Memory for absolute pitch.

Originally published in Studies in Psychology, Titchner commemorative volume, pages 43-78, 1917.

John Wallace Baird, Clark University

Contents

I. Introduction

II. Experiments

1. The identification of notes of various clang-tints:  Piano; pipe-organ; human voice; flute; clarinet; tuning- forks; notes beyond the piano scale
2. Identification-time
3. Reproduction of pitches (Tonvariator)

III. Results

1. Note-errors

a. Individual differences in efficiency
b. The influence of clang-tint
c. The distribution of errors over the tonal scale
d. The distribution of errors over the octave
e. The direction of deviation
f. The magnitude of error
g. Most frequent confusions
h. Errors in pitches beyond the piano scale

2. Octave-errors
3. Identification-time
4. The reproducing of designated notes

IV. Summary and conclusions

I.  Introduction.

When a note is struck upon a piano or other musical instrument and the auditors are asked to determine its pitch from hearing alone, one finds that their behavior is of three wholly different sorts: (1) Certain individuals succeed in determining the pitch more or less accurately by a procedure which consists in bringing it into relation with the known pitch of a standard note. (2) A few exceptional individuals are able to identify the pitch immediately, without resorting to any process of comparing or relating. (3) The majority of the auditors, however, are able only to state in the most vague and general terms that the given note is of high pitch or of low pitch, or that it belongs approximately to this or that region of the tonal scale; and if pressed to name the note they can only hazard a hesitant guess, which proves to be wrong in about ninety percent of the cases.

Those individuals who are able to identify pitches without having recourse to any process of comparing or relating are said to possess a memory for absolute pitch.[1] Their identifications are instantaneous, requiring but a fraction of a second (see Abraham, op. cit.) these individuals recognize the pitch of a note no less immediately and directly than they recognize the color of a ribbon or the taste of an apple. This capacity is relatively rare; but instances of it are to be found in most communities. A sharp line of demarcation is to be drawn between the capacity possessed by this exceptional group of individuals and the capacity possessed by the group whose procedure consists in relating the given pitch with a known standard. In the latter group the process of relating is accomplished by means of a knowledge of musical intervals. And the standard pitch is either obtained from an external source-- for instance, by striking the a' on the piano; or, in cases where the individual has a definite knowledge of his vocal compass, it may be derived from his own vocal apparatus. In order to obtain a note of known pitch, as a point of orientation for his act of relating and identifying, he need but sing the lowest note or the highest note of which he is capable. This type of procedure is available to most students of music; and most cases of alleged memory for absolute pitch prove on examination to be cases in which the pitch of a given note is determined not in an absolute but in a purely relative fashion-- a fact which may be revealed by the individual's habitual tendency to hum or to "feel about with the voice" in his endeavor to assign the given note to its proper place in the tonal series. This tentative humming is never present in a case of genuine memory for absolute pitch. A survey of the literature shows that writers on this topic have frequently failed to differentiate between memory for relative pitch and memory for absolute pitch.

II. Experiments.

The investigation which is here reported was undertaken in cooperation with two members of the faculty of the School of Music at the University of Illinois-- Professor Frederick L. Lawrence, Director of the School of Music and Professor of Music (piano), and Mrs. Constance Barlow Smith, Instructor in Sight-Singing and Ear-Training (in charge of public school methods). The author is under obligation to both of them for helpful criticism and suggestions, as well as for aid in discovering observers who possessed a memory for absolute pitch; he is also indebted to the various observers, mentioned elsewhere, who cooperated in the investigation.

The investigation was begun some ten years ago; but the work has frequently been interrupted, at times by the pressure of other duties and at other times by difficulty in securing observers who possessed a memory for absolute pitch. In consequence of this, it has not yet been possible to complete the program as originally planned; but since there seems no prospect of resuming the investigation in the near future, the writer ventures to publish certain of the findings which have already been obtained in the hope that even though incomplete they may throw light upon certain features of this baffling problem.

Among the series of experiments which were included in our original plan were the following:

1. The Identification of the Pitch of Notes of Various Clang­Tints

a. Piano Notes. This series of experiments consisted in asking our observers to identify the pitches of notes from the various regions of the piano scale. Before the experiments began we prepared lists in which the eighty-eight notes of the piano were arranged in the order in which they were to be presented for identification. In preparing these lists we endeavored to avoid easy and familiar intervals in consecutive notes, in order that the participation of a knowledge of relative pitch should be eliminated. Three such lists were prepared; and since the notes of each were sometimes presented in a backward order and sometimes in a forward order, we really employed six lists; and it seems probable that no remembrance of the order of presentation could be carried over by the observers from one sitting to another. 

The observers were asked to specify not only the name of the note (d, a-flat, c-sharp, and the like) but also to indicate the octave to which the note belonged. In order to facilitate the recording of their identifications, a Vergil Practice Klavier was employed throughout[2]-- the observer being asked to indicate upon the keyboard of the klavier the position of the note which she had heard. The observer sat before the keyboard of the klavier, with her back to the experimenter's piano and at a distance of about eight feet from the latter. The experimenter sat before the piano, with a mimeographed copy of one of the six lists of notes upon the music-rack before him; and his procedure consisted in presenting the various notes in successive order, pausing after each presentation until the observer had identified the pitch and had recorded the identification.' Above the keyboard of the klavier was fastened a strip of cardboard which extended the full length of the keyboard and which bore the indices of the various octaves (c5, c4, etc.) in order to facilitate the observer's designation of the octave to which she assigned the given note. The time required for presenting and identifying a complete list of eighty-eight notes averaged about fifteen minutes, the extreme times being twelve minutes and eighteen minutes.

The observers who took part in this group of experiments (with the number of attempted identifications in parentheses after the name of the observer in each case) were as follows: Miss Augusta S. Cottlow (176); Mrs. Edwin G. Boring (Miss Lucy M. Day, Ph.D., 304); Miss Marie von Engelken (352); Miss Rosa Lee Gaut (817); Miss Bertha I. Howe (264) ; Miss Mamie Lewis (88) ; Miss Elva Pease (182) Miss Gertrude L. Peck (229); and Miss Sarah White (425). These nine observers are of course a selected group; they proved to be the only genuine cases of memory for absolute pitch in several score of alleged cases which were brought to the writer's notice. Miss Cottlow is a concert pianist of international reputation; she has been a student of the piano since early childhood and has spent many years of study under the most prominent teachers of Germany and she has subsequently made various tours as a piano virtuoso in America, in England and on the Continent.[3] Miss Howe was, at the time of the investigation, an instructor in piano in the University of Illinois School of Music. Mrs. Boring was a graduate student in psychology in Cornell University. Miss Gaut was a resident of Champaign, Ill. The other observers were students in the University of Illinois School of Music. All of the observers were more or less highly-trained musicians.

