An experimental study of pitch recognition.

Originally published in Psychological Monographs, 6, 1-124, 1932.

Laurence A. Petran

I.  Introductory statement.

By "absolute pitch" is understood the remarkable ability possessed by certain few musicians (and an occasional idiot savant) to give quickly and correctly, without reference to any standard tone, the names of tones that they hear, and also the ability which still fewer musicians have to sing or whistle any tone which may be called for by name. This ability has long been coveted and more or less revered by musicians, and has been the topic of no little psychological discussion since the time of Stumpf. The main questions that have been asked are: (1) By what means are absolute pitch judgments made? (2) With what accuracy can they be made? (3) What factors facilitate or interfere with absolute pitch judgments? (4) How did possessors of absolute pitch acquire the ability? (5) Is it possible for anyone to acquire the ability? (6) What is the ability worth to its possessor?

This study first presents a discussion of the answers that have been given by psychologists and musicians to all six questions; then reports two experiments. The first is aimed at answering definitely the second question and thereby throwing some light on the first. In the first experiment nine reactors with absolute pitch, four with relative pitch, and four control reactors tuned a Stern tone variator to violin a purely from memory, ten times a day for ten days. In all cases the reactors had heard no music or tones for half an hour or a much longer period before they began tuning the variator. The second experiment was designed to study the method which has been used by practically all previous investigations on the subject, but which has inherent in it so glaring a fault that the method can hardly be called a test of absolute pitch at all. In this method the reactor who is to make absolute pitch judgments has been given at one sitting a long series of notes which he is to name one after the other: a test in which it would be impossible to say that the reactor in judging any note other than the first was not influenced to an unknown and unascertainable degree by the judgments he had made on preceding notes. In the second experiment this method is used, and results from it are compared with results from a test in which the same series of notes was given to the reactors one each morning before the reactor had heard any music or tones, and therefore had no chance of making a relative pitch judgment.

II.  Analytical survey of the literature.

A.  Importance of research on absolute pitch.

Numerous reasons for the further investigation of absolute pitch have been given by writers on the subject. These reasons may be grouped under five headings: (1) the bearing of the phenomenon of absolute pitch on theories of hearing; (2) the similarity of the mental activities involved in judgments of absolute pitch to processes usually included within the psychological categories of memory, discrimination, and simple restricted association; (3) the possible value of absolute pitch as an indicator of musical talent; (4) the advantages that the possession of absolute pitch gives musicians in the analysis and enjoyment of music; and (5) its importance to singers in the maintaining of tonality in unaccompanied vocal music.

1. Bearing of absolute pitch on theories of hearing.

The existence of the phenomenon of absolute pitch fits in more readily with those theories of hearing (the resonance and the extensity) which allow for the existence of local sign in the end organ than with other theories such as the telephone theory, although it puts no insuperable difficulty in the way of the latter. The current and undisputed conception of sound stimuli is that, when ranged according to pitch, they form a continuous linear series from the lowest audible to the highest audible, and each audible pitch has its position or local sign in this line. Thus Zwaardemaker [118] states that "in the auditive line in which are found the sounds audible to man . . . each point offers its own local sign which makes us attribute a certain height to the sound. This evaluation is absolute or relative." Hein [30] extends this concept by saying that " if each resonating fibre in the cochlea were connected individually to the brain center we should expect universally fine absolute pitch", and Chiloff [16] makes a similar statement. Wilkinson [112], who advocates the resonance theory in a recently developed form, states that the existence of absolute pitch implies the association between certain zones of maximal stimulation and the names of corresponding musical tones, and that these zones remain at a practically constant level in the end organ. Thus, on a resonance hypothesis, an absolute pitch judgment would depend on a rather definite, unequivocal association between a certain resonating fibre or narrow group of fibres in the cochlea and the corresponding musical pitch name; or, as Chiloff [16] contends, between the pitch name and the pattern formed by all the fibres resonating to the fundamental and upper partials of the stimulus tone. It could be argued that on the resonance theory absolute pitch should be as easily and quickly acquired for pure tones as for complex.

