The nature of absolute judgment of pitch.

Originally published in Journal of Experimental Psychology, 17, 485-503, 1934.

Carl H. Wedell, Princeton University

I.  Introduction

"Absolute pitch" is the ability to name a tone that has just been heard without comparing its pitch to that of a standard tone. This ability has always been regarded by the musician as an exceptional power or gift, and many examples have been recorded in the literature of the remarkable feats of those who possessed it. Stumpf's discussion of Mozart's sense of pitch marks the beginning of psychological interest in the problem, and of efforts to determine accurately the factors involved in this judgment.

The present study is designed to ascertain whether unmusical persons can acquire the ability, to find out how accurate they can become, and to investigate the effect of different series of tones on the learning. The last problem will be explained more fully in the next section. For the present, we are interested in previous experimental attacks on this elusive gift held so much in awe by the musician.

Although v. Kries and others, fortified by the testimony of trained artists, had denied that absolute pitch could be acquired, Meyer and Heyfelder set out to test the statement by attempting to train themselves. Meyer (6) reports that with the use of tuning forks, the percentages of correct judgments were 83, 78, 70, and 56, on 9, 11, 14, and 16 forks respectively. Likewise with notes of the piano, the percentage of correct judgments decreased as the number of notes increased. The results for Heyfelder were about the same. It is not clear why Meyer thinks that the influence of training is shown in the experiment, for it is quite evident that both subjects had a certain amount of training or ability to start with.

Köhler writes that after two weeks of practice on the white notes of the piano from C to b3, 112 out of 220 judgments were correct. Since he does not state how accurate he was at the beginning of the experiment, it is not possible to tell how much benefit he derived from the practice. He maintains that his accuracy was due to paying especial attention to the "tone-body."

The effect of a long period of practice in recognizing notes is shown clearly, however, by the experiment of Gough (4), who trained 90 Smith college students on the piano. On the average, the group of subjects improved from an average error of 5.5 semitones on the first trial to 4.5 semitones on the last trial. The improvement was not uniform, however, with all subjects, and the curves show a gradation in ability from those who could identify correctly 83 out of 88 notes to those who could accurately name only one. The individual practice curves, which are given for only five subjects, give no evidence of a plateau at any point. They are extremely irregular, but show a decrease in the average error per trial as a result of practice. As for the distribution of errors over the keyboard, the fewest errors were made in the middle octave, the number increasing toward either end of the scale, except that the highest note and the lowest note had the fewest errors of all. The exact order of octaves from that with the smallest number of errors to that with the largest number was once-accented, twice-accented, small, thrice-accented, and great. This is a frequency distribution of errors over the scale similar to that which Stumpf (9), Baird (2), Weinert (10), Abraham (1), Whipple (12), and Petran (8) have found. These experimenters do not agree exactly on the order of octaves from easiest to hardest, but they do agree that the middle regions of the scale are not as difficult, judging by the number of errors made, as the extremes. This is interesting in view of the results of the present experiment which are discussed below.

The data obtained by Mull (7) also show that practice has a definitely favorable effect on the ability to estimate pitch in an "absolute" manner. She trained 12 subjects, but the most pertinent facts are those obtained from "Group 1" which consisted of six persons who practiced identifying the pitch of middle c. This group gave judgments that were correct 40 percent of the time before training, with an average error of 285 cents (100 cents = 1 semitone). After training, they were correct 82 percent of the time with an average error of 33 cents. When the same group attempted to learn to select middle c from a scale consisting of nine tones, one separated from the next by only 8 ~/sec, their final performance was an average error of 29 cents. It is to be noted that decreasing the distance between tones in the scale did not change the size of the average error appreciably.

These experiments have established a few important facts. They have shown that a certain amount of absolute pitch ability can be acquired. Further, Gough's and Mull's work has indicated that the greatest amount of improvement takes place during the very first part of the learning period. The results of the former also have made it plain that in a large group of persons there are a few who possess the ability to a high degree, some who do not have it at all, and a great many who stand between these two extremes.

