The acquisition of absolute pitch.

Originally published in The American Journal of Psychology, Volume 36 (1925), pages 469-93.

Helen K. Mull, Vassar College

History of the Problem

The problem of absolute pitch came to psychology from the musical world, where, as early as Mozart's time (b. 1756), the ability to identify notes upon hearing them was recognized among musicians as an unusual gift. It was Stumpf[1] who introduced absolute pitch anecdotally, theoretically, and to some degree experimentally, to psychology, which only within the last few years, however, has brought it into the laboratory in true scientific fashion. Here the work has been chiefly upon individuals who already possess absolute ear, and who, as it turns out, can furnish no introspective clue to the basis of their judgments, which come too easily and immediately for inspection. Neither are the objective results of different Os similar or clear-cut enough to point unequivocally toward any particular explanation. This state of affairs turns psychologists again theory-ward in their search for an understanding of the nature of absolute judgments, and discussion centers around tonal attributes. There is naturally little agreement as to what attribute, or combination of attributes, is chiefly accountable for such judgments, inasmuch as there is no unanimity of opinion as to what actually are the attributes of tone. Even the meaning of absolute pitch cannot yet be narrowly defined by either an ob­jective or a subjective criterion. For if we say, as Baird does, that it is the ability "to identify pitches without having re­course to any process of comparing or relating "[2] (to the pitch of a known standard note), we are still being indefinite upon the matter of the degree of ability a person must have in order to qualify. Again, positive definition by a subjective criterion is impossible, since the experimental basis of judgment is unrecognized by those who have absolute ear, and is consequently the subject of most varied speculations on the part of theorists.

In presenting the historical setting of the problem of absolute pitch, it seems advisable to give first place to a discussion of the principal facts which have come out in the course of observation and experiment upon it, and afterward briefly to mention various systematic accounts of the phenomenon.

Degrees of Precision. That there are degrees of precision among the "gifted" individuals, is generally recognized, but it is stated nowhere more convincingly and explicitly than in Baird's (lbid., 53) work upon 9 such persons. Here are exhibited all degrees from 100% to 0%, both by the group and by individuals, under the various experimental conditions given by different kinds of instruments, different pitch regions, and different notes to be judged. Baird claims that his Os possess absolute ear, however, because their averages on each of the instruments are in every case higher than would be due to chance, which he says is the extent to which the normal individual would judge correctly. Boggs[3] also found that the percentage of correct judgments made by her 6 "gifted" Os upon piano notes chosen at random from a certain arbitrarily selected number of octaves ranged from 100% to 16%. Both of these scores were made by the same individual.

What degree of precision shall be reached seems, then, to depend both upon the experimental conditions and upon the individual himself. We are now concerned to discover, further, upon just what external and subjective factors absolute ear may rest.

Pitch Region. Typically, the greatest precision occurs in the middle pitches-- typically, hut not invariably; for Boggs (Ibid., 202) found that pitch region makes very little difference to accuracy in the ease of some of her Os. Nor does the middle region seem particularly favorable to Meyer[4] and Heyfelder, if we are to judge from the results of the experiments in which they took part. On the other hand, Baird (op. cit., 75)  found quite generally that the middle range is easiest to judge. Von Kries[5] also, who has absolute ear, finds this to be true in his own case. He attributes greater precision in the middle region to its greater musical value, and to the fact that pitch discrimination is there finest. Stumpf (op. cit., I, 313) likewise recognizes this regional superiority, but attributes it rather to greater use and consequent familiarity, discounting fineness of relative pitch discrimination as an explana­tion, since, for his Os, regions of greatest accuracy for absolute pitch were not always coincident with those of greatest accuracy for relative pitch.  Révész[6] notes the greater familiarity of the middle register, but speaks also of a possible fundamental superiority which it may have. Just what he means by "fundamental superiority" or what von Kries means by "musical value", is difficult to say; but the terms seem to emphasize the nature of the stimulus. All of the writers, however, recognize that individual, subjective differences are also of importance; there must be some "individual coefficient", as Stumpf (op. cit., I, 315) calls it, which enables an individual to respond adequately to the stimulus. Otherwise there would be nothing unusual about absolute ear. We shall see in the systematic accounts what each writer considers the "individual coefficient" to be.

Naturals vs. Accidentals.  It is not only pitch region that influences accuracy. According to Baird (op. cit., 61) certain notes namely "f", "e", and "g", are generally more favorable for absolute judgments, though these notes are not easiest for every one. Generally, also, naturals are better judged than accidentals, though there seems to be no reason for believing in the tradition that each, as a class has a distinctive character. Boggs (op. cit., 202), it is true, found one of her Os able almost invariably to distinguish naturals from accidentals, but she attributes it to the fact that in this case the naturals had names of their own, whereas the accidentals did not. In the case of the other Os, the accidentals had distinctive names as well as the naturals. In her opinion, one essential requirement for absolute pitch is that there shall be invariable association between a note and its name.

As early as Helmholtz[7] we find a discussion of the allied subject of key-character, which Helmholtz himself believes to exist, but not to be a matter of absolute pitch in so far as it depends upon incidental physical characteristics of the stimulus. Incidental characteristics, however, will not explain all cases. The most general explanation Helmholtz offers, and the only one which he considers really to he a matter of absolute pitch, is that the cue may come from g'''', which is the "proper tone of the human ear", and so has a special brilliance. The extent to which this tone is present as an overtone in other notes may be a determining factor, though he does not believe it to be a very important one (op. cit., 487).  This latter explanation might be applied to absolute pitch for single notes, which Helmholtz himself does not discuss, as well as to key-character.

Timbre.  We noted, in treating of degrees of precision, that some timbres are more accurately judged than others. It may be that overtones are in some way important per se or on the other hand, it is possible that it is the familiarity of the clang which should receive the emphasis. Or it may be that both factors contribute.

Stumpf (op. cit., I, 305) admits the importance of timbre and, consistently with his views concerning pitch region, sets some store here also by familiarity. The most familiar timbres are the easiest to judge. But there are other factors as well. "Alles hangt hier von der tlbung, vom Gedachtms, eben damit aber auch von einem individualen Koeffizienten, ab." Von Kries (op. cit., 261, 264) is not entirely in accord with Stumpf; for, though he recognizes the importance of timbre and of the individual coefficient, he minimizes the role of frequency. If richness of overtones, which according to von Kries need not be consciously present to the Os, is in some way important for accuracy in absolute pitch judgments, then chords ought to be easier to judge than single tones. For von Kries himself they are, especially harmonious chords.  Nevertheless, they are by no means as frequently heard as single tones (von Kries, op. cit., 271). Boggs (op. cit., 202, 204) also finds her Os keen in hearing out overtones, and more adequate to chords than to single tones. But, as von Kries points out, overtones cannot be all-important, since pitches produced by the human voice, rich in overtones, are for him harder to identify than those produced by tuning- forks which are practically lacking in overtones.

