Pure Tone Frequency Discrimination:
An Examination of Experimental Methodology
Robert Mannell
Macquarie University, 2007
Abstract
This series of experiments examines the concept of "just noticeable differences" (jnd's) in frequency
(also known as frequency difference limens or DLF). This is the difference in frequency (Δf)
between two tones presented in series that can just be detected. Frequency jnd's vary for different
frequencies. The higher the frequency of a tone, the greater the change of frequency must be for the
second tone to sound different in pitch.
This paper examines a number of experimental methodologies for determining frequency jnd's. The
experiments progress form very simple and rather naive experimental designs to more complex and
carefully controlled designs. Issues examined include token timing, subject training and response
tasks. This paper clearly illustrates the sensitivity of experimental results in psychoacoustics to
issues of experimental design and subject training.
Readings
1. Moore, B.C.J., 2003, The Psychology of Hearing, Academic Press, 5th edition.
o Frequency Discrimination: Chapter 6, esp. pp 197-204
2. Mannell, R.H., 1994, The perceptual and auditory implications of parametric scaling in
synthetic speech, Unpublished Ph.D. dissertation, Macquarie University
o Frequency Discrimination: Section 2.2.1 "Frequency"
3. Mannell, R.H., 2007, SPH307 Psychoacoustics lecture notes (only available to SPH307
students via WebCT on the MyMQ Portal).
Experiment 1
In this experiment we attempted to determine the frequency jnd at 1000 Hz using a very simple
experimental procedure.
To do this we present a series of 10 conditions. In each condition there are four pairs of tones. Each
condition has a fixed frequency difference (Δf) between the two members of each pair. For two of
the pairs, the first of the two is set at 1000 Hz and the second is Δf higher. For the other two pairs
the second is set at 1000 Hz and the first is Δf lower. Δf ranged from 1 to 10 ms. For each group of
four pairs the presentation order is randomised. In each of the four tone pairs, each tone was 500 ms
in length and the two tones were separated by 250 ms. Each of the tone pairs was separated by
about 1 second. (These tokens are from an audio CD published by the Institute for Perception
Research Eindhoven, The Netherlands and the Acoustical Society of America. Houtsma, A.J.M.,
Rossing, T.D, and Wagenaars, W.M., (1987) Auditory Demonstrations)
Each condition had a smaller df value than the preceding condition. We attempted to determine
which condition was the first condition for which less than three of the pairs were discriminated by
each subject. The jnd was then assumed to be the df value for the proceeding condition.
Results
There were no valid results for this experiment. All 18 subjects failed to achieve a stable perception
of frequency j.n.d. at 1000 Hz.
Design Issues
Possibly the factor most affecting the negative results for this experiment was the timing of the tone
pairs. Firstly, the two member tones of each pair were too far apart in time. Previous work on the
determination of frequency j.n.d.'s suggests that tones are discriminated best when they are very
close together. The closer together they are, the less the influence of short-term memory on the
performance of the subjects. The other timing factor that may have impacted on the results was that
the different tone pairs may have been too close together. What is needed is for intra-pair tone
separation to be smaller and inter-pair tone separation to be greater.
Also, a few more extreme tone differences (say of 20 Hz) at the beginning of each condition may
better prepare the subjects for this discrimination task. Perhaps most importantly, subjects received
no training before attempting this task.
Experiment 2
This experiment was essentially identical to the experiment carried out in experiment 1, except
that:•
•
the two tones in a tone pair were abutted together (rather than having a 250 ms gap between
them)
subjects were presented with a questionnaire that asked about their hearing and musical
experience and training
Results
18 subjects participated in the experiment. The results for one subject was excluded because of
significant hearing loss.
Of the remaining 17 subjects, 3 subjects failed to discriminate any tokens and 1 subject made only
one discrimination. These subjects were excluded from the following analysis. An additional
subject reported discrimination of all tokens. This result might be due to this subject attending to
some feature other than the frequency difference (such as temporal discontinuities [ie. clicks] or
phase shifts) or it might be that this subject has above average frequency discrimination abilities.
This subject was also excluded. Another 3 subjects provided anomalous results, such as
discriminating the least discriminable pairs better that the most discriminable pairs or having a
significant drop or increase in the middle conditions relative to the most and least discriminable
conditions. All subjects who were included reported discrimination for at least 12 tokens and
reported no discrimination for at least 4 tokens.
Only 9 subjects were finally included in the analysis. Of these nine, eight reported musical
experience. That is, of the nine subjects who reported musical experience, only one was excluded
from the analysis and this was because of significant hearing loss. Only one of the subjects who
reported no musical experience was included.
In the following figure the results for all 9 included subjects are shown against the ten frequency
differences (1 to 10 Hz).