Dunlap (19, 20, 21) has shown that the extensity theory explains very clearly the different degrees in fineness of pitch perception found between unmusical and musical ears. "An individual who has an ' unmusical ear' judges pitch differences in a rough way, as if mere gross sizes of objects were directly compared. On the other hand, the person with a ' musical ear ' judges in a more exact way as if he noted the point to which each tone extends." Since on this theory all vibratory extents in the cochlea are coterminous at the basal end, the dominant pitch characteristic of each sound might come to be associated with stimulation of the hair cells at the upper end of the vibrating extent, and these particular hair cells would thus provide a local sign for each pitch. This local sign would not necessarily be focal in the tone sensation for the great majority of people, while it would necessarily be more so on the resonance theory. Hence it might be expected on the extensity theory that only those having much to do with music would have developed the ability to recognize pitches to any extent, and that there would be gradations in this ability corresponding to the attention which had been given the local sign feature of each tone, rather than to the whole vibrating extent. This is in accordance with what is known about absolute pitch.

2. Relation of absolute pitch to other mental processes.

Correct absolute pitch judgments furnish outstanding examples of memory and, to a certain extent, of tonal discrimination. Stumpf (95) and others assert that a well-developed memory for absolute pitch operates even after long periods of disuse, and while evidence on this point is mainly anecdotal there is enough of it to warrant consideration. None of the investigations of memory for specific tones (Wolfe, Angell and Harwood, Angell, Whipple) seem to have studied it over periods longer than ninety seconds, and practically all the work on pitch discrimination, except some of Gough and Mull, has been done with time intervals of only a few seconds between successive tones. But people with absolute pitch have been able to make pitch discriminations over long periods of time with a comparatively high degree of exactness. Finally, absolute pitch has several of the characteristics of simple association. As von Kries points out (48), it works in one direction (from tone to name) better than in the other, just as to us a foreign word suggests its English equivalent much more quickly than the English word suggests the foreign. Also, a given tone may be associated with several things: a piano key, a letter name, musical notation, a familiar song, etc. The process of naming heard tones is very similar to the controlled association reaction.

3. Absolute pitch as an indicator of musical talent.

Evidence of absolute pitch in children has not generally found a place in the schemae or tests of musical talent which have been made up by psychologists, but it is likely that music teachers have always been impressed by the ability when it appeared in their scholars, and have encouraged such to go on in music. Psychologists are unanimous in stating that absolute pitch is not in itself necessary or especially important as a constituent of musical talent, but Rupp (87) raised the question whether its appearance in children might not be an indicator of musical ability. Schoen (90) gave absolute pitch tests of varying rigidity as a part of a musical talent examination to ten children selected by their music teachers. In all the resulting profiles the absolute pitch score occupies a position close to or below the average. He concludes that absolute pitch "is closely allied with other musical powers, and has a high diagnostic value." Révész (80), in his tests of 62 children for musical talent, found that the ability to locate on the piano the eight notes scattered over a wide range that were played to them correlated "highly" (.68) with what he considered the "Hauptmerkmal" of musical talent. This was the ability to sing two-measure fragments of a Schumann song after it was played to them. Some of the children without musical training performed better on this test than some of those with training. Mjøen (63) concluded from questionnaire data on musical traits found in families over several generations and reporting on a total of 2,452 people that absolute pitch was one of the most important indicators of native musical ability, more important than any other criterion except composing. König (46) suggests that the extent (number of notes a child can name correctly) and time in which absolute pitch is acquired may serve as a measure of musical talent. Mull (65) feels sure from her experiments on the acquisition of absolute pitch that there is such a relation. On the other hand, Bartholomew (11) found only negligible correlations between scores on absolute pitch ability and scores on the Seashore pitch, intensity, and consonance tests with twenty-one adults, all with musical training. Since the validity of the Seashore tests is seriously questioned, this result is not necessarily prejudicial to the suggestion that absolute pitch may be a factor indicative of musical talent, as it most certainly is of interest in things tonal.

4. The value of absolute pitch to musicians.

Most of those who write from only a general information of the subject state that absolute pitch, while in no way essential to musical achievement, may be a potent source of enjoyment in following the course of music as it is heard. Following are some typical evaluations of the ability:

Stumpf (95): "Musical capacity to an unusual degree, penetrating understanding, and most complete enjoyment of great works, however, presuppose this ability. It aids substantially the hearing out of a relatively weak tone in a tone mass, certainly of attack in singing, and unity in modulation."

Wallaschek (104) thinks that absolute pitch facilitates comprehension of melody, but is necessary to musical enjoyment only when complicated passages are being followed.

Meyer (57): "Absolute pitch may indeed be scarcely of importance for the aesthetic enjoyment of music; however, this assertion cannot be made with certainty."

Abraham (1): It is an advantage mainly to composers, because those having it can work freely with units of one tone and hence can be more original than those without it, who must work with intervals (units of two tones).

Liebscher (53): " Comprehension of pitch is a means of orientation in hearing music; therein lies its only superiority to relative pitch."

