An Examination of Error Frequency and Magnitude in the
Melodic Dictation of Professional Musicians
Philip Baczewski and Rosemary N. Killam, University of North Texas
Presented at the Annual Meeting of
The Society for Music Theory
New York, 1995
This presentation examines data resulting from the authors' methodology that enables the capture of professional musicians' notation through three identical performances of a musical stimulus. Previously it has been shown that correct responses within this task tended to follow the musical structure, and that interaction could be observed in the relationship of correct and incorrect responses. The continuation of this research examines the frequency and magnitude of error occurrences. Of particular interest are whether notation errors in earlier performances relate to correct responses in later performances, whether frequency of error relates to tonal or metric structure, and whether the magnitude of error relates to tonal or metric structure. This and previously reported research leads to an understanding of the successful strategies used by trained musicians when faced with the task of transcribing an audio source to music notation.
Previous research has shown that musically trained and experienced subjects can accurately notate the pitch structure of a W.A. mozart duet for violin and viola (Figure 1) after hearing it performed three times, and that patterns of correct responses yield insight into the strategies employed by the subjects (Baczewski and Killam, 1989).
Further experimentation showed that melodic character and voice position affect transcription accuracy (Baczewski and Killam, 1990). An examination of both correct and incorrect notational responses has shown a greater degree of attention to and notation of the top line of the duet and that an early and successful recognition and notation of notes occurred with a shifting of attention from top line to bottom line as the experiment progressed (Baczewski and Killam, 1994).
Recent analyses of these data have proposed a model of the processes that musicians use for a successful transcription task. This work explores existing models of tonal hierarchy and how they relate to the transcription process (Krumhansl and Kessler, 1982, Bharucha and Krumhansl, 1983, Butler and Brown, 1989, Butler, 1992). Performing musicians base their transcription strategies on melodic information within individual contrapuntal melodies. When the stimulus is further complicated through inversion of contrapuntal lines, subjects' accuracy decreases dramatically, but they continue to invoke strategies of melodic motion and scale degree function (Killam and Baczewski, 1995).
The present analysis examines the size and frequency of notational errors resulting from the task of transcribing the mozart duet. When all responses are considered, the total mean error size is 3.60 half steps (between a minor and Major third). The mean error size for top line notation was lower, at 3.34 half steps, than that for the bottom line at 3.89 half steps. When examining the progression of error size over the three times that subjects heard the duet, we see a general increase except for top line, where the lowest mean error occurs after the second time the subjects heard the duet (Figure 2).
Combined mean error, however, shows a increase over the three times that subjects heard and notated the duet (Table 1).
Top Line, Bottom Line, and Combined Mean Error Size
for the Three Times the Duet was Heard and Notated
Time 1 Time 2 Time 3
Top Line 3.32 3.29 3.40
Bottom Line 3.68 3.80 4.00
Combined 3.40 3.47 3.71
When frequency of error sizes is examined, errors of a major second (two half steps) are seen to be most common. Five error sizes (half step, whole step, minor third, major third and perfect fourth) account for 88 percent of all errors, and errors of a major second, major third, and perfect fourth account for about 66 percent by themselves, showing a preference to these errors over those of a minor second or minor third (Table 2).
Frequency of Error Size
Error Size Frequency Percent Cumulative
(Half Steps) of occurrence of Total Percent
1 69 11.8 11.8
2 183 31.2 43.0
3 62 10.6 53.6
4 105 17.9 71.5
5 97 16.6 88.1
6 13 2.2 90.3
7 17 2.9 93.2
8 6 1.0 94.2
9 16 2.7 96.9
10 3 0.5 97.4
11 10 1.7 99.1
13 2 0.3 99.5
14 1 0.2 99.7
16 2 0.3 100.0
In Table 2, It is interesting to note that all error sizes of perfect fifth or larger are each less than 3 percent of the total errors made in the transcription process (also, see Figure 3).
About 43 percent of the time, experienced musicians' notational errors fall within a whole step or half step of the actual pitch.