b. The Identification of the Pitch of Pipe-Organ Notes. The procedure employed here was essentially identical with that described in the foregoing section, excepting that the strip of cardboard containing the indices of the various octaves arranged in order was here employed alone, without the klavier, since it was not feasible to transport the latter instrument to the auditorium where these experiments were carried through. The sixty-one notes of the organ were arranged in lists in such a sequence as to eliminate the participation of the observer's familiarity with musical intervals. Four qualities or "stops" of pipe-organ notes were chosen for presentation--  flute, diapason, reed, and string, an equal number of each being presented. Five of the observers who had taken part in the piano experiments also took part in the experiments of this section-- D (73), E (415), G (1645), H (976) and W (415).

c. The Identification of Notes Sung by the Human Voice. In this group of experiments the notes to be identified were sung by four vocalists who had been recommended by the Director of the School of Music-- Miss Lois McCobb, contralto (instructor in voice), Mrs. W. C. Bradford (Miss Florence M. Pruitt), soprano (special student in music), Mr. Leon U. Everhart, tenor, and Mr. George R. Wade, bass.  Lists of notes which lay well within the compass of the voice of each of these vocalists were prepared in advance, a total of fifty-nine notes ranging from B-flat to g#2; each note was struck upon the piano in a distant room and transmitted, by means of a telephone, to the vocalist who thereupon reproduced it in the presence of the observer. Five of our observ­ers took part in these experiments-- H (59), G (59), Pk (59) and Ps (59).

d and e. The Identification of the Pitch of Notes of the Flute and of the Clarinet. Here a list of notes which had been prepared in advance was presented, by means of the flute and the clarinet, by Mr. Albert A. Harding, a member of the faculty of the School of Music. These notes were selected from the once-accented and the twice-accented octaves. Five observers took part in these experiments-- H (26, 26), G (26, 26), Pk (26, 26), Ps (26, 26) and E (26, 26).

f. The Identification of the Pitch of Tuning-Forks. In this group of experiments the tones of fourteen tuning-forks were presented for identification; the forks were of standard make (König, Kohl) and they were mounted upon resonance boxes. The pitches varied from c to c3. These were presented in irregular sequence at each of three sittings.

g. The Identification of Notes beyond the Keyboard of the Piano. For a description of these experiments see pp. 68f.

2. Identification-Time

In this group of experiments we measured the observer's reaction-time in her act of identifying the pitch of a given note. The Hipp chronoscope was employed; the piano key was struck by means of an instrument which closed the electric circuit at the instant when it came in contact with the key, and the observer's reaction consisted in speaking into a voice-key. These time-measurements were made, in adequate number, only in the case of Observer C. The averages, presented elsewhere, are computed from 731 reactions to piano notes, and 645 reactions to organ notes. The stimuli, in these reaction-experiments, were distributed uniformly over the various octaves of the keyboard; and the reaction consisted simply in naming the note presented, the reagent here not being required to designate the octave.

3. The Reproducing of Notes by Means of the Tonvariator

In this group of experiments the observer was asked to reproduce the various notes of an octave by means of the Tonvariator. The Variator was actuated by means of a current of compressed air, of constant pressure. The observer sat with her back to the Variator. The experimenter designated any note of the octave, in random sequence; and then proceeded to adjust the instrument, under her direction, varying the pitch in a constant direction until the observer signalled that the designated note had been reached. Determinations were made in both an ascending direction and in a descending direction, twelve determinations being made for each note of the octave.

III. Results

In identifying the note presented, our observers were asked not only to name the note but also to name the octave to which it belonged. A perfect identification, therefore, would be one in which the observer stated the name of the note correctly and also stated the name of the octave correctly. Now it frequently happened-- and this seems to us to be one of the most surprising and significant features of our results-- that the observer succeeded in naming the note correctly but erred in her identifying of the octave to which it belonged. These "octave-errors" will be discussed in a later section (pp. 69f). In the present section the only errors which concern us are "note-errors"; for instance, if the observer identified c3 as c2 (as she frequently did) it will for our present purposes be regarded as a correct identification.

1. Note-Errors

The numerical results of this part of our investigation are presented in Tables I to VIII. In Table 1 will be found a record of our observers' percentage of note-error in identifying pitches of the various clang-tints. a. Individual variation. A reference to this table shows that memory for absolute pitch proves to be a capacity whose perfection varies from individual to individual; and that the limits of this variation are exceedingly wide.

Table I.
Percentage of error in identifying pitches of various clang-tints.

Observer C made but 2 erroneous identifications in a total of 176 attempts to identify piano notes-- an average of 1.1 percent of error; while Observer E made 262 errors in 352 attempts-- a percentage of error amounting to 74. The scores of the other five observers are distributed more or less uniformly between these two extremes-- at the points 3, 11, 27, 39, 49, 59 and 68. The same state of affairs is revealed in the identifying of notes of other clang-tints. For instance, the extreme scores in the case of pipe-organ notes are 4.7 and 84.5, while the intermediate scores are 25.2, 68.5 and 69.2. In the case of notes sung by the human voice the extreme scores are 18.5 and 94.9, while the intermediate scores are 58, 69 and 93. And a similar state of affairs is found to be present in the case of every other clang-tint-- flute, clarinet and tuning-fork.

It is to be noted, however, that our observers were a selected group-- they all possessed some degree of memory for absolute pitch--  and the least successful member of the group represented a degree of efficiency in the identifying of pitches which is far above that of the average member of the human family. If an individual who possesses not the slightest degree of absolute pitch memory had been asked to identify pitches under the conditions of our experiment, his responses (provided he responded at all) would have been nothing more than random guesses. And since in any given case he might respond with the name of any one of the twelve notes of the octave, his guesses would be correct in approximately eight percent of the cases; our least successful observer was correct in approximately twenty-six percent of her identifications.

b. The influence of clang-tint. Accuracy in identification varies with the clang-tint of the note presented for identifica­tion. For instance, Observer H had a percentage of error of 3.4 in her identification of piano notes; her percentages of error in the identification of pipe-organ notes, voice notes, flute notes, clarinet notes and tuning-fork tones were 4.7, 18.5, 15.4, 30.8 and 8.3 respectively. G's percentages were 11.1 for piano, 25.2 for pipe-organ, 58.4 for voice, 30.8 for flute, 30.8 for clarinet, and 75.0 for tuning-fork. A similar variation of accuracy with clang-tint is found to be present in the case of every other observer. If now we endeavor to arrange the clang-tints in the order of ease of identification, we find that this order varies somewhat from individual to individual; the general averages indicate, however, that the pitch of piano notes can be identified more easily than notes of any other clang-tint. Notes sung by the human voice are usually the most difficult to identify. In so far as the averages of our results warrant any seriation in order of increasing difficulty, the order seems to be piano, organ, flute, clarinet, voice; the relative position to be assigned to forks and to certain other clang-tints employed in our experiments is uncertain.