Seashore (88) : "(Absolute pitch) is a source of pleasure in itself in creating a feeling of familiarity and mastery in tonal environments."

Braine (14): "Those with absolute or relative pitch make many times the progress of those not so gifted."

Auerbach (7, 8) is inclined to ridicule absolute pitch as having no place in musical aesthetics and as being useful only to the Chef of a railway station, who might recognize different train whistles thereby. Abraham (2) rebuts Auerbach's contentions in detail.

Wilson (114) states that absolute pitch, like the telephone, can be a great nuisance, and sometimes feels his own to be a curse.

Slonimsky (91) values it and adds that therewith he has been able to estimate from the motor hum the speed at which his car is going, and in the war could tell when a shrapnel shell was coming his way.

Of Weinert's (107) twenty-two musically proficient reactors with absolute pitch, only two thought that it contributed to musical enjoyment; others felt it was disturbing. Only a few of them, and those only occasionally, noticed individual keys and tones when hearing music.

On the whole, the ability is rather highly prized by musicians and is considered especially valuable for singers, for violinists, and above all for composers. Slonimsky (91) however states that absence of it does not seem to interfere with a composer's creative powers.

5. The value of absolute pitch as a basis for tonality

That primitive songs begin on a high sustained note to which return is made at the beginning of subsequent stanzas has been noted by Stumpf (97) and others. Myers (68) considers this an evidence of the awareness of absolute pitch in primitive people, and as such considered it the basis for the tonality of their music, guiding their use of intervals. However, it could as well be said that the customary tonality could be the basis for whatever absolute pitch these people may have. It must also be remembered that practically all races have musical instruments such as pan's-pipes whose scales are fixed, thereby fixing the tonalities used. Also, as Stumpf (97) points out, primitive people readily transpose their songs, often starting them according to the pitchpipe sounded as the phonographic recording is started. Hence, in many cases at least, the return to the initial note is a matter of relative, not absolute, pitch.

B.  Definitions of absolute pitch

Since the abilities and performances included under the name of absolute pitch vary from author to author, these abilities will first be discussed individually and in detail. After this survey is completed an attempt will be made to develop a definition including only the essential factors.

1. The performance included in absolute pitch by practically every writer on the subject is that of designating a heard tone correctly with a name from a customary nomenclature, and from memory alone, without any other aid. Stumpf (95) speaks of this performance as dependent on comparison of the heard tone with a memory tone, such as the a' of violinists. Wallaschek (104) and Rupp (87), however, base the ability on a whole scale of tones imprinted in the memory. Undoubtedly both types of judgment are found, but the second must be considered the more highly developed and the more truly characteristic of absolute pitch.

There is little agreement as to the immediacy (quickness with which the judgment is given), accuracy, and time interval since the last hearing of tones which are required if the naming of a heard tone is to be called absolute pitch. Boggs (13) emphasizes that with her reactors the more immediate judgments were nearly always the more accurate, and this conclusion is validated by Baird, Gough, and Weinert. Ogden (71) attaches great importance to the immediacy feature, saying that " absolute pitch is not a judgment in which the observer compares the tone heard with a standard he has in mind, and which he can imagine or imitate vocally; for judgments of this type are erudite and rational, compared with the immediacy of absolute pitch."

The accuracy required in order that a naming judgment may be called a satisfactory absolute pitch judgment is put by many authors (Abraham, 1, Dunlap, 21, von Kries, 50) at within a semitone above or below the correct tone. Slonimsky (91) would demand that the notes from the five central octaves be judged immediately and with no errors. Jodl (37) thinks that the only limit to the possible accuracy of absolute pitch judgments is the difference sensitivity of the ear, but an approach to this limit has been experimentally tried only by Abraham (1) and Gough (24) on themselves, and by Mull (65) on a few of her reactors. All these fell short of Jodl's limit, as might be expected. Exhaustive practice would undoubtedly be necessary for the attainment of such fineness of discriminative memory.

2. von Kries in his first article on the subject (48) mentions that a heard tone may be recognized not as b or d but as agreeing with a certain familiar bell or pipe. He adds, however, that the " learning of systematic designations of pitches is an extraordinary help; a learning of many definite pitches without it is scarcely possible."

3. Revesz (78) broadens the definition of absolute pitch into the " ability to express always the same ways of behavior with respect to individual tones" ("die Fähigkeit, den einzelnen Tonen gegeniiber stets ganz gleiche Verhaltungsweisen zu äussern"). This is perhaps the most satisfactory definition of the passive (naming) judgment, and could be applied to animals and primitive peoples, if the occasion should arise. Likewise there can be no objection to von Kries' extension of the definition except that such an extension would be needed infrequently. Thus far, the essential thing in absolute pitch judgments is the unequivocal association of individual musical tones by their pitches with a definite response pattern.

