Detecting intonation errors in familiar melodies
Nancy E. Kelley
Manchester College
North Manchester, Indiana
Experiments on musical pitch perception have shown that intervals with equal frequency
ratios are not always perceived as the same by musicians, but are affected by the tonal context, or
key, in which the intervals are heard (Krumhansl, 1979; Krumhansl & Keil, 1982; Krumhansl &
Shepard, 1979). Memory for the pitch of single tones has also been shown to be affected by
whether a series of tones intervening between the standard and comparison tones is tonal or
atonal (Dewar, Cuddy, & Mewhort,1977; Krumhansl, 1979). These findings are thought to result
from the use of an internal frame of reference (the scales) in the encoding of pitch. The present
study is a test of the hypothesis that nonmusician's recognition memory for pitch in the form of
intonation judgments concerning notes in familiar melodies will be affected by the tonal context
in which the tones are heard. Specifically, it is expected that differences in the tonal functions, or
tonal stabilities, of the tones in their respective tonalities will contribute to differences in the
ability of listeners to perceive small changes in frequency when the notes are out-of-tune. Since
the more consonant steps in the scale are more easily remembered, it is predicted that they will
also be more discriminable from close neighboring tones.
Experiment One
In the first study, participants made intonation judgments concerning notes which were
the second and fifth degree of the scale in the key of the melody in which they were heard. On
half of the trials, the tone being judged had an absolute frequency of 256 Hz (middle C). On the
other half, the frequency was 384 Hz (the G above).
Method
Participants: 27 musically-untrained listeners participated as part of one of the options for
fulfilling the experimental methodology activity requirement for an introductory
psychology course at Indiana University Purdue University Fort Wayne.
Materials:
Eight melodies which were familiar to the listeners were synthesized and
presented using the Hypersignal software by Hyperception, Inc. The following
four melodies contained target tones that were the fifth degree of the scale:
America; Jingle Bells; Row, Row, Row Your Boat; and Doe, A Deer. The next
four melodies contained target tones that were the second degree of the scale: The
Alphabet Song; When the Saints Come Marching In; Happy Birthday; and Here
Comes the Bride.
Procedure:
Each participant was asked to judge whether a particular note, the “target” in each
of eight melodies, was in tune or not. The melodies were heard free field and
judgments were entered on an answer sheet. Six judgments were available which
reflected the listener’s judgment about whether the note was “right” (in-tune) or
“wrong” (out-of-tune; sharp or flat) and the degree of confidence: definitely right,
right, maybe right, maybe wrong, wrong, definitely wrong. Each listener heard
nine versions of each melody in random order for a total of 72 trials. Each version
differed in (1) whether or not the target was in tune and, if not, (2) the degree to
which the target was out of tune. The nine possible targets were separated by
eighth-tone steps. Version one was a half-tone flat, version two was 3/8th-tone
flat, and so on up to version nine, which was a half-tone sharp. Participants were
informed of which note was the target by using the words of the songs. The words
were presented in written form with those words corresponding to non-target
tones in black, lowercase type and those for target tones in red, uppercase type.
For example, while listening to “Row, Row, Row Your Boat”, participants would
see the following:
Row, row, row your boat
Gently down the STREAM
Merrily, merrily, ...
They then made their judgment concerning the note corresponding to “stream”.
These judgments were made without feedback.
Results
An initial analysis showed that responses did not differ according to the absolute
frequency of the target. Therefore, the data were collapsed across both frequencies. Figure 1
shows the total number of “right”
responses of any sort as a
function of the number of 1/8
tones the target note was out-oftune. The bell shape of the curves
are typical for frequency
discrimination data with two
exceptions. (1) The point at
which the target was most likely
to be heard as in-tune for the P5
condition was not centered on the
objectively in-tune frequency, but
was slightly higher in pitch. (2)
Figure 1
The curves are steeper (better
discrimination) when the target
was flat than when the target was
sharp for both P5 and M2.
The signal detection analysis shows a similar pattern. For both P5 and M2, two separate analysis
was performed for when the targets were sharp and when they were flat. Hit rates were the
percentage of correctly responding
“right” when the targets were in-tune.
