Originally published in Archives of Psychology, Volume 7, pages 1-98, 1922
Evelyn Gough, Ph.D.
It gives me pleasure to express here my gratitude to the many people who aided in the progress of this investigation. John W. Baird, under whose instruction I first became interested in the problem, directed the initial stages of the work. He also brought me into communication with Professor C. A. Ruckmich who generously contributed the report of a similar experiment conducted by a student in his laboratory. Professor C. A. Seashore in correspondence suggested new aspects of the problem and methods of approach. I am especially indebted to Professor R. S. Woodworth for his constant encouragement and criticism throughout the investigation.
I wish to thank my fellow students, Miss R. S. Clark and Miss H. J. Sleeper, my sister, Mrs. E. S. Boegehold, and the many undergraduates at Smith College, who cooperated so heartily in this study. I also extend my thanks to the Department of Music at Smith College for affording the necessary facilities for carrying on the experiments.
Many striking cases of absolute pitch memory have already been investigated, yielding interesting and valuable results. Individuals who possess this ability in a high degree are, however, unable to analyze their means of recognition and trace its development. They identify a particular note as c1 in the same way that they recognize any familiar percept or respond to any elementary experience. This attitude has led to the belief that certain highly favored people are endowed by nature with an unusual tone-recognizing mechanism which has been denied to others.
The present study has undertaken to investigate to what extent the average individual is able to identify notes, and to what degree his initial ability may be improved by training. By an analysis of the introspective reports given at these tests and a comparison of these reports with the objective results, it is possible that some light may be thrown on the general problem of judgments of absolute tone.
A review of the literature on this problem brings out many casual observations of the ability, many speculations as to its nature and its relation to other abilities and to practice effects, and also a number of systematic studies in this field.
Stumpf[1] writes as early as 1883 that he believes the individual differences in memory for pitch to be due to such variable factors as practice effects, general retentiveness and a certain inexplainable individual coefficient.
In tests on a group of musicians he finds that the different regions of the keyboard have varying degrees of difficulty, and that clang-tint affects the ability to identify notes to a great degree. Different observers require different lengths of time for judgment, and the same observer varies according to the region to be judged. Stumpf's own results from six tests on the piano are as follows:
His errors are mostly intervals of a semitone or a whole tone. A few extend to the tritone, but never include fifths or sixths. Little account is taken of octave errors, because musicians make slight use of the symbols designating the octave and consequently do not easily differentiate them. The effects of practice are noticeable in these results.
Stumpf reports a test he made on a girl eight years old, using the sixty piano notes between C and c4[2]. Thirty-nine notes were correctly named. Most of her errors lay in the three-accented octave and occurred among the accidentals. Black keys were confused with other black keys, as c#3 with f#3. She was less able to identify chords than single notes.
He reports the case of a man who could recognize the keys of chords played on the piano or played by an orchestra, but not played on an organ. And he was unable to identify individual notes. Stumpf explains this on the basis of the direction of musical interest.
Several people are recorded who possessed interval memories inferior to their memories for absolute pitch. If a piece was played in an unfamiliar key, even though it might be only a semitone or a whole tone higher or lower than the accustomed key, it was necessary for them to transpose individually each note to the new key before being able to sing or play the melody.
Further conclusions from Stumpf's investigation of the subject are that absolute pitch memory appears very seldom among women, and that it is not an indispensible factor in musical ability. He attributes much importance to the element of frequency in establishing a good memory for pitch, but regards as more fundamental the individual's initial discriminative ability and his inherent retentiveness for certain kinds of auditory impressions.
ln 1892 von Kries[3] cites a number of observations which he made on himself and on a few others who possessed a good memory for absolute pitch. Violin pieces are occasionally written for violins to be tuned a semitone higher than normally. Some violinists find it impossible to play music written in this way, others experience no difficulty. Hence von Kries conjectures that the latter do not have absolute pitch memory. He agrees with Stumpf in finding the middle range the easiest and the surest to judge. The notes above c4 and below C are difficult to hear distinctly.
Arranging the different musical instruments in order of ease of judgment, the piano comes first, then the greater number of string and wind instruments, then the voice, tuning forks and whistles. Since the different clang combinations influence greatly the ability to judge pitch, he concludes that memory images are not the essential condition-- in other words, that absolute pitch memory does not involve a comparison judgment. He explains this form of memory from the Lehmann association point of view. It is based on a kind of limited association, which holds only for certain claI2gs. He finds in studying the different clangs that recognition may have all grades of clearness. A sharp line is not to be drawn between the recognizable and the non-recognizable tones. With long practice he was able to reduce the limits of the unrecognizable, but was never able to pass from indirect to direct judgments.
He rejects the theory of muscular accompaniment, for in his own case he has more success in judging the pitch of soprano voices than male voices, and tones which he himself cannot sing at all. Frequency of hearing certain notes does not fully explain results for him, for in spite of his wide experience with male voices and his slight experience with the violin, judgments of pitch in the first case are poor and in the second good. He hears one-part singing oftenest yet can judge the pitch of several-part singing more easily. He finds -many cases of people who can recognize keys and chords, but not single notes.
Richness in overtones seems to be the most predominant factor contributing toward absolute pitch memory, although these tones need not be present consciously to the observer. The fact that the human voice gives difficulty he thinks may possibly be explained by the interference of the vowel sounds in singing.
A report is made by Meyer[4] in 1889 of an investigation in which he and one other observer attempted to develop absolute pitch memories through practice. They worked two months using the notes produced by sixteen tuning forks varying from 100 v. d. to 4000 v. d., and four months using from ten to thirty-nine notes produced on the piano. More than half their judgments were correct and the size of the errors was very small. After discontinuing practice for several years Meyer found they had lost the greater part of what they had acqnired.
The following questionnaire was sent to one hundred musicians by Abraham[5], who bases his conclusions regarding memory for absolute pitch in part upon the replies he received:
1. How long have you possessed absolute pitch memory?
2. Do you play or sing? How long?
3. Do you compose? Do you improvise on some instrument? Is it difficult for you to find the correct bass for the melodies you know?
4. Does your memory for pitch include the ability to produce by singing or whistling certain notes as well as the ability to name correctly notes you hear?
5. How do you arrive at your correct judgment? Is it immediate judgment by a conscious comparison with a note in memory or by singing the note heard? Can you think of a note without singing it or hearing it? What timbre has this note? Do you compare the note heard with the relatively lowest or highest singing tone which you can produce?
6. Is it easier for you to recognize a note in a melody or the key of a chord than a single note?
7. In singing correctly a note from memory do you image its notation on the staff, or do you think of a song which begins on this note?
8. Has your pitch memory upper or lower limits in range? Do you judge one octave better than another?
9. How loudly and how long must the note be sounded for you to judge it easily?
10. What errors in judgment do you sometimes make? Octave, fifth, semitone, etc.?
11. Have all the as for example, some likeness which distinguishes them from b, c, etc.? Is this similarity present in a lesser degree between a and e?
12. Can you tell when an instrument is a quarter or an eighth of a tone higher or lower than another if a long period of time intervenes between the two sounds?
13. When a song is transposed by an accompanist can you sing it easily, or must you transpose it yourself mentally?
14. Does difference in timbre affect your ability to judge notes?
15. Have you a good memory for melodies? Must you think of a melody always in its correct key, or can you imagine it in any key?
16. Did you develop or improve your memory for pitch by practice? Is it hereditary?
17. Do you think of colors in connection with notes?
Abraham also made experiments in regard to the influence of pitch, intensity, duration of sound, time-interval between notes and tone-color on memory for absolute pitch. He found that the range of the ability is wide and variable, and does not coincide with the range of ability for sensible discrimination. Loud notes in which the high overtones are prominent are judged higher than they are. The pitch judgment does not require a longer stimulus time than that necessary for perception, but repetition of the stimulus increases the assurance. Notes without overtones are judged lower than they actually are.
According to Abraham's results some people possess absolute pitch memory without special practice, others are able to acquire it through practice, and others are never able by any means to acquire it. He attributes this ability to an individual factor which may be due to a certain fineness of sensory apparatus by which individuals recognize separate tone qualities in their finer differences, or to certain unique cerebral conditions. This memory depends on associations formed in the auditory realm alone, and therefore lacks the many aids to memory which are found in other types of learning. "If a child is shown a clock, he sees it, feels its shape, hears it tick, feels the coldness of it, etc. The different senses help him to realize the object, so that he can always recognize it as a clock in the future... Absolute color consciousness seems to be more common than absolute tone consciousness. Very fine differences of color are recognized, and color shades are produced in imagination by the name. However, I find that the color always attaches itself to some definite object. I cannot imagine brownish red purely as a color, but must think of the portière in my room. We cannot use instances like this to help us in our decision of pitch. We can only fix the pitch by itself in our memories." Other factors which hinder the development of absolute pitch memory are the variations in the keys in which a child hears the same song sung and played, the variations in the standard pitch for different instruments for different purposes and the use of the tonic sol fa system, where do may sometimes be c, sometimes e-flat, etc.
Certain indirect methods may aid in determining the correct pitch of a note. The pain sensations which accompany very high notes, "colored-hearing," feelings of tension in humming a note, emotional reaction, and the characteristic pitch of the ear drum might be used as bases for inference. Visual images of the note or the key of the piano, or of oneself sitting at the piano, or the scene from some opera are sometimes used. These devises have no part in a good tonal memory, but they may lead to a firm impression of the note on the memory.
A person who has the "power of true tone imagination," or the ability to call up a note at will, is able to make exceedingly fine judgments of absolute tone, such as judgments of notes less than a quarter of a tone apart, because he can compare each note he hears with the note in his imagination. These two aspects of tonal memory are inseparable, but each marks a different stage in the development of the ability.
Absolute key consciousness is often confused with the recognition of certain physical differences in the notes of different instruments. The white keys on the piano give a louder sound than the black keys, partly because one uses a more powerful touch on pressing them down, and partly because the subduing effect of the hammer, as the white keys are played more frequently, is very soon lessened disproportionately. The open strings of bowed instruments sound brighter than the other notes, so that they give the keys in which they are used a great deal, especially those in which they are the key notes, a brighter character. The natural tones of wind instruments sound brighter than those made by stops, etc. One's feeling for keys is undoubtedly affected by assocations of various kinds. If a composer has written a powerful piece in d-minor, later musicians come unconsciously to associate that key with power.
Experiments made by Abraham on a man who claimed to be able to recognize keys but not single notes, show that only f#-minor could be correctly recognized, and only when played on his own piano. Abraham concludes that the existence of absolute key consciousness without absolute tone consciousness is very uncertain.
Abraham believes this ability is an important part of a musician's equipment, but taken alone need not indicate musicianship. He finds it frequently accompanies imperfect melody memory, which he explains on the theory that the association paths within the auditory area from tone to tone are more numerous or more closely knit together than the paths from tones to other sensory areas, as to a word, a visual image, etc.
Other possible explanations for the decidedly different character of different keys on piano and bowed instruments are offered by Helmholtz.[6] "C-major and the adjacent d-flat major have different effects. That this difference is not caused by difference of absolute pitch can be determined by comparing two different instruments tuned to different pitches. The d-flat of the one instrument may be as high (sic) as the c of the other, and yet on both the c-major retains its brighter and stronger character, and the d-flat its soft and veiled harmonious effect." This may be due, as Abraham has said to the method of striking the short black keys of the piano, or as Ellis suggests to the different leverage of the black keys, so that each key has a different distribution of the stronger and gentler quality of tone among the varying degrees of the scale. Further the difference made in the tuning of those fifths which the tuner keeps to the last, and on which are crowded the whole of the errors in tuning the other fifths in the circle of fifths, may be regular and contribute to this effect.
On bowed instruments the notes from the open strings color the key by the inequality of intonation. The open strings give perfect fifths, but in playing in different keys if each note has the same sound throughout, the other fifths will not be perfect. Hence the scales of the various keys will differ in intonation and in character. Wind instruments illustrate this in an even more striking manner.
Another possibility is that g4, the proper tone of the human ear, which sounds peculiarly shrill at all times, may color those notes which possess it as an upper partial, as g3, c3, g2, and give to them a brighter and more piercing character than other notes.
Boggs[7] investigated memory for absolute pitch in a group of especially endowed individuals, all of whom had a musical inheritance and early musical training. Her observers displayed immediateness of recognition and sureness of judgment. Concentration of attention was found to be of great importance. Extraordinarily good discrimination of pitch was not observed and imagery did not seem to be particularly necessary. A strong emotional feeling for music as a whole was shown, but not for isolated notes. Her observers reported that they were conscious of overtones and that the pitch of the particular piano used made practically no difference in their judgments.
This factor of attention to overtones led Boggs to believe that each note is heard in its relationship to other notes as part of a tonal system. This view is supported by the fact that chords are frequently more easy to identify than single notes. This tonal system is a qualitative one comparable to a phase of the spectrum in vision, each system being regulated in part by differences in vibration rate. The tonal scale corresponds to the brightness variations. Hence the average person might hear the scale in the same way that a colorblind person sees the spectrum as graduated succession of brightnesses.
Writing on tests for musical ability, Rupp[8] states that memory for absolute pitch is in general indicative of musical ability. Although it does not constitute the essence of this ability, it is closely bound up with other musical qualities. Since he examined only a small number of cases, he cannot attach a high degree of certainty to his correlation.
He suggests the method of minimal changes as advantageous for the study of the upper and lower thresholds for the memory of notes. For instance by slowly changing the pitch on a variator, one can discover within what limits the sounds seem like a1, c1, etc.
He finds, as has been before mentioned, that the sureness and exactness of memory is not the same for different notes and octaves. More mistakes were made in the extremes than in the middle octaves. A and c in the different octaves were recognized more quickly than other notes which were named with hesitation and sometimes by reference to c and a. The differences in the tone color of different instruments was a hindrance which led to indirect judgments such as comparing the tone of new timbre with more familiar tones. By continued practice Rupp believes it is possible to reach correct absolute pitch judgments without intermediary aids. A long series of impressions of notes would lead in time to a firm, lasting impression. This may be either acoustic or kinaesthetic memory.
In reproducing notes as distinguished from recognizing notes heard, the individual's technique in handling his instrument is an important factor in his success. Hence a good vocalist without absolute pitch memory might make a better showing than a poor singer with memory for pitch.