The fact that clang-tint is an influential factor in determining ease of identification of pitch has been reported by other investigators of this topic[4]; and various conjectures have been advanced as to the reason for this difference in difficulty and in accuracy in the identifying of pitches of different clang-tint. For instance, it has been supposed that those clang-tints which are most frequently heard are most easily identified; and that the reason for the difference in ease of identification is to be found in difference in degree of familiarity[5]. But while this hypothesis may furnish a plausible explanation for the relative ease of identifying the pitch of piano notes, which undoubtedly are frequently heard by the average member of modern society, it wholly fails to account for the extreme difficulty in identifying the pitch of the human voice, which is of course heard much more frequently than the piano. Nor does it seem possible to find any correlation between simplicity, complexity or other characteristic of sound-wave on the one hand and ease or difficulty of identification on the other. That identification of pitch is not facilitated by purity of tone is shown by our experiments with the relatively pure tones of mounted forks, which usually proved to be difficult to identify. Even Observer H who was much more successful here than any other member of the group was less successful here than in her experiments with piano notes and organ notes.

c. The distribution of errors over the tonal scale. In Table II the record of the errors of the various observers in identifying piano notes (Table I, second column) has been thrown into a form which shows their distribution over the tonal scale, and the direction of their deviation from correctness. It turns out that the middle section of the tonal scale offers least difficulty in identification-- the average percentage of error in the once-accented octave is approximately 20; while both extremes of the tonal scale offer much greater difficulty-- the percentage of error in the highest octave of the piano keyboard is 43, and in the contra and subcontra octaves, 52 and 57 respectively. The other octaves are distributed more or less uniformly between these two extremes-- the percentage of error as we pass up the keyboard from the contra octave being 42, 29, 20, 24 and 31 (expressed in terms of the nearest whole number). And this state of affairs which is revealed from a survey of the averages of all the errors is found to hold true, completely or approximately, in the case of each individual observer. Whether there is any definite correlation between the position and extent of the region of least diffi­culty, and the position and extent of the observer's vocal range, is problematic. There is of course a general correlation in that those pitches which the observer can sing are most accurately identified; but there is far from being a perfect coincidence between that region of the tonal scale which can be sung and that region of the tonal scale within which pitch identification is most accurate.

TABLE II.
Piano errors: Their distribution over the tonal scale by octaves, and the direction of their deviation.

Observer C, for instance, had 2 errors in 24 attempts to identify the notes of the contra octave-- a percentage of 8.3.  The data at the foot of the table show the direction in which the observers erred-- for instance, in 100 percent of their mal-identifications of the notes of the sub-contra octave they over-estimated the pitch of the given note (identifying a as b-flat or as b, etc.).  The vocal ranges of our observers are as follows: C, a-a2; H, g-f2; G, a-c3; L, g-g2; W, f-a2; Pk, g-b-flat2; Ps, e-f2; E, d-b1.

A similar relation appears in Table III which shows the distribution, over the tonal scale, of errors in the identifying of pipe-organ notes. Here we find a tendency toward greater accuracy in the identifying of notes from the middle region of the scale than in the identifying of notes of higher or lower pitch; but the distribution of errors over the tonal scale is less regular here than in the case of piano notes, and it varies somewhat from individual to individual.

TABLE III.
Pipe-organ errors:  Their distribution over the tonal scale by octaves, and the direction of their deviation.

The results are recorded in percentages-- Observer H, for instance, had 7 errors in 48 attempts to identify the "flute" notes of the lowest octave, a percentage of error amounting to 14.6. The data at the foot of the table indicate the direction in which the observers erred-- for instance, in 96.7 percent of their erroneous identifications of notes of the lowest octave they overestimated the pitch.

d. The distribution of errors over the notes of the octave. Are all of the twelve notes of the octave equally difficult to identify? Or are there certain preferred notes, which prove to be more readily identifiable than other notes? In Tables IV and V the record of errors for piano notes and organ notes is compiled in such fashion as to show their distribution by notes. Table IV shows, in its first column, the percentage of error made by each observer in all her attempts to identify the pitches of the eight c's of the piano keyboard, while the second, third and other columns of the table record similar data for the c-sharps, the d's and other notes of the octave. Table V records the note-distribution of errors made in the organ experiments.

A survey of these tables shows that the naturals are usually identified with greater accuracy than the accidentals (Here and elsewhere in this paper we shall, for the sake of brevity, employ the term naturals to indicate the white notes and accidentals to indicate the black notes on the keyboard of the piano or organ)-- the average percentage of error being 30 for the naturals, and 40 for the accidentals in the case of piano notes, while the percentages are 41 and 50 in the case of organ notes. There are, however, notable exceptions to this general rule. G's most difficult organ note was a natural (d, 38 percent, of error) and her easiest organ note was an accidental (a-flat, 9 percent of error); indeed, her average percentage of error for the sharps and flats was somewhat less than her average per­centage of error for the naturals-- 22 percent as compared with 27 percent And we find that a natural, if not the most difficult note, is at least in the most difficult group of notes for both C and L.

Our tables show that every observer is more successful in identifying certain notes of the octave than in identifying other notes of the octave. In the experiments with piano notes Pk never succeeded in identifying any of the d's, but she failed in only one-third of her attempts to identify the c's. L never failed to identify the c's and the d's, but she failed in one-half of her attempts to identify the a's. H invariably succeeded in identifying the c-sharps, the d's, the e's, the f's, the f-sharps and the b's, but she frequently had difficulty with the c-flats. G never failed with the f's and failed only once with the c's, but she had 19 errors with the b-flats. D had only 11 percent of error in her attempts to identify the f's, while she had 75 percent of error in her identifications of the b-flats.

TABLE IV.
Piano errors:  Their distribution by notes.

This table shows the percentage of erroneous identifications of each note of the octave. For instance, Observer H had 1 error in her 24 attempts to identify the various c's of the keyboard-- a percentage of error amounting to 4.2.

TABLE V.
Pipe-organ errors:  Their distribution over the octaves by notes.

This table shows the percentage of error in identifying each of the twelve notes of the octave. In the case of the "flute" notes, for instance, Observer H had two errors in her 24 attempts to identify the various c's (C, c, c1, c2, c3, and c4)-- a percentage of 8.3.