Another argument against the sufficiency of an explanation on the basis of familiarity is the fact that there seems to be a determinable order of difficulty among the various instruments. Von Kries (op. cit., 264, 272) finds general agreement among musicians that the order, from least to most difficult, is as follows: piano, strings, wind-instruments, voice, whistling, tuning-forks, and bells. Baird's (op. cit., 50, 74) order is strikingly like that of von Kries: piano, organ (diapason, reed, string, flute), voice, and tuning-forks. Though it is possible that this order of difficulty might be, in general, the order of familiarity as well, neither Baird nor von Kries thinks that familiarity has much to do with the situation, and both cite in support of this view the fact that the voice, which is most familiar, is among the most difficult to identify (von Kries, op. cit., 275, 276; Baird, op. cit., 52). The argument seems fallacious, however, because it is not a single human voice which is repeatedly heard, but many different human voices, among which there is much less uniformity than among mechanical musical instruments. Moreover, as Köhler[8] points out, any particular voice is unstable because of vowel differences which considerably affect its tone-body. He finds that persons with absolute ear are inade­quate to unfamiliar clangs. And, unlike von Kries' and Boggs' Os, his Os were not more adequate to chords than to single notes (Köhler, op. cit., 168).

Timbre, then, is probably important both per se and also by reason of its familiarity to the individual; at least we do not seem justified in leaving out either factor in an explanation of absolute pitch in general. In any individual case a different conclusion might be reached.

Errors. Errors in absolute judgments, we have seen, are made in all degrees, depending upon the individual and upon the conditions under which he is rendering his judgments. But there are certain alleged peculiarities in the nature of errors made by "gifted" individuals which are sometimes considered important. Foremost of these is the fact that a note is often given its proper name, but is assigned to the wrong octave. Baird (op. cit., 65, 66, 76) bases his explanation of absolute ear largely upon these "octave-errors." He discusses the possibility of their occurrence by reason of the extreme community of overtones in notes an octave apart, but rejects it finally, in the face of the fact that the next most frequent errors arc thirds and sixths, which do not have as high a degree of community of overtones as fourths and fifths, which come after thirds and sixths in order of frequency. He considers this fact to he evidence which justifies the assumption that there is a certain something, "quality" he calls it, after Révész, which is alike for all "c's", alike for all "d's", but different as between "c" and "d". It is an attribute, "obscurely present" in all tones, but clearly experienced only by those who have the gift of absolute pitch. Such an attribute would explain very neatly the likelihood of one "c" being mistaken for another.

There are, however, other explanations of octave-errors. Stumpf (op. cit., I, 311) considers them to be due simply to misapprehension or ignorance as to what pitch-regions the different octave designations signify. Accordant with this explanation is Köhler's (op. cit., 172) belief that such errors do not occur on familiar instruments. To Watt[9] they are an indication of the extent to which absolute ear is subordinated to relative ear. The placement of the note within the octave, that is, its interval, is of primary importance, and the placement of the octave a secondary matter. Ogden[10] believes that the reason errors of fourths and fifths are of comparatively infrequent occurrence, as against thirds and sixths, is that they are more prominent divisions of the octave, and so get more attention and individuality. As may be surmised, neither Watt nor Ogden explains absolute pitch without reference to the musical interval, upon which they both base their systems of hearing.

Since it is Baird who places most importance upon the nature of the errors, let us examine his results somewhat more closely. Usually, he finds, errors do not exceed three semitones, and those of one semitone are most frequent. He gives no data to show the relative frequency of octave-errors to the other errors. Errors of thirds and sixths are frequent, but one can not be sure in the case of sixths that the 0 did not mean to place the note, say, in the octave above, and judged it a minor third too low. Again, he gives no date to show the relative frequency of errors of tritones and sevenths. It is also possible that a different statistical treatment of errors might result in a different order of frequency (cf. pp. 4841).

Kinaesthesis and Imagery. If one were not disposed to call in a special attribute of tone, which only those persons gifted with absolute ear could clearly perceive, one might think first of kinaesthesis as a possible explanation of the phenomenon. Absolute judgments might be based simply upon the remembrance of the vocimotor feeling of the various notes, or of the feeling of one note, to which all other notes are related by interval. It is hard to disprove the sufficiency of such an explanation, especially when one remembers the "implicit" responses urged by the behaviorists. But if kinaesthesis is important, its influence is, to say the least, often very obscure and unconvincing. With regard to the relating of all notes to one note, there is ample testimony that there are many persons, who possess absolute ear, who do not have good sense of interval (Köhler, op. cit., 160; Stumpf, op. cit., I, 269; von Kries, op. cit., 276).  And with regard to the possibility of each note having a different feeling, it is not clear why kinaesthesis should take precedence over auditory sensations. But let us examine more closely the evidence for and against the importance of kinaesthesis in absolute judgments.

There are many cases where recognition of a given pitch is possible without reproduction of the same pitch when it is designated by name (Köhler, op. cit., 174).  This fact certainly obscures the role of kinaesthesis, though it proves nothing against it; for recognition is always an earlier stage in association than recall. Again von Kries (op. cit., 271, footnote 2) affirms that he can judge female voices, whose pitches he cannot reproduce, better than male ones, and that he can never estimate his own vocal or whistling tones correctly. A third argument against kinaesthesis is the fact that absolute ear often dates from childhood and children's voices change as they grow older, although it is possible that readjustments might occur. A more conclusive argument lies in the fact that some individuals can judge notes correctly without being able to carry a tune, to reproduce a given pitch, or even to misrepresent it consistently. Nevertheless, this argument is not entirely conclusive, for there may still be some consistent kinaesthesis adequate to the single note. Granting this, we have still to account for the undeniable fact that some timbres are more easily judged than others.

When we turn to the introspective reports, we have Stumpf's (op. cit., I, 308ff) evidence that the transposition of a tone to the middle register sometimes occurs to advantage. Boggs (op. cit., 204) found that there may be various accompaniments, such as humming and visual or motor imagery. But she also finds that there is a positive correlation between immediateness and accuracy of judgment and that, typically, accurate judgments are immediate both in time and in experience. Baird (op. cit., 69, 72) found that, though humming is sometimes successfully employed, nevertheless, in test series in which his Os were given all the time they wanted to make their judgments, a smaller degree of accuracy was shown than in those experiments in which only sufficient time for immediate judgments was allowed. Like Boggs, he found that, even without the necessity imposed by time, judgments were immediate. This is enough evidence to show that, although kinaesthetic sensations and imagery of various kinds have been known to occur in judgments of absolute pitch, accompanied sometimes by success and sometimes by fail­ure, they are usually lacking. What, now, can be the basis of the typical judgment? Has it anything to do with musical ability?