The results from experiments on absolute pitch memory, conducted by a student in the Psychological Laboratory at the 'University of Illinois, were made available for the writer through the kindness of Professor C. A. Ruckmich[9]. In order to investigate the problem, "Can absolute pitch be cultivated," practice experiments were made individually on two musical adults who possessed varying degrees of accuracy in pitch memory, two children, nine and twelve years of age, and the students in an ear training class. The observers began by trying to impress on their memories the notes c1, e1 and g1. After a time all the white keys in the once accented octave were undertaken and later the range was extended to two octaves. The black keys in the middle range were then added. The class in ear training was given notes taken at random from the entire keyboard.
The results from this practice evidence a degree of improvement. Both the size and the percentage of error are decreased. The average time from all the experiments for the correct judgments is slightly less than that for the incorrect, although this does not always hold in single tests. The writer concludes that accuracy of judgment varies directly with the speed.
In testing the children the experimenter found it impossible in spite of his efforts to lead them to think of a note in terms of absolute pitch. They insisted on making their judgments relative to some other note, usually c, which they seemed to remember remarkably well.
On account of the difficulties involved in explaining the many aspects of memory for absolute pitch as due either to the complexity of the sound wave, or to the familiarity with certain clangs, Köhler[10] is led to believe that recognition of notes is in many cases the result not of a memory for pitch, but a memory for some other feature of tonal body. He quotes such aspects as the immediateness of the recognition of those who possess good tonal memory, their proverbially poor interval memories, their incompetence in the face of some new clang tint, the superiority of the recognition of chords over the recognition of single tones, and the frequency of errors of the octave interval, of fifths and of fourths.
With the importance of tonal body in mind, Köhler made an experimental study on himself trying to learn the notes of the white keys between c and b3. After fourteen days practice he was convinced of the value of this method. Half his 220 judgments were correct and the majority of his interval errors corresponded to the errors of individuals in whom absolute pitch memory was native, i. e., errors of the octave, fifth and fourth.
His results lead him to the conclusion that memory for tonal body may be the criterion for correct tonal judgments and affords a plausible explanation for many of the striking characteristics alleged to belong to memory for pitch. Neither pitch nor tone body alone cover all cases, therefore either one may be effective in the judgment. He explains the difficulty in judging tones from human voices as the result of the continual shifting of the register by the variation in vowel sounds. He quotes Max Meyer and Heyfelder as supporting his view that pitch alone is not adequate to explain the problem.
The most extensive investigation of the nature of absolute pitch memory was made by Baird[11]. All his observers were more or less highly trained musicians who possessed some degree of memory for absolute pitch. Nine observers took part in identifying the pitch of the eighty-eight notes of the piano, taken in random order (i. e., naming the note definitely as c3, A2, etc.), and five observers took part in identifying sixty notes of the pipe-organ, using the flute, diapason, reed and string stops, fifty-five notes ranging from B-flat to g# sung by four vocalists, soprano, contralto, tenor and bass, twenty-four notes, c1 to c3, of the flute and the clarinet, fourteen tuning forks ranging from c to c3, twenty-three notes beyond the keyboard of the piano from d5 to c8, using Konig bars and the Galton whistle. In another group of experiments he obtained the reaction time by means of a Hipp Chronoscope. The observer was asked to name notes of the piano and organ without designating the octave. In a third group of experiments six observers were asked to reproduce the notes of an octave by means of the Tonvariator. Determinations were made in an ascending and a descending direction.
His results in regard to note errors show great individual variation.
(1) Although the observers belong to a highly selected group, their average error in identifying piano notes varies from 1.1 percent to 74 percent This is true also for the identification of notes of other clang tints.
(2) A variation of accuracy with clang tint is found in the case of each observer. Arranging these in order of the ease of identification for each person, marked individual preferences are found. On the whole the piano notes are most easily identified. Then follow in approximate order the notes from the organ, the flute, the clarinet, and the voice. The results from the other clang tints are uncertain.
(3) The middle range of the piano is in every case most accurately named. The average percentages of error distributed over the tonal scale by octaves are for nine observers as follows:
Greater individual variation occurs in identifying pipe-organ notes.
(4) The naturals are usually identified with greater ease than the accidentals, although here again great individual variation is found. Every observer was more successful in naming certain notes of the octave than others in the case of both piano and organ notes with little coincidence of preference in the same individual with these two instruments. The averages from all observers show that f and c are most accurately identified on the piano and g and c on the organ, whereas c# and b-flat are least accurately identified in both cases.
(5) A central tendency of judgment is noticeable. Low pitched notes tend to be judged too high and high pitched notes too low. Overestimations of pitch are relatively more frequent for piano notes and underestimations for organ notes.
(6) The size of the error varies from one semitone to two octaves. The proportion of gross errors increases with the decrease in number of correct judgments from one person to another and with the same persons from one instrument to another.
(7) Certain observers habitually make the same mistakes. Errors of a fifth occur in 51 cases, errors of a fourth in 54 cases, errors of a sixth in 70 cases, and errors of a third in 80 cases. (Baird's observers show a tendency to call many of the uncertain notes g, for c, d, e, f, b#, and b are wrongly identified as g a large number of times.) From these findings Baird concludes that the notes least subject to tonal fusion are most subject to confusion. Although the observers believed they were aware of qualitative differences between naturals and accidentals, no evidence is found to support their view. In the case of errors among the accidentals, 38% are misidentified as naturals, 12.1% as accidentals. On the other hand in the case of errors among the naturals, 20.1% are misidentified as accidentals, and 29.8% as naturals. This shows that the response of 'natural' occurs more than twice as frequently as the response of "accidental."
(8) Some slight ability to identify pitches beyond the range of the piano is found. The observers report that above c7 the pitch is indistinct and smothered by noise.
Octave errors are common in the identifications of all the observers in every kind of clang tint, but are subject to much Individual variation. They are more frequent in the more accurate observers with one notable exception, and more frequent with relatively easy clang tints. Baird distinguishes two stages in the process of identification, 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. These two responses are usually separated by an appreciable interval, and the degree of subjective assurance is less for the octave identification than for the name of the note.
The results for identification time show that piano notes are more quickly recognized than organ notes, that the notes in the middle range are more quickly recognized than those at the extremes, and that a fairly close correspondence exists between accuracy and promptness of response.
Wide individual differences are shown in the ability to produce given notes by means of the variator. The degree of accuracy of each observer corresponds fairly well with her degree of accuracy of identification of notes. Wide tonal "bands" with considerable overlapping of neighboring notes satisfy those who are least accurate in their identifications. Those most accurate in the previous tests reproduce notes with relatively narrow bands, without overlapping, located at appropriate regions in the tonal scale.
Baird rejects as inadequate the theory that complexity of Sound wave is the important factor in the identification of pitch. He advances an alternative explanation which is supported by results of investigations on vocality.* This states that distinctive qualities attach to different regions of the tonal scale. One may experience these qualities a single time possibly and from that time be able to recognize them when they recur just as the normal individual recognizes the elementary experiences after a single occurrence. On examining the process of recognition in his observers Baird does not find an initial learning period filled with a variety of mental content, which later fades out as recognition becomes immediate, such as is necessary for acquisitions of mental or motor skill. His observers claimed that they had never attempted training of this kind, but had simply discovered at an early age this ability, which apparently remained unchanged. The literature on practice experiments in this field strengthens his belief 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. . . . Given this base as the advent of the capacity to recognize pitches is inevitable and abrupt."
[*Kohler found in using tuning forks as stimuli that a series of tones ranging from 163 v. d. to 4000 v. d. gives a series of vowel qualities which can be arranged like those of color. As red shades gradually into Otange and orange into yellow, similarly in the tonal system the vowel quality u (moon) passes through u-o, o-u to o, and so on to a (father), e (prey), and i (machine). Later in using Stern variators with interference apparatus he obtained the pitches of the pure vowels and added é, f and oh fo the upper range and m to the lower. His pure vowels fell regularly into octaves.]
The importance in pitch recognition of the so-called tonal attributes of quality and vocality, defined by Révész[12] as that which recurs at every octave and that which is different in different octaves, has been emphasized by a number of writers. Max Meyer, writing in 1914, believes that the distinction between tonality and vocality is essential for an understanding of memory for absolute pitch. Révész states that there may be several kinds of memories for absolute pitch, in which one or the other or both attributes play a part. A musical interval can be either a span in vocality, or a relation of tonality, or both.
The psychological status of these two characteristics is a matter of dispute. Do they rank as attributes of sensation, or as perceptions, or are they completely outside the tonal series? Stumpf[13] denies on the basis of introspection that vowel qualities are comparable to the color series, and explains octave similarity as due to the degree of fusion, an ultimate fact of hearing. In 1914 he writes that the primary qualities lie within a single octave[14]. Rich[15] reports a recent experimental study of tonal attributes in which he concludes that vowel quality judgments are perceptions, but he is in doubt whether to regard tonality as attributive or perceptuaL Watt[16] denies the view that vowels are primary qualities of hearing or in any sense attributive. He believes vowels hold a mid-position between tones and noises. Also octave similarities do not require a theory of octave qualities in explanation but can be interpreted as the result of the symmetry of volumic relations.
Watt offers an explanation for absolute pitch memory on the basis of his analysis of tones. Tones are systems of sound possessing six attributes, (1) intensity, (2) extension or volume, (3) systemic order, under which heading pitch falls, (4) a single quality characteristic of all tones, (5) temporal order, and (6) durance. Pitch is not to be identified with tone, but is to be regarded as the intensively predominant order of the whole volume, which is symmetrically balanced in relation to pitch. Differences in pitch illustrate the ordinal series in sound as distinguished from a qualitative series. A unit in the tonal series is better described in quantitative terms as "this one," and "that one" and "the next one," than in qualitative terms as "this sort of one," "that sort of one," and "the other sort of one." A scale is a series of volumes of constant proportions, an octave simply a pattern of volumic relations, which has set an artificial standard for the whole range, and a musical interval an intensive volumic outline. Both absolute ear and relative ear are based on these relationships. For the former a point of reference in auditory orders is required. Says Watt, "Absolute ear emerges when the natural absoluteness of tonal orders maintains its efficiency in spite of the tremendous emphasis laid on relativity or proportion in. music."
Naming tones correctly is on a par with localizing accurately a point touched on the skin. Each is dependent on the attribute of order. The chief reason why many fall short in the first case is due to the extraordinary emphasis laid by music on the relationship of pitches. The variation in absolute pitch of musical instruments is in part responsible for the defect. Some people may have a special refinement of hearing, such as a greater delicacy of volumic outline and especially of predominance than others have. Or a highly favored auditory disposition might give them the power to maintain their absoluteness of ear in spite of the universality of musical relativity. In this case everyone naturally possesses absolute ear, and later loses it, or loses the power to convert it into absolute nomenclature. Octave errors in absolute ear are the inevitable results of the relativity which the octave brings. Even a well-maintained absolute ear is in part subdued to musical relativity, regarding as of first importance the placing of the pitch in the octave, and of minor importance accuracy in specification of the exact octave.
E. M. von Hornbostel (Ueber vergleichende akustische und musikpsychologieche Untersuchungen, Zeitschrift für Augewante Psychologie, 1910, 3, pp. 465ff.) states that children can be trained to develop absolute pitch memories, and that the less contact they have had with music, the better this training. Parrots and starlings have been ohserved to reproduce melodies only in the original keys in which they were sung.
Myers and Valentine[17] made a study of the different attitudes which different people assume toward tones. They analyzed four possible attitudes (1) the intra-subjective attitude, which involves certain physiological sub-aspects in which the observers characterize the note as 'strident' or 'piercing' and conative subaspects such as impulses to motion and efforts to determine meaning, pitch or interval; (2) the objective attitude, in which the observer relates the sound to some standard of purity, pitch, etc.; (3) the character attitude in which the observer tends to personify the tones heard; and (4) the association attitude including musical (fused) associations and other than musical (non-fused) associations. Their results for single tones are as follows:
The attitude which an individual assumes when listening to isolated notes will affect the possibility of his regarding tones as part of an ordinal series with absolute points of reference. These results show that the highly musical observers are more apt to have the analytical point of view for single tones than the less musical observers.
Summarizing the results of these writers, we find many points of similarity and of difference. The reason why the ability is so restricted is believed according to Abraham to depend on the facts (1) that absolute pitch forms its associations in only one sense realm, the auditory, (2) that songs are transposed freely from one key to another, (3) that the standard pitch of instruments varies greatly, and (4) that the use of the tonic sol fa system emphasizes the side of relativity in music. Watt also stresses this last factor of relativity in musical training.
Various characteristics and accompaniments of the ability are: (1) the middle range is universally regarded as the easiest to judge and gives the surest judgments. Baird finds f and c on the piano most frequently judged correctly and g and c on the organ. (2) Clang tint directly affects judgments. Arranging the instruments in order of ease of identification Baird puts the piano first, then the organ, the flute, the clarinet and the voice. Von Kries places tuning forks and whistles after the voice. (3) Stumpf found that the speed of judging time varies from person to person and with the same person from one clang to another. Ruckmich's student adds that speed and accuracy vary together. (4) Stumpf's errors in identification were mostly semitone and whole tone errors diminishing gradually in number as their size increased. No errors of the fifth or sixth occurred. Baird's errors ranged from a semitone to two octaves. He found a large number of octave errors, 70 errors of a sixth, 51 errors of a fifth, 54 errors of a fourth, and 80 errors of a third. Köhler emphasizes the predominance of errors of a fifth, a fourth and an octave amongst observers who possess genuine absolute pitch memory. (5) Stumpf found that errors of black keys were due to confusions with other black keys. Baird's results contradict this. (6) Abraham suggests that poor melody memory is apt to accompany memory for absolute pitch.
Chords are frequently claimed to be easier to identify than single notes. One of Stumpf's observers could name single notes correctly but not chords, one could name chords but not single notes. Abraham's results led him to feel doubtful of the existence of absolute key consciousness without absolute tone consciousness.
Baird found the ability to reproduce given notes to run fairly parallel with the ability to name notes heard. Abraham thinks the two abilities need not necessarily be at the same level of development, but that both represent the same general capacity.