II.  The problem.

It was the object of the experiment to determine whether the subject learns to recognize individual notes, or whether he learns the extent and character of a whole scale. Stated in a different manner the question is, does the observer learn a number of tones individually so that if given some other notes he would have to learn their pitches in turn? Or does he learn the position of the notes relative to a whole scale, so that he could judge almost any number of pitches with the same degree of accuracy?

This problem has not gone unnoticed, it is true. Gough states, "In acquiring a memory for absolute tone the observer does not remember well one or several notes and the others not at all, but he builds up a more or less cohesive structure about a few or many notes." And again, "By repeatedly directing attention to the unity of the series, one may acquire the mental adjustment which finds little trouble in quickly assigning to random notes a position in a relatively well organized whole" (4, p. 92). Mull also writes, "Rather does it seem that, after a very rough initial placement of the notes as high, low, or intermediate, some feature in its relation to the total tonal configuration furnished the basis for judgment" (7, p. 490).

It is evident that some of the later experimenters are aware that even in absolute pitch, the judgment is at least in part one of relation. The quotations cited are all based upon introspective reports, and they could be balanced by as many quotations from the older literature to show that the observer learns to respond to an individual note. It is hoped that the results of the following investigation will be at least the beginning of an experimental solution of the problem.

III.  Apparatus.

In order to carry out the experiment, a means of producing a large number of relatively pure tones was required. The tones were generated electrically by a Western Electric 6010-B vacuum tube oscillator. With this instrument, it is possible to produce a tone of any frequency from 35 to 50,000 ~/sec, and although the intensity of the overtones could not be measured, they were estimated to be about as prominent as in the tones produced by tuning forks. Since the ear is relatively less sensitive to the low frequencies, the overtones were more noticeable to the trained ear in that part of the scale.

The current was conducted from the oscillator through a potential attenuator and a two-stage, transformer-coupled amplifier to two Western Electric Type B, 552-W ear phones connected in series. The potential attenuator was a means of varying the tone from below the threshold to a painfully loud sensation.

Subject and experimenter communicated by means of a telephone since all the work was done with the observer in a sound proof room. Therefore, while the experiment was in progress, both E and O wore two headphones, one in which they heard the stimulus tone, and one through which they received communication from each other.

The subject had before him a large cardboard chart on which were represented at appropriate points on a logarithmic scale the tones which he was learning. They were designated by numbers indicating their vibration rates.

The Subjects.

Seven persons in all served as subjects in the experiment, four in the first part and three in the second part. Three were graduate students, and four were members of the departmental staff. None was actively engaged in the field of music, nor did any play an instrument regularly. Ka, Ho, Mo, and Ba had never had any formal musical training. We had had only two years of piano training in early life. Hu had had about six years of piano training, and Br had had about thirteen years of rather intensive practice in playing the same instrument.

IV.  Results.

The experiment itself can be described most easily under two headings. In Part I the general procedure, the method peculiar to this part of the experiment, and the results obtained by this procedure will be discussed. In Part II, the method will be mentioned only insofar as it differs from Part I.

Part I

Procedure.

In order to rule out so far as possible the influence of intensity, the tones were all given at a loudness level equal to the loudness of a sound of 1000 ~/sec raised 40 dB in intensity above the threshold. (The intensity of a sound in db = to login Ix/Io where Ix is the given physical intensity (say in ergs/sec) and Io is the threshold intensity.) The low frequencies do not have to be raised 40 dB to sound equally loud with 1000 ~/sec at that level. The graph on p. 230 of Fletcher (3) was used to determine how much to increase the intensity of each tone above the threshold. Inasmuch as all of the subjects were practiced observers, a modified method of limits with six judgments with the tone increasing in intensity, and six with it decreasing in intensity were used to determine the threshold for each tone.  Because of the fact that the output of the oscillator could not be measured in any absolute terms, this procedure involves the assumption that the curve of the threshold values for these Os was of the same form as that indicated on Fletcher's graph.