Musical Ability. Discussion on the preceding topics has indicated that good sense of interval, fine pitch discrimination, and ability to carry a tune are not necessary accompaniments of absolute ear. Stumpf (op. cit., I, 289, 306ff), however, considers interval-sense to be the only dispensable musical ability. Ogden (op. cit., 161) and Boggs (op. cit., 204) also think it likely that all persons "gifted" with absolute ear are also gifted with musical ability. On the other hand, Köhler, von Kries, and Watt emphasize rather its unimportance, and von Hornbostel states that it is not an invariable accompaniment. We can hardly estimate the musical talent of parrots and starlings, but it is not likely to be as highly developed as it is in human beings. They might be said, however, to possess absolute pitch, since they repeat melodies only in the keys in which they were learned.[11]

The foregoing facts which have been ascertained with respect to absolute pitch leave us chiefly with a realization of their contrariness. Conclusions drawn from them can be only of the most general kind. It does seem, however, that (1) something depends on the stimulus, and that (2) something depends on the individual.

To account more explicitly for the phenomenon displayed, two general explanations have already been indicated: (1) the individual may possess a special ability, differing in kind from anything possessed by the average person; or (2) he may possess merely a high degree of some ability which is found to some extent in all persons.

The most unconditioned exponents of the first explanation are Boggs, Révész, and Baird. They believe that quality is the distinguishing feature of a tone in absolute pitch judgments. Boggs (op. cit., 202-204) was at first inclined to think that ability to hear out overtones was the cause of the absolute ear, but later changed her view from timbre to quality. Quality, she holds, enables a person to hear tones in much the same way as those with color vision see colors.

Baird's (op. cit., 77, 78) view is similar. He bases it chiefly on octave-errors, as we have seen, and on immediateness of judgment, which he thinks did not become immediate by practice, but was originally immediate, like the recognition of red when once it has been pointed out as red.

Révész (op. cit., 90-101) makes a definite division between those who recognize tones by pitch, and those who recognize them by quality. Both have genuine absolute ear, but it is the latter group whose judgments are most immediate and most correct. Ability to distinguish quality is innate, like color-vision, and cannot be acquired. Pitch-memory, on the other hand, may be acquired and perfected by diligent practice. Those who have quality usually have pitch also, and the two work in conjunction, so that the octave-errors are comparatively infrequent and can soon be eliminated by regional pitch-memory. Qualitative memory may be present for certain regions only. To explain the influence of timbre, he says it is possible that, when other parts of a tonal complex are changed, the quality cannot be recognized in the new combination.

Révész' position is based largely upon the results of his investigations on an abnormal O, von Liebermann, for whom "pitches" were abnormal, so that he could not judge intervals correctly, while "qualities" of the component notes remained unchanged. Von Liebermann's case allows, however, of other interpretations. Ogden (op. cit., 161) attributes his confusion of the fifth with the octave, for instance, where the judgment of their "qualities" remained intact, to "a reduction of von Liebermann's musical ability to that of an unmusical person." The defect is an integrative one, of central origin presumably, since the disturbances were binaural.

Stumpf and von Kries hold similar positions, though that of Stumpf seems less extreme. Both speak of Anlage, which they do not further define. For von Kries (op. cit., 267, 262), however, it is something which cannot be acquired, while Stumpf leaves the question more open, and gives more weight to familiarity, musical ability, feeling, and interest, as displayed in practical musical activities.

It is almost impossible to disprove theories of special ability, but it is certainly undesirable to multiply entities unnecessarily. Rich[12], in 1919, made an experimental study of tonal attributes by a method of independent variability. He finds some evidence for an attribute of "tonality," defined as "that attribute by which (musical) tones are named." His Os, it is true, had difficulty in knowing what to observe when asked to observe tonality; but that proves nothing against the tonality (quality) which we have been discussing, since the Os, who were not gifted with absolute pitch, would not be expected to observe it easily. But Rich found that the DL for what his Os took to be tonality increases steadily without following Weber's Law. Just why the middle pitch-region should be easiest to identify in absolute pitch is not explainable by this fact, if the Os in his experiments were judging quality, and if judgments of absolute pitch rest upon the same attribute.

The most convincing proof of the spuriousness of tonality, in Baird's sense of the term, would be success in training average individuals in absolute pitch to the point where they were similar to the "gifted" individuals in every respect.

Explanations of absolute pitch which do not rest upon a special ability are held by Meyer, Köhler, Watt, and Ogden.

Meyer (op. cit., 514) holds that every one has absolute ear to some extent-- that there is no sharp line of distinction, which, if it existed, would indicate a physiological difference between normal and "gifted" persons. He considers some features of the tone-body, rather than pitch, to be the basis of absolute judgments. The theory that tone-body, and not pitch, is important, has been developed by Köhler (op. cit., 161ff). Tone-body includes brightness, vocality, volume, and intensity. It is recognized immediately, that is, without the intervention of a memory image. Experiments on himself, in which he tried to learn the white notes between C and b''', showed a great improvement in correct pitch-naming after he changed from a pitch Aufgabe to one of tone-body. In judging upon this latter basis he found himself relying upon gross brightness for regional placement and, further, upon a characteristic which was different for each note. Some notes were "geschlossen", others "zwiespaltig", and so on. These features of tone-body were not present in pure tones, and pure tones are notably difficult to place. (On an attributive explanation it would he difficult to explain why pure tones should offer any special difficulty, since they have the same attributes as those presented by complex ones.) For unfamiliar timbres, recognition is quite impossible, Köhler holds. He explains his errors of fourths and fifths by claiming that, when attention is upon tone-body, it is away from pitch, and if two pitches, not too different, have similar tone-bodies, one may quite easily be taken for the other. Watt (op. cit., 85, 263ff) disagrees with Köhler's list of attributes and considers that he has merely shown that timbre is important. Watt believes the attributes of tone to be two, pitch and volume; pitch is ordinal, volume extensive. Both are taken into account by absolute ear, where there may be either a special refinement of sensory apparatus or a better auditory memory. But he thinks that in many cases of absolute pitch there is required also an absolute point of reference in auditory orders (pitches). The problem is analogous to that of localization on the skin, where, however, the great influence of relativity does not exist. It is due to this lack of relativity that tactual localization is possible for all persons. Auditory localization is possible only to a few who have not allowed the relative ear to dominate the absolute ear. According to this view, we all have had a chance to possess absolute pitch, but because of our education in musical relationships we have lost it through disuse. We do recognize noises and the sounds of our friends' voices, where the influence of musical relationships does not impose itself. Ogden, who, as we noted, bases absolute car upon a refined sensitivity to different clang-patterns, also insists upon the necessity of reference to a scale with which the individual who possesses the talent is familiar. "The tone must find its place within the setting of an octave and thus establish its interval before its pitch can be named" (Ogden, op. cit., 163). This explanation is essentially like Watt's. With Ogden, however, the point of reference seems to be introduced for purely systematic reasons arid to be considerably overemphasized, especially when one remembers that good interval-sense is not a requisite for absolute pitch and that relationships are generally considered to be a hindrance rather than a help. A note must have a name, and the name is likely to imply musical relationships; but unless the relationships are properly comprehended and help to make the perception richer or more definite, they seem gratuitous.