Many possible aids in making absolute pitch judgments are enumerated by Helmholtz and Abraham. They are (1) feelings of tension in humming, (2) emotional reaction, (3) pain sensations caused by high notes, effects of the characteristic pitch of the ear drum on g4 and on notes which possess g4 as one of their overtones, and (4) the quality or intensity of tone as a result of the method of striking the black and white keys. In judging keys on the piano the effects of constant errors in tuning, and in judging keys on bowed and wind instruments the variation in intonation of the fifths might serve as secondary criteria.
The essential criteria for absolute pitch memories vary from writer to writer. Writers are fairly agreed that the muscular accompaniment cannot be wholly responsible for these judgments. Overtones or complexities of tone are rejected by Baird, and are held to be important by von Kries and Köhler, who explain the discrepancy found for singing tones as due to the influence of vowel sounds which continually shift the register of the voice, and also by Boggs, who believes that they lead us to a knowledge of the extended tonal system, comparable in many ways to the spectal series. The place of frequency and of practice in establishing memory for pitch is much disputed. Stumpf finds it important, provided other criteria are present. Von Kries thought it reduced the limits of the unrecognizable, but never to the extent of converting an indirect judgment into a direct judgment. In Meyer's experiments practice developed a temporary ability which soon was lost through disuse. Abraham thinks practice may be beneficial with some people, wholly unnecessary for others and quite useless for still others. Baird denies that any evidence exists that training will originate the ability if it is not to some degree present already. On the other hand Rupp and Köhler agree that repetition will produce a firm lasting impression which according to Rupp may be either auditory or kinaesthic.
The ultimate basis for absolute pitch judgments is finally (1) for Stumpf the inexplicable individual coefficient, (2) for Abraham either exceptional fineness of the sensory apparatus which enables an individual to recognize separate tone qualities in their finer differences, or certain unique cerebral conditions, (3) for Baird a discovery of the distinctive quality present in every c, in every d, etc., and (4) for Watt the attribute of order which is inseparable from every auditory sensation. This may be overshadowed by circumstances and is probably preserved either by an individual's greater delicacy of volumic outline or by a more highly favored auditory disposition.
Observers who were already trained to some degree in introspection were selected to take part in the experiments. The nine members of an advanced laboratory course in psychology and two instructors in the department formed the first group of observers in the practice series. Group 2 was made up of eighty students, members at that time of the required introductory course in psychology. The majority of these students were juniors, a small number were sophomores and seniors. They ranged musically from a few who excelled in violin or piano study in the department of music through varying degrees of ability to a few who had had no training of any kind or interest in music. Although this group, totally unselected, taken from a required course at the college, represents as widely distributed a sampling as is possible in a college community, it has, however, already been subject to much selection of entrance and cannot be taken as representing the average person. The training in analysis and introspection which the observers were obtaining in their psychology course was believed to be a valuable asset for this study. Group 3 contained three selected members, a junior and a sophomore of exceptional ability in music, who possessed an evident degree of absolute pitch memory, and the instructor in Ear Training and Harmony classes under the Department of Music, who did not possess memory for absolute pitches. During the summer tests were given individually to observer Bd, who had had considerable musical and psychological training.
The members of Group 1 took part in the first series of practice experiments. The method of conducting these tests was as follows: The observer was seated with her back to the piano, facing a cardboard piano keyboard which bore the symbols for the different octaves.
A new upright Knabe piano tuned relatively high (a1 = about 445 v. d.) was used in all the different series of tests unless otherwise specified. The piano was located in a music practice room containing no hangings to soften its exceptionally clear resonant tone. During the year it was used only by the observers in these tests, and was tuned at frequent intervals.
The experimenter seated at the piano held a list of the 88 piano notes arranged in random order avoiding octave sequences and any sequence less than two octaves apart. (About fifteen of these lists were compiled during the course of the experiment.) The experimenter gave a signal, played a note mediumly loud and with a stop watch noted the time necessary for the observer to respond aloud with the name of the note. The note was repeated as often as the observer wished to hear it. As soon as the response and the time were recorded by the experimenter, the next note was sounded, continuing in this way until all 88 notes were given. A sitting lasted from about twenty minutes to forty minutes according to the speed of the observer.
Each of the ten members of Group 1 was given an individual preliminary trial with instructions only in regard to the distinctive symbols for each note. The notes were to be definitely located within their proper octaves. Before this trial the observers were allowed to play a few moments on the piano in order to gain a general idea of the quality of its tone. At the close of this first sitting the group was divided into two sections.
Six of its members were instructed to practice the entire keyboard, using this piano always, for about forty minutes a week, in four ten minute periods, if possible, and to attempt to devise some method by which they might be able to retain the pitches of the different notes. Memory for absolute pitch without reference to any secondary criteria was to be the goal, but any method might be used to reach this. Tests followed weekly the periods of practice throughout the greater part of the college year, 1917-1918, with some slight irregularities. At the end of each sitting introspections were written by the observer, especially regarding the method attempted in practice and its usability in the test. After a few weeks the writer acted as experimenter for all the other observers throughout the remainder of the investigation. Each of the other observers was at some time experimenter when the writer was observer. This brought about a fair uniformity of general procedure. The experimenter attempted always to employ a constant method of striking the notes producing equal degrees of intensity for the full range of notes. The duration of the notes differed for the different observers. Some asked for a number of quick repetitions, others preferred to have the tone ring out without interruption. If the response was immediate the sound was at once stopped; if there was hesitation, it was continued until the note was named.
Four members of Group 1 undertook a somewhat different procedure. Instead of attempting to familiarize themselves with the entire keyboard at once, they began with a single octave, the once accented octave, and increased the range gradually, adding first the next higher octave, then the next lowei~ octave after practicing for two weeks before each new addition. The presentation order of notes used by the experimenter was as varied as was possible, but at first, when the range was small, it was necessary to have an interval of fifteen seconds betweeen the notes during which time the observer's attention to the previous note was distracted by unharmoi~ious chord combinations extending over a wide range. Aside from this difference test II was conducted in the same manner as test I. This test continued through a part of the academic year 1917-1918.
t the same time a test was begun in which the 31 notes on the violin, from a-flat to d3, were used instead of the 88 piano notes. One observer from Group 1 carried this through as a practice experiment for half the year, then later joined the group in test I. The method of procedure was identical with that of test I. Another member of Group 1, an excellent violin student, produced the violin notes in the earlier tests and at first during the practice periods. Later the writer was the experimenter and the observer practiced herself on the violin.
During the middle of the year all the members of Group 1 were similarly tested once on the pipe-organ. Four stops were used: the flute, the diapason and the viola stops with 60 notes each, and the oboe stop with 42 notes.
At the close of the practice series with Group 1, nine of these observers attempted to reproduce the pitch of c1 and a1 singing into a Seashore tonoscope. Three trials were made for each note at wide intervals apart. The subject was instructed not to "feel around" audibly with her voice to reach the pitch, as for example, to sing the extremes of her vocal range and estimate the pitch by that means. She was to sing directly with but slight modifications the pitch which she believed to be approximately c1 or a1. All of the subjects had had opportunity during the year to use the tonoscope, which had been adapted by Professor D. C. Rogers for the high pitches of women's voices, and gave readily clear readings for these pitches.
(a) This test extended through the period following the spring vacation to the end of the college year. The eighty members of Group 2 were observers in this practice series. It was necessary that the procedure differ somewhat with so large a number of observers, hence the experiment was adapted for a group test in which about twenty observers could take part at one time. They sat with their backs to the piano facing the card keyboard and kept themselves a written record of their 88 responses. They were asked to attempt to place the note as near as possible to its actual position in every case.
The experimenter (the writer) presented the notes at fixed intervals, one every twenty seconds (this interval seemed to be a fair average judging from the results of Group 1, which was allowed unlimited time), sounding each several times during the first 10 seconds, then pausing 10 seconds before striking the note. This made a trial last exactly 28 minutes. At the end the observers wrote introspections regarding the various mental processes involved in the judgments. These were read each week and criticized from the point of view of accurate psychological analysis.
The observers were given two preliminary trials without practice and six other trials at intervals of a week apart, following two ten minute periods of practice. The same Knabe piano was used both for the weekly practice and the group sittings. The correct notes, the semitone errors and the octave errors were designated in red after each trial to serve as an index to the observer of her achievement. Suggestions as to advisable methods of practice, based on results from Group 1, were made to this group. Further each observer was assigned a certain note (the observers' names were arranged alphabetically according to class, and the notes were distributed to them in order from A3 to f#4) with which she was to make special efforts to become familiar. It was recommended that she think of her own note in a definite setting as belonging to a certain chord or scale, or possibly as the beginning note in some piecer They were to acquaint themselves with the general range of the piano and the tone-quality of each octave, and endeavor in some way to fix the individual notes in their memories, so that taking notes at random they could assign to them names with some degree of accuracy.
At the close of the practice series the following questionnaire was given to the observers from Groups 1 and 2:
MEMORY FOR PITCH.
Training.
If you were to be graded on a scale of ten, where would you place yourself for (1) musical ability, (2) musical appreciation?
What instruments have you studied, and how long?
What vocal training have you had?
Have you taken ear training or harmony courses?
Have you a good, fair or poor memory for music?
What was your threshold for pitch discrimination? (The pitch discrimination of a large number of the observers had been obtained at a class test earlier in the year.)
Are other members of your family musical or unmusical?
Type of Imagery. (Adapted from Seashore's tests for imagery, Elementary Experiment, ¼ Psychology, 1908, pp. 107-110.)
Answer the following questions by writing after the question the number which denotes the degree of vividness characteristic of your image. Follow the order: I 1, II 1, III 1, I 2, II 2, III 2, etc. Compute the averages for each type of imagery.
Degrees of Vividness.
0. No image at all.
1. Very faint.
2. Faint.
3. Fairly vivid.
4. Vivid.
5. Very vivid.
6. As vivid as in perception.I. Visual.
1. Can you imagine the color of (a) a red rose? (b) a green leaf? (c) a yellow ribbon? (d) a blue sky?
2. Can you imagine the brightness of (a) a white teacup? (b) a black crow? (c) a gray stone? (d) the blade of a knife?
3. Can you image the form of (a) the rose? (b) the leaf? (c) the teacup? (d) the knife?
4. Can you form a visual image of (a) a moving express train? (b) your sharpening of a pencil? (c) an up and down movement of your tongue?
5. Can you image simultaneously (a) a group of colors in a bunch of sweet peas? (b) Colors, forms, brightnesses and movements in a landscape view?
6. Can you compare in a visual image (a) the color of cream and the color of milk? (b) the tint of one of your finger-nails with that of the palm of your hand?
7. Can you hold fairly constant for ten seconds (a) the color of the rose? (b) the form of the rose?II. Auditory.
1. Can you image the sound of (a) the report of a gun? (b) the clinking of glasses? (c) the ringing of church bells? (d) the hum of bees?
2. Can you image the characteristic tone-quality of (a) a violin? (b) a cello? (c) a flute? (d) a cornet? (e) an organ? (f) an orchestra?
3. Can you repeat in auditory imagery the air of (a) the Star Spangled Banner? (b) the Marseillaise?
4. Can you form auditory images of the intensity of a violin-tone (a) very strong? (b) strong? (c) weak? (d) very weak?
5. Can you form auditory imagery of the rhythm (a) of men's marching to the beat of a drum? (b) "Dixie" or other air played? (c) "Tell me not in mournful numbers" spoken by yourself?
6. Can you form auditory images of (a) low tones on the piano, high tones, those in the middle range? (b) your own note on the piano? (c) middle c?IlL Motor.
1. Can you imagine, in motor terms, yourself (a) rocking in a chair? (b) Walking down a stairway? (c) Biting a lump of sugar? (d) Clenching your fist? (c) Dancing?
2. Does motor imagery arise in your mind when you recall (a) cutting cloth with a large pair of scissors? (b) a facial expression of fear? (c) two boys on a teeter-board?
3. Aside from the actual inceptive movements, do you get motor imagery when recalling (a) a very high tone? (b) a very low tone? (c) middle c? (d) words like "Paderewski," "bubble," "tête a tête?"
4. Can you form a motor image of (a) the weight of a pound of butter? (b) your speed in running a race? (c) the motion of a boat? (d) being swung around rapidly in a chair or in a swing?Method.
On hearing the note did you try to recognize the octave first, then the note, or did you try to name the note first, then place it in an octave, or were the two simultaneous? In all cases?
Did the note to be judged seem to have a setting in an imagined chord, scale or keyboard? If so, did you think of the chord, scale or keyboard in visual, auditory, kinaesthetic or any other terms?
Did recognition ever come instantly, without intervening images or associations?
To what extent were you conscious of overtones?
Did you notice perseveration of preceding tones? Did you judge the pitch of one tone in reference to the pitch of the preceding tone?
Did you notice a difference in quality between the sound of a note immediately after it had been struck and after it had sounded a while? Did you prefer to judge at the initial sound of the note or after it had been sounded a few moments?
Explain fully what meaning c has for you. Do you think of it as having distinctive quality, coloring, setting, emotional value, or relation to other notes? Go through each of the twelve notes in this way: (c, c#, d, d#, e, f, f#, g, g#, a, a#, b. How is c2 related introspectively to c1?
What sort of associative devices did you attempt?
Name some of the interferences which prevented the formation of these new associations, and some of the facilitations which aided their formation.
Did you feel special confidence in judging any tone or tones? Which ones? Did your practice aid in this?
By what method do you think you reached the best results?
What part of the keyboard did you find hardest? Which easiest? Why?
How would you criticise the length of interval or the manner of striking the notes in your own case?
Did you find the first, second or last third of the judgments in one sitting easier or harder than the others? Why?
Did you find the experiment interesting, indifferent or uninteresting?
(b) One year after the close of the practice series in which Groups 1 and 2 took part, twenty observers from Group 2 selected on the basis of availability and two observers from Group 1 were given similar tests as before. The members of Group 2 were given the group test and the members of Group 1 were tested individually with unlimited time for response. Introspections regarding the judging process were again written after the identifications were made.
(c) This same year Group 3, consisting of three especially selected music students, undertook a practice series similar to that of Group 2, in which the time for presentation and. response was limited to twenty seconds. A concert grand piano located in the office of a member of the musical department was used for these trials. Introspections were recorded at the end of each sitting and the questionnaire was filled out at the close of the practice series.