As a further check upon intensity, during sessions i8, iq, and 20 for Ba and Ho; 17, i8, and 19 for Br; and i6, 17, and i8 for Mo, the loudness level of the tones was changed to determine whether this characteristic was being used as a cue. In the first of these three sessions, all of the tones were raised 10 db in intensity. In the next, they were lowered 10 db, and in the following session, they were presented at haphazard values varying between 10 and 3o db from one another. It will be seen from the results shown in Fig. 1, where the asterisks indicate the point at which the intensity was changed, that the size of the average error was not affected.
The series of twenty-five tones used in Part I is shown in Table I under the heading "Series 5." The tones were spaced an approximately equal number of dl's apart. To obtain this number, the value of the threshold as given on p. 152 of Fletcher (3) was used. Since the size of the dl is continuously changing, the number of dl's between any two points could be accurately calculated only if the equation of the curve were available. As this equation is not known, the distance in terms of dl's between two tones as shown in Table I was obtained by a method of approximation.

The musical interval between the tones can be compared with the intervals on the piano by computing vibration ratios. Thus in Series 5, the interval is a minor sixth between the two lowest notes, and from there upward decreases gradually to about a minor third between the fourteenth and fifteenth, after which it remains constant to the upper end of the series.  (The standard piano range, with middle c tuned to 256 ~/sec is from 26.6 to 4096 ~/sec. So the scale used here had an upper and a lower limit about an octave higher than the piano.)

Each experimental session, of which there were three a week, consisted of one test repetition of this series, and three practice repetitions. The test presentation always came first each day. In this, the O was presented a tone for five seconds and then required to identify it. After a short interval of ten seconds or so, a second tone was presented. In this manner the whole series of twenty-five tones was given once. The practice repetitions which followed immediately were the same, except that the subject was corrected every time that he made a mistake.

TABLE I.
Showing the stimulus tones used, and the number of dl's between adjacent tones in each series.

The instructions to the subject were as follows:

You will be presented a series of tones in haphazard order, and you are to identify each tone in terms of the number of double vibrations per second shown on the scale in front of you. Two seconds after the experimenter says "ready," he will present a tone for five seconds. As soon as the tone stops, you are to tell him which one it is. A certain number of tones each day will constitute a test series, during which you will not be corrected, but after that you will be corrected each time that you make a mistake. The object of this experiment is to see how quickly you can learn to recognize each tone correctly each time that it appears. Make every attempt to fix each tone in your mind in terms of its pitch.

A tone was repeated if the O desired it, but this did not happen more often than once each session, and although after-singing was allowed, the subjects were encouraged to respond quickly. Corrections were accepted only when they were made before the next tone was presented.

Thus the three practice repetitions each day constituted the learning period. A session took slightly less than an hour, and as there were 23 sessions for two of the subjects, and 22 and 21 for the other two, the Os spent three hours a week for over seven weeks on the experiment.

A haphazard order was used in presenting the tones, and this was arranged in such a manner that there were an equal number of large and small steps, but two adjacent tones were never presented following one another. Furthermore, the order was begun at a different place at each session so that the same tone never commenced either a test or a practice series twice. The order was the same for every session throughout Part I except that after the 16th session for Ba and Ho, and the 15th and 14th for Br and Mo respectively, it was changed to ascertain whether the subjects had memorized it. The new order can be seen on Fig. 3 under the heading "Series 5." That this change had no effect on the results can be seen in Fig. 1, where the small cross lines on the graph indicate the point at which the new order was introduced. The average error of two of the subjects is less following the alteration of order, while that of the other two is greater. It would have been almost impossible for them to have memorized the order in the test repetition anyway, because they never knew whether they were correct.

In the next to the last session, nine tones were replaced, unknown to the subjects, with tones near them in frequency, and in the last session, the entire scale of tones was shifted slightly. In Table II, the original 25 tones (Series 5) are given in the first column, the nine new ones are shown in boldface type in the second column, in the third column the new series is given, while the fourth column indicates the difference in semitones between the old and new series.