Problem and Observers

Problem. From the foregoing discussion, it seems that there is little reason for calling in a special attribute of tone to explain absolute pitch. There would be even less reason if average individuals could be trained in absolute pitch until they were just like those "gifted" with it. The following experiments were undertaken to test this possibility, and to discover, if possible, the basis of absolute judgment. The results point to still another explanation than any so far given-- to one which stresses the importance of attention. Stumpf hints at it when he speaks of interest and practical musical ability. Boggs also implies it when she remarks that there is great need for con­centration in judging pitches absolutely, as is shown by requests for repetition of the notes, and by the distraction caused by outside disturbances. Ogden thinks the most favorable clangs are "striking and uniform." Köhler too notes that one direction of attention is more effective than another, but his emphasis is chiefly upon that which is attended to. What justification we find for emphasis upon attention itself will be dis­cussed in connection with the results.

Observers. There were 12 Os in these experiments. Miss E. W. Amen (A), Mr. A. M. Brues (B), Mr. J. G. Beebe-Center (B-C), Mr. L. R. Frazier (F), Mr. W. S. Hulin (H), Mr. J. M. McGinnis (MeG), Mr. K. E. Zener (Z), and the writer (Mu), were graduate students in psychology at Harvard University. Dr. A. A. Roback (H) and Dr. M. B. Pratt (P) had the doctorate from Harvard and Clark Universities respectively. Mrs. E. C. Gilbert (G) and Miss K. Miller (Mi) were college seniors majoring in psychology. These particular individuals were selected in order to make up a group representing various degrees of musical ability and training.

Preliminary tests soon made it apparent that none of the Os was "naturally" gifted with absolute ear. Three, B, R, and MeG, had never had any musical training outside of that af­forded by secondary schools. Moreover, these three Os had the greatest difficulty in reproducing vocally a given pitch that was well within their vocal compass, though one of them (R) had no difficulty whatever in carrying a tune. A and G had had only a few piano lessons, but did not "keep up" their music. The others had had considerable training, and still engaged in some sort of musical activity. The Seashore tests of musical ability show Mi, B, Mu, F, P, and Z, as ranking in the first quartile in the order given; H, G, and R, in the second; and A, C, and McG, in the third.

General Procedure. The experiments and the Os fall into three groups, according to the phase of the problem with which they are particularly concerned.

The first group dealt with the acquisition and perfection of absolute ear for one note. The Os were trained with respect to one note only, in the belief that a greater though limited training would yield more rapid and more precise results than the casual acquaintance with many notes. The assumption was that, if one note could be learned, all could be learned, in time. In this group the problem of the transfer of the acquired ability to some instruments other than the one learned also arose. In the second group, the ability to judge notes correctly, before special training, was investigated more thoroughly than in the case of the first group. The rate of forgetting after special training, and the correlation between speed and accuracy of judgment, were also determined. The third group of experiments dealt with the acquisition of absolute ear for all the notes of the chromatic scale of an octave in the middle pitch-region.

Results: Group 1

Procedure. Six persons, A, B-C, F, H, Mi, and R, took part in the first group of experiments. Each observed one hour a week throughout most of the college year, excepting that A and R came once a week through the first semester, and twice a week during the second semester.

Preliminary tests, consisting in the presentation of various single notes of the diatonic scale, selected from three octaves in the middle pitch-region, were made to make sure that the Os were not already possessed of absolute ear. After it was suffi­ciently demonstrated that none of them was so "gifted", intensive training was begun.

The Appunn tonometer was used throughout all of the ex­periments, excepting that in the first few, when the tonometer was not available, the Ellis harmonical was used.

With Os B-C, H, and Mi, middle c (c'; 264 d. v.), the note selected to be learned by this group, was sounded once every minute for i 5 mm. Each presentation lasted 5 sec. To the other three Os, A, F, and R, it was sounded continuously for i 5 mm. In these trials attention was called to the note once every minute for five sec., and between attentive periods the Os were instructed to distract themselves by reading or study­ing. These two modes of training were adopted in order to discover whether a stimulus unattended to would be of advan­tage in the acquisition of absolute pitch. During the 5 sec. attentive periods, all the Os were allowed to sing the note, or to "do" anything else they pleased with it; and they were encour­aged to observe everything they could about the note. Introspections were required at the end of the 15 min. Then, after a short but effectual period of auditory distraction, which prevented the continuance of after-images, the test experiments were begun.

In the test experiments the O, seated with his back to the instrument, was presented with a series of notes chosen from among the naturals from c to b' inclusive. The possibility of melodic clues was avoided by making the series as musically nonsensical as possible; by using, in any series, only some of the notes; and by the occasional introduction of accidentals in extreme regions. The O was to respond by saying "yes" when he judged the note presented to be c', and "no" when he judged it to be a "not c" note. Any note was repeated upon request, and requests turned out to be frequent, for outside disturbance was very distracting. The series ended automatically with a "yes" judgment. Then the O was told whether he had judged correctly or not and, if not, what the note was, in order that he might know the direction and magnitude of his error. Then c' was presented again for 5 sec. to offset the tendency to form habitual errors. There were usually 20 of these test series given at one sitting, with auditory distraction between them. Free introspections as to the basis of judgment were called for, often after single judgments, and sometimes at the end of an hour.