4. The sense of absolute pitch has also been taken to include the ability to tell whether a piano is tuned too low or too high. Warren definitely states this (105), Wilson agrees (114), and Wallace (103) says that the term "absolute pitch" "appears to be applicable to a condition in which the ear is hypersensitive to a fixed standard of tuning and rejects as false in intonation all other sounds which do not coincide with it." Braine (14) extends this concept to the active judgment, thus: "He (a possessor of absolute pitch) can keep his violin tuned to correct pitch without use of tuning-fork or pitch-pipe." The former ability, mentioned by Warren and Wallace, seems to be much more widespread than absolute pitch, and there is no evidence as to how much the two are correlated. Not a few violinists claim to have the latter but there has never been any extensive check-up on them, and probably their accuracy would vary with the amount their violin was out of tune at the beginning of the test. Hence it would seem better to consider the former ability as at most a corollary of absolute pitch, not a constituent feature of it.

5. We now reach the active judgments of absolute pitch, as opposed to the judgments in which a heard tone is named, or passive judgments. The ability to sing with a fair degree of accuracy a tone called for by name is included under absolute pitch by some writers, but this phase has received comparatively little attention in the experimental work, Gough's and Weinert's being the only ones to treat it in any detail. There is the same lack of agreement as to the immediacy and accuracy to be required as in the case of the passive judgment, and, except for Dunlap (21), no mention as to the interval since tones have been heard previously. It is interesting that only occasional writers (Baird, Braine, Myers, and Schoen) have mentioned the extension of this ability to the tuning of an instrument such as the monochord or tone variator to a "tone held in the memory".

6. As in the case of the passive judgments, there is no reason why the verbal element may not be left out altogether on occasion. For instance, Schoen (90) suggests as a test for absolute pitch that a tone may be sounded to the reactor and that after a certain length of time he be asked to reproduce the tone.

7. Somewhat related to the last mentioned performance is the singing of a melody at the pitch at which it is learned. Konig (45) states that a child who can do this may be said to have absolute pitch, but the objection to this is that the reproduction of a melody involves a different degree of difficulty of performance and of evaluation of performance than does the reproduction of an isolated tone.

8. Meyer, in two articles published in the same year, states in one (57) that for absolute pitch "a certain degree of exactness is necessary" and in the other (58) that he does "not see any reason for refusing this name in any case where the individual is unable to determine the pitch with an average error less than a certain interval, viz., a third." Von Kries (49) accepts the latter `statement by saying that recognition of high tones as high and low tones as low may be considered a form of absolute pitch, and several writers agree with them. However, there seems to be little advantage in extending the term to cover such cases, except to emphasize the infinite number of gradations in the ability to name or reproduce tones. Recent experimental studies (Baird, Bartholomew, Gough) amply demonstrate this gradation. It would seem more useful and in accord with custom to reserve the term absolute pitch for the ability to name a given tone or intone a given note with a rather high degree of accuracy. This degree could not be set satisfactorily until studies of the distribution of the ability had been made and compared.

9. Musicians writing on the subject frequently include related abilities, such as the ability to analyze chords and counter-melodies without undue deliberation, under the head of absolute pitch. Urbach (101) sinned in this respect and drew deserved criticism from Altmann and others (3, 53, 64, 86), for including too much in his definition and thereby befogging the issue.

In this study the pitch series from the lower to the upper limits of perception will be considered as linear, that is, as made up of an infinite number of points. This is in accordance with the nature of the physical correlate of pitch ( frequency of vibration) and on the psychological side is an inherent assumption of the extensity and telephone theories. With this assumption in mind, judgments of absolute pitch may be defined as judgments based on associations learned between more or less narrowly limited ranges of the pitch series and the terms of any unequivocal nomenclature, these judgments being without reference to or aid from any tone or tones recently heard which have been given as a standard or attended to in any degree as being of a certain pitch or familiar pitch position.

Three points in the above definition require further elaboration. First, how narrow should the pitch ranges be? Von Kries in 1892 (48) stated that judgments erring by a fourth or more are valueless for musical purposes; Meyer (58) answered that no interval could be arbitrarily set up as a boundary line. Abraham ( 1) from experiments on himself concluded that judgments erring by a half tone should be considered correct, and while some psychologists have accepted this, most musicians writing on the subject assume that absolute accuracy should be required. If this is to be the basis, no reactor on whom any extensive investigation has been reported has absolute pitch. While the whole question may appear academic, it would seem more fitting on the basis of experimental results to confer the name, if at all, on those who were say eighty to ninety per cent accurate in the central part of the scale, something like fifty to sixty per cent accurate in the outer regions, and whose accuracy was not disturbed to any great extent by timbre differences.