TABLE 2.
Showing vibration frequencies of original 25 tones, and of new tones substituted during the last two sessions of Part I.

The final procedure in Part I was the relearning of the tones after an interval of three months. Then two test presentations were obtained with a series of 49 tones, consisting of the former 25 plus 24 new ones whose frequencies were just halfway between each pair of the original 25. This series, together with the number of dl's between adjacent tones is shown as "Series 6" in Table I.

Results.

Figure 1 gives the results for the four subjects for the test repetitions of each session. The abscissa gives the number of the session, and the ordinate gives the average error in dl's for the session indicated on the abscissa.

Figure 1.  The effect of practice on the ability to recognize pitch. Short cross lines indicate where order of presentation was changed, and asterisks indicate first of three sessions in which intensity was varied.

The curves are quite typical of learning curves, since they show the sharp descent during the first few sessions, and the more gradual slope later. By the fourth session all Os had made their large gains, and by the eighth all had reached a level of performance around which they varied during the rest of the experiment. It is impossible to tell whether longer and more concentrated effort would have enabled them to do still better, but they seemed to be on a plateau, so the experiment was discontinued. The sudden increase in errors made by the two subjects in the 19th and 10th sessions is probably due to fatigue or some emotional disturbance.

A sharper initial drop, and a definite plateau, are the chief differences between these curves and those given by Gough (4). There is no doubt, however, that the subjects did cut their errors about in half as a result of the practice.

The curves of Fig. 1 show a great irregularity for the individual subject. Some of this was caused by a wavering interest in the problem, and a consequent variation in effort. This is especially true of the slight tendency of the curves to rise in the last few sessions.

Distribution of Errors by Tones.

One of the noticeable things about all of the previous work in absolute pitch is that the fewest errors were made in the middle regions of the scale, with the exception of the end tones in some cases. Yet in the present experiment almost opposite results were obtained. Fig. 2 gives the average error per tone in terms of dl's for the test repetitions of each session of Part I. In spite of the irregularity of the curves, a general rise is apparent from each end toward the middle, with the middle more or less level from 500 to 1910 ~/sec.

Figure 2. Average error per tone.

The fact that there is no tone upon which all of the Os did better than upon any other is a fairly good indication that there were no constant differential cues. One or two of the tones did develop an attendant noise in a session, and if this remained constant throughout a session, it was immediately seized upon by the Os. So that had it continued, it would certainly have been evident in the results shown in Fig. 2.

The subjects were unanimous in declaring that there was considerable qualitative difference between notes in various regions of the scale. The lowest note was a flutter or rumble, the next higher ones had less of the rumble and more of a buzzing quality; from about 160 to 710'-/sec was a region which seemed to have a unity, while from there up to 3710 sec the tones were thought of as being "somewhere in the middle." But at the upper end of the scale a shrill, sharp quality was distinguished. These observed differences may have been due in part to the purity of the tones. The overtones in an instrument like the piano have the effect of somewhat concealing pitch differences.

In an experiment of this type, the O presumably makes his judgment on the basis of some scale that he carries within himself (cf. Weyer and Zener, 11). Also, this subjective scale has some point or points of reference. Probably it is at these places that the 0 makes the fewest errors. With the subjects in this experiment, the ends of the scale served as points of reference, and they seldom made a mistake in judging them. The Os agreed that the middle of the scale was by far the hardest to judge, and this testimony is corroborated by their performance as seen in Fig. 2.

Just why previous experimenters have found the fewest errors in the middle of the scale, it is difficult to tell. With experienced musicians, this might be explained as due to their greater familiarity with that region (cf. Petran 8, p. 27 and p. 116), but Gough's results can not be explained on this basis since she used inexperienced observers. However, some of her subjects started practicing the middle octave, and the others who were free to use their own method may have done the same thing.

There is in the data no evidence of a consistent tendency to overestimate or underestimate on the part of any one subject, or of all of the subjects taken together. Neither do the results indicate that the higher tones were underestimated, and the lower tones overestimated, as Mull (7) and others have found. (But cf. Petran 8, p. III).