After a month, other experiments were begun, in which the notes used were much closer together than those of our musical scale. Nine notes, including the c' already being learned (264 d. v.), separated by equal increments of 8 vibrations, were selec­ted between 232 and 296 d. v. inclusive, and were presented in test experiments of the same nature as the previous ones, except that this time the series did not end with the giving of a "yes" judgment: all 9 notes were presented, in haphazard order, in every series. The Os were told, however, that c' might be presented more than once in a series, or that it might not be presented at all. This method has the advantage of presenting all the notes an equal number of times, and thus facilitating computation of the results.

Experiments of these two sorts were made alternately every two weeks. Toward the end of the year, tests of the first kind were made with three different organ stops (diapason, string, and flute) to study transfer of learning.

Amount of Learning. If, for purposes of comparison, we select from the pre-training records of all the Os only those cases where c' was presented and judged, we find that judgments were correct only 40.4% of the time, and that in 59.6% of the cases c' was mistaken for a note not c'. The average error com­puted from all the notes that were judged as c' is 285 cents (100 cents = 1 semitone). The untrained O was correct with respect to c' less than half the time, and made on the average an error between a musical second and a musical third. The final records show that judgments were correct 82% of the time, that is, that in only 18% of the cases was c' mistaken for a note not c'; the average error was reduced to 33 cents. These averages are representative of the individual records (see Table 1). There was, then, decided improvement; but can we say that, at the end of their training, the Os had acquired absolute ear for middle c? Baird's (op. cit., 57, 59, 61) figures show an average error of 24.5% (as against our 18%) with the most favorable stimulus, piano notes; and of 37.9% with organ notes. The magnitude of individual errors of 4 of his 9 Os was rarely greater than 3 semitones. The same thing may be said of 5 of our 6 Os, as can be seen from Table 1. It thus appears that our Os acquired absolute ear for middle c to the degree that Baird's Os had it.

(Table 1 and 1A forthcoming.)

Importance of Marginal Stimulus. It will be recalled that to three of the Os of this group, B-C, H, and Mi, c' was presented intermittently and only under attention; and that to the other three, A, F, and R, it was presented continuously, but part of the time under distraction. The duration of attention was alike for both groups. A scrutiny of the individual records reveals no striking superiority of the second over the first group. The records of the first are, if anything, superior; individual differences, however, seem to be the potent factor rather than the difference in methods of training.

Rate of Learning. By far the greatest amount of learning occurs in the very beginning, during the period of intensive training preceding the first test experiments. The latter show an average of 70% correct judgments, with an error of 84 cents, as against the 40% and 283 cents of the pre-training experiments. Table 2 shows that there is on the average a steady improvement, although as can be seen from Table 1 there are irregular fluctuations in the individual records.

Transfer. Table 2 shows that there was a high degree of transfer of learning to notes of the diapason, string, and flute organ stops. As contrasted with the 40.4% correct judgments of the pre-training records, diapason notes show an average of 76.3%; string notes, of 77.1%; and flute notes, of 77.7%. From Baird's experiments we have these corresponding figures; diapason, 59.2%; string, 52.4%; flute, 49.7%. The order appears to be opposite in the two cases; but when we remember that the flute errors amounted to 42 cents in the average, and the diapason and string errors to 25 and 24 cents, respectively, a modification of the order indicated by the percentages above seems advisable, especially since it is not representative of the individual cases. Two of the Os made the highest percentages of correct judgments upon diapason notes, two upon string, and two upon flute notes. A slightly more representative order is given by the average errors, where we find that the flute errors are greatest in three cases, string errors in one case, and diapa­son errors in one case. It does not seem reasonable to attach much importance to the difference of our percentage order from Baird's, which also, like ours, is not completely representative of the individual cases.

Table 2.

The average errors in cents are calculated on a basis of the number of judgments made in any test, instead of upon the number of times the notes were presented, as is done with the percentages in Table I. It is difficult to decide which figures to use when comparing our results with Baird's. In his case the two methods would have yielded identical results, since every note that was presented was judged by its own name. Our "not c" judgments of c' introduce errors of omission taken into account by the percentages but not by the errors in cents. The latter, however, are the best single estimate of performance.

There is the possibility that by the time these new stops were used, the Os' general method of judging had become per­fected; so that, after the new c' was once heard, they knew how to recognize it subsequently. This factor may indeed account partially for the results; for, as we have already noted, learning is fairly rapid; but transfer is the only explanation of the fact that, of 24 initial presentations of new c's, 16 were judged correctly, or in other words that 16 c's out of 24 were judged correctly the very first time they were heard.

Magnitude and Direction of Errors. Baird states that the errors made in judgments of absolute pitch seldom exceeded three semitones except in the case of 4 of his 9 Os. Table 1 shows that this is true of our Os also, with the exceptions B-C and H. The direction of our errors is chiefly that of overestimation of c', both for the tonometer notes and for the organ stops; but with respect to the notes presented, the terms in which Baird speaks, the errors are underestimations. The average error calculated from the notes below c' that were judged as c' is 20 cents for tonometer notes, and 11cents for organ notes; whereas the error calculated from the notes above c' mistaken for c' is 6i cents for tonometer notes and i6 cents for organ notes. Baird (op. cit., 61) also finds that with organ notes underestimation is relatively more frequent.

Results of Experiments with Notes of 8 d. v. Differences. The results of these experiments in all essential respects confirm those already discussed, as Tables 3 and 4 will show, except for the fact that in this case we have no record of the Os' ability previous to training; when these experiments were begun, c' was already well established.

From an average of 43% of c' presentations correctly judged, with an average error of 68 cents in test 1, the Os attained to 57% correct judgments in the final performance, with an average error of 29 cents. There is average improvement from test to test in respect of the diminution in size and number of errors. In respect of the percentage of presentations correctly judged, there is one inversion.

The individual records naturally show greater irregularity than the average. It is interesting, however, to note that here, where the task is harder and the percentage of correct judgments is less than in the experiments with notes of the diatonic scale, the individual errors are of less magnitude, that is, they are grouped more closely around c'.

From the total number of errors made upon each of the various vibration rates, an approximately normal curve could be drawn, though it would be somewhat skewed in the direction of pitches above c', indicating that, as in the case of the diatonic notes, the pitch of c' is usually overestimated. The average error of overestimation is 31 cents, whereas that of underestimation is 15 cents.

Table 4.

