system.
Using the two finite-state musical grammars described in the
previous chapter, we explore the learning of new music via
passive exposure. In all experiments in the next two chapters,
participants are assigned to either Grammar I or Grammar II.
During a passive exposure phase, participants hear a set of
melodies composed according to their assigned grammar. Pre- and
post-exposure tests are conducted to assess various aspects of
learning. 

Experiment 1

In this experiment, musically
trained subjects are exposed to melodies in either Grammar 1 or
Grammar 2. To understand the extent to which participants
acquired their grammar, we ask the following questions
regarding learning:

1.      Can participants
recognize melodies they had heard?

2.      Can they generalize
their knowledge towards new melodies composed from the same
grammar?

3.      Can they predict
frequencies of events in the new musical system?

4.      Can they form
preferences for any aspects of the new musical system?

To address questions 1 and 2,
we employ two-alternative forced choice tests of recognition
and generalization, where participants hear familiar and
unfamiliar melodies in both grammars, and are asked to choose
the more familiar melody. Question 3 is addressed using
probe-tone tests before and after the exposure phase, where
participants hear a melody followed by a probe tone, and rate
the degree to which the probe tone fit the preceding melody.
Finally, to answer question 4 we conduct a subjective rating
task where participants gave preference ratings for each melody
after hearing it. To presage our results, we found extensive
learning based on several of these tests. 

Method

Subjects. Twenty-four
undergraduate students from the University of California at
Berkeley participated in this study for course credit. All
participants had normal hearing and more than five years of
musical training. Only participants with musical training were
used in this first study because musically trained individuals
have been shown to demonstrate less variability in their data,
especially in probe tone tests (e.g. Krumhansl, 1990). Each
subject was assigned to either Grammar 1 or Grammar 2.

Stimuli. All auditory stimuli
were generated and presented using Max/MSP (Zicarelli, 1998)
and presented via headphones at a level of 70dB. Twenty
individual melodies (10 in each grammar) were constructed and
presented in pure tones ranging from 220Hz to 660Hz, spanning
one tritave in the current tuning system. The musical grammars
and melodies generated from them were described in the previous
chapter.

Procedure. Experiments were run
in a soundproof chamber. Each experiment included five
phases:

1)      Pre-exposure probe
tone ratings: thirteen trials were presented in this phase.
Each trial consisted of the same melody in the Bohlen-Pierce
scale, followed by a probe tone which varied across trials. The
melody for Grammar I was {6 6 4 3 6}, where each number stood
for n in the Bohlen-Pierce scale formula, Frequency = 220 *
3^(n/13). The melody for Grammar II was {0 7 4 6 6}. The probe
tone of each trial varied randomly from 0 to 12 in the B-P
scale. In each trial, after hearing the melody and the probe
tone, the participant's task was to tell the experimenter how
well the probe tone fit the preceding melody, on a scale of 1
to 7 (where 1 was least fitting and 7 was best fitting). The
experimenter entered the participant's response into the
computer, and then initiated the next trial.

2)      Exposure: The second
phase consisted of five melodies generated from the assigned
grammar being played in randomized order for 25 minutes. See
Appendix 2 for a list of all melodies presented during the
exposure phases of experiments in this chapter. Participants
assigned to Grammar I were exposed to melodies 1 through 5 of
Grammar I, whereas participants assigned to Grammar II listened
to melodies 1 through 5 of Grammar II. One of the five exposure
melodies in each exposure set was the same as the melody used
to obtain probe tone ratings in the previous phase of the
experiment. Each tone in each melody lasted 500ms, and a 500ms
silence separated any two melodies. Each melody was repeated
100 times over the course of exposure. While listening to the
melodies, in order to alleviate boredom participants were given
the option of drawing on provided paper as a distracter
task.