The ability to recognize the fundamentals of tonic chords evenly struck in the twelve different keys between c1 and c' and the improvement in this ability by practice was investigated during the summer of 1918 (for these experiments a relatively new baby grand piano was used). Two observers (a new observer, B, who possesses marked musical ability and observer G, who had taken part in the tests of Group 1) carried this on as a practice experiment. Each of the twelve chords was presented twice at a sitting, all twenty-four being arranged at relatively wide tonal intervals apart and given after pauses of a minute, in order to eliminate as fas as possible relative judgments. During the following winter one of the music students from Group 3 did the experiment as a single test in identification following the same procedure as was used for the previous series. Introspections were recorded during the practice tests.
Since the psychological laboratory at Smith College had at this time ready for use a set of instruments for detecting slight movements during the thinking process[18] it seemed worth while to apply these instruments to the field of pitch judgments. Consequently while two observers, members of Group 1, judged the pitch of 31 violin notes selected at random and played at uniform intervals of fifteen seconds, kymograph records were made of thoracic breathing, horizontal movements of the throat, tongue movements and the movements and changes in volume of the left arm. Both observers were familiar with the quality of sound and the technique of the violin and with the rather elaborate apparatus necessary for taking these records. About two yards of smoked paper was stretched from a roller over a very slowly rotating kymograph drum, so that it was possible to proceed without break through the test which lasted nearly eight minutes.
Professor Seashore suggested to the writer that an accurate test for detecting genuine absolute pitch memory would consist in presenting the observer with a tuning fork early in the morning before he had heard any music which might set up a temporary relative "set" and ask him to judge its pitch. Smaller differences than musical semitone intervals ought to be judged accurately if the observer's memory is strictly a memory for absolute pitch. A set of tuning forks containing the standard fork of 435 v. d. and the ten increment forks 0.5, 1, 2, 3, 5, 8, 12, 17, 23 and 30 vibrations higher than the standard furnished the material for the test. Each morning for 66 fairly consecutive mornings, as far as was possible :~fl suburban surroundings before hearing any musical sounds, observer G from Group 1 was given one of the eleven tuning forks, to sound as often and as long as was desired, and to pass judgment in regard to which of the eleven forks it might be. Each fork was presented six times in random order during the experiment. The observer was already familiar with the sound and range of the tuning forks and after each daily identification sounded all the various forks and listened carefully to their tones. The results of the test were not made known to the observer until the close of the experiment.
Since many of the investigations of this kind had begun their study of memory for tones by using first a small number of notes and gradually increasing the number, it seemed advisable to include this method as well as one by which the entire keyboard is attempted at each trial. After continuing the two methods in Group 1 for several months the piecemeal method was abandoned for these reasons. It was less interesting to the observers and called forth less responsiveness from them. The narrow range allowed little opportunity for variety in forming chord combinations in practice and for testing octave similarities and differences. This method also complicated the procedure of the tests somewhat. The different notes could not be presented at relatively short time intervals without distractions, for relative pitch operated too readily within the narrow limits. It made the interpretation of results a more complex affair which was disadvantageous in an experiment with a large group. Therefore when weekly tests on eighty observers were undertaken, simplicity in procedure became essential.
(Tables I through XII and the corresponding Figures 1 through 8 are based on the results from the tests using the 88 notes of the piano for identification.)
Table I.
The results given in Table I show that the errors of the observers from Groups 1, 2 and 3 approximate a normal curve of distribution. (See Figure 1). No sharp break occurs between any two divisions although the observers range from those who claim to be tone-deaf and those who had practically no musical education, through all stages including the unmusical who have received good training and the musically inclined who have had little training, to the especially promising students of music. The average error for the various members of these groups is less than an interval of a perfect fourth per note, for the poorest observer is a little over a minor sixth and for the best observer slightly over a semitone. Evidently the ability to identify notes is not an all-or-none trait, but may be found in all grades of accuracy. Even the least successful observers are able to assign positions to notes within certain relatively narrow limits.
Figure 1.
Frequency-Distribution of Error per Note measured in Semitones and
averaged from Total Number of Trials from Groups 1, 2 and 3.
Table II.
The curve showing the frequency of errors for the first trial (See Figure 2) assumes also the general form of the probability curve. After a period of practice the distribution remains approximately the same, although the central point has moved about 100 semitones nearer the line of no errors. (See also Tables II and III.)
Figure 2.
Frequency-Distribution of Error per Note measured in Semitones from First and
Last Trials of the Practice Series. First Trial in Broken Line. Last Trial in
Continuous Line.
Table III.
The improvement per person, however, was not as uniform as this graph might indicate, for using the Pearson formula for the coefficient of correlation2 to obtain the degree of relationship between initial and final trials in the practice series as measured by the size of the error, it is found that in Groups 2 and 3, r = +.439 p. e. .06, and in Group 1, r = -.132 p. e. .219.
Certain individuals improved rapidly after a poor beginning, others who did better in their first performance gained slowly in comparison. This is most marked in Group 1. An important reason for the difference in the correlation of Groups 2 and 3 and that of Group 1 lies in the fact that the period of practice varied greatly among the observers in this latter group, some continuing this special form of the experiment for only six trials, others for fifteen to twenty-four trials. The longer, the periods of practice the more chance for accentuating the factors of individual difference. Also those who began at a high level of ability had less chance for conspicuous improvement than the less able ones.
Greater deviation from the normal curve of distribution is shown in Table IV, Figure 3, based on individual records for correct notes, than in the curve for error distribution. The curve is skewed toward the side of little ability and is very irregular at the opposite side. On the whole the observers in Group 1 whose practice extended over longer periods average much better than the observers in Group 2 whose practice lasted six weeks. The relationship between the average number of correct notes and accuracy as measured by the size of the average error proved to be r +.602 p.e. .047 for Groups 2 and 3, and r= + .895 p. e. .044 for Group 1. It will be remembered that the tests as given to Groups 2 and 3 were in the form of group tests with a definite time limit for response. The observers in Group 1, on the contrary, were tested individually and given unlimited time for response. This factor together with the variation in length of the practice series would tend to produce a greater degree of correspondence between the general correctness of response as measured negatively by the size of the errors and positively by the number of correct notes. Since this high correlation is found between the two methods of grading, it makes it possible to use either of the two more or less interchangeably as a basis for estimating an individual's record.
Figure 3.
Frequency-Distribution of Correct Notes averaged from Total Number
of Trials from Groups 2 (Continuous Line), 1, added to Group 2 (Dotted Line),
and 3, added to Groups 1 and 2 (Broken Line).
Table IV.
The Frequency-Distribution of correct notes in the first trial is also skewed toward the poorer extreme. (See Figure 4, Tables V and VI.) Practice draws the entire curve over a little to the opposite side but does not change its original form. It seems even to accentuate individual differences by increasing the number of fluctuations in the curve for the last trial. This is in contrast to the fairly normal curve & distribution found in the curves of average error. This greater variety on the side of the curve representing greater achievement may perhaps be explained as the result of the advantages in general education and musical training which the observers in these tests have had.
Figure 4.
Distribution of Correct Notes in First and Last Trials of the Practice Series.
First Trial in Broken Line, Last Trial in Continuous Line.
Table V.
Although the members of Groups 1 and 2 represent as wide a sampling as is possible in a college community, it is however true that that community is already narrowly selective.
Table VI.
Improvement in naming correctly the individual notes is steady in the group as a whole and alters but little the form of the curve, but individual improvement is at times somewhat uneven. The correlation between the number of correct notes per individual in the first and in the last trials for Groups 2 and 3 is: r = +.845 p. e. .031 and for Group 1: r = +.516 p. e. .266. On the whole those who begin well are apt to be the ones to finish well, especially when the practice periods are of equal length. Where the length of the practice series varies greatly as occurred in Group 1, the record for the first trial cannot be taken as an accurate gauge of the results of different individuals after unequal intervals of practice.
Figure 5.
Total Frequency of Interval Errors obtained from all Records. Broken Line
represents Underestimation of Interval, Continuous Line Overestimation of
Interval.
Table VII.
It was of great interest to find the relative frequency of the different interval errors taken from over 700 tests in which the 88 notes of the piano were used. (See Figure 5, Table VIII) Underestimations of pitch are fairly consistently less than overestimations. The largest number of misjudgments were only a semitone too high or too low. The next lower frequency was found for the whole tone, then the minor third, the major third and so on down step by step. The larger the interval error the less frequently it occurred. Instead of a distinct rise in frequency for octave errors the curve continues downward, a little more slowly at that point than a few intervals before or a few intervals afterward. In the records of 31 observers out of 89, the frequency for the positive octave error rises one point or more above the frequency for the error of the major 7th interval. In only nine cases is this rise conspicuous and in only three cases does it occur among the negative interval errors. In four cases the frequency for the octave error rises above all preceding frequencies except, in one case, that of the semitone error, and, in the other three cases, that of the whole tone error. Not the slightest evidence is found in any record of a preference for errors of a fourth or a fifth, as is sometimes claimed to be the case. The major 3rd has the modal frequency of error in two cases, the minor 3rd in three cases, the major second in seventeen cases, and the minor second in all other cases (numbering 67).
The time for each response of the observers in Group 1 was taken by means of a stop watch. The average time per note in each trial was found for the five observers who continued the experiment by the same method throughout the academic year, and recorded in Table VIII. (See Figure 6, page 62.) Wide variations from trial to trial are shown in each record. C in her introspections admits that she followed very different methods on different occasions. This would account for fluctuating from 13.6 seconds per note to 18.7 seconds to 10.4 seconds. The desire to improve upon the accuracy of past records had a tendency~ to lengthen the time, for instead of making an immediate quick judgment the observers weighed their decisions several moments to assure themselves of the approximate correctness. Fatigue and changes in the level of the attention affected the speed of response. Many of the tests were given late in the afternoon when concentration on a task which taxed one's auditory perceptions to so unusual a degree was difficult.
Figure 6.
Average Time per Note in each Trial of the Practice Series for 5 Observers.
TABLE VIII.
The observer with the best record of accuracy in the test had the lowest average time, but the observer with the next best record had the highest average time. The observer who was second best in time had the least successful record of accuracy of the five observers. (See Table IX.) Comparing the average time and average accuracy measured by the amount of error in each trial of the practice series of these five observers, the coefficient of correlation in each case is as follows:
B r = + .028 p.e. .153
C r = + .528 p.e. .152
E r= + .807 p. e. .056
F r= + .308 p.e. .014
G r= -.216 p.e. .136
In the case of E, the longer the time taken for response the fewer the errors. There is but slight indication of this for C and F, none at all for B and the barest indication that the reverse is true in the case of G. On the whole the time per response is a very inadequate gauge of ability in these tests. Correlating the time per individual response with the degree of accuracy in G's trial 17, r = - .037 p.e. .071. In this trial 50 of the 88 notes were correct and only one octave error occurred which might over-emphasize the size of individual errors.
Figure 7.
Average Time for Correct and Incorrect Notes in Seconds. Continuous
Line represents Time for Correct Notes, Broken Line Time for Incorrect Notes. 5
observers.
Table IX.
The average times for correct and for incorrect notes found from all the trials of the five observers show a slightly longer time for the incorrect responses in four instances and a longer time for the correct responses in one instance. (See Figure 7, page 63.) This last observer admits that she made use of relative pitch in a large measure; and in consequence of hei roundabout method all her times are long. It is natural that the correct judgments should be the somewhat quicker responses. The observers knew their own limitations fairly well and would pause to consider certain notes in the keyboard which were invariably difficult to judge and try to find in them distinguishable pitch or other tonal characteristics which might facilitate judgment on later occasions.
Figure 8.
Practice Curves for Observers B, C, E, F and G, based on Average Error per Note
for each Trial.
Table X.
The reduction in error in the individual practice curves of the five observers of Group 1 is exceedingly irregular. (See Table X, Fig. 8.) The interruptions caused by the vacation and mid-year examination periods are responsible in part for this, although variations in method and attitude are more important factors. All observers made definite initial progress. With possibly one exception no definite plateaus occur at any place, and the curves indicate on the whole a tendency toward improvement which at the end of the test had by no means reached a level. F alone did not progress in her last five trials. Her method, which was based mostly on the use of relative pitch whenever possible, or what seemed to be non-essential associative devices, may have hindered her improvement. G's lack of progress during the summer is partly the result of the use of a piano with a wholly different quality of sound, and partly the result of the inability to sustain a high level of attention on oppressively hot days.
In order to study the effect of the amount of time spent in practice on improvement, and the effect of previous musical training on improvement, the Pearson coefficient was obtained from the data given by 84 members of the three groups. Improvement was measured in an arbitrary manner. Because of the fact that those who started out poorly had much more opportunity to improve than those who began well, a definite advantage increasing in arithmetic progression was added to the actual amount of improvement of the last trial over the first trial in each case.
The largest total amount of error found in trial 1 was 745 semitones. Using this as a starting point, those having an error of 745 and 744 in their first trials had zero added to their amount of improvement. The observers starting with 743 and 742 errors measured in semitones received an increment of one point each, those starting with 741 and 740 errors an increment of two points each, and so on with regular increase to the observer having the smallest amount of error which proved to be 223. To the improvement in this case was added 261 points.
The correlation between this arbitrary amount of improvement and the amount of time spent in practice gave r = + .391 p.e. .061; the correlation between improvement and previous musical training gave r = + .205 p.e. .049. In both cases the positive relationship is barely existent. Evidently frequency of hearing the piano notes is alone no guarantee that memory for absolute tone will result. It must be noted that the specifically directed practice for this experiment gave a slightly higher correlation with improvement than the general musical training of past years gave.
The average degree of accuracy per person was corr~Thted with the number of years of musical training and gave r = + .436 p.e. .055. This shows some tendency for the musically trained to make a smaller amount of error on the whole than the musically untrained.
Sixty of the observers had taken part in a group test for pitch discrimination, in which the standard set of tuning forks was used. The standard fork and each of the ten increment forks was repeated ten times and 70% accuracy was taken as the threshold for discrimination. The results from these tests were correlated with the average error of these sixty observers and gave r = + .376 p.e. .073. That means roughly that a low threshold has a slightly better chance for accompanying a record with few errors than a higher threshold. The best records were made for the most part by those with the keenest ears.