Figure 1: This figure displays the mean number of tokens perceived as having a change in
frequency for each of the frequency differences. The error bar represents one standard deviation.
It should be noted that these results, whilst demonstrating some stability in subject responses, do not
provide us with a reliable measure of frequency discrimination at 1000 Hz. From previous research,
we would expect a flat maximal response (ie. a response of 4) for the larger frequency differences
(say above 4 Hz), but this was not achieved.
Design Issues
In experiment 1 the tone pairs were separated by a silent gap. In experiment 2 there was no
separation between the two tones in each pair. They were spliced together with no gap between
them. In experiment 1 no subjects were able to perceive changes in frequency whilst in experiment
2 all musically-trained subjects were able to detect frequency changes. Previous work on the
determination of frequency j.n.d.'s suggests that tones are discriminated best when they are very
close together. The closer together they are, the less the influence of memory on the performance of
the subjects.
Another problem with this experiment is the presence of clicks in some tone pairs. The abutting of
two tones together may result in clicks and possibly also in audible phase changes. In future, tones
should more gradually change from one frequency to another over several cycles to avoid clicks and
to minimise phase artifacts.
Subjects with no musical training or experience typically responded poorly to this experiment with
patterns of no discrimination or inconsistent discrimination. A few more extreme tone differences
(say of 20 Hz) at the beginning of each condition may better prepare the subjects for this
discrimination task.
It was determined that subject training should be considered in much greater detail before trying
this experiment again.
Experiment 3
In this experiment subjects were provided with extensive pre-test training (made possible by the
purchase of an integrated audiovisual token presentation and respone system). Responses were
simple Yes/No responses to questions of the type "Did this tone change in frequency?".
Procedure A: Tone Step
In this experiment we utilised a number of 2 second tones of a frequency about 1000 Hz which
either increase or decrease in frequency near the tone's temporal mid point. The change in frequency
occurs smoothly between the two frequencies over a period of 0.2 seconds. For each frequency
change two tokens were created, one in which the frequency increased by Δf Hz and the second in
which the frequency decreased by Δf Hz. For example, for a frequency change of 10 Hz, one tone
changed from 995 Hz to 1005 Hz whilst the other tone changed from 1005 Hz to 995 Hz.
Thirty three (33) tones were created. These included one tone in which the frequency did not
change, plus two tones (rising and falling) for each of 16 frequency changes (50, 45, 40, 35, 30, 25,
20, 18, 16, 14, 12, 10, 8, 6, 4, 2 Hz).
All tokens were presented to experimental participants using an "audience voting system" created
by IML (Innovative Group Response). Each token was played to participants via high quality
headphones. A computer screen prompted responses from participants and provided feedback when
required. Using a hand held device, participants responded to each tone by pressing "1" if a change
was heard and "2" if no change in frequency could be heard.
Training occurred before the test session. Training was divided into three sequences:1. The first sequence used tones with very clear frequency changes (50, 45, 40, 35, 30, 25 Hz)
presented in order from the largest change (50 Hz) to the smallest change (25 Hz) with
rising and falling tones paired and presented in random order. Tones with no change were
randomly presented within this sequence. The purpose of this sequence was to familiarise
subjects with the sound of rising and falling tones.
2. The second sequence consisted of the 20, 18, 16, 14 and 12 Hz changes presented randomly
and interspersed randomly with non-changing tones. These tones were regarded to be
reasonably discriminable tones and that would be repeated in the test sequence.
3. The third and final sequence consisted of the least discriminable tone changes (10, 8, 6, 4,
and 2 Hz) presented in order of decreasing frequency change interspersed with nonchanging tones. This order was selected to gradually familiarise subjects to increasingly
hard to discriminate frequency changes. These tones were also repeated in the test sequence.
During training, feedback was provided in the form of bar charts showing the total yes and no
responses of the current group of experimental participants and information on whether or not each
tone actually did have a change in frequency.
The test session immediately followed the training sessions and comprised of the 20, 18, 16, 14, 12,
10, 8, 6, 4, and 2 Hz changes (both directions) presented randomly and interspersed with nonchanging tokens. No feedback was provided during the test session.
Procedure B: Frequency Modulation
In this experiment we utilised 3 second tones that varied sinusoidally in frequency around the centre
frequency (1000 Hz). The modulation rate was 4 Hz. That is, each tone varied smoothly between its
upper and lower frequency limits 4 times per second. For example, a tone with a frequency change
of 50 Hz varied sinusoidally 4 times per second between 975 Hz and 1025 Hz.
Seventeen (17) tones were created. These included one tone in which the frequency did not change,
plus one tone for each of 16 frequency changes (50, 45, 40, 35, 30, 25, 20, 18, 16, 14, 12, 10, 8, 6,
4, 2 Hz).