3)      Forced-choice
recognition and generalization: In the third phase,
participants were given two forced-choice tasks, one assessing
whether they could recognize the melodies they had heard during
the exposure phase, the second assessing whether they could
recognize novel melodies generated by the same grammar (thus
demonstrating generalization). One block of five recognition
trials was followed by a block of five generalization trials.
In both types of trials, two melodies were played one after
another, with an inter-onset interval of 5 seconds (i.e. the
time delay between the start of the first melody and the start
of the second was 5 seconds). Participants' task was to
indicate which melody (the 1st or 2nd)
sounded more familiar. The alternative melody (the incorrect
answer) was always a melody drawn from the alternative grammar.
Thus, while the same melodies were presented to both groups of
participants, the right answer for participants exposed to
Grammar 1 was the wrong answer for those exposed to Grammar 2,
and vice versa. Participants indicated their response verbally
(by responding "first" or "second") to the experimenter, who
then recorded their answer and initiated the next trial.

4)      Post-exposure probe
tone ratings: In order to measure sensitivity to occurrence
frequencies of tones as a result of exposure, we administered a
second probe tone rating task after exposure. This task was
identical to the first probe tone task, allowing direct
comparison between the two sets of data.

5)      Preference ratings:
To assess the degree to which learning influences musical
preference, the fifth and final block consisted of twenty
trials of preference ratings. Participants heard a different
melody in each trial, with melodies chosen randomly without
replacement among melodies 1 through 10 of either Grammar I or
Grammar II (see Appendix 2 for lists of melodies 1 through 10
of Grammars I and II). Participants responded by telling the
experimenter a preference rating for each melody after it was
played once. Ratings were on a scale of 1 to 7, with 1 being
the least preferable and 7 being the most preferable. The
experimenter recorded the participant's response, and then
initiated the next trial.

Results

Figure 1 shows the data from the
recognition and generalization tasks, plotted as percent
correct. A participant's response was scored as correct when
they selected either the melody that they had heard during
exposure (recognition items) or the novel melody generated with
the same grammar as their exposure melodies (generalization
items). When the participant selected the melody generated by
the other, non-trained grammar, their answer was scored as
incorrect.

As is evident in the figure,
participants were significantly above chance in identifying the
melodies they had heard, but were not above chance in being
able to identify new instances of the same grammar as more
familiar.  We observed successful recognition of old
melodies with very high accuracy (M = 97%, SD = 23%; two-tailed
t-test against chance: t(20) = 33.1, p < 0.001, d = 7.17;
prep > .99), but only chance levels of
generalization (M = 54%, SD = 24%; two-tailed t-test against
chance: t(20) = 0.67, p = 0.41).

 

Figure 1. Two-alternative forced
choice results from Experiment 1.

Probe tone ratings collected
before and after exposure were both significantly correlated
with the exposure frequencies (mean pre-exposure r = 0.36, SD =
0.23; post-exposure r = 0.64, s.e.0.19; see Figure 2). When
effects of the melody used to obtain the ratings were
partialled out (see Appendix 1), post-exposure ratings were
still significantly above chance (average r' = 0.26, SD = 0.26,
two-tailed t-test against chance level of 0: t(20) = 3.00, p
< 0.01, d = 0.66; prep = 0.96) but pre-exposure
ratings were not significantly correlated with exposure (r' =
0.05, SD = 0.26, t(20) = 0.60, p = 0.55).

 

Figure 2a. Probe tone ratings
for Grammar I from Experiment 1.

 

Figure 2b. Probe tone ratings
for Grammar II from Experiment 1.

In the preference ratings task,
participants rated the five old melodies as more preferable
than new melodies in either grammar. Ratings for old melodies
in the same grammar were significantly higher than ratings for
new melodies in either grammar (average rating: old melodies
same grammar: M = 4.7, SD = 0.3; new melodies same grammar: M =
3.9, SD = 1.4; new melodies different grammar: M = 3.8, SD =
1.4, one-way ANOVA comparing three conditions: F(2,63) = 3.42,
p < 0.05, d = 0.75, prep = 0.89, see Figure
3).

Figure 3. Preference ratings.