Table XI.
One year after the close of the tests with Groups 1 and 2, sixteen members of the groups were retested in a similar manner. Observers from Group 2 were given the group test with a time limit for response and those from Group 1 were tested individually with unlimited time (these observers were selected simply on the basis of availability, consequently include good, fair and poor observers). An examination of the results given in Table XI shows that one-fourth of the observers did better as measured by average error the following year than at the last trial of the previous year. One-half made a better record in the retesting than the average of thir practice series records, and fourteen of the sixteen in their retesting improved on their records for the first trials of the series. The correlation between the size of the error of the last trial of the practice series and the size of the error at the retesting gives r = + .68 p.e. .09. This indicates that the amount retained over a period without practice is to some degree proportional to the degree of ability acquired from the practice. Four of the six observers who said they had not attempted to identify notes during the year just past, made records poorer than the results averaged from the total number of trials of the practice series. Six of the ten observers who had made some attempts at tonal recognition in the year's interval made better records than the average record of their practice series.
The frequency with which the correct names were given to each note on the piano keyboard is given in Table XII. The c's have the highest frequency of correctness, then in order come a, b, g, d, f, e, a# (or b-flat), g# (or a-flat), and d# (or e-flat), c# (or d-flat), and f# (or g-flat). C5 has the largest number of correct responses. The next eleven in order are: A2, b4, a4, c1, c2, B2, a#4 (or b-flat4), A#2, (or B-flat2), g4, D1 and d1. The twelve in order with the smallest number of correct responses are: c#3 (or d-flat3), F# (or G-flat), g#3 (or a-flat3), G# (or A-flat), D# (or E-flat), d#3 (or e-flat3), C# (or D-flat), c# (or d-flat) and d# (or e-flat), f#1 (or g-flat1) and c#4 (or d-flat4), and f#1 (or g-flat1). Excluding the three notes of the subcontra octave and c5, the seven octaves arrange themselves according to frequency of correct responses as follows: four-accented octave, once-accented (or middle) octave, contra octave, twice-accented octave, small octave thrice-accented, and great octave. It is to be expected that the results from these groups of observers who did not at the start possess memory for absolute tone will be markedly different from results obtained from the selected, especially gifted group. However, if we leave out of consideration the subcontra octave and the four-times accented octave (which by pure chance the observers might name correctly more frequently than the central octaves), and give the remaining five their rank in this respect, the results from these groups coincide exactly with Baird's results (see page 21), namely:
Table XII.
The assignment of individual notes to the observers in Group 2 had definite value. First they aided in making the task more concrete and stimulating. Little stress was laid on the notes after they were assigned, for it was thought that emphasis on individual notes might divert the attention from a study of the entire range. The observers, however, took readily to the idea of mastering a single note and frequently practiced the other notes in relation to this one. Second the results from the notes assigned illustrate the value of specially directed practice. In comparing the frequency of right responses for individual notes with that for the average note, it is striking that the assigned notes were correctly named approximately two and a half times as often as the average note.
Figure 9.
Range of Positive and Negative Errors and Median Position for each
3-Semitone Division of the 87 Piano Notes.
Figure 10.
Average Error per Note per 3-Semitone Division based on 725 Trials from
Groups 1, 2 and 3.
Table XIII.
c5 was omitted in order to preserve the 3-semitone grouping.
The results from experiments in pitch discrimination show that absolute differences in discriminative ability measured in terms of vibration rates tend to remain constant over a limited range[19]. Hence an increase in keenness follows a rise in pitch when measured relatively, that is, in terms of a fractional part of a tone. These facts would lead one to expect a similar gain in accuracy in judgments of absolute pitch. The data, however, do not bear out this supposition. The correlation between average accuracy, based on the average error measured in semitones from 725 records, of the 35 "naturals" from the five octaves C to c5 and the absolute size of the semitone interval measured in terms of vibration rates, gives r = -.24 p.e. .024 (the overestimations and the underestimations per note were added, together and correlated with the semitone interval above and below each respective note). The accuracy remains fairly steady between C and f, where the average error is about five semitones, then improves between g and e2, c1 having the smallest amount of error, namely, 3.6 semitones, and from e2 decreases and remains with an error of slightly over five semi-tones up to c4. The median positions for the individual notes taken in groups of threes (Fig. 9) show remarkably little variation from their true positions.
Other factors were obviously operating against this adrnitted increase in discriminative ability. Frequency of hearing the notes in the middle range was undoubtedly a very important element. Loss of distinct changes in volume with rise in pitch might counteract the benefits derived from relative improvement in pitch discrimination. Rich tested for volume limens at three levels, 275 v.d., 550 v.d. and 1100 v.d., and from his results concludes that volume tends to follow Weber's Law[20]. Whatever the status of volume it proved influential in judgments of absolute pitch and a progressive lessening of its efficiency in these regions tested would affect the accuracy of pitch judgments.
The chief factor which can account for the sharp turns of the curve at c and at c3 (Fig. 10) is the "end-error." The largest possible negative error at c is 27 semitones, and the largest possible positive error at c is 24 semitones, owing to the extremes of the pianoforte. An error of approximately these amounts is found to occur fairly regularly throughout the intermediate range of notes. On approaching the extremes of the piano the size of the plus or minus error is necessarily reduced and the curve falls correspondingly.
Table XIV.
The experiments on the organ were undertaken with the idea of making a study of the effects of different timbres upon tonal judgment. Many difficulties were met in the attempt. The organ was less accessible than the piano and the range of the stops varied considerably, so that a comparison of results was difficult. Therefore these experiments were not carried as far as was originally intended. The results from three of the observers are given in Table XIV. The average error per note differs but little from the average error for piano notes. The flute stop has a slightly larger amount of error than that found in the first trial on the piano, whereas the other stops have for the most part less error than that of trial 1 on the piano and slightly more error than the average error of the practice series on the piano. All the observers when tested on the organ had the advantage of three months' practice in judging notes on the piano. Since the range of notes is smaller for the organ stops than for the piano, the observers had less chance for making gross errors with organ notes than with piano notes. This factor must be considered in comparing their results. The average time per notes for the four organ stops does not differ to any considerable degree from the average time needed to judge piano notes.
Table XV.
Co's progress in the violin practice series is similar to that of the piano series-- an irregular decrease in the size of the average error per trial together with an irregular increase in the number of correct notes. C and G were tested a single time in identifying the violin notes one year after the close of their long practice series on the piano. It is significant that but one octave error occurs in any of the results from these tests on the violin. Co often mentioned that the notes on the A and the D strings seemed alike, but never that octave differences could not be distinguished. Co's interval errors vary from overestimations of a semitone to a minor sixth, and from underestimations of a semitone to a minor seventh. C's interval errors extend to overestimation of a maj or third, plus one octave error, and to underestimations of a major sixth. G's interval errors are two semitone overestimations and four semitone and one whole tone underestimation.* In these experiments the accuracy of the pitch of the notes depends on the experimenter's keenness of hearing and technique with the instrument. Slight inaccuracies necessarily occur, which make these results in a measure less reliable than those from the study of the piano keyboard.
*G has always noticed the sympathetic vibration of the open string when that note is played on the adjacent string in one of the higher positions. This would invariably give a clue to the names of certain notes. The other observers apparently made no use of this factor in their identifications.
Two kymograph records measuring the breathing curve, movements of the larynx, movements of the tongue and changes in volume in the arm were taken during the tests for judgments of violin notes for C and G (see Figures 11, 12. The plethysmographic records were discarded because they did not give sufficiently clear readings). During the early part of the experiment C's records show little movement of the larynx or the tongue, and fairly regular although shallow breathing. The breath was usually suspended on hearing the sound until the judgment was made, as is characteristic during tense attention. Later on in the test more movement of the tongue and the larynx is found and the breathing curve becomes increasingly irregular. Absence of any gross movement, except at times during the initial adjusting period characterizes the interval for judgment.
Figure 11.
Kymograph Records of Movement during Period of Judging Violin Notes by
Observer G.
Figure 12.
Kymograph Record of Movement during Period of Judging Violin Notes
by Observer C.
G's curves show more general movement than those of C. The irregular crests of the erratic breathing curve with its periods of held breath indicates also very strained attention (due in part to the observer's interest in the production of the tones as well as in her own task). The curve for movements of the larnyx shows usually a gradual depression during the presentation of the note, indicating a lessening of pressure. The curve for tongue movement shows a fairly uniformly slight rise during the judging period, the result of pressure. On the whole there is comparative quiet during the interval between presentation and response irt contrast to the continual slight movements recorded at other times. Kinaesthesis, was, therefore, a negligible factor in this experiment in identifying notes. The average time for judgment was 12 seconds for C and 6 seconds for G, which corresponds closely with the average judging time for piano notes.
Table XVI.
The practice series of observers Bd and G for judging the fundamental tone of the twelve tonic chords based on each note within the middle octave show an initial relatively low ability and fairly regular improvement. The most frequent errors for Bd are in order: semitone, whole tone, minor third, major third, fifth, fourth and augmented fourth; for G: semitone, whole tone, minor third and fourth. H's errors consisted in two semitone errors. Only Bd responded at any time with names of other notes contained in the chord, and only in trial 1 do responses of the fifth occur. Here as in the tests with single notes the errors on the whole were less frequent the larger the interval. Both Hr and G did relatively poorer in this test than in the tests for judgments of single piano tones in the same tonal region. Only two semitone errors out of 84 responses occurred in Hr's judgments in the middle octave and G's errors in this region, out of 276 responses, seldom exceeded a semitone. This is contrary to the views expressed by von Kries, Abraham, Boggs and Köhler. Stumpf reports a similar case. All of the observers in this test had had sufficient musical education to make chord analysis comparatively simple. Some new factor of fusion was entering in to complicate this situation rendering the new tonal blends baffling. That these difficulties could be met by continued practice is evidenced by the improvement in the successive trials.
A certain amount of ability in identifying the ten increment and standard (435 v.d.) tuning forks was shown by G (Table XVII). The results for the higher pitched forks are well beyond the limits of pure chance. When the increment from fork to fork is very small the judgments seem little better than guesses. The number of times each fork was responded shows a preference for naming the 3 v. d. and 5 v. d. increment forks. This may be due to the fact that the standard fork (435 v. d.) was always thought of as a1, which has a somewhat shifting value, a1 at concert pitch being 440 v. d. and 435 v. d. for ordinary purposes. Hence the 3 v. d. and 5 v. d. increment forks might on this account be confused at times with the standard fork.
The ability to reproduce a tone depends to as large a degree on one's ability to sing the note that one is imagining as on one's accurate formation of an image. False attempts are confusing and interfere with the voluntary production of adequate images. The nine observers who took part in singing the notes c1 and a1 into the tonoscope were more successful as a group with c1 than with a1, both in regard to the average vibration rates and the average deviations (Table XVIII). The three violinists F, B, and G, and Co who had completed the practice series for the violin, have the best results of the group for a1. It is natural that a1, the note to which violins are tuned, should persevere with some accuracy in their minds. The large amount of underestimation in singing a1 is undoubtedly due to the increased muscular strain in producing higher notes. The largest amount of error for c1 for all but one observer, A, does not exceed a whole tone; for, a1, with the same exception, is nearly a major third. Observer A had the poorest record of any member of Group 1 who took part in identifying piano notes. The relatively small errors of the other observers do not offer much ground for comparison with their results in the tests in judging piano notes. The variations in standard pitch of the different pianos make it difficult to arbitrarily select 435 v. d. or 440 v. d. as the basis for grading. Generally speaking in this test the best observers have also been those who excelled in the tone identifications, and the poorest observers those who were relatively less successful in judging piano notes.
Table XVII.
Table XVIII.
The responses to the questionnaire, which are given in full on pages 30-33, bring out many striking features. First, the observers in Groups 1 and 2 have had distinct musical advantages. Only four observers had no practical music training of any kind. A summary of the frequencies of individual ratings for musical ability on a basis of 0 to 10, from 74 observers is as follows:
| Ratings | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Frequencies | 7 | 2 | 4 | 6 | 12 | 14 | 6 | 14 | 7 | 2 | 0 |
The frequencies of rating for musical appreciation are as follows:
| Ratings | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Frequencies | 1 | 0 | 1 | 1 | 3 | 13 | 9 | 15 | 19 | 9 | 3 |
The median frequency for musical ability falls on grade 5, and for musical appreciation on grade 7. The frequencies for individual estimates of good, fair and poor in musical memory are as follows:
| Memory | Good | Fair | Poor |
| Frequencies | 22 | 38 | 14 |
The tests for imagery yield the following results:
| Most Vivid Type of Imagery |
Visual |
Auditory |
Motor |
Mixed |
| Frequencies |
48 |
10 |
8 |
8 |
Half of the observers who possess a predominance of auditory imagery rank very near the top in ability to identify notes, the others are scattered throughout the middle ranks. None with good auditory imagery are found near the poor extreme in this ability. No similar correspondence is found for the other types.
The literature on tonal identification assumes that people with marked ability in this respect always recognize first the note-name, as c or d, then after momentary reflection give it a place in an octave, as c3 or d4. The questionnaire reveals the fact that fourteen observers were accustomed to identifying the note directly, not for example as some d or other, but as d1. The observers who made this a single process include some of the most able in identification and others less able. Seven of the 79 reporting recognize the names of the note first and later its octave. Three of these seven were notably good in their judgments, the other four only fair. Forty-six observers named the octave first and then gave the note. Twelve occasionally named the note first, occasionally the octave first.
In reporting direct or indirect judgments twenty-six usually gave the immediate or direct judgment, thirty-four usually delayed judgment for consideration, ten at some times gave direct judgments at other times indirect judgments.
Thirty-eight preferred strongly to judge the note from its initial sound, immediately after it was played (which necessitated many short repetitions of the note), twenty-five preferred to have it sound a few moments before trying to make a judgment, and two were impartial. Those who judged from the initial sound had on the whole the best results.