When mean error sizes are ordered by their association with the tonal scale degree functions of the correct pitch, we see that supertonic, leading tone, mediant and tonic pitches all fall toward the lower end of the mean values (see Figure 4).
The lower mean error size for tonic, supertonic, mediant, and leading tone is consistent with a previously reported model for accurate perception of pitches within a melodic structure (Killam and Baczewski, 1995).
Finally, mean error sizes are seen ordered by type of melodic motion (see Figure 5).
Motion types which involve progression by step are seen to yield smaller mean error sizes than those which involve melodic progression by leap.
The increase in combined mean error over the three times that the subjects heard the duet strengthens our previously reported notion (Baczewski and Killam, 1994) that accurate recognition of pitch elements early in the task yields a more successful transcription.
A large majority of errors (88 percent) were within a perfect fourth or less of the correct pitch. The proportion of errors occurring within a whole or half step of the correct pitch (43 percent) indicates the possible perception of melodic details which were not successfully transferred to the notation process.
In examining the ordering of mean error size by association with the tonal scale degree of the correct pitch, the relatively high mean error size associated with tonic may be the result of a lack of recognition of the modulation occurring at the end of the duet's second phrase. Chromatically altered pitches are seen to have a lower mean error size, possibly explained by the omission of an appropriate sign (flat, sharp, or natural).
The ordering of mean error sizes by melodic motion type helps confirm a preliminary hypothesis that step-wise motion should yield lower degrees of inaccurate notation.
Summary and Prospects
Analysis of the size of notation errors strengthens some previously reported hypotheses as well as raises issues for further study. Relationships between mean error size and stimulus presentations (Table 1) reveal a marginal increase in top line mean error size over three performance times. For bottom line notation, mean error size increased consistently over the three times. Previous analyses have also shown that top line accuracy was greatest after time one and gradually decreased, while bottom line accuracy steadily increased over the three times the duet was heard and notated. Thus, early accuracy can be associated with smaller mean error sizes for top line notation, but not for bottom line notation, supporting the concept of different cognitive strategies for notation of top and bottom line.
In examining the association of mean error size and melodic motion, the largest mean error sizes occur with leap-unison and unison-leap approach resolution motion pairs, pointing towards a need for future research into possible time and precedence factors. Further, it is suggested that melodic contour has an influence on the mean size of errors. Although some step-wise motion is associated with lower mean error sizes, the simple step-step motion type does not produce the smallest error magnitude. This finding suggests that certain contour elements may provide stronger perceptual keys than simple step-wise motion. Extension of the authors' established methodology may provide additional insight into these and other questions.
Baczewski, P., and Killam, R. N. (1994). Investigation of
Musicians' Cognitive Processes through Analysis of Notational
Errors. Presentation at the annual meeting of the Society
for Music Theory, Tallahassee, FL.
Baczewski, P. and Killam, R. N. (1990). Melodic character versus
voice position in the perception of a two-voice musical
structure. Journal of the Acoustical Society of America, 88
(Supplement 1), S90.
Baczewski, P., and Killam, R. N. (1989). Perception of a musical
construct by professional musicians. Journal of the
Acoustical Society of America, 86 (Supplement 1), S17.
Bharucha, J., and Krumhansl, C. (1983). The representation of
harmonic structure in music: Hierarchies of stability as a
function of context. Cognition, 12, 63-102.
Butler D. (1992). The musicians's guide to perception and
cognition. NY: Schirmer Books.
Butler, D., and Brown H., (1989). Describing the perception of
tonality in music: A proposal for a theory of intervallic
rivalry. Music Perception, 6, 219-241.
Killam, R. N., and Baczewski, P. (1995). Identifying
Professional Musicians' Strategies for Accurate Transcription
of Two-Voice Contrapuntal Music, In Submission.
Krumhansl, C.L. and Kessler, E.J. (1982). Tracing the dynamic
changes in perceived tonal organization in a spatial
representation of musical keys. Psychological Review, 89,