Conclusion

After 25 minutes of exposure to five
melodies in one grammar, participants were able to recognize
the melodies they heard, but could not generalize their
knowledge to new instances of the same grammar. Preference
ratings revealed that melodies presented during the exposure
phase were preferred over novel melodies. This suggests that
preference arises partly from familiarity, and that being
exposed to an input repeatedly can have a positive influence on
subjective preference. This is similar to the Mere Exposure
Effect, reported by Zajonc and others in various studies (e.g.
Zajonc, 1968; Bornstein & D'Agostino, 1992).

Experiment 2. Effects of Set Size on
Learning

Experiment 1 showed highly successful
recognition but chance levels of generalization. This failure
to generalize may be due to the small number of melodies during
exposure. Having been exposed to only five melodies for 25
minutes, participants may have learned those five melodies by
rote memorization, instead of acquiring a deeper and more
flexible understanding of the underlying grammatical rules.
This is supported by findings in statistical learning showing
that variability can be a useful cue in learning of structures
(Gomez, 2002).

In an attempt to induce generalization,
the second experiment in this chapter employs a larger number
of melodies (15 instead of five) during exposure.

Method

Subjects. 24 undergraduate
students participated in this study. Recruitment criteria were
the same as Experiment 1. None of the participants in
Experiment 2 had been in Experiment 1.

Stimuli. In addition to the 10
melodies for each grammar from Experiment 1, 10 new melodies
were generated for each of the two grammars. All other stimulus
parameters were the same as Experiment 1.

Procedure. Experiment 2 was
identical to Experiment 1 in procedure, except for the
following modifications:

1)      Pre-exposure probe
tone ratings: a different melody (i.e. one not presented during
the exposure) was played prior to the probe tone in both pre-
and post-exposure ratings. Grammar I participants were
presented with the melody: {10 6 7 3 0 4 6}, and Grammar II
participants heard the melody: {10 6 7 4 3 6 0}.

2)      Exposure: we
increased the set of presented melodies from five to 15. Each
melody was presented 33 times over 25 minutes of
exposure. 

3)      Forced-choice
recognition and generalization: 10 more trials were added to
the recognition block, such that this phase of the experiment
contained 20 trials, 15 in the recognition block and 5 in the
generalization block.

4)      Post-exposure probe
tone ratings: this was identical in materials and procedure to
the Pre-exposure probe tone ratings phase of Experiment 2.

5)      Preference ratings:
participants gave preference ratings for 40 melodies (20 in
each grammar), using the same scale and procedure as Experiment
1.

Results

Data from the recognition and
generalization tasks are shown in Figure 4. Data are shown
separately for the two groups of participants based on the
presentation grammar due to a significant main effect of
grammar (F(1,44) = 7.18, p = 0.01) and a significant
interaction between grammar (Grammar I vs. Grammar II) and task
condition (recognition vs. generalization): F(1,44) = 11.8, p =
0.001. Forced-choice tests showed that both groups of
participants recognized the presented melodies at significantly
above-chance levels (Grammar 1 recognition accuracy: M = 76%,
SD = 0.17, t(11) = 5.17, p < 0.01; Grammar 2: M = 79%, SD =
14%, t(11) = 7.25, p < 0.01). In addition, participants
exposed to Grammar 1 significantly generalized their
familiarity to the new instances of the same grammar (M = 70%,
SD = 20%, t(11) = 3.46, p < 0.01; see Fig. 4a), whereas the
group exposed to Grammar 2 did not generalize their familiarity
to new melodies (M = 38%, SD = 20%, t(11) = -2.03, n.s.; see
Fig. 4b). Pooled data from both exposure grammars revealed
significantly above-chance performance in recognition
(recognition accuracy: M = 78%, SD = 15%, t(23) = 8.72, p <
0.01) and above-chance, but not significant, performance in
generalization (M = 54%, SD = 25%, t(23) = 0.81, n.s.).

 

Figure 4a. Grammar 1 forced choice
results.

 

Figure 4b. Grammar 2 forced choice
results.