In response to the question regarding the setting which each note was given, forty-five gave the note a spatial position on either an imagined piano keyboard or on the cardboard chart placed before them. Seven thought of it as belonging to a particular scale, nine as belonging to a chord, one as the fifth of a chord, others as the fundamental of a tonic chord, and others as the tonic or the dominant seventh of a chord followed by its proper resolution, ten combined a number of the settings already mentioned, and five claimed to have no definite namable setting for the note. Several referred the note frequently to imagined violin notes, and one had an imaginative ladder scheme which represented the ascending and the descending scales. Those who gave the notes definite settings in chords had on the whole the best objective results.
The aids to recognition which are enumerated in the reports are, (1) kinaesthetic sensations (vocal motor and other forms), (2) knowledge of the vocal range, (3) auditory memory of the individual notes assigned, (4) auditory images of the tonic chord or other chord combinations with harmonic resolutions, (5) auditory images of notes a third or a fifth or an octave above the note presented, (6) auditory memory of the violin a1 and other notes, and the piano c1, and in general the c's, b's, and f's on the piano, (7) recollections of certain pieces, (8) recognition of certain tonal characteristics, and (9) tonal volume. The hindrances to recognition enumerated in the reports are, (1) a shifting standard of some pitch or pitches in memory, (2) distracting noises (including distant music, occasional faint humming, not permitted in the group, the sounds of lawn mowers and bursts of song from nearby birds, which could not at all times be eliminated), (3) wavering of the attention through fatigue or distraction, (4) the unfamiliar tone-quality of the piano, and (5) the inability to produce voluntarily auditory images.
The majority of the observers regarded the first part of the sitting as the easiest because then 'they felt fresh and could control their attention better, and the last part of the sitting the hardest, because as the experiment continued their imaginations flagged increasingly through fatigue and distraction. A few observers felt that the task grew easier during the course of the sitting, as they overcame the first strangeness of the situation and adapted themselves to a kind of temporary auditory set which facilitated judgment.
Twenty-seven observers report that they found the middle range of the piano the most difficult to judge and the extreme octaves the easiest. Twenty-five observers found the middle range the easiest and the low notes hardest, and eight observers thought the reverse to be the case. (See Table XII). In explanation many said that the middle octaves were more familiar to them on account of the frequency with which they had heard them, and on account of their ability to form auditory kinaesthetic images of notes in this range. On the other hand, many said this range was the hardest for them to judge because the character of all the sounds was very much the same. The extremes were claimed to be difficult because of the lack of definite pitch there. Others noticed distinguishable characteristics at the extremes not found in the middle of the keyboard. The fact that within limits underestimations could not be made at the lower end of the keyboard or overestimations at the upper end eliminated a source of error found in the middle range.
Forty-five observers expressed themselves as having enjoyed the experiment throughout its course. They were interested in watching their progress and anticipating results. Fifteen found it very difficult and tedious. Eleven claimed to have maintained a neutral attitude.
A survey of the introspections recorded by the observers at each trial throws light on some of the problems involved in tonal recognition and possible methods of meeting them. No attempt to direct the course of the introspections by suggestion was made at any time. As was stated, these reports were read each week and criticized in regard to clearness of expression and completeness in order to stimulate the observers to attentive analysis. All the observers had used Titchener's A Beginner's Psychology and were familiar with his terminology in the chapter on Sensation. It is striking how few allusions are made directly to the pitch of the notes. Several observers write:
"Tried to get the general range and tonal qualities of the different piano notes. The quality gets deeper and more resonant as the notes go down. Each octave has a different quality of its own."
"After practice noticed that the different notes seem to have different volumes."
"The volume of the note helps to place it in the right octave."
"The last octave has a certain metallic ring."
"Prefer low notes because they jar less than high ones and can be attended to better."
"The difference between octaves is one of intensity." (This observer claims to be tone-deaf.)
"Tone color helped."
"The higher notes do not last (resound) as long as the lower ones. Many notes almost pained the ear."
"Listened for the vibrating quality which differentiates the high notes from the lower. High notes are thin, the low ones deep and full."
"Determined approximate position by volume."
"Nearly always judge the notes in relation to whole keyboard rather than to a particular note. Have a feeling of spacing. There is a certain point at which the note must lie."
"A sense of position seems to be the only guide. I hear the sound and then by reasoning place it where it seems to belong on the keyboard. Octaves help little. I have simply a notion of the total position."
A few of the difficulties encountered were:
"Octaves at the center of the piano are harder to distinguish than those at the ends."
"Seem to be a great many notes in the small octave."
"After listening to a number of notes, it sounds as if the same notes were repeated many times, especially those near the middle of the piano."
"Too many notes between c and c2. Do not know what to do with them all. Forget that the octave c2 to c3 exists."
"Practice seems to make many notes sound alike."
For the most part practice tended toward impressing octave differences on the observers. "Practice makes it easier to decide on the octave than before, but it is just as difficult to find the right note in the octave." (This observer had the poorest record of all.)
Various methods were employed to overcome these difficulties.
"Tried to recall c1 and judge from that."
"At first tried to refer all notes to c1."
"Judge from memory of the notes in the middle octave. The lower and higher notes seem to resolve into one of the notes between c1 and c2, not when first sounded, but after the second or third striking. Judge better by listening for overtones. Keep in memory the tone quality of c, e and g."
"If I thought the note sounded like f#, I imagined g as following it and estimated the probability."
"The first, third and fifth notes in the octave have a more finished tone than the others, which helps in locating the note."
"Some notes have a familiar sound, but I cannot always tell whether it is a c or an f."
"The notes begin to have a definite letter attached to them when they are struck. I do not have to hunt for a place on the chart as was necessary at first. Something familiar in the quality of c."
"This time I did not have to think so long what note it might be. A name just seemed to come into my mind."
The members of Group 1 had more opportunity to attempt and develop new methods in their longer series of practice. Quotations from their weekly introspective reports show their progress.
Observer Co, practice series for the violin.
Trial 1. "No particular method. All guesses, I think."
Trial 2. "Still guesses. Tried to use relative pitch without much success."
Trial 3. "The c's are getting easier to identify, also the f's which have a 'squeezed in' compressed quality as a rule."
Trial 7. "Several times I fdund myself having a feeling of familiarity when a certain note was struck. Usually I thought it was c or a, or g or b, and then had to decide, sometimes by humming, which of the two it was. With the other notes, I identified the string on which they were being played and then the position of the note."
Trial 9. "Although I succeeded in confusing the d and a strings to some extent, the notes on these two seemed to possess something of a 'quale'."
Trial 10. "Usual method now is either (1) immediate or almost immediate recognition, after which I usually try to verify; or (2) visual image of string and kinaesthetic imagery with little auditory; or (3) absolute blank, followed by an attempt to follow out procedure (2)."
Trial 11. "It is seldom a note is absolutely certain in my mind upon hearing it. Usually I have to go through a series of checks after I have decided what it is. In general these checks are kinaesthesis (vocal motor sensations), related auditory images and a few visual images in connection with the auditory."
Same observer Co, practice series on the piano, following the series on the violin.
Trial 1. "All the octaves save the middle one and a few notes on either side were guesses. With the notes of the middle octave, I used kinaesthetic sensations and actual humming to identify them. The other notes I tried to relate to the corresponding notes in the middle octave."
Trial 2. "Related the notes to those on the violin. G seems to me to be the lowest note which has real 'roundness'."
Trial 4. "Tried to do away with the humming in my judgments this time. Took my snap judgment and then tried to find out the peculiar 'quality' of that particular note, and fitted them together. If they did not fit, I had to discard my snap judgment and try the humming method or else let it go as a mere guess."
Trial 6. "The notes seemed to have 'qualities' for me for the first time. It seemed as though I could have finally distinguished many of them if I had taken time to associate that 'quality' with the same note in the middle octave."
Observer B, practice series on the piano.
Trial 1. "Tried at first to relate the notes to a remembered c'. Found I could not remember c', when another note was played. Noticed I could remember the violin a1, so related notes to it. Related the extreme octaves to the middle octave."
Trial 2. "When a note was struck I hummed it in the middle octave calling it do, and hummed the me, sol, do above."
Trial 13. "The following factors help me in naming a note, (1) humming the note and its diatonic scale. If the note is not within my range, I give it a position in the scale I can hum, and later place it in its right octave. (2) I seem to tell whether the note is a sharp or a natural by the way it is struck. (3) The highest and lowest notes I tell by the amount of tone."
Observer E, practice series on the piano.
Trial 1. "Felt absolutely helpless when I first heard the notes. Could not tell one octave from the other. I had an idea of c1, but could not tell when it was heard."
Trial 2. "Felt a little surer of myself. During the practice periods of this week I spent most of the time on the middle, the second and the highest octaves, trying to detect slight differences between notes. Certain notes like e and / seem to have the same quality, which make them difficult to distinguish. I gave up the idea of singing the notes and attempted to tell directly by their sound. This seems to be more satisfactory."
Trial 4. "Notice that the thrice-accented octave has a marked difference in quality from the others. It is more rasping."
Trial 10. "The placing of the octave does not bother me a great deal. I felt fairly sure of the octaves except the two lowest."
Trial 11. "The middle octaves I sing to be sure of the notes. Others I judge entirely by their pitch. By having the note repeated if I am not sure at first, I can get an immediate judgment or nearly that."
Trial 12. "Feel that I am improving. The quality of the note rather than the pitch locates it for me in the scale."
Observer F, practice series for the piano.
Trial 5. "When I started this trial I had an auditory image of a1 firmly in mind, as a result of previous practice. The first few notes were correctly named through relative pitch. Then a low note threw me off. A great deal of the time I first listened carefully to the sound of the note and tried to think what note it was without using indirect means, and then compared the result with a muscular sensation in the throat. Some times no comparison was necessary, for I was certain what note it was without any comparison. Whenever I came across one of these notes of which I felt certain, which were a's, d's, e's, and c's, I used relative pitch with the succeeding notes until some wide interval skip between notes put me off."
Trial 6. "Depended mostly on humming the note in the singing range. Sometimes just listened to the notes. Got more right by the latter method."
Trial 10. "The notes now seem to have different qualities-- some are open, some vibrate more than others and some are dull. They also seem to have more place on the scale.
Trial 14. "It is very difficult for me to keep my attention fixed. My ears feel strained listening for overtones or purity of tone. I recognize the sound of some of the notes and then forget the name to be associated with it. It seems an interminable task to differentiate between so many notes." (F had twenty-five correct judgments in this trial.)
Characteristics which F associated with some of the notes:
C real tone not heard.
G funny overtone wave.
D weaker after it is held a few seconds.
E-flat very strong.
E not as strong as E-flat.
A buzz or low rattle-- hard.
B-flat thump when struck.
B funny sound when key is lifted.
c flats after a second.
c# second overtone rings out.
d flats when struck-- strings not tuned together.
e-flat deep, hollow sound.
c1 flat--no overtones--harsh.
c#1 after a few seconds part of tone flats.
f#1 rattle when played softly.
g#1 thump.
a1 open, rings out, not as much as e2.
d2 rings out but softer.
d#2 hollow when key is lifted.
e2 rings out more than c2.
g4 sharp as a knife.
a4 very sharp and clear.
b-flat4 muffled.
b4 woody, longer sound than c5.
c5 woody.
Observer C, practice series for the piano.
Trial 1. "A feeling of amusement at my helplessness in such a situation. However, a strong determination to do as well as possible. When seated before the scale, listening for the note, my eyes were resting upon the middle of the scale. When the note was struck my eyes turned either to the right or left, according to whether the note sounded high or low, and continued to move until they seemed to reach the note heard. There was no conscious analysis of tones. But my idea of the position of the note was so definite in mind that my eyes readily stopped at some fixed place, and the judgments were made with slight hesitation. This made me conclude that discriminations need not be due to conscious comparison, but that a method of training to develop immediate judgment would be adequate."
Trial 2. "During period of practice I sounded the various C's on the piano in order to get a clear idea of the characteristics of the different octaves. I j~oticed when the low notes began to have distinct overtones and where the high notes disappeared into their more prominent overtones. I tried to differentiate the timbre of the lowest two bass octaves and also that of the highest two octaves. At the end of the practice I felt confident that at least I could place a note in its proper octave.
"This test was made after my partner had been tested. She used a method of conscious comparison, humming to get the interval more clear in mind. Her results were on the whole quite accurate. I realized that that method was probbably more reliable than mine, so I undertook my own trial with some hesitation. At first I tried to use her method, but realized that I had not had sufficient training for it. I then resorted to the method of immediate judgment which had previously appealed to me. I found I was reduced largely to guessing and that my practice to try and differentiate the octaves had amounted to little. The lowest and highest notes were not as distinct from each other as I had anticipated. Feeling of discouragement."
Trial 3. "During the practice period I endeavored to learn to differentiate the octaves, as before. I tried to analyze the quality of each, so that I could at least place the note in the proper octave. More attempt to get the note placed in the right octave, than to get the correct name of the note. The name of the note usually came readily to mind without conscious comparison, but the determination of its octave was still perplexing. Feeling of helplessness usually with very little confidence, especially in regard to the high and low notes."
Trial 4. "During the practice period I was anxious to be able to name the note correctly as well as place it in the octave. I played over the middle octave many times trying to fix it in mind, in pitch and relative variations in pitch. When I found I could hum it readily and accurately, I hit at random notes on piano to see if I could name them correctly. Result-.--small percentage of right answers. Used method of conscious comparison. I tried to place the note heard in the scale of c1-c2 and then place it in the proper octave. My reaction took longer but I had more of a feeling of confidence. There was difficulty in being able to keep pitch of ~ very clearly in mind. I did not attempt to locate sharps or flats to any extent. Not entirely satisfied with this method."
Trial 5. "During the practice period I tried to fix separate intervals clearly in my mind. From the sound of middle c I would try to work out the pitch of notes at various intervals from this. I sang the notes, trying to train my ear to become more accurate. After I had secured the note I played it on the piano, in order to see how correct my judgment had been. There was great inaccuracy at first but I found improvement before the practice was completed. The pitch was determined by singing do mi sol do from middle c to try and locate the given tone. I still felt very hesitant about my ability and I could not see in what way my practice had helped me. During this sitting it occurred to me that I could use my highest and lowest singing notes for standards which would be less likely to vary than my memory of middle c. I determined to attempt that at my next practice period." Trial 6. "During the practice period I played the various high and low notes in order to try and hum their octave in middle range. I found that I frequently judged their pitch a fifth or a third off so I continued my practice until I could readily distinguish the octave of the note struck. Then I tried to discover my high and low thresholds for humming tones so that I could use them for bases for comparison. I found I could get the pitch of the given tone more clear in mind than at any previous sitting. But it was still hard work to name the note. I sang down the scale as far as I could and tried to learn from the last note what scale I had been singing. I felt still very uncertain about my accuracy. In the case of middle c I judged it correctly more from the feeling of familiarity accompanying it than from its relation to my lower threshold."