As to the influence of nomenclature, it is probable that very few people will ever build up absolute pitch associations for pitch ranges narrower and closer together than those for which definite names are available.

The time interval since tones or music have been heard previously is obviously important, as the work on memory for isolated tones shows, but consideration of it has been neglected by practically all investigators of absolute pitch. Any attempt to control it would seriously affect any of the techniques that have been used, and would make most of them impossible. Rupp (87) recommends a half hour interval between work on different test tones, and Seashore (88) and Dunlap (21) regard the giving of a test in the early morning before any other tones or music are heard as the only complete control.

Abraham (1) gives a list of the names current in Germany in his time for the ability under discussion, and finds the name "Absolute Tonbeuwußtsein" most frequent, but "memory for absolute pitch" most suitable. In English the following names have also been used: "absolute determination of pitch" (Myers), "absolute ear" (Watt), "judgments of absolute tone" (Ladd and Woodworth), "positive pitch" (Copp). One hears also the a term "perfect pitch" used to mean or include this ability. However, the great majority of writers in English use the term "absolute pitch", and the term seems quite satisfactory. The same phrase has been used by physicists (Rayleigh and others) to designate the vibration frequency of a tone, but there is little likelihood of confusion thereby.

C.  Methods of testing and evaluating absolute pitch judgments.

Methods of testing and rating absolute pitch judgments can be grouped under three heads: active, passive, and threshold. The third necessarily makes use of the first two methods, but with pitch differences much smaller than are commonly used in the first two.

The case in which the reactor names a tone presented to him is best designated by the name "passive". This method has been the one used in the great majority of investigations on the subject. The active judgment, in which the reactor reproduces a specified tone by singing, whistling, or by manipulating some instrument such as the monochord or tone variator, has received only incidental attention.

Schoen (90) distinguishes various degrees of rigidity in tests made by the active and passive methods. The most rigid test is to designate pitch after a single hearing of the tone, or to produce a tone of specified pitch. A less rigid test is to sound a tone several times till it is impressed on the hearer ; after a while a second tone is given and the reactor is asked to state whether the comparison tone is the same, or higher, or lower than the first tone. Or instead of sounding the second tone, the experimenter may ask the reactor to reproduce the first tone from memory. Again, a tone may be played or sung for the reactor several times; then the experimenter may play or sing a phrase of several tones, whereupon the reactor is to state whether or not the first tone appeared in the phrase. All these tests are undoubtedly significant for diagnostic work with music students but, except for the most rigid, can not strictly be called tests of absolute pitch.

Rupp's proposals for the investigation of musical talent (87) are by far the most thoroughgoing in the field, and show evidence of musical as well as psychological knowledge. His discussion of methods for the investigation of the threshold of absolute pitch is so fundamental that it is summarized here in detail. He states that methods for determining absolute pitch are complicated by four considerations : (1) With those who do not play or sing a threshold test is merely a test of hearing; with those who do play or sing it tests also training and education of the ear. Such training may help the reactor by giving him other points of view (associations with piano keys, tuning of strings, larynx and muscle sensations) which can be got at only through introspection. An " inner singing " is possible in all cases and can hardly be excluded. But this, and violin and piano cues may make the judgment worse, if technical accuracy and facility are lacking. (2) When the judgment-finding method is used the reactor passively makes one judgment; with the stimulus-finding method the procedure may be passive also. In this case the reactor is told which note he is to look for and then is given a series of tones which he judges as too high, too low, or correct. Or he may actively find the correct note by singing, tuning a string, or finding a piano key. With these latter methods there is much greater self-activity, and concentration increases as the tone approaches the goal. (3) a' is not sharply distinguished from not a', therefore, especially when using the stimulus-finding method, we need to find for each individual a distribution curve, range, central measure, and measure of deviation. It is also important to find averages of several lower limits and higher limits to get an average range. If tuning a string is the method used, the resulting values may be influenced by the fact that strings are usually tuned from a low pitch up. Also, thresholds for higher than a' and lower than a' should be found by starting the stimulus tone at a' and moving up or down. Results from the stimulus-finding method should be compared with results from the same procedure with the judgment-finding method. When the direction of the test series is upward to a', the point at which fifty per cent of the judgments are lower than a' and the rest equal to a' or higher than a' may be considered the average threshold. (4) Three methods are possible. (a) Konstanz-inethode: a series of equally separated steps more than covering the range must be presented; each must follow each other an equal number of times and have positions equally distributed at the beginning, middle, and end of the series. Piano steps are too large for this; tuning forks or the Tonniesser may be used, and the monochord and tone variator if they can be set at exact pitches. (b) Herstellungs-inethode: giving the reactor control of the stimulus. Difficulties here are that the range may not be equally gone over by all reactors, and that tuning too often comes from below. To obviate the first difficulty the reactors may be told not to vary over too wide a range; otherwise tones may be too much influenced by their predecessors, and not equally with all reactors. Continuous tuning is the most feasible method, but this is not possible on an instrument with discrete steps. Individual habits of tuning are influential. Most of the objections fall away with sung tones, unless the voice varies and "searches around". (c) Grenz-inethode: getting thresholds (upper and lower) by method of small steps in one direction, later reversed. This is possible with calibrated tuning forks, monochord, or variator.