Probe tone tests revealed that subjects
significantly learned the tone frequencies within the corpus of
melodies. Both the pre-exposure ratings and post-exposure
ratings were correlated significantly with the melody set
(pre-exposure r = 0.32, SD = 0.31, t(23) = 5.14, p < 0.001;
post-exposure r = 0.46, SD = 0.34, t(23) = 6.47, p < 0.001)
(Fig. 5). An increase in correlation is observed for
post-exposure ratings, but this difference is not significant
with 24 participants (t(23) = 1.42, n.s.). When effects of the
probe melody were partialled out (see Appendix 1 for details on
partial correlations), both pre-exposure and post-exposure
ratings were still above chance level (pre-exposure r = 0.20,
SD = 0.32, t(23) = 3.04, p < 0.01; post-exposure r = 0.26,
SD = 0.37, t(23) = 3.47, p < 0.01).

Figure 5a. Pre- and post-exposure probe
tone ratings versus frequencies of occurrence of pitches during
exposure to Grammar I of Experiment 2.

Figure 5b. Probe tone ratings versus
frequencies of occurrence of pitches during exposure for
Grammar II of Experiment 2.

Preference ratings were not different
for old grammatical, new grammatical, and ungrammatical
melodies (ratings for old grammatical melodies: M = 3.5, SD =
1.2; new grammatical: M = 1.2, SD = 1.2, ungrammatical: M =
3.4, SD = 1.0; one-way ANOVA comparing three conditions:
F(2,33) = 0.96, n. s.; see Fig. 8), showing that this
experiment did not elicit a change in preference.

 

Figure 6. Preference ratings from
Experiment 2.

Conclusion

Both groups of participants recognized
the melodies they had been exposed to. One group of
participants was able to generalize this information to new
melodies composed according to the same grammar. This suggests
that participants in this group successfully learned the new
musical grammar.  While results are still difficult to
interpret at this stage, the possibility of successful
generalization may mean that when given exposure to a
sufficiently large set of exemplars of a musical grammar, the
human brain could infer structure within music.

Probe tone ratings showed some increase
in sensitivity as a result of exposure, but results were not
significant in this experiment. Changes in preference due to
exposure were not observed in this experiment. Thus the
melodies that participants had previously encountered, which
the forced choice tests showed that participants could
recognize, did not influence their musical preferences. While
it was possible that the artificial musical sounds we use were
simply insufficient to induce a change in affective response,
it could also be that the current exposure parameters (15
melodies repeating 27 times each) were insufficient to cause
changes in preference ratings. Based on observations from
Experiment 1 of this chapter showing preference increase
following repeated exposure to a smaller number of melodies, we
expect that repeated exposure to melodies may lead to changes
in preference, whereas an increase in number of exemplars leads
to grammar generalization.

General Discussion

Experiment 1 showed that after
participants were exposed repeatedly to five melodies for 25
minutes, they recognized and preferred melodies they had heard,
but could not generalize their knowledge to new melodies
composed in the same grammar.

In Experiment 2 we exposed participants
to a larger number of melodies (15 instead of five) for the
same overall length of time. Thus, participants heard each
individual melody fewer times than participants in Experiment
1. This increase in exemplars and reduction in repetition
affected participants' performance in the forced-choice tests:
participants now showed only marginal recognition, but also a
trend toward generalization. Learning of the musical system was
also demonstrated in the probe tone task, where probe tone
ratings showed that participants became more sensitive to the
underlying frequencies of tones in the new music system after
exposure. 

Taken together, these experiments
suggest that given limited exposure to exemplars of a novel
musical system, humans can exhibit rapid learning to develop
expectations that conform to the musical grammar. Increasing
the number of exemplars of the musical grammar may a) help to
enhance sensitivity to the underlying statistics of a grammar;
and b) aid learners in generalizing the learned statistics to
new instances of the same grammar. However, increasing the set
size of exemplars also seems to be detrimental for developing
preferences for familiar melodies. These results suggest that
the subjective experience of musical preference is not directly
related to the increase of statistical sensitivity or to the
understanding of grammatical structure; instead, preference may
be a result of item recognition and familiarity. We plan to
conduct follow-up studies to further examine the link between
familiarity and preference.

Having observed the possibility that
humans can learn new musical grammars, we now attempt to
identify individual components of the input that may optimize
learning.