Results: Group 2

Procedure. The results of the first group of experiments-- particularly the immediateness of learning, the irregularity in individual records, and the unimportance of the marginal stimulus-- suggest that an important factor in the acquisition of absolute ear may be simply the giving of attention to the task in hand, that is to say, interesting oneself in the note for its own sake rather than for its melodic or harmonic significance. Accordingly, in a second group of experiments, we made atten­tion the variable factor, by putting 4 new Os, B, G, McG, and Z, through two series previous to any training, of which the first was just like the pre-training experiments of Group 1, where the various notes presented were to be judged by their own names; and the second consisted in running through the same experi­ments once more with the Os asked to judge merely whether the note presented was "b" or "not b" (the b below middle c, 248 d. v.). We had it in mind to discover whether the heightened attention which a narrowed Aufgabe insures would influence the results.

After these two sets of pre-training experiments were completed, the Os were trained intensively to b by being asked to listen attentively to it for 5 sec. once every minute for 10 mm. Thereafter tests were given at the end of 3 min., 1 hour, 1 day, 1 week, and 1 month, to determine the persistence of learning. These test experiments consisted of the presentation of the diatonic notes from f to e' inclusive (176-330 d. v.), and in addition two accidentals in a non-critical region (a'-flat and b'-flat) to offset the possibility of melodic cues. The series, in each of which all the notes were presented (as in the experiments of Group I with a difference of 8 d. v.), were constructed so as to insure their being as melodically nonsensical as possible. Reaction times were taken to discover whether any relation existed be­tween speed and accuracy of judgment.

Pre-training Experiments: (a) Degree of Precision (Set 1). The purposes of this group of experiments were to discover the influence of heightened attention upon absolute pitch, the amount of forgetting, and the relationship between speed and accuracy of judgment. The pre-training experiments, moreover, proved interesting for comparison with Baird's results in certain other respects.

For the group as a whole, the order of correctness for the various notes, as shown by their percentages of presentations correctly judged, is as follows:

The figure for b is higher than that shown in Table 6 because in this case neither the octave-errors nor the "b" judgments of b-flat were counted as errors (cf. Baird, op. cit., 49)

Chance would give .11, since the 7 diatonic notes plus 2 accidentals were used. We must realize, however, that if all the judgments made had been, for instance, "c" judgments, c' would have been judged correctly 100% of the number of times it was presented, and obviously this figure would misrepresent the actual state of affairs. Our Os did not use such a method, that is, they did not respond invariably with the judgment "c", or or any other one note, but as a matter of fact a comparatively large proportion of their judgments were "c" judgments. The order of frequency of judgment in terms of the various notes, regardless of octave, is:

The positive correlation between the two orders is .81. If we now look for an order of correctness by getting the percentage of correct judgments for the various notes, on the basis of the number of judgments made in terms of each note, we obtain the following:

(The figure of b is high chiefly because of one individual's score.) The notes e and f, then, are both frequently judged and frequently judged correctly, though on the whole the positive correlation between frequency and correctness is insignificant (.009).

No matter which order is considered, it is apparent that, even before training, the Os give correct judgments in a greater percentage of cases than would be due to chance. It is also noteworthy that judgments in terms of accidentals were almost never given, even though the Os were told that some accidentals would be presented. The Os thought in terms of naturals, and in terms of some naturals more than others.

For Baird's Os the case is similar: c, f, and g are the notes best judged. He claims, however, that "c-ness", "f-ness", and "g-ness" are peculiarly easy to detect, whereas it is possible that these notes had merely received more attention and emphasis in the course of the O's previous casual experience.

(b) Errors. Another very interesting phenomenon as shown by this first set of pro-training experiments is the occurrence of octave-errors. Baird considers these errors peculiar to the absolute ear; but, as we have seen, they are sometimes thought to be due simply to unfamiliarity with musical instruments. Altogether, there were 14 octave-errors in the present experiments, and 13 cases of errors of more than one octave.

Baird gives the percentages of octave-errors to correct-note judgments, for 4 of his 9 Os, as .31, .22, .10, and .03. Three of our 4 Os show corresponding percentages: .27, .21 and .05. Octave-errors are not, apparently, peculiar to the absolute ear.

If, in order to parallel Baird's results as nearly as possible, we consider simply, as he did, the actual number of confusions of the different intervals, our order from greatest to least is: seconds, fourths, minor thirds, semitones, fifths, thirds, tritones and sixths, minor sixths, and sevenths. This is not exactly Baird's order, since for him sixths come before fifths; but neither wit an order of community of overtones, and so it paral­lels Baird's in this respect. Our orders, then, confirm Baird's conclusion that commumty of overtones cannot be the basis of confusion in judgments of absolute pitch.

The order of frequency for confusion of intervals for our Os is not easily determined. If we count, for the moment, octave-errors as errors, we have this order:

When we consider, however, that the Os judged in terms of naturals only, and that the number of different intervals possible among the natur­als is not uniform, some revision of the above figures seems necessary. On the basis of one diatonic octave there are possible 7 different cases of correct-note judgment, 2 different cases of semitone errors, 4 of seconds, 4 of minor thirds 5 of thirds 6 of fourths, 2 of tritones, 6 of fifths 3 of minor sixths, 4 of sixths 5 of minor sevenths, 2 of sevenths, 7 octaves etc. If we divide the number of errors of each interval made by the number of times it is possible for that interval to occur on the basis of the diatonic notes of one octave, the frequency of the errors will be found generally to fall off directly with the size of the interval.

Pre-training Experiments: Influence of Aufgabe (Set 2). Table 6 shows that under a narrowed Aufgabe the Os were considerably more adequate, even before training. For, if we select from the first set of pre-training experiments those cases where b was presented and judged, we find that it was judged correctly only 5% of the time. The average error, calculated from the notes wrongly judged as "b", is 259 cents. When judgments merely in terms of "b" or "not b" were asked for, they were correct in 36% of the cases, and the error was reduced to 222 cents.

In the case of B, we do not find any improvement under the narrowed Aufgabe. Of course if the individual had absolutely no notion of the pitch-region of a note, a heightened degree of attention would be of no avail; and it is true of B that he had no practical experience with musical instruments.

Other casual experiments not recorded here were made by the writer during the summer of 1924 on still other persons, and without exception there was a decided improvement under heightened attention brought about by such narrowing of the task.

Proportional number of:

Baird did not have so difficult a problem in determining which intervals were most frequently confused, since his Ss did not restrict themselves to judging in terms of naturals, but inspection of his results (62) shows that they rendered more natural than accidental judgments.

Rate of Forgetting. Table 6 shows that this learning persisted for a month, and that it was even slightly augmented by the practice obtained from the test experiments.

Reaction Time. The average reaction time for correct judgments is 5.9 sec.; for incorrect judgments, it is 6 sec. There is even in the individual cases a slight difference in the direction of shorter time for correct judgment, but the difference is never striking.