The same state of affairs is found in the case of the organ notes. E's identifications of the g's were more than twice as accurate as her identifications of the c's, the c's, and the b's. C had approximately four times as many errors with the b-flats as with the a-flats. And W's identifications of the c's were approximately twice as accurate as her identifications of the d's, the e's, the f's and the b's.

For each individual, then, there are certain relatively easy notes and certain relatively difficult notes; and this phenomenon of preference appears both in the identification of piano notes and in the identification of organ notes. But there is a general lack of coincidence between the note which is preferred in the case of piano clangs and in the case of organ clangs. It is true that for E the d's and the f's are among the easiest notes in both cases, while the b-flats, the e-flats and the f-sharps are among her most difficult notes in both cases; the f's and the c's are relatively easy for C in both cases while the b's and the b-flats are relatively difficult; c is relatively easy for W in both cases while c-sharp and f-sharp are relatively difficult; and there are other coincidences of this general sort. But if for each observer we arrange the twelve notes of the octave in order of difficulty as regards piano and as regards organ, we find that there is a striking lack of conformity in our two lists. For example, in the case of organ notes, a stands in the first quartile 61 W's list, while for the organ notes it stands in the last quartile. And in C's lists we find that c-sharp shows a similar shift of position.

Nor is there any unanimity among the observers as to which note of the octave is most accurately identifiable either in the case of piano notes or of organ notes. It is true that f proves to be the easiest note, or at least to be a member of the easiest group of notes, for four of the nine observers; and it stands in the first quartile for three other observers. But it stands in the second half of the list for the remaining two observers-- in the last quartile for one of them. And while d is the easiest note of the twelve for two observers, and in the easiest group for two others, it is the most difficult note of the twelve for one of the observers. A similar lack of agreement is present in the case of organ notes. One observer finds that d is the most difficult note of the twelve, while two others find that it is relatively easy; b is easy for one but difficult for two others; g proves to be easy for three observers but relatively difficult for the fourth. The most difficult note of the twelve is f-sharp for one observer, c-sharp for another, d for another, and b-flat for the fourth.

The averages of all observers show that f and c are most accurately identified in the case of piano notes and g and c in the case of organ notes; while c-sharp and b-flat are the least accurately identified in both cases.

e. The direction of deviation. The data at the foot of Tables II and III show, for each octave, the percentage of cases where the mal-identification erred in the direction of an overestimation of pitch, and in the direction of an underestimation of pitch. These data reveal the presence of a central tendency of judgment-- the pitch of low notes tends to be judged too high, and the pitch of high notes tends to be judged too low. A second general tendency manifests itself in the finding that overestimations of pitch are relatively more frequent (57.1 percent) in the identifying of piano notes, while underestimations of pitch tend to be relatively more frequent (58.7 percent) in the identifying of organ notes.

f. The magnitude of error. The errors varied in magnitude from one semitone to two octaves. Apart from the illusion of the octave, however, the magnitude rarely exceeded three semitones excepting in the case of four of our nine observers. The proportion of grosser errors increases with decrease of accuracy in estimating pitch (Table VI). Eighty-seven percent, of all the piano errors made by the three most successful observers were errors of small magnitude (one semitone), while only 43 percent, of the errors of the three least successful observers were errors of small magnitude; and the same relation obtains in the case of organ notes. When the task becomes more difficult, as in the identifying of organ notes, not only do the errors become more numerous but they also increase in magnitude. This principle is especially evident in the case of the more successful observers, where the percentage of larger errors (two or more semitones) increased from 19 percent of the total number of errors, in the case of piano notes, to 39 percent, in the case of organ notes.

TABLE VI.
The relative frequency of errors with various magnitudes.

The results are expressed in percents-- for instance, 78 percent of H's errors in identifying the pitch of piano notes were errors of one semitone, 11 percent were errors of two semitones, and 11 percent were errors of more than two semitones, etc.

g. Most frequent confusions. If we examine the errors with a view to determining whether there are any notes which are especially subject to being confused with each other-- and which may therefore be presumed to be especially similar in sound-- we find that there are certain errors which recur over and over again in our records; and that certain observers are especially prone to certain errors. For instance, our records show that on four occasions H identified c#2 as a-flat2 (organ; flute, string). This is a most unexpected confusion. No other observer ever confused any c# with any a-flat; H's identifications of c2, c#3 and c#4 were invariably correct, but she twice identified a-flat as c# (organ; flute, diapason). The cases in which any given pair of piano notes was most frequently confused with one another by any individual were as follows: W confused b-flat and e-flat 9 times. This confusion was always made in one direction, e-flat being identified as b-flat but b-flat never being identified as e-flat; this pair was confused only once, and in the opposite direction, (H) by all other observers. (See next paragraph.) W confused b-flat and c-sharp 7 times, all other observers only twice. E confused e-flat and a-flat 5 times; this confusion was never made by any other observer. Certain confusions were common to more than one observer: c and g were confused 7 times by E, 6 times by W, 5 times by Pk, but never by any other observer; c-sharp and e-flat were confused 5 times by W and 4 times by Ps, never by any other observer; e and g were confused 7 times by W, 6 times by E, 4 times by all other observers.

The most frequent confusions of piano notes with the total number of times they recurred in the identifications of all observers are as follows: c and g, i8 times (c being identified as g, 12 times; and g as c, 6 times) ; e and g, 7 times (4+3); b and g, 13 times (9+4); f and g, 11 times (9+2); g and d, 10 times (8+2); e-flat and b-flat, 10 times (9+1); a and c, 10 times (10+0); c-sharp and e-flat, 9 times (9+0); c-sharp and b-flat, 9 times (7+2); b-flat and g, 9 times (6+3) ; e-flat and a-flat, 7 times (5+2); b and d, 8 times (6+2); e-flat and a, 7 times (4+3).

The most striking confusion of organ notes occurred in the case of b-flat and e-flat; b-flat was identified as e-flat 15 times by H and 5 times by W, never by any other observer, and e-flat was never identified as b-flat by any observer. It will be remembered that H and W, but no other observer, confused these two notes in the piano experiments.  Of these 15 confusions, 4 occurred with string stop, 6 with reed stop, 4 with diapason, and i with flute; the errors were distributed by octaves as follows: b-flat, 2; b-flat1, 3; b-flat2, 6; b-flat3, 4.  It seems worthy of mention in this connection that on several occasions Pk volunteered the remark that e-flat and b-flat sounded very much alike; and she added that these two differed from all other notes of the octave in that both of them were peculiarly "soft and mellow." Yet our records show that Pk never identified e-flat as b-flat, nor b-flat as e-flat. It is also to be noted that E identified e as g, 9 times and W identified e as g, 6 times; H and C never failed to identify these notes correctly, and E and W never identified g as e.