Trial 7. "During the practice period I found that my humming ability at the highest limit varied more than at the lowest limit, so I decided to adopt only c, my lowest limit, as my standard. I hummed it over and over, endeavoring to fix in mind the auditory and kinaesthetic sensations. Then I studied out how I could infer the pitch of any note on the piano with reference to this standard. When the note was heard I tried to hum it, or its octave equivalent within my range, then, by means of do mi sol do, I tried to relate it to c. This method seemed dependable, and, although some notes were hard to determine, on the whole I felt quite confident in my judgments."
Trial 8. "During the practice period I decided that do mi sol do was not detailed enough, so I attempted to study out the relation of each note on the piano to c in terms of half notes, not larger intervals. I decided to sing every note in the scale, upon approaching c, not merely do mi sol do. Although this method seemed more accurate, it took more time. Moreover, I felt throughout that my judgment of c was not entirely fixed. Therefore, more of my judgments might be wrong than before. The method seemed quite unsatisfactory.
Trial 9. "During the practice period I realized I could not make use of the method of singing every note as it took so long. I therefore decided to go back to the method of do mi sol do, still attempting to keep the pitch of c more surely in mind. Throughout I felt confident in my judgments. But I did feel, too, that the method of humming was not an ideal one, as it involved too much time and had at best a good deal of variability, as shown in my results."
Trial 10. "During the practice period I struck a few notes to see if I could guess their pitch immediately. I found I guessed a few right, the others being very nearly so. So I decided to abandon my former method of determining pitch by humming and to adopt the new way of judging immediately. I tried to fix in my mind the qualities of the various notes at the top of the piano, analyzing them as carefully as possible. Afterwards I attempted to do the same with the lower notes but I did not have time to differentiate them as well. It was as interesting as a game. I judged the pitch of each note as accurately and quickly as possible, running my eyes up or down on the chart until they seemed to reach the right spot. On the whole, I felt quite confident, especially with the higher notes. When I was not certain of the octave, I would resort to my old method of humming."
Trial 11. "During the practice period, as before, I tried to differentiate the notes at both extremes of the piano. I also tried to single out significant points, above or below which the notes seemed to have a certain quality. I practiced especially the lowest notes. I tried to judge the pitch of each note immediately as before. Some I felt confident about, but most of them seemed doubtful, especially those in the middle range. I did at times fall back upon my old method of humming."
Trial 12. "During the practice period I practiced especially the notes of the middle range, trying to get the characteristics of the various octaves. I found significant differences, but they did not limit themselves to the octaves. Some octaves were very much alike throughout while others seemed to have several distinct differences within them. I made my judgments with no great feeling of confidence. But I had become convinced that this was the better method to follow and that in time I might make marked improvement."
Observer G, practice series for the piano.
Trial 1. "Began the test with the idea that I could identify a great many notes by immediate judgment, but was surprised by the unusually penetrating, brilliant sound of the piano notes. This together with the high pitch of the piano confused me thoroughly. I felt some degree of certainity about the octaves, although attention was not always steady on this point which resulted in failure to distinguish between the different octaves. I was more certain about the middle range than other parts of the keyboard. At the extremes, I used chiefly guessing, with no foundation at all for my judgments."
Trial 3. "Attention was very strained, so that genuine fatigue entered in. At these times octave differences are apt to be overlooked. As each note was struck I seemed to go through a definite period of orientation. No vivid imagery of any sort appeared, but fleeting, hazy, concrete visual and auditory images were present. A slight process of comparison and judging occurred frequently. For instance, a very high note was thin, wiry, penetrating and short. That would be judged as belonging to highest octave, its place in the octave depending mostly on its metallic quality. At the extreme upper and lower ends of the piano pitch entered little into the judgments. Within the other five octaves recognition often came instantly, as distinctly a b or an f quality, though usually I weighed this judgment a little, considering that this piano was tuned high. If it was difficult to tell at once, I regarded the note as the seventh of a dominant chord and resolved it downward or considered it as the seventh in a scale and thought of the note above, or considered it as the fundamental, third, fourth, or fifth of a tonic chord. If this were too prolonged I forgot the tone, or became quite confused. My memory for the note struck seems exceptionally short. In the once-accented octave I try to attach a certain quality to each note, and believe I am partially succeeding. By transferring this octave's relationships to other octaves, I may be able to extend the range of the ability."
Trial 4. "A heavy cold at this trial made me feel that this experiment were progressing more poorly than others. It seemed as if it were impossible to make use of some standard for judgment to which I was accustomed. I had never consciously used kinaesthetic sensations or images in order to judge by the "feel" or by comparing with my singing range but was led to think by this fact that I actually had used one or the other. However, my results were better than usual, so this may or may not have been a factor. When I tried humming the tone given I was thrown off completely. At no time did it seem to help."
Trial 6. "In practicing I played simple scales, usually the scale of c, over and over, noticing the octave variations. Then I tried arpeggios from one end of the keyboard to the other, and simple chord progressions. I spent considerable time practicing the first and last octaves. Their pitches are not very obvious to me as I play them, although each note is sufficiently different from the adjacent ones. At the upper extreme everything from b3 to b4 sounds like e4. c4, even when I am playing it myself, has nothing clearly in common with the lower c's on the piano. I can call up at will good auditory images of the piano notes from C through a3. Below that I can imagine only a general, rough sound, and above that oniy a metallic sound without definite pitch relations. Practice seems to be giving these tones slightly more individual character."
Trial 12. "Like to have the note sounded fairly strongly but not pounded. Frequently ask to have it sounded again softer and louder with a pause in between. The initial sound seems especially important and while the note is still sounding, I ask to have it repeated in order to get that initial sound. Try to free my mind from any bias and 'set' in regard to what note is coming. When the note is heard I place it instantly unless it is very high or very low (when I am usually in doubt and make guesses). Then I like to have the note repeated in order to verify my judgment, and think of it mentally as belonging in a particular chord or scale. On some days it seems hard to judge octaves. The bare, undecorated room in the Music Annex reenforces the overtones to a great extent, and I seem to be judging the width (extensity) of the sound to make sure of its octave. Occasionally I hum the octaves--seldom individual notes. On this account, I like the intensity kept constant and the note struck decisively.
"Have come to know certain peculiarities of our piano; c1 to me sounds a bit flat; a1 has an individual quality of tone which is almost never mistaken; d, b1, c2, e2, c3 and d3 seem to be exactly in tune and are always judged correctly when heard and almost never given when not heard. D1, b, g1, a1 and b2 I am beginning to recognize as having a certain quality. Other notes are placed as 'not being these,' but as having an approximately definite place. Except at the extremes of the piano, and except when attention is distracted, am certain that the note lies within a very small range of possibilities. c#2 and d2 do not seem to be in tune, i.e., d2 sounds flat, but I am beginning first to judge d2 correctly. The highest octave is beginning to have recognizable quality of tone, but it takes much more attention and activity on my part than the lower ones. The notes below G1 I judge by width of tone and roughness, except, I think, D1 and C1.
"Feel as if attention were a very large factor. It is partly attention to discriminable tone-qualities, not wholly pitch. For instance, when g1 was played, I knew it to be lower than g#1, but was not sure whether it should be called g1 or g#. I could not tell at once whether the difference lay in pitch or in volume." (This confusion occurred on several occasions.)
At the close of the trial which occurred one year after the practice series with piano notes the following reports were made by members of the group.
|
Observers |
Number of Notes Correct at This Trial |
Reports |
| 1 | 11 | Judgments were made quickly, based upon an estimate of the octave in which the note lay. Timbre and length of time note resounds after it is struck aided in this. |
| 2 | 44 | Several devices remained from the previous practice. Remembered the type of quality of c1, c2 and c3. All seemed very clearly c's this time. No great assurance throughout. Gave note instant location in some octave. Afterwards tested judgment of note to make sure of it. Remembered octaves well. Verbal imagery (suggesting possible responses to myself) came in. Used the chart very little. |
| 3 | 5 | Remembered that I was apt to omit entirely the octave c to c1, and tried to place unfamiliar notes there. Remembered peculiar qualities of certain notes. |
| 4 | 5 | Used last year's method. Auditory images of the successive octaves above or below the one presented to determine position on the keyboard. Much tension in throat for low notes, less for those in middle range. |
| 5 | 10 | Remembered the peculiar ring of some notes. |
| 6 | 6 | Could decide more quickly than last year. Referred all notes except those in extreme octaves to c1. |
| 7 | 10 | Seemed easier and quicker than last year. Remembered the low and high notes better than the middle ones. |
| 8 | 15 | No definite method of discrimination. Some visual, auditory and motor imagery. |
| 9 | 8 | Decisions made more quickly. |
| 10 | 19 | Tried first to recognize the octave, then the note. Some notes sounded familiar, others I had to guess at. |
| 11 | 9 | Last year I thought of the notes in their relation to C1. This year, I thought of their relation to each other in the scale. |
| 12 | 21 | I do not remember anything from last year's practice, but in the past year I have found myself constantly trying to tell in what key a piece is being played, and to pick out certain notes by name. |
After the tests in identifying the fundamentals of tonic chords the following introspective reports were given:
Observer Bd, "At first tried to pick out the lowest note and sing it to myself; later just listened for the effect of the whole."
Observer G, "Tried to pick out the individual notes from the chord struck and judge from them. This was very difficult to do for the notes were evenly struck and blended well. In a general way I felt a slight emotional (or kinaesthetic) reaction to the chord as a whole. c e g c was instantly recognized. db I knew as being not c but approximately in that region."
|
Fundamental of chord |
Bd's characterization of chord |
G's characterization of chord |
|
c |
Blended, hollow |
Most complete of all |
| c# or d-flat | Tiresome | Unsatisfied |
| d | Not clean cut | Wistful, not at all self-sufficient |
| d# or e-flat | Hard, ringing | Some independence |
| e | More clear cut | Cold, impersonal |
| f | Hollow | Finished effect |
| f# or g-flat | Not clear cut | Cold, powerful |
| g | Slightly blended | Very complete |
| g# or a-flat | Clearer than some | Self-complacent |
| a | Ringing quality | Powerful and brilliant |
| a# or b-flat | Blended | Wistful, appealing |
| b | Clear | Self-sufficient |
([The effect was] different on different pianos.)
The following introspections were recorded by Observer G after the experiment in identification of tuning forks (observer G's threshold for pitch discriminations obtained by means of the Seashore Columbia Record disc was 98 percent):
These identifications were much harder than those of piano or violin notes. Attention was mainly on the pitch, but there was also a sort of vocal motor reaction aiding the pure memory for pitch. A comparison with imagined pitches a few vibrations higher or lower always took place in order to suggest or to verify the vibration rate. I always thought of the standard pitch (435 v.d.) as slightly flat. As I struck the fork I tried to observe any relaxing or tightening motor sensations, or any flatness or sharpness in comparing it with an auditory image. The four highest forks seemed distinctly high or sharp. It seemed almost impossible to distinguish between the first four or five forks whose differences are only one-half or one vibration.
These introspective reports emphasize the fact that pitch is only one of many elements that enter into judgments of musical notes. Other important factors are the variations in apparent width and intensity of sound as you pass from the low tones to the higher ones. In some cases what seem to be directly ordinal judgments occur. The judgments are based upon a knowledge of general position and tonal spacing. Practice tended toward improving octave discriminations more than discrimination among the individual notes.
Frequent methods employed to determine the notes were, reference of all notes to an imagined c1 or a1; reference of all notes to their representatives in the middle octave; placing the note in a scale within the vocal range; placing the note in a chord followed by various harmonic progressions. Judgments were sometimes based on the so-called finished quality of sound which certain notes seem to possess. c1 is characterized in this way most frequently. Observers report "snap judgments," or immediate judgments, followed by an attempt at verification by indirect means. A few observers in Group 2 and more in Group 1 had feelings of familiarity for certain notes leading to immediate identifications as a result of their practice.
During the practice series more certainty of judgment was developed in observers who began the experiment with mere guesses. Direct judgments not infrequently occurred during the progress of the tests. A knowledge of octave differences came first in most cases, and later a feeling for individual notes.
Some observers attempted to build up a memory for separate notes by the formation of non-essential associations, such as: B has a funny sound when the key is lifted. In c# the second overtone rings out. f# rattles when played softly. Noticed where low notes begin to have distinct overtones and where high notes disappear into their more prominent overtones. The association that c, e and g have a finished quality may be the result of some habitual motor or perceptual reaction to these sounds. The notion that several observers had that certain notes are not quite in tune indicates also that they may have established a temporary or moderately lasting "set," auditory or motor, which gives rise to the feelings of the "in-tuneness" or the flatness.
The introspections following the experiment with the tuning forks emphasize again the effectiveness of a possible auditory or motor neural adjustment. This gives rise to an immediate judgment of higher, lower or the same, eliminating the comparison judgment with the aid of images.
The effect of the different distributions of black and white keys in the various chord combinations is illustrated by the observers' characterizations of the chords. The tonic chords built up on c, f, and g, which possess no accidentals are uniformly called hollow or complete. The rise in pitch also changes the feeling-effect for the chord. The higher pitches are thought of as more ringing or powerful.
After the lapse of a year with no deliberate effort to preserve any of the previously acquired ability to identify piano notes it is found that a number of essentials are still retained. The observers could still make use of their knowledge of octave differences, or more accurately differences in volume, for, as was remarked, some octaves have more than one change in them. In some cases the mental set for c's remained, although other adjustments were much less clear. Former inaccuracies of the attention were recalled to aid this later test. Interest in this sort of tonal judgment was retained by one observer, who found herself constantly trying to tell the key of a piece and to pick out individual notes.