The two False Alarm rates were the
percentages of incorrectly responding
“right” when the target was either a
quarter-tone flat or a quarter-tone sharp.
While Hit rates were basically the same
in all four cases, False Alarms were
greater when the out-of-tune targets were
on the sharp side.
Experiment Two
In the second study, participants made intonation judgments concerning notes which were
the sixth and eighth degree of the scale in the key of the melody in which they were heard.
Method
Participants: 18 musically-untrained listeners participated as part of one of the options for
fulfilling the experimental methodology activity requirement for an introductory
psychology course at Indiana University Purdue University Fort Wayne.
Materials:
Eight melodies which were familiar to the listeners were synthesized and
presented using the Hypersignal software by Hyperception, Inc. The following
four melodies contained target tones that were the eighth degree of the scale: This
Old Man; Santa Claus is Coming to Town; All I Want for Christmas; Brahm’s
Lullaby; The next four melodies contained target tones that were the sixth degree
of the scale: Highlands; Oh, Shenandoah; Bicycle Built for Two; and Amazing
Grace.
Procedure:
The same procedure was used as in the first experiment.
Results
Once again, an initial
analysis showed that responses
did not differ according to the
absolute frequency of the target
and the data were collapsed
across both frequencies. Figure 2
shows the total number of
“right” responses of any sort as a
function of the number of 1/8
tones the target note was out-oftune. The peaks of both curves
are at the point where the targets
Figure 2
are in tune. The overall
steepness of the curve for P8 is
greater than for M6, showing the
P8 to be more easily
discriminated from near
neighbors. There is an
asymmetry in the curves for both P8 and M6 with a steeper fall-off on the flat side indicating
better discrimination.
The signal detection analysis shows overall better discrimination for P8. There is a
conservative bias to respond “wrong”
when the target is P8 and a bias to respond “right” when the target is M6.
Discussion
First of all, musically-untrained listeners are able to hear relatively small changes in
intonation. For all the P8, P5, and M2 scale degrees, they are able to detect a quarter-tone change
from the point of subjective equality (which is slightly sharp in the case of P5). For the M6, a
change of a 3/8 tone is required for reliable discrimination.
Secondly, there are clear differences in the discrimination functions for the different scale
degrees. Therefore, it is evident that musically-untrained listeners' pitch intonation judgments
are sensitive to the tonal functions of the tones. It is not so evident what mechanism(s) is(are)
responsible for these differences. It is not a simple case of more consonant tones being more
discriminable than less consonant tones. While P8 targets were most discriminable, P5 was no
better than M2. The differences in response bias for the different tonal functions suggest that the
accuracy of their memory representations may influence the criteria that is used in accepting a
tone as in-tune. In other words, if one has a good idea concerning what a note such as P8 should
sound like, one will have a more strict criteria for what one calls in-tune. Of course, that begs the
question of why certain tonal functions are better represented than others. Another possibility is
that a perceptual quality associated with the different tonal functions changes at a different rate in
the tones surrounding the target tones used in this study. The differences in the discrimination
functions may reflect the degree of change in this subjective quality at 1/8, 1/4, 3/8, etc. tone
differences from the in-tune note. The
greater the local change, the better the
discrimination.
References
Dewar, K.M., Cuddy, L.L. & Mewhort,
D.J.K. (1977). Recognition memory for
single tones with
and without context. Journal of
Experimental Psychology: Human
Learning and Memory, 3,
60-67.
Krumhansl, C.L. (1979). The
psychological representation of musical pitch in a tonal context.
Cognitive Psychology, 11, 346-374.
Krumhansl, C.L. & Keil, F.C. (1982). Acquisition of the hierarchy of tonal functions in music.
Memory & Cognition, 10, 243-251.
Krumhansl, C.L. & Shepard, R.N. (1979). Quantification of the hierarchy of tonal functions
within a diatonic context. Journal of Experimental Psychology: Human Perception &
Performance, 5, 579-594.