The most frequently confused organ notes were as follows: e-flat and c-sharp, 30 times (21+9); b and d, 24 times (14+10); b-flat and e-flat, 20 times (20+0); e and g, 15 times (15+0); b and g, 14 times (8+6); e-flat and a-flat, 13 times (7+6); c and g, 12 times (7+5); c and e, 11 times (8+3); b-flat and g, 11 times (8+3); b-flat and e, 9 times (8+1); a and c, 9 times (6+3); c-sharp and a-flat, 8 times (5+3); d and g, 7 times (5+2).

If, now, we arrange these pairs of confused notes in order of frequency of confusion in the piano experiments, and if we make out a similar list showing the relative frequency of confusion of the various pairs in the organ experiments, we find that c and g is the most frequently confused pair of notes in the piano experiments and that this pair stands seventh in order of frequency in the organ experiments; the e and g pair comes second in the piano list, fourth in the organ list; b and g comes third in the piano list, fifth in the organ list. That is, the three pairs whose members are most frequently confused with one another in the piano experiments stand among the first seven of the most frequently confused pairs in the organ experiments. It is a remarkable fact that g is a member of all three of these pairs. Indeed, g is a member of each of the first six pairs of the piano list ;12 but it is present only twice in the first six pairs of the organ list. This would seem to indicate that g is much more readily identifiable when presented in organ clang-tint than when presented in piano clang-tint.

This fact seems surprising in view of the data presented in Table IV, where g proves to be one of the easiest notes of the octave to identify-- the averages of Table IV show that only three other notes of the twelve are more readily identifiable than g. But an examination of the data which appears within the parentheses on the present page shows that the vast majority of these confusions in which g played a part were not cases in which g was mistaken for another note but cases in which other notes were mistaken for g.

If we add the number of times that each of these pairs was confused in the piano experiments and the number of times of confusion in the organ experiments, we obtain the following totals: e-flat and c-sharp, 39 times (21+18) (As indicated in a preceding paragraph, these symbols mean that c-flat was identified as c-sharp 21 times, and that c-sharp was identified as c-flat 18 times.); e and g, 32 times (29+3); b and d, 32 times (20+12); b-flat and e-flat, 30 times (21+9); c and g, 30 times (19+11); b and g, 27 times (17+10); b-flat and g, 20 times (14+6); c-flat and a-flat, 20 times (12+8); a and c, 19 times (16+3); g and d, 17 times (10+7). When we classify these most frequently confused pairs of notes, employing as our basis of classification the degree of community of overtones or of musical relationship existing between the two members of the pair, we find the fifths were confused in a total of 51 cases-- 31 times in the piano experiments and 20 times in the organ experiments; the corresponding data for the other musical intervals are: fourths, 54 times (14+40) ; thirds, 80 times (28+52) ;14 sixths, 70 times (38+32).

There were 24 cases of confusion of the major thirds and 4 confusions of minor thirds in the piano experiments; 14 confusions of major thirds and 38 confusions of minor thirds in the organ experiments. Major sixths were confused 15 times, and minor sixths 23 times in the piano experiments; major sixths were confused 21 times, and minor sixths xi times in the organ experiments.

One would expect, on a priori grounds, that liability to confusion would be a function of community of overtones; and that notes would be subject to being confused with one another in proportion as they possess overtones in common, or in proportion as their relationship is such as to give rise to a relatively perfect fusion with one another (especially in view of the fact that octave-confusions are so frequent). But the reverse proves to be true. The findings reported in the preceding paragraph do not furnish complete data as to the relative frequency of confusions of seconds, sevenths, and tritones; but they do show that notes between which the relationship of the fourth obtains are more frequently confused with one another than are notes between which the relationship of the fifth obtains; and that thirds and sixths are confused much more frequently than fourths or fifths. We have already pointed out that errors of a semitone constitute a very considerable proportion of the total number of errors made by our observers-- a fact which further confirms our paradoxical finding that those tones are most subject to confusion which are least subject to tonal fusion. This finding is of course not surprising in the case of errors which reach a magnitude of only one or two semitones, for it is rather to be expected that observers should frequently fail to differentiate between notes which lie at adjacent points upon a continuously graduated series. But it is a remarkable and significant fact that in such a considerable number of cases those notes which are subject to confusion by individuals who possess a memory for absolute pitch should prove to be notes which are so clearly and so readily differentiated by individuals whose reactions to tones are determined largely by a memory for relative pitch.

Several of our observers reported that the sharps and flats possess a peculiar sound-quality which differentiates them from the naturals; and on various occasions they remarked that they had recognized that the given note was a natural (or an accidental) before they had recognized which natural (or accidental) it was. This belief in the existence of a specific accidental-quality which differs from the specific natural-quality seems to be widespread among individuals who possess a memory for absolute pitch. When asked to describe these two qualitative characteristics they find it impossible to find words which can do justice to the minute nuances of sound-quality involved in the differentiation; and they usually have recourse to metaphor. "The naturals are cool while the accidentals are warm" is the way in which one observer expressed the distinction; another reported that the accidentals are brilliant, the naturals dull.

Now if this peculiarly elusive criterion were of service to the observers in our experiments, one would expect to find that in cases of erroneous identification the observers would tend to confuse naturals with naturals and accidentals with accidentals rather than to confuse naturals with accidentals. Accordingly we have prepared a tabulated statement of the percentages of errors (Table VII) in such form as to show the relative frequency of these various sorts of confusions. These data show that the most frequent type of error consists in identifying accidentals as naturals-- that is, in reporting that a given accidental is a natural; and that the least frequent type of error consists in confusing one member of the accidental group with another member of the same group. This tendency is common to all of the observers; indeed, two of the observers recognized in only about five percent of the cases that the (erroneously identified) accidentals were accidentals. And the averages of the eight observers show that in more than half of their mal-identifications they failed to recognize that accidentals were accidentals and that naturals were naturals-- that is, they reported that the given stimulus belonged to a group which is alleged to be qualitatively different from the stimulus; and in less than half of their erroneous identifica­tions did they assign the stimulus to the group with which it is alleged to be homogeneous. In view of these facts it is impossible to accept the statement that all accidentals are perceptibly similar to one another, and perceptibly different from all naturals.

TABLE VII.