It has been said that no judgment is "absolute" unless a long time, say 12 hours, has intervened since the last hearing of a tone. Following this line of reasoning in the present experiment, the only absolute judgment would be the first one each day. It must be admitted that there is some basis for this assertion, because some of the subjects seemed to compare the notes with one another deliberately. In addition to this, a subject would sometimes correct a previous judgment by saying, "Oh, that other one must have been [so and so]."

Table III gives the error for the first judgment each day in the test repetitions. The average error shown at the foot of each column of this table is of about the same order, except for the subject Mo, as those shown in Fig. 1. There is no indication that the first judgment differed from the rest. But as Petran (8, p. 43) has pointed out, this does not preclude the possibility that the first tone judgments were absolute and the following ones relative, since especially with untrained observers a relative judgment may be wrong as well as right.

To investigate the effect on the learning curve of the substitution of new tones for the more familiar ones, nine tones differing slightly from some of those in Series 5 were substituted in the next to the last session while the other i6 remained the same. Then in the last session, an entirely new series was given as shown in Table II. The Os had to make their responses on the basis of the old chart, and were not told beforehand that new tones had been introduced. The average error for these two trials or sessions is given in the last two points on each curve of Fig. i. A glance at the curve shows that these figures are of the same order of magnitude as those of the last eight or nine sessions. Thus the introduction of new tones displaced anywhere from 1/5 to 4 semitones from those with which they were familiar did not disturb them at all. However, one of the subjects (Ba) did recognize that new tones had been introduced, and one other thought that 50 ~/sec sounded queer. In both cases, this was the result of the large difference between so and 40 ~/sec. The tones did not sound unfamiliar enough to the others to elicit any comment.

TABLE 3.
Showing the error in terms of dl's on the first tone presented each day, part 1

After an interval of two months for three of the Os, and four months for the other (Br), they were all retrained on the old tones until their average error per session was the same as it had been when they stopped learning. This took only two sessions with three of the subjects, and three sessions with the other (Ba). They were then given two test repetitions of a 49 tone series made up of the old 25 plus 24 new ones (Series 6, Table I). The repetitions were separated by an interval of 48 hours. The subjects had before them a new chart with the tones indicated by their vibration rates at appropriate points on a logarithmic scale.

Table IV shows the average error for each of the four subjects at the two sessions. Three rows of figures are presented for each subject so that the error made on the series as a whole can be compared with that made on the original 25 tones in this series and on the new 24. Comparing the average error on the 49 tones (Table IV) with that made during the last ten or eleven sessions on Series 5 (Fig. i), we see that only one of the subjects (Mo) did worse on the 49 tones than he had been doing during the latter part of the training on the 25 tone series.

When we look at Table IV and compare the average error on the more familiar tones with that on the less familiar, we find that in seven out of eight cases it is larger for the new tones. Only in the case of Ba on the second session is the error significantly larger on the new tones. That is, only in this case is the average error definitely outside the range of variation of previous sessions as given in Fig. 1.

TABLE 4.
Showing the average error in dl's made in the two sessions on series 6; as a whole (all 49), on the previously-learned tones (old 25), and on the new tones (new 24).

Summing up then, we find that three out of four Os were not appreciably disturbed by being presented a series of tones in which the distance between any two was just half that which they had become accustomed to. Moreover, they made nearly as many errors in judging the more familiar tones in such a series as in judging those which were strange. This can only mean that in this experiment, the training had the effect of establishing a familiarity with an auditory range. It did not serve to establish a response to specific tones. This is seen more clearly in Part II which was designed to investigate the phenomenon more thoroughly.

Part II

Procedure.