Direction of Error. As in Group 1, underestimation of the notes presented is commoner than overestimation. (See Table 5.)

(Table 5 and 5A forthcoming.)

Table 6.

Procedure. Mu and P undertook to learn all the notes of the chromatic scale from g (196 d. v.) to f# (369 d. v.) inclusive. With P the tonometer was used. Pre-training ability was determined in the usual fashion; intensive training was given by sounding each of the x 2 notes 3 times, under attention; and subsequently tests in which each note appeared twice in irregular order were given 3 times a week for 4 months. In these tests auditory distraction was always introduced between notes to prevent the formation of judgments on the basis of interval. After the learning was well under way, P was asked at alternate sessions to make her judgments immediately; in all cases where time was allowed, introspections were called for.

In the summer of 1924, Mu trained herself to the same pitches. No pre-training record could be made in this ease because of Mu's experience as E in training the Os of Group 1. Common brass organ reeds, and the method of random selection at widely separated intervals of time, were found convenient for self-experimentation. Since the reeds were almost urn- form in size, tactual clues were inconsiderable in comparison with the primary auditory ones. In this case, all judgments were made ad libitum, and except in those cases where the pitch was named immediately, introspections were recorded after each judgment.

Amount of Learning. With respect to the 12 notes to which they were trained, the degree of adequacy attained by both of the Os of this group places them easily among those who have absolute pitch. In the case of Mu, the final 96 experiments were 75% correct, and the average error was 27 cents; for P, the final 96 experiments were 62% correct, with an average error of 65 cents. Table 7 shows that again the learning was largely immediate, and in this case the fact is brought out more strikingly than before, since more notes are learned with less intensive training than was the case with either of the other groups. We also find in this group the usual variation in the records from day to day.

Errors. The results of the pre-training experiments of P show most of the characteristics of those of Group 2. Only 5 out of 192 judgments were made in terms of accidentals al­though accidentals were being presented; "c" judgments were more frequent than those of any other note (38); next in order come the "e" (33) and "f" (31) judgments; "a" stands next with 17. As a group, "c" ,"e", and "f" judgments embrace g out of the total number of 13 correct judgments. Errors are chiefly in the direction of underestimation of the notes presented. P, who has had considerable practical musical experience, did not make any octave-errors; her errors never exceeded the interval of the minor seventh.

Table 7.

After training, errors are usually less than a minor third. In 455 experiments, Mu never made an error of more than one tone, and in 500 experiments P made only 34. Underestimation was more frequent than overestimation for both Os.

Both Os made a proportionately larger number of natural than of accidental judgments; but though Mu was slightly more adequate to the naturals, P found the accidentals easier to judge. The individual notes which were best judged included both nat­urals and accidentals in both cases; for Mu the two easiest notes were g and b, and for P, g and e'.

Immediate vs. Mediate Judgments. Table 7 shows that P's accuracy was slightly diminished when she was asked to judge notes immediately upon their presentation. Baird, on the contrary, found his Os somewhat more adequate under these conditions. His Os, however, were in this case responding in accordance with their habits, whereas P was accustomed to take her own time in forming her judgments ("natural judgments", see Table 7) with only a few notes had learning progressed to the stage where immediate response was natural. In the experiments in which she was allowed to take her own time, the average reaction time for correct judgments is slightly less than that for incorrect judgments.

Introspective Results

The objective data show that our Os acquired absolute ear for the notes to which they were trained. We have still to consider their introspective reports to discover, if possible, the basis of absolute judgments. First we shall inquire whether there is enough uniformity in the introspection to indicate that there is some single basis upon which absolute judgments rest. The reports do not warrant such a conclusion, for we find a great variety of clues not only among the various Os but in the introspections of each individual as well. There are clues from pitch, timbre, kinaesthesis, synaesthesia, association, and logical processes, acting sometimes alone, and sometimes in various combinations.  (By "timbre" is meant gross qualitative differences between notes that are not fundamentally differences of pitches. The physical nature of these qualitative differences is unknown.)

There are, however, a few general statements that can be made. In the first place, all Os have recourse to some kinaesthetic placement of the notes, like implicit singing or whistling. In the early experiments these cues frequently served as the principal basis for judgment. More and more, however, kinaesthesis tends to drop out, though it is usually summoned in difficult cases. Concomitantly, there is developed a finer analysis of the timbre of the note, and upon it, then, the greater burden falls. Especially for the 8 d. v. differences do the kinaesthetic cues seem inadequate. This fact is explicitly stated by 4 of the 6 Os of Group 1, and is implied in the reports of the other two. A stated that singing did not give a sufficiently exact placement, and that timbre seemed a finer criterion. B-C stated that in these experiments he gave practically no attention to pitch. M said that she determined c' mostly by timbre, but discarded extreme notes immediately by pitch. (This is the most explicit statement of what is very generally implied in many of the introspective reports. Taken with the facts that extreme notes were in general discarded immediately, it means that pitch is a rough, immediate criterion, which serves to give a rough immediate placement of the note.) R asserted that pitch seemed a rough criterion, and often his reports upon individual cases show that, though pitch seemed satisfactory enough for c', the timbre was not right for it, and that on the latter basis the note was rejected. It is also apparent from the reports of F that he usually relied upon a feeling of familiarity based upon pitch and timbre. H definitely passed from the stage where kinaesthesis predominated to that where he says he found relaxation better, with attention to timbre. The synaesthetic, associative, and logical cues are comparatively few, and were used by only 3 Os, chiefly in the early experiments. They include such experiences as colors, visual placements, sounds of boat whistles and sawmills, and such reasoning as that a note which came early in one series would come late in the next.

In general, also, the Os pass from a rich experience in the early experiments to a poorer one, which is sometimes so im­mediate that it cannot be analyzed at all. Sometimes the basis of judgment can be described as a feeling of familiarity, and sometimes as an outstanding feature of the total Gestalt of the note.

With respect to the correlation between speed and accuracy of judgment, we have already noted that in Group 2 there is too slight a correlation to be statistically valid, but in this group training did not proceed very far. With P, forced immediate judgments were found to be somewhat less accurate than the slower natural ones; but where the judgments were made ad libitum, reaction time for right cases was found to be slightly less than for wrong ones. It seems probable that with further training the degree to which our Os would make immediate judgments would approach that shown by Baird's.