Practice has a marked effect on an individual's ability to identify musical notes, that is distinct from the inital capacity of the individual, or from the type of instrument used in producing the notes. The observers in these tests improved irregularly from trial to trial in identifying piano notes, violin notes and the fundamental notes in tonic chords. A short period of practice covering an interval of about eight weeks with two ten minute practice periods a week brings an increase in the number of correct identifications and a corresponding decrease in the size of the errors made. Longer periods show continued improvement more or less irregular in its progress. Little sign of fixed plateaus is apparent in any of the results. The amount retained after the lapse of a year without practice is in some measure proportional to the degree of ability acquired through practice. In most cases some of the ability is lost over this period, although in a few cases progress rather than forgetting seems to have taken place.
Baird's results from tests on people possessing a high degree of ability to identify pitches show that "cases of absolute pitch memory may 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." The results presented on the preceding pages of this paper show this to be true not only within the limits of a selected group, but in a much wider field. The series of gradations extends without recognizable break below the obvious case of absolute pitch memory through all ranks of individuals who are familiar with our diatonic scale down to those who are tone-deaf.
The curve representing the frequency distribution for errors measured in semitones forms a fairly typical curve of normal distribution, and includes all grades of responses from a case in which 83 of the 88 piano notes were correctly identified down to cases in which only one tone is accurately named. The curve for the frequency distribution of correct notes is skewed a little toward the lower end and remains somewhat so after practice. To explain the absence of an occasional exceptionally bad case to offset the occasional very good cases the limitations of sampling within the group has been suggested. The error curve represents the individual's ability in a more comprehensive way and is less affected by random correct guesses.
The attempt to reduce the size of errors shows no tendency toward preferred intervals, such as those of a fourth or a fifth. On the contrary we find the overwhelming majority of the errors to be those of a semitone, and the larger the error the less its frequency in consecutive order from the halftone error to those over two octaves in magnitude. In a few cases octave errors show a slight increase in number over the errors of the major seventh, and in still fewer cases the rise in number of octave errors brings the frequency of this interval error next in order to that of the semitone or the whole tone.
The naturals on the piano all have a higher frequency of correctness than the accidentals. The notes at the extremes of the keyboard and those in the middle octave were most often named correctly. On the whole the accidentals in the thrice-accented octave received the fewest correct responses. The order of frequency of identifications for the seven octaves is as follows: four-accented, once-accented, contra, twice-accented, small, thrice-accented and great octave.
The practice curves for the five observers from Group 1 show considerable variation in progress. With the observers who continued the experiment very nearly throughout the year, it holds true that the longer the period for practice, the smaller the error, irrespective of the initial error. The irregularities in the curves are due partly to changes in method of approach to the problem, partly to variations in attention and fatigue. Interest wavered at times, then received new spurts as the experiment progressed, and lagged again.
The time curves are more fluctuating than the error curves. These same factors affect the results here also. Accuracy, however, was made much more the goal in these tests than speed, so that reductions in the identification time are more or less incidental. The correlations between the average time per trial and the average error for each of these five observers are negligible. The correlation between the size of the error per note and the time per response for one observer is zero. On the whole the time for incorrect responses is slightly longer than that for correct responses.
The identification of notes from different instruments presents new situations which are more or less adequately met by the observers. The results from experiments on the pipe-organ using the four stops, viola, diapason, oboe and flute do not reveal striking differences between the average error or the average time per note for judging piano notes and for judging the notes of each of these stops. Since these tests were made after the observers had had several months of practice on the piano, it is possible that some of their methods gained through special practice with piano notes were transferred to the organ notes and aided identification. This may account for the fact that these observers show less variability than is usually the case in estimating notes of different timbre.
In the experiments judging the fundamental notes of various tonic chords, the observers found the task more difficult than identifying single notes. This contradicts the reports of a number of writers. The fusion of sounds with their new intensity orders confused the observers and made chord analysis necessary before the fundamental note could be identified. Small interval errors resulted rather than errors of the third or fifth as might have been expected.
The tests with tuning forks indicate some ability to remember the tone of relatively simple sounds over long periods of time. The forks with the larger vibration differences were better discriminated than those with small differences. These identifications seemed to be more dependent on the factor of memory for pitch than on recognition of tonal volume or brightness changes within these narrow limits. This pitch memory was expressed in both auditory and kinaesthetic terms.
during the judging period Good auditory imagery seems important in recognizing tones, more so, these experiments indicate than kinaesthesis. This fact is brought out by comparing the results from the tests for vividness of imagery with the individual's ranking in the tonal identification tests. It is further illustrated by the results from the kymograph records of movement of the larynx and the tongue, and the breathing curve during the judgment periods. The usual shallow irregular breathing curve representing quick adjustments of the attention occurred, together with noticeable cessation of movements of the tongue and the larynx.
Ability to reproduce accurately by means of a tonoscope the vibration rate of designated notes depends partly on the ability to image the correct note and partly on one's technique in singing the imaged tone. On the whole in these tests the abilities to reproduce and to identify notes correctly run parallel. The experiments in singing the notes took place at the end of a year's practice in identifying notes. The earlier experiment had laid emphasis on auditory images and must have aided somewhat in this later experiment.
Writers are agreed that frequency of hearing certain notes can not alone be made the basis for tonal memory. The results of special practice are held to be important by some writers and negligible by others. Many different theories have been advanced to explain the type of association involved in the identification of notes. Practice and memory plus an individual coefficient are made the basis for correct identification by Stumpf. A kind of limited association with particular pitch-blends is responsible according to von Kries for memory for pitch, because the instruments most frequently heard are not invariably the ones remembered. The ability is attributed by Abraham to associations of pitch built up in the auditory realm. In some people the sensory equipment may be finer so that finer differences of tone quality are recognized, or certain association paths in the brain may be more numerous or more closely knit together than in other people. The mechanism of the instrument producing the sounds may be such as to give to the different notes definite coloring which becomes associated with them, or the structure of the ear itself may affect the character of certain notes.
The tonal series may be regarded in two ways, first as a qualitative series, constituted by variations in pitch, and second as a quantitative series with the single quality of tone which may vary in ordinal terms, namely in pitch. The first interpretation is adopted by Boggs, who puts pitch on a par with color in the visual series. One may be color blind and still recognize brightness differences, so one may be pitch deaf and recognize only the brightness differences in tones. Memory for absolute pitch is, therefore, not the result of learned. associations but the result of a capacity for elementary experiences. Similarly Baird regards the recognition as dependent on the ability to observe in each note some distinctive characteristic c-ness, d-ness, etc., which can not be learned, but simply perceived if we are endowed with the capacity.
Other non-pitch attributes of tone have been stressed by writers, who have found experimentally that keen discrimination of tone-body or tone-color may with practice lead to a memory for the correct names of notes in the same way as pitch. The so-called attributes of tonality and vocality have an important bearing in memory for tones, for if attributive, they would greatly affect one's method of approach to the problem of absolute pitch memory. But it has yet to be proved that the similarity of octaves is attributive in that vowel sounds are not themselves the result of a previous association. The experimental evidence is strongly in favor of the latter view.
Watt advances the second interpretation of the tonal series as a quantitative system and regards pitch as an attribute of order. According to this, absolute ear is the natural condition of hearing, just as localization in any sense realm is a natural development from the primary attribute of order. This tendency in hearing is counteracted by the emphasis which music places on harmony and key relationships which are purely arbitrary and result according to Watt from the adoption of the volumic pattern of the octave as the standard of the whole range. People who are able to retain their original absoluteness in spite of the pressure toward relativity possess an unusual auditory "disposition" or a greater delicacy of volumic outline and predominance.
The results from the present investigation support the view that certain factors other than pitch have importance in tonal judgments. The variations in the brightness and the volume of the notes afforded a cue that was used by all the observers. These factors were obvious to the poorest observer and were readily synthesized by the non-musical with the data from other sensory experiences. No evidence of aid from a recognition of vowel qualities occurs in these tests. Reports of differences between octaves are always translatable in terms of brightness or of extensiveness, or of certain incidental features. Most of the observers reported a likeness existing between the same notes in the different octaves, at least in the octaves toward the middle range. At the extremes this similarity disappeared for some. Confusions in identification arising from the octave illusion are rare, only three observers showing high susceptibility to this error. Judgments of tonal position in a large number of cases involved naming a note within its octave in a single act, instead of dividing the process into first naminga note and then placing it into a particular octave, or vice versa, although all three methods were used to some extent during the course of the experiments. Observers occasionally confused volume differences with pitch differences, as for example when g1 was played, the observer knew the note was lower than g#1, but was uncertain whether lower was to be interpreted in volume and the note named g# or in pitch and the note named g1.
Complexity of sound was not found to aid in these experiments. Chords, in which no single predominance of pitch occurred, were more difficult to recognize than single notes. The identifications of notes from the four organ stops vary little from the results with the piano and the violin. Even when complexity of sound was entirely eliminated as in the test with the tuning forks, correct identifications and relatively small errors in judgment were possible.
The experiments bring out clearly the importance of frequency of hearing notes, provided attention is directed toward essential tonal characteristics. First, the individual notes assigned to the observers in Group 2 for special practice had a much higher frequency of correctness than the other notes; and second, practice over the entire keyboard produced a marked improvement in efficiency both as regards general reduction in error and increase in the number of correct responses. Furthermore, special practice correlates higher with improvement than the number of years of previous musical training.
The recognitive consciousness in identifying musical tones may be interpreted as similar to that in any typical judgment process. It is based on frequency, recency and satisfyingness of the individual's experience and is subject to the usual laws of practice and forgetting. Interest plays an important part and is probably dependent on the delicacy of the sense organ and the wealth of clear auditory images. Without these factors attention tends to wander to extraneous aspects of the sound and learning will not proceed. If the observer is interested he will frequently attend to the correct factors without being analytically conscious of his task.
In acquiring a memory for absolute tone the observer does not remember well one or several notes and the others not at all, but he builds up a more or less cohesive structure about a few or many notes. Octave similarities, or the series of repeated relations within the octaves and the likenesses, existing between notes an octave apart, whatever their origin, make the task of apprehending the tonal series of eighty-eight steps much easier. These recurrent relationships may be wholly arbitrary, fixed in our minds by repetition, or they may be elementary. For many of the observers the tonal series did not contain very distinctive recurrences of chord or scale relationships from octave to octave. The series was one-dimensional without these regularly repeated units which facilitate the task of comprehending so long a range. Instead of calling the volumic series one of brightness changes, and the pitch series one of qualitative changes, it seems more appropriate to regard tones as belonging to a discrete series which the mind many apprehend in its diversity or as a unified whole consisting of even divisions of smaller units. By repeatedly directing the attention to the unity of the series, one may acquire the mental adjustment which finds little trouble in quickly assigning to random notes a position in a relatively well-organized whole.
This system of sounds when well incorporated is not a rigid inflexible affair. If an instrument is tuned lower or higher within limits (so that the tension of the strings is not altered too greatly), the system can be adjusted to the new situation and correct responses made. Also an observer may have given the correct name to a note in many previous successive trials, and at the next one place it a half tone higher or lower than it should be.
In immediate correct judgments of notes the observer has already established an accurate and (moderately lasting) 'set' or adjustment toward the tonal system so that responses then occur without reflection or comparison. It is conceivable that the set may be the result of vocal motor reaction arcs aroused by the stimulus, or it may be wholly auditory. Whatever its pattern the feeling of familiarity, or the feeling of completeness or relaxation which accompanies the sound of certain notes, as c1, can be explained as the result of definite establishment of associative connections, which with repetition will tend to drop out of consciousness. Thus one is not born with a sense for absolute pitch which is lost as a result of musical relativity but one learns to acquire a memory for individual notes through the analytic and synthetic processes involved in apprehending the originally discrete tonal series as an organization of recurrent parts and the development of well established associative connections giving rise to relatively permanent mental adjustments for the various musical tones.
1. C. Stumpf, Tonpsychologie, 1883, pp. 286-313.
2. C. Stumpf, Tonpsychologie, II, 1890, pp. 553 f.
3. J. von Kries, Ueber das absolute Gehör. Zeitschrift für Psychobogie und Physiologie der Sinnesorgane, 1892, 3, pp. 257-279.
4. M. Meyer, Is the Memory of Absolute Pitch Capable of Development by Training? Psychological Review, 1899, 6, pp. 514-516.
5. O. Abraham, Das absolute Tonbewusstein. Sammelhefte der internationalen Musikgesellschaft, 1901, 3, pp. 1-86.
6. H. von Helmholtz, Sensations of tone, Trans. by A. J. Ellis, 1895, pp. 310-830.
7. L. P. Boggs, Studies in Absolute Pitch. American Journal of Psychology, 1907, 18, pp. 194-205.
8. H. Rupp, Ueber die Prufung musikalischer Fahigkeiten, Teil I, Zeitschrift für angewandte Psychologie, 1914, 9, pp. 1-76.
9. Can Absolute Pitch be Cultivated? Manuscript, 1916.
10. W. Köhler, Akustische Untersuchungen, Zeitschrift für Psyohobogie, 1915, 72, pp. 159-177.
11. J. W. Baird, Memory for Absolute Pitch, Studies in Psychology, Titchener Commemorative Volume, 1917, pp. 43-78.
12. M. Meyer, Review of Révész, Psychological Bulletin, 1914, 11, p. 349.
13. Quoted from G. T. Rich, A Study of Tonal Attributes, American Journal of Psychology, 1919, 30, pp. 121, 125.
14. R. M. Ogden, Tonal Attributes, Psychological Bulletin, 1917, 14, pp. 161-162.
15. G. T. Rich, A Study of Tonal Attributes, American Jour'auzl of Psychology, 1919, 30, pp. 121-164.
16. H. T. Watt, The Psychology of Sound, 1917, pp. 41-53.
17. C. S. Meyers and C. W. Valentine, Individual Differences in Attitude toward tones. British Journal of Psychology, 1914, 7, pp. 68-ill.
18. See R. S. Clark, An Experimental Study in Silent Thinking, Archives of Psychology, No. 48, 1922.
19. C. E. Seashore, The Psychology of Musical Talent, 1919, p. 73.
20. G. T. Rich, A Study of Tonal Attributes. AmeDican Journal of Psychology, 1919, 50, pp. 149-153.