As with the Tone Step condition, this experiment commenced with three training sequences similar
to the training sequences used for the tone step experiment.
The test session immediately followed the training sessions and comprised of the 20, 18, 16, 14, 12,
10, 8, 6, 4, and 2 Hz changes presented randomly with interspersed with non-changing tokens. No
feedback was provided during the test session.
Subjects
56 subjects participated in this experiment. The majority (about 90%) of subjects were female and
their mean age was about 20. Subjects provided information about their hearing and musical
background.
A small number of additional subjects participated in this experiment but were excluded because of
false positive and/or false negative trends during training. A false positive trend occurs when a
subject consistently reports a change in frequency for tokens that don't change in frequency. A false
negative trend is a trend that exhibits a much greater than average history of negative responses
during training to tokens that are reliably identified as having a clear change during training. A false
positive trend might indicate that a subject is responding to some aspect of the signal other than the
change that is being trained. Nearly always (in the present experiments), however, it is accompanied
by false negative trends and is a possible indication of hearing loss. In all cases, subjects excluded
on these grounds also self-reported hearing problems.
Results
Results for the frequency discrimination experiment are summarised in figure 2.
Figure 2: This figure compares the frequency step and frequency modulation results for the
experiment 3 discrimination tasks.
Chi-square statistics were applied to the raw data. The Frequency Step and Frequency Modulation
results for a frequency change of 4 Hz were significantly different (p=0.001). No other frequency
change showed a significant difference between the two conditions.
For the frequency step condition all frequency changes ≥4 Hz were perceived correctly,
significantly above chance (ie. above 50%, p<0.01). For the frequency modulation condition all
frequency changes ≥6 Hz were perceived correctly, significantly above chance (p<0.01).
Musical training and musical experience did not significantly affect the outcome of this experiment.
Note however, that there were significant differences in the time it took different subjects to obtain
a stable pattern of results. Some subjects obtained a stable pattern of responses immediately whilst
others took nearly the entire (rather long) training session to obtain a stable pattern of responses. It
may be that musically trained subjects had a tendency to obtain a stable pattern of responses more
quickly than other subjects, but this was not tested (this would be a good hypothesis for a future
experiment).
Experiment 4
In this experiment an important modification to the experiment 3 experimental method was tried.
The experiment 3 yes/no training procedure was repeated, but then it was followed by additional
training in an AB decision task. The AB decision task presents two tokens, one of which contains
the targeted change whilst the other does not change. In the simple AB decision task the subject
must answer "A" if token A was perceived to change or "B" if token B was perceived to change. A
response was forced, so the subject had to make a decision, even if it was only a guess.
Figure 3 summarises the results for these experiments. 26 subjects participated in this experiment
and all of them are included in these results as none exhibited false negative or false positive trends
during training.
Figure 3: This figure compares the frequency step and frequency modulation results for the 2005
frequency discrimination experiments. In these experiments a forced AB choice was made. In the
above diagram the horizontal line labeled"A" indicates a perfect chance response (ie. 50% A and
50% B responses). Responses equal to or greater than the line labeled"B" are significantly above
chance for p=0.05. Responses equal to or greater than the line labeled"C" are significantly above
chance for p=0.01.
It should be noted that for p=0.01 the results for this experiment are similar to those in the
preceding experiment in that for the frequency step condition the 4 Hz token was significantly
perceived above chance whilst for the frequency modulation condition the 6 Hz token was the
smallest change that was significantly perceived above chance. Note, however, that in the previous
experiment the 4 Hz FM token was not significantly above chance for p=0.05 whereas it was in this
experiment.
General Conclusions
The general conclusions and observations for this series of experiments are:1. Similar results are obtained for frequency step and frequency modulation designs.The
frequency step condition provides a slightly better discrimination for a yes/no decision task,
but there is no significant difference for an AB choice task.
2. The AB choice task resulted in more consistent results for the frequency step and frequency
modulation designs than did the yes/no decision task.
3. Pre-test training is essential. Prior musical training only partially compensates for absence of
pre-test training. The inclusion of larger differences in training may increase the efficacy of
training by better familiarising subjects with the kind of changes being tested, but this needs
to be tested by carrying out training using only the Δf values used in the test stage of the
experiment.
4. Token pair timing appears to be critical. Token pairs need to be abutted in order for clear
discrimination patterns to emerge.
5. Abutting two tones together without a period of transition results in audible clicks which
could affect experimental results. The effect of these clicks was not investigated in this
series of experiments but the perceptual effect of such clicks is well attested in
psychoacoustic literature. Masking the clicks by adding to the tones a small amount of
background white noise may remove any such effect, but this would be likely to occur at the
cost of increased uncertaintly in the decisions as is seen in the gap detection experiments
reported upon in the Gap Detection paper.