It is unfortunate that Rupp never investigated musical talent experimentally in accordance with his prolegomena. Only three investigators have reported using threshold methods, and none of these extensively. Abraham (1) after practice came to locate violin a on the Tonmesser within a range of eight vibrations; the absolute position of this range was three vibrations lower with the Auswahl-methode than with the method of right and wrong cases. Raif, his co-worker, had a somewhat wider range. Gough (24) tested herself with the Whipple increment forks on successive mornings and found that she could recognize the greater increments as being different from the 435 fork tone she was trying to hold in her memory, but her success in naming individual forks was no better than chance. Mull's reactors (65) learned to a certain extent to distinguish a tone she had taught them from other tones less than a half step away.

Table 1 (page 20) on which the salient features of previous experimental work are summarized shows some rather striking characteristics common to many of the investigations. The piano is used predominantly for the presentation of tones, other instruments being used mainly for accessory investigations. Of all the authors who report tests in which a piano other than the reactor's own was used only Gough and Weinert mention anything about the make and tuning of the test piano. The duration of the stimulus has hardly ever been regularly controlled; the only case mentioned being that of Gough, who in one experiment sounded each note several times for ten seconds. Otherwise the general practice seems to have been to hold each note until it died out, or to strike it an irregular number of times. In spite of this irregularity, authors draw conclusions as to the relative familiarity of various notes of the scale, although it is rather obvious, as von Kries (48) says, that unfamiliar tones must have a greater duration than familiar tones in order to be recognized. In practically all cases a number of notes have been presented in series with pauses after individual notes for the reactor to give his judgment.  Of all the studies using this method, only those of Katz (39), Revesz (80), and Bartholomew (11) give the serial order in which the notes were presented. This striking omission by all other authors of an important phase of the experimental technique can be explained on the assumption that they either underestimated the influence of notes in a series on each other, or thought that other phases of their techniques eliminated this influence. The whole subject of the effect of preceding notes on the judgment of a note will be considered in detail later. However, the following means of distraction between individual stimulus tones have been used, although there is no way of knowing whether or not the distractions accomplished their purpose. Stumpf employed conversation between test tones; Abraham, conversation and unusual modulations on the piano, which he thought the ear could not follow by interval sense; Revesz used "meaningless sound combinations" and Mull "a short but effectual period of auditory distraction"; neither of the latter two is more specific. Weinert reports some unintentional distraction, not always auditory, indulged in by some of his reactors to relieve themselves from boredom in a test period of some hours.

Very few writers specify the directions given the reactors as to how to judge the tones presented. Perhaps the majority of the reactors understood readily what was wanted of them. Neither is there much mention as to whether or not after-singing was allowed, but to judge from other points mentioned in the reports it was not indulged in with great frequency. Weinert, however, says he had a great deal of difficulty in keeping one of his reactors, a coloratura soprano, from singing arpeggios after each note. Stumpf, Gough, Mull, Bartholomew, and Weinert took systematic introspections.

A very satisfactory aid to the reactor in making his judgment is to provide him with either an actual model of the piano keyboard or a keyboard chart on which he can point out or from which he can give or record his judgment. Without such a device octave errors are bound to creep in, due to the general lack of familiarity with the octave names (as contra, once-accented, etc.). With it there is more likelihood that the letter name the reactor intends to give will be correctly given. Abraham (1) used the keyboard of a toy piano (this had only one octave) and Baird (9) a Vergil clavier—an instrument that contains the piano keyboard but which makes no musical sound. Gough (24) and Bartholomew (11) used charts of the keyboard with the name of each note written thereon.