Quantitative treatment of the introspection of P and Mu shows that the majority of their judgments were made chiefly upon the auditory clues offered by the note. It is impossible to say to what extent obscure kinaesthesis may have been present and determinative. Nevertheless, auditory features, especially of timbre, furnished the outstanding clues. Rarely did it happen, however, that pitch was so much overlooked that a very different pitch of similar timbre was mistaken for the correct note: the two criteria of pitch and timbre were not so divorced. Rather does it seem that, after a very rough initial placement of the note as high, low, or intermediate, some feature in its relation to the total tonal configuration furnished the basis for judgment. In difficult cases, kinaesthesis was consciously introduced, more often successfully than otherwise. Sometimes decision was arrived at by a process of the mental elimination of neighboring notes.

To the Os of all three groups, outside disturbances were very distracting, and requests for repetition of the presentation of notes were frequently made.

Summary of Results

(1) Average persons frequently possess absolute ear in some degree inasmuch as they can judge notes correctly, previous to training, in a greater number of cases than would be due to chance.

(2) Ability to judge notes correctly can be greatly im­proved by training, and in the region of 264 d. v. can be extended at least to notes only 8 d. v. (about 50 cents) apart.

(2) The improvement is largely immediate, and is relatively lasting in its effects.

(4) In making judgments of absolute pitch a high degree of attention to the notes is more effective than a lower degree; and a note which is not attended to has no noticeable effect.

(5) The majority of errors are small, and the frequency of error falls off directly as the size of the interval increases. Previous to training, some octave-errors occur.

(6) Errors of underestimation predominate for both men and women in the region between g (196 d. v.) and f'# (369 d. v.)

(7) A high degree of transfer of learning occurs when various organ-stops are used.

(8) There is a very slight correlation between speed and accuracy of judgment, except where the O is forced, prematurely, to make all his judgments immediately; then accuracy is slightly diminished.

(9) Ability to acquire absolute pitch correlates better with practical musical ability than with ability in the Seashore tests.

(10) From the introspective reports it appears that, in the course of learning, experience becomes less rich. Kinaesthesis, especially of the throat and mouth, has an important part in the beginning, but tends to give way to auditory features of the note. When judgment is difficult, kinaesthesis is summoned as an aid, and it is possible that kinaesthetic factors are always obscurely, if not clearly, functioning.

In the later stages of learning there is, typically, a rough immediate placement of the note presented for judgment; and, secondly, a finer placement made upon a clue furnished by some outstanding feature of the total tonal configuration. Some­times judgment is based simply on a feeling of familiarity, and sometimes it is too immediate for analysis.

(11) There is no objective evidence which necessitates the postulating of an attribute of quality, or tonality, which recurs in successive octaves, and upon which all judgments of absolute pitch rest; nor do the introspective reports disclose the exist­ence of any such attribute.

In connection with these results upon the specific question of the acquisition and nature of absolute pitch, there have been some which have a wider bearing; namely, those which show the influence of Aufgabe. It was found that when, previous to any training, Os were asked to name every note presented by its own name, they were less adequate to any single note than they were when asked to judge all the notes simply by reference to the name of one particular note. It was also found that, where the task was harder, as in the experiments with 8 d. v. differences, the frequency of correct judgments was less, but the number of large errors was also less, than in the easier experiments where only diatonic notes were presented.

Conclusions

(1) The average person can acquire absolute pitch. This statement is based on the fact that there is a similarity of per­formance between Baird's "gifted" Os and our group of average persons after intensive training. Similarity between the two groups is shown in respect of degree of accuracy, of nature of errors (size, direction, and individual differences), and to some extent in respect of immediateness of judgment, inasmuch as judgments became more immediate as learning progressed and, even where immediate judgments were forced, a high degree of adequacy was maintained. Indeed, we may go further and say that it seems true that most persons who are familiar with music have absolute ear in some degree even previous to training.

(2) The possession of absolute ear seems to rest simply upon the giving of attention to notes as phenomena: that is to say, upon an interest in the notes themselves rather than in their melodic or harmonic relationships, which, because of their much greater musical importance, usually monopolize attention. The im­portance of attention is indicated (a) by the immediateness and permanence of the learning; (b) by the individual variability from day to day; (c) by the increased accuracy under a narrowed Aufgabe; (d) by the fact that a stimulus which is not attended to has no noticeable effect; and (e) by the fact that a good hearing of the note is necessary before judgment can be made.

There still remains the question why certain individuals, without having been trained, possess absolute ear so much more completely than others. An answer may lie in the suggestion that such persons, probably when they were children, found notes interesting in themselves, perhaps because of an unusual degree of ability to deal with notes in this way. Vivid associations which the notes suggested[13], establishing them thus in their own right and then in time fading out, may have been the counterpart of the experiences which our Os underwent in learning. In support of this suggestion it may be said that many persons who have absolute ear discovered it when they were very young; and that, in certain schools of music which claim to teach absolute pitch, frequent successes are said to occur with the children, who are taught according to the system of "fixed do", in which each note has only one name-- "c" = "do", "d" = "re", etc.-- acquiring thereby more individuality than in the system of "movable do" commonly taught in the public schools.

Footnotes

1.  C. Stumpf, Tonpsychologie, I, 1883, 280, 305ff; II, 1890, 380, 553.  [Return to text]

2.  J.W. Baird, Memory for Absolute Pitch, Titchener Commemorative Volume, 1917, 44.  [Return to text]

3.  L.P. Boggs, Studies in Absolute Pitch, this JOURNAL, 18, 1907, 194-205.  [Return to text]

4.  M.Meyer, Is Memory of Absolute Pitch Capable of Development by Training? Psychol. Rev., 6, 1899, 514-516.  [Return to text]

5.  J. von Kries, Ueber das absolute Gehör, Ztschr. f. Psychol., 3, 1892, 263, 268.  [Return to text]

6.  G. Révész, Zur Grundlegung der Tonpsychologie, 1913, 101.  [Return to text]

7.  H.L.F. von Helmholtz, Tonempfindungen, 1870, 485-488.  [Return to text]

8.  W. Köhler, Akustische Untersuchungen, Ztschr. f. Psychol., 72, 1915.  [Return to text]

9.  H.J. Watt, The Psychology of Sound, 1917, 85.  [Return to text]

10.  R.M. Ogden, Hearing, 1924, 163, 164.  [Return to text]

11.  von Hornbostel, Ueber vengleichende akustische und musikpsychologische Untersuchungen, Ztschr. f. angew. Psychol., 3, 1910, 465-487.  [Return to text]

12.  G.J. Rich, A Study of Tonal Attributes, this JOURNAL, 30, 1919, 121-164.  [Return to text]

13.  R. Rolland, Jean Christophe, I.; F. Galton, Inquiries into Human Faculty, 1883, 99, 182, 183.  [Return to text]