The method devised was as follows. Three Os learned first a series of five tones (Series 1, Table 1) which were an approximately equal number of dl's apart, and covered the same range of frequency as Series 5. Next, they practiced nine tones (Series 2), then thirteen (Series 3), and seventeen (Series 4). Lastly they had two test repetitions, separated by 48 hours, of the same series (Series 5) as was used in Part I. A series was considered learned when an O had made one errorless test repetition, but during the learning of the 13 and 57 tone series, it was necessary to advance some of the subjects to the learning of the next longer one before they had been able to satisfy this requirement. Otherwise, the experiment would have taken more time than was available. However, a subject was not allowed to proceed until he seemed to be making no further progress with the series at hand.

Another change in method in Part II was that throughout there were only two practice repetitions per session instead of three.

Results.

The results of using this method are shown in Fig. 3. The graph is a combined one giving the data for the three Os on all five series, for the test repetition of each session. The abscissa gives the number of the session, and the ordinate the magnitude of average error in dl's. Above each set of curves the tones are shown in the haphazard order in which they were presented.

It is evident that only two or three sessions are necessary for a subject to learn to identify tones as far apart as those in Series 1. The addition of four more makes the problem a great deal more difficult. However, one O had mastered it in five sessions, and the other two in seven and eight, respectively.

When the thirteen tone series is considered, it can be seen that it has really become a difficult task to assign the correct vibration number to the tone. None of the subjects mastered the problem, even though one of them was allowed 13 sessions.

We was given two, Ka and Hu were given three complete sessions (test repetition and practice repetitions) on the 17 tone scale (Series 4). Their performance shows that one of them (We) did much better than he had on the previous series, while the other two remained the same.

As to Series 5, on which they were given two test repetitions, one subject (Hu) again reached a level of performance he had formerly attained in Series 2, and the other two subjects stayed remarkably close to their previous performance.

Figure 3. The effect of number of tones in the series on pitch recognition ability. Above each set of curves is shown the corresponding series of tones in order of presentation.

At the end of this long training period, during which the distance between adjacent tones had become smaller and smaller, the Os were making an average error of between 12 and 70 times the limen, with the median for the three Os being around 5o. This compares very favorably with the record made by the subjects in Part I. The best of the latter was averaging about 45, and the worst about 70 when the training was discontinued. This means that the former method results in as good a final performance as the latter.

In order to compare the results obtained in this experiment with those reported by others, it is necessary to translate the error into semitones. Throughout most of the tonal scale, a semitone contains about 20 dl's. As the Os at the conclusion of both parts of the experiment were making an average error of about 50 dl's, this means an error of 212 to 3 semitones. Petran (8, p. 106) reports the same error in his experiment on the testing of musically trained reactors, and it is somewhat less than that given by Gough (4, p. 37 f1). The individual practice curves in both this experiment and that of Gough are so irregular that such an average is not very reliable. Yet the considerable agreement with diverse methods of attacking the problem may mean that an average error of from three to four semitones is the normal limit of ability in this problem, and that any considerable advance beyond this limit can only be attained by a few persons after most intensive practice.

The striking thing about the experiments of Part II is the fact that after Series 3 had been reached, the average error was not increased by increasing the number of tones between two limiting frequencies. This points to the fact, as suggested in Part I, that the person who acquires a pitch-naming ability is really acquiring a knowledge of the limits and characteristics of an auditory extent, rather than of individual notes within that extent. Otherwise the errors should have increased as each new series was introduced.

V.  Conclusions.

1. Relatively unmusical observers can learn to increase their accuracy in assigning pitch numbers to pure tones.

2. The greatest increase in ability takes place during the first few practice sessions.

3. The limit of ability reached in this experiment was an average error of about three semitones.

4. The course of the learning process is very irregular, and there are large individual differences.

5. Unmusical observers can learn accurately and easily to recognize tones that are eight and one third semitones apart, but they fail to learn to judge the tones correctly when the interval is decreased to five and one half semitones or less.

6. Observers build up a subjective scale in which they can place unfamiliar tones as accurately as familiar ones.

7. Contrary to previous experimental results, the greatest average error was made in identifying tones from the middle of the scale, the size of the error gradually decreasing toward the ends.

(Manuscript received May 15, 1933)

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