Measurement of the time taken for judgment has usually been taken, when at all, by the stop-watch. Abraham tried to measure the response time by means of a lip key, but finding this unsuccessful fell back on the toy piano keyboard connected with a chronoscope. Baird used a voice key and chronoscope with one reactor.

All degrees and manners of statistical treatment have been used in the more extensive investigations, but the older and smaller ones give this very inadequately. Weinert (107) in 1929 criticized severely all previous work on the subject as (1) being based on too few reactors and too few series of tests, (2) employing inadequate analysis of errors, spontaneous corrections, and cases in which the tone could not be named, (3) undervaluing the importance of reaction times, etc. But he makes no reference to any American work later than 1907, thus ignoring the work of Baird, Gough, and Mull, who in their work have taken care of most of the considerations Weinert mentions, and very pertinently.

The method of average error in making an active judgment seems to have been used only twice: by Revesz (81) , who had the young prodigy Erwin Nyiregyhazi set a tone variator to four notes, and by Baird (9), who operating the tone variator himself set it to each note of the diatonic scale according to the directions of each of eight reactors.

The evaluation of a passive judgment as correct or not could hardly involve any sources of error if the tone has been accurately produced on a musical instrument or other calibrated device for producing tones. But the evaluation of judgments of the pitch of bells, glass tones, etc., when done by the experimenter's unaided ear (Stumpf, 96, Revesz, 81) may in itself be erroneous. Weinert (107) had his reactors sing or whistle tones whose pitches were estimated, apparently by Weinert himself, in steps as fine as one-eighth of a whole tone. Needless to say, no matter how fine a musician's ear may be, it should not be given the responsibility of making such fine degrees of judgment for scientific work. Gough (24) used the Seashore tonoscope for similar tests.

The table of experimental work shows the number and kind of reactors in each investigation. Obviously, for experiments other than on acquisition, reactors must be selected from those in whom to a certain extent associations between tones and names are already set up. In the more extensive studies professional musicians and music students have been used. Normal children who have been taught to know tones by names constant for each pitch (Eitz, 82, or other method) have been studied, as well as three who would fall into the musical prodigy class (23, 81, 96). In the experiments on acquisition of absolute pitch adults, both musical and unmusical, have reacted. Stumpf, Abraham, von Kries, Meyer, Köhler, Gough, and Mull have used themselves as reactors.

D.  Results of experimental work on pitch identification

The chart on the next three pages gives the more salient points concerning the reactors and techniques in previous investigations. The points immediately following are those on which agree the five most extensive investigations on identification of notes given in series.

1. White notes are more often correctly judged than black.

2. The more accurate judgments are usually made more quickly than the less accurate.

3. Notes in the middle range are judged more accurately than notes in the extreme ranges.

4. There is a tendency to judge high notes lower and low notes higher than they actually are.

Table I.
Survey of previous experimental work.

Tones in order of correctness, from the most often correctly judged to the least often correctly judged:

Baird (9 reactors):  F, C, D, G, E, A, B, D#, F#, C#, A#, G#

Gough (90 reactors):  C, A, B, G, D, F, E, A#, G#, D#, C#, F#

Mull (4 reactors):  G, C, A, F, B, D, E

Bartholomew (21 reactors):  C, G, F#, A, E, D, F, G#, B, A#, D#, C#

Weinert (22 reactors): D, E, F, G, A, C, D#, F#, B, G#, C#, A#

Specific results from individual investigations follow:

1. Individual reactors tend to give a certain note name (such as a or f) more frequently than other names (Weinert).

2. There is a rather regular decrease in the number of errors with increase in the size of error (Gough, Weinert). These two investigators found no evidence of any special tendency to make errors of a fourth or fifth.

3. Women tend to make more errors of overestimation than of underestimation (Gough, Bartholomew). Men tend to underestimate (Bartholomew).

E.  Factors involved in judgments of absolute pitch.

The numerous factors which have been claimed to have an influence both on absolute pitch judgments and on judgments of isolated tones in general may be conveniently grouped under four headings. These are : (1) objective features of the tones presented and the manner of their presentation, (2) subjective, general psychological factors, (3) practice, whether of the customary musical sort or specifically designed for the acquisition of absolute pitch or related abilities, (4) matters somewhat under dispute, but best classed in the field of tone psychology.

1. Stimulus tones and their presentation

Stimulus tones for passive judgments may vary in timbre, in intensity, in duration, and in the range or extent of the scale covered by a series of them. For each stimulus tone the time interval since music or tones were previously heard will be a variable.