This table shows the relative frequency with which, in identifying the given note erroneously, the observers made the various sorts of accidental-confusions and natural-confusions. For instance, in 44.4 percent of H's erroneous identifications, accidentals, presented by the experimenter, were identified as naturals, etc.

h. Errors in the identifying of pitches beyond the range of the piano. Our findings had shown that the possessor of a memory for absolute pitch can readily and correctly assign a given pitch to its proper place within the octave, i.e., can name the note; but that she frequently hesitates and frequently errs in her attempt to name the octave to which this note belongs. This remarkable finding, together with such descriptions of mental procedure as the observers were able to furnish, raised the question as to whether one might assume that these observers find in each of the notes of the octave a certain quality-- a c-ness, a d-ness, etc.; and whether in consequence of this peculiar characteristic each note differs from its fellows within the octave but resembles the corresponding note of other octaves. This conjecture led to an additional series of experiments in which we employed the Galton Whistle and the König bars. The series of notes presented by means of the König bars were eight in number-- e5, g5, c6, e6, c7, e7, g7, and c8. These eight notes were each presented three times, in irregular sequence. Observer C reported that in all of the notes beyond c7 the pitch was so indefinite and so completely smothered by noise as to be incapable of identification. In the 15 identifications which she attempted she had 10 errors, a percentage of error amounting to 66.7. C also failed to perceive any distinct pitch in any note above c7 she had 5 errors in her 15 identifications, a percentage of 33.3. H attempted to identify the pitch in twelve cases and she had but 3 errors, a percentage of 25.0.

In the series with the Galton Whistle we presented the fifteen naturals extending from d5 to d7; these were presented, in irregular order, at each of three sittings. C usually reported that the sound of the two highest members of the series was not sufficiently clear to be identified. She had 11 correct judgments in the 41 cases where she attempted an identification, a percentage of error amounting to 73.2. C also found that certain of the higher pitches were unrecognizable but she attempted 39 identifications with a percentage of error amounting to 41.0. H's percentage of error in 33 attempts was 51.6.

2. Octave Errors

One of the most striking features of our findings is a phenomenon which may be called the illusion of the octave. It frequently happens that an observer who possesses absolute pitch memory is able to name a given note correctly but fails to designate the octave to which the note belongs. As we point out elsewhere, the process of identifying the pitch of any given note is made up of two distinct stages: An initial stage, which consists in a prompt naming of the note; and a subsequent stage, in which the observer names the octave to which the note belongs. In many instances, the observer is able to name the octave only after devoting an appreciable time to a process of deliberating and groping. The note-response and the octave-response were usually separated by an appreciable interval; and the degree of subjective assurance attaching to the octave-identification was usually very much less than that attaching to the note-identification. The octave-error was common to the identifications of all nine of our observers; and it was present in the identifying of notes of every variety of clang-tint.

An examination of our records shows that the octave-error occurred with the following frequencies: In 5.1 percent of the cases where Observer C designated the (piano) note correctly, she designated the octave incorrectly; H, 40.8 percent; C, 27.6; L, 7.9; D, 12,9; W, 13.6; Pk, 6.9; Ps, 11.4; E, 2.5. The illusion was somewhat less frequent in the identifying of organ notes-- the percentages here being: H, 31.5; G, 21.7; W, 10.3; E, 3.2. These data show that the illusion of the octave is of frequent occurrence, that it is subject to individual variation, and that it varies with the clang-tint of the note presented. It is usually more frequent in the more accurate observers, although we have in the case of C a notable exception to this general principle; and it is more frequent with relatively easy clang-tints. This illusion is undoubtedly a phenomenon which is especially characteristic of memory for absolute pitch as compared with memory for relative pitch. The individual who estimates the pitch of a given note in relation to a standard is characterized by the presence of note-errors alone; he has no difficulty in locating the general region of the scale to which the given pitch belongs. And it seems a remarkable phenomenon that in the possessor of absolute pitch memory we have an individual who is especially successful in assigning the given note to its position within the octave, but is frequently at a loss as to the general region of the scale to which the note is to be assigned.

3. Identification-Time

The naming of the note was usually an instantaneous process. It is true that the observer hesitated in certain instances; but her identifications were almost invariably erroneous when they were not made with the utmost promptness. The hesitations were more frequent with notes of very high pitch and very low pitch, and with notes of difficult clang-tints. One observer stated: "As soon as I hear the note I know its name. If I do not recognize it immediately I am lost; but I usually require some little time to discover the octave to which it belongs." And this statement describes the typical reaction of all observers. In order to determine the relation between immediacy and accuracy, we arranged a series of experiments in which organ notes were presented in rapid succession in one ca~, -and with pauses intervening between presentations in the other case. In the former case the observers were instructed to record their decisions as rapidly as possible, and as a matter of fact, if they hesitated they found that the next note had been presented before they had recorded their identification of the preceding note; in this series the notes were presented at the rate of about ten per minute. In the slow series the observers were instructed to take as much time as they re­quired for accurate identification, and no note was presented until its predecessor had been identified and recorded by the observer; the rate of presentation in this series was about one per minute. It turned out that every observer identified the rapid series more accurately than the slow series, the average percentage of error being 41.8 for the rapid series and 49.6 for the slow series. The data for the individual observers were: H, 3.3 percent and 6.1 percent; C, 24.4 and 27.6; W, 59.1 and 75.5; E, 80.3 and 89.3. In numerous instances the observers, in the slow series, were found to be engaged in a process of humming and feeling about with the voice in an endeavor to identify a particularly difficult note.

This was clearly an employment of the relative pitch criterion. That this criterion may be employed successfully, but that it was not employed in the ordinary identifications of our observers is shown by the following incidents:

1. When in her regular series an observer made an erroneous identi­fication of any note, it was the custom of the experimenter to proceed as follows: Instead of then presenting the note which stood next in order upon his mimeographed list, he introduced an extra note of such pitch that it was separated from the erroneously identified note by some such easy and familiar interval as an octave or a fifth. This expedient was employed in the hope that if the observer were judging in terms of her "sense of interval" she would betray herself by now committing a second error of the same magnitude and direction. In not a single instance did we succeed in trapping one of our observers by this device.

2. In additional experiments notes were identified by means of relative pitch alone. Miss Winifred Forbes, instructor in violin, Mr. George F. Schwartz, instructor in violin, and Director Lawrence-- all of whom possessed a highly-developed "sense of interval"-- were kind enough to serve as observers in these experiments, the detailed results of which can not be discussed here. We employed the same lists of notes as in bur other experiments. But here, in our experiments with Miss Forbes and Mr. Schwartz, each note was preceded by an a' struck upon the piano, and the observer was instructed that the pitch of the note which followed was to be identified in relation to the a'; while in the experiments with Director Lawrence we first made an accurate deter­mination of his vocal compass and then he was instructed that the pitch of the given note was to be estimated by means of his voice alone. The percentage of error varied, in the three observers, between 12 and 37-- which shows that relative pitch suffices for identification provided appropriate conditions are furnished. It turned out, however, that the procedure of these observers was wholly different from the procedure of the observer who possesses a memory for absolute pitch; and the identification-time, instead of being a fraction of a second, frequently amounted to several minutes.

Yet notwithstanding their recourse to this additional expedient, and notwithstanding the fact that in the rapid series there were occasional blanks in the record on account of the observer's lack of sufficient time for record­ing her identification, the identifications were considerably more accurate in the rapid series.

In our measurements of the identification-time-- which were sufficiently numerous to be of value only in the case of Observer G-- we obtained the following results (all of these results are expressed in terms of sigma) : The average identification-time, for piano notes (731 reactions) was 754.4 ± 187.3. The times, averaged separately for each octave of the piano, were: A2--B2, 1241.3±274.1; C1--B,, 957.7 ± 205.5; C--B, 798.8 ± 184.9; c--b, 726.5 ± 153.1; c1--b', 658.3±127.0; c2--b2, 615±133.3; c3--b1, 636.3±151.8; c4-- c5, 765.2±209.5.

G's average identification-time for organ notes (645 reactions) is somewhat longer, 957.8 ±204.9. The average times for the four stops were: Flute, 1078.c ± 226.4; diapason, 822.6 ± 189.6; reed, 993.0 ± 219.5; string, 935.3 ± 183.9.

A survey of these data shows that the pitch of piano notes is identified more promptly than the pitch of organ notes; that the identification of pitches of the central region of the scale requires less time than the identification of very high or very low pitches; and that there is a fairly close correspondence throughout between accuracy of identification and promptness of identification.

4. The Reproducing of Designated Notes

Six of our observers were asked to reproduce each of the notes of an octave, by means of the Tonvariator. The results of these experiments are given in Table VIII. A survey of this table shows wide individual differences in accuracy of reproduction-- the degree of accuracy of any given individual corresponding fairly well with her degree of accuracy of identification as recorded in Table I. Indeed, in certain instances it was found that in the case of those individuals who had proved to be least accurate in their identifications, the notes reproduced upon the Tonvariator represented broad bands of the tonal region; and these bands were sometimes so broad that the zones of neighboring notes overlapped. For instance, in one of her attempts to "find" the note e2, Ps reported that a stimulus of 691 vibrations per second seemed to her to be e2, while on another occasion she reported that a somewhat lower pitch, 676 vibrations, was f2. E's reproductions also overlapped in several instances. In those observers, however, who had been most accurate in the identifying of notes, namely, C, H and G, no overlapping ever occurred; their "found" notes represented relatively narrow bands, located at appropriate regions of the tonal scale.

TABLE VIII.
The reproducing of designated pitches by means of the Stern Tonvariator.

IV. Summary and conclusions.

Our results show that memory for absolute pitch is not an "all-or-none" capacity as has sometimes been supposed, but is a capacity whose degree of perfection is subject to variations and limitations of various sorts:

a. Individual variations. Certain individuals who possess this capacity are found to be exceedingly inaccurate in their identifications of pitch, even when the most favorable conditions are present; these individuals differ but slightly from normal capacity to identify pitch. In other individuals, however, the capacity is present in such a high degree of perfection that erroneous identifications are exceedingly rare; these individuals represent an extreme degree of supra-normality. Other possessors of the capacity are distributed more or less uniformly between these two extremes. Cases of absolute pitch memory may, therefore, be represented as a series of gradations which extends from normality at the one extreme to a high degree of deviation from normality at the other extreme.

b. Variation with clang-tint. Clang-tint proves to be an influential factor in determining the efficiency of absolute pitch memory. Pitches of certain clang-tints are relatively easy to identify, while pitches of other clang-tints prove to be difficult-- even impossible in the case of certain individuals. An observer whose percentage of error with certain clang-tints is less than 4 percent may have a percentage of error amounting to nearly 40 percent in other clang-tints. Piano notes are relatively easy to identify, while tuning-fork notes and notes sung by the human voice seem to stand at the opposite extreme.

c. The influence of tonal region. Notes chosen from the central region of the tonal scale are identified with a much higher degree of accuracy than very high notes or very low notes; an individual who is fairly successful in identifying notes of the once-accented octave may wholly fail in his attempts to identify notes selected from either end of the keyboard.

Errors in identifying pitches are of two wholly different sorts: Note-errors and octave-errors. In the former case the observer errs by a few semitones; in the latter case he names the note correctly but assigns it to the wrong octave. This illusion of the octave is of frequent occurrence in cases of absolute pitch memory. Note-errors vary in magnitude; but errors of small magnitude tend to predominate in pro­portion as the observer in question ranks high in efficiency.

Observers tend to be especially accurate in their identification of the pitch of certain notes of the octave, and to be especially inaccurate in their identification of the pitch of other notes. But there seems to be little agreement among observers as to which is the preferred note of the octave; and the note with which a given individual is most successful in her organ identifications may not be identical with her most successful note in piano identifications.

In experiments with higher pitches than are employed in music one finds that identification is still possible although accuracy is somewhat impaired. It is doubtful if in any previous experience of our observers these high pitches had ever been heard in conjunction with their note-names; and it seems remarkable that their identifications should have been accurate in such a large proportion of the cases. This phe­nomenon, together with the illusion of the octave, suggests that overtones may have played a prominent role throughout in the identifications of our observers; but although the physical composition of the sound-wave may be cited in support of this view, there are certain features of our findings which can not be brought into conformity with this hypothesis-- for instance, how are we to account for the fact that a note is much more likely to be confused with its third or its sixth than with its fourth or its fifth?

The fact that observers are much more successful throughout in identifying the pitch of certain notes of the octave than in identifying others would seem to indicate that certain notes of the octave possess a distinctive and recognizable individuality. And this suggests an alternative explanation of absolute pitch memory. Recent writers have advocated the view that certain specific "qualities" or "characters" attach to certain specific regions of the tonal scale; that besides its pitch, its clang-tint and its other traditional attributes, the sound of middle c, for instance, has an attribute of c-ness which not only differentiates it from its fellows within the octave, but relates it with the c's of other octaves.[6]  If this view be granted one finds a ready explanation for certain of our findings which otherwise prove to be mysterious and baffling.

When one seeks to determine what relationship exists between the ordinary process of recognizing, as it runs its course in the everyday experiences of normal individuals, and the process of recognizing pitches, as it runs its course in the exceptional individuals who served as subjects in our experiments, one finds that the known facts of the recognitive process support the following conception of this relationship. A comparison of one's consecutive recognitions of a recurrent stimulus reveals the fact that the ordinary process of recognizing has a typical genetic history and passes through a series of typical developmental stages. Especially in those cases of recognizing where one has to do with perplexing situations and where the process of recognizing is hesitant and difficult, the initial stages are characterized by a wealth and variety of mental content; and the subsequent stages are clearly distinguishable from one another. A difficult recognition is characterized at the outset by hesitancy and deliberation; it is the product of a process of discriminating, relating and comparing, and it is accomplished by means of imaginal and affective components which are definitely present to con­sciousness. But just in proportion as we become progressively more proficient in dealing with the recurrent situation, and as we 'learn to recognize' the datum in question, the affective and imaginal content becomes progressively more sparse and vague; and the process of recognizing becomes progressively and proportionately more prompt and facile.[7] There are of course hosts of experiences where, because of the simplicity and ease of the recognitive process involved or for other reasons, we pass directly and at once from the initial stage of development to the final stage; for instance, the normal individual recognizes reds and sours and warmths after but a single experience with them. The process of recognizing as delineated in the foregoing follows a general law of mental functioning which is illustrated, for instance, in every acquisition of mental or motor skill and in the formation of all mental and motor habits.

Now the process of recognizing pitches, as exemplified in our observers, bears a close resemblance to the final habituated stage of the ordinary recognitive process as exemplified in normal individuals. Every one is capable of recognizing promptly and accurately in certain domains; and one individual's efficiency of recognition in a given domain may be much superior to that of other individuals, The practiced student of geology never fails to recognize that a trilobite is a trilobite; and the efficient student of German invariably recognizes that this neuter noun is neuter, and that that masculine noun is masculine. Mr. A finds it possible to differentiate and recognize the twins in his neighbor's family, although he formerly failed to do so and although many of their acquaintances still fail. (The reason for his success lies in his discovery that Lottie has a tiny mole on her cheek, while Tottie has no such distinguishing mark; and immediately on the discovery of this obscure criterion his efficiency of recognition mounted from zero to nearly one hundred percent) Now the recognizing accomplished by the exceptional individuals who served in our experiments is, in its present perfect form, so similar in kind to the student's recognizing of trilobites that one might be tempted to assume that this final goal had been reached by the same general route and after the same toilsome journey in the two cases. But nothing could be farther from the truth. In the first place, such experimental evidence as the literature affords makes it seem very doubtful that absolute pitch memory can be acquired by training.[8] And in the second place, all of our observers report that their memory for absolute pitch is not a product of training; they simply discovered at an early age-- in some cases at the age of five years-- that they possessed this capacity, and possessed it apparently in quite as perfect form as at present. In view of all of these circumstances, may we not therefore assume that memory for absolute pitch is based upon an ability to detect the presence of the c-quality which is obscurely present in every c, of the d-quality which is obscurely present in every d, etc.? And that given this basis upon which to build, the advent of our observers' capacity to recognize pitches was as inevitable and as abrupt as was the advent of Mr. A's capacity to recognize Lottie on discovering that she possessed a distinguishing mark?

Footnotes

1.  This term is not wholly free from objection, but so far as the writer knows, no less objectionable term has ever been proposed. See in this connection: J. von Kries, Ueber das absolute Gehör. Zeitschrift für Psychologie and Physiologic der Sinnesorgane, III., 1892, p. 257; Otto Abraham, Das absolute Tonbewusstsein. Sammelbände der internationalen Musikgesellschaft, Jahrgang III., I., 1901, pp. 1f.  [Return to text]

2.  This practice klavier is an instrument which has been devised for the purpose of affording students an opportunity to acquire a playing technique under optimal conditions. The instrument consists essentially of a piano keyboard (eighty-eight keys) of standard size and form, but it has no piano-strings or other internal mechanism of a sound-producing sort. This silent keyboard proved to be peculiarly well-adapted to the purpose for which it was used in the present investigation.  [Return to text]

3.  Miss Cottlow possesses a remarkably clear and definite chromaesthesia (colored hearing) which she has represented in colors for the author, who hopes to publish a detailed description of it in the near future. [Return to text]

4.  For instance, C. Stumpf, Tonpsychologie, I., 1883 pp. 235f.; II., 1890, pp. 553f.; von Kries, loc cit., pp. 264 and 269ff.; Abraham, loc. cit., pp. 25ff.  [Return to text]

5.  Stumpf, loc cit., I., p. 235; see Abraham's discussion of this point, loc. cit., pp. 25ff.  [Return to text]

6.  Köhler has discovered that a specific "quality" or "vocality" (a u sound) attaches to a pitch of about 262 vibrations (pure tone, unmixed with overtones) ; that a second specific 'quality' or 'vocality' (an o sound) attaches to a pitch of about 522 vibrations; that a third (an a sound) attaches to a pitch of about 1055 vibrations; and that a fourth (an e sound) attaches to a pitch of about 2090 vibrations. (W. Köhler, Akustische Untersuchungen. Zeitschrift für Psychologie, LIV., 1910, pp. 241ff., and LVIII., 1911, pp. 59-140, especially p. 128; Ueber akustische Prinzipalqualitäten. Bericht flber den IV. Kongress für experimentelle Psychologie, 1911, p. 234.) And Révész reports that even unmusical observers, who are unfamiliar with musical intervals, are able to detect a "similarity" in the pitches of pure tones which are selected from points an octave apart on the tonal scale-- from which he concludes that the c's possess a specific and common "character" of c-ness, the d's a specific d-ness, etc. (G. Révész, Nachweis dass in der sogenannten Tonhöhe zwei voneinander unabhãngige Eigen­schaften zu unterscheiden sind. Nachrichten. der leöniglicheu Gesell­schaft der Wissenschaften .ru Gottingen, Math-physik. Kiasse, 1912, pp. 247-252; Ton psychologie, 1913, pp. 90-101.) See also J. D. Modell and G. J. Rich, A Preliminary Study of Vowel Qualities. American Journal of Psychology, XXVI., 1915, pp. 453-456.  [Return to text]

7.  For a detailed description of the genetic stages in the development of recognition see E. L. Woods, An Experimental Analysis of the Pro­cess of Recognizing. American Journal of Psychology, XXVI., 1915, pp. 313-387. [Return to text]

8.  Max Meyer reports a series of experiments from which he seems to infer that memory for absolute pitch may be developed by training; but an examination of his findings leaves one in doubt as to whether any improvement actually took place during the progress of the training. Meyer's investigation throws no light on the question as to whether an individual who possesses no memory for absolute pitch can acquire that capacity by training. (Max Meyer, Is the Memory of Absolute Pitch Capable of Development by Training? Psychological Review, VI., pp. .514-516.)  [Return to text]