The earlier investigators, mainly von Kries, Abraham, and Ki5hler, were much concerned over the effects of timbre on judgments of absolute pitch. From their own experience or from anecdotal reports they concluded that notes of certain timbres were much more difficult to name correctly than those of other timbres. Because of the non-quantitative nature of their reports it would hardly be useful to give a tabular summary here of the degrees of difficulty reported by them and their observers in this respect. But an average rank order from the most easily and accurately judged to the most difficult would be: piano, violin, woodwind, organ, voice, tuning fork and pipe, bells, and glass tones. The two explanations most frequently offered for this order were (1) that the more familiar a timbre was, the easier it was to judge, and (2) that everything depended on the relative complexity of the wave form of the tone. Von Kries (48) rejects both explanations: (1) on the ground that voice tones, although frequently heard, are very difficult to judge, and (2) on the ground that the complex bell and glass tones were about as difficult to name as the pure tones of tuning forks and variators. Abraham (1) makes similar statements, but adds that the intensity of the upper partials may be more of a factor in causing confusion than the relative number of them. The strong inharmonic partials in bells and human vowel sounds would make these difficult to judge. As an explanation of the fact that certain moderately rich timbres are judged more easily and accurately than purer ones, Stumpf (95) suggests that with an increasing number of overtones the fundamental increases more in importance in comparison with the partial tones, thus making its pitch more salient. But Abraham and von Kries agree that the pitch of a clang is associated not with the fundamental alone but with the fundamental and its upper partials. This latter idea reappears in Köhler (44), who asserts as a result of his experience and experimental work that pitch is a minor feature of tones, and that letter names are associated not with the pitch of a tone but with its "tone-body". This affords a convenient explanation for the timbre effect, since whatever it is that Köhler calls tone-body is supposed to vary from timbre to timbre, while pitch obviously need not. But as might be expected, Köhler was astonished to find a twelve-year-old boy whose accuracy in absolute pitch seemed not to be affected at all by timbre. From this Köhler had to conclude that the boy associated the letter names with pitch after all, not with tone-body. Chiloff (16) is more analytic and states that since the higher a tone is, the fewer perceptible overtones it has, "a complex sound of different height possesses a timbre characteristic of its height". From this consideration and from the fact that his reactors were much more successful naming complex tones than pure, he concluded that absolute pitch depends on the faculty of determining the timbres of sounds of different heights. Baird (9), who worked with reactors highly trained in music, found them less accurate with tones from the clarinet, flute, four organ stops, and tuning forks than with those from the piano. Perhaps they would have become equally accurate after a little practice. Gough (24), who trained musical and unmusical reactors in pitch recognition, found only comparatively slight differences in accuracy of judgment with different timbres.

Hence, the familiarity of a timbre seems to be much more important for pitch recognition than its relative complexity. It is difficult to make pitch judgments on human voice tones for three reasons: (1) while the human voice is heard very frequently, individual singing voices are heard quite rarely, compared to the piano, and voices vary greatly in timbre; (2) the range in both pitch and speed of the vibrato in the human voice is variable from voice to voice and may constitute a disturbing factor; (3) singers not infrequently sing "off key". Tuning fork tones may be hard to judge because, besides being rarely heard, they are often tuned to a scientific scale both lower than and of different proportions from the tempered scale with which musicians are familiar.

Seashore (88) in his discussion of absolute pitch states that the faculty depends on differences of timbre, since one can readily see by running a scale on the piano that its notes differ in timbre. Until oscillographic studies now being made of the wave forms of tones throughout the piano are completed it seems safe to assume that, aside from individual variations in the piano, notes not too far apart are probably quite similar in wave form; the significant variation is in frequency. At any rate it is doubtful that the timbre differences between notes lying close together on a piano could compare with pitch differences in furnishing unequivocally different stimuli for absolute pitch judgments. For example, on ten well-tuned pianos any given note (such as d') would have practically the same pitch, but the timbre of this note (or any other) would vary from piano to piano, especially if the makes and styles were different; besides that, each piano would have more or less slight timbre variations within its own scale which were peculiar to itself.

Inasmuch as there has been until quite recently no satisfactory method for the measurement of the intensity of tones, only suppositions can be made as to the effect of intensity on absolute pitch. Abraham (1) believed that the intensity threshold for judgment of absolute pitch was higher than that for sensation alone, since tones had to be of a certain intensity before he could name them. On the other hand, he thought very loud trombone, bell, and other tones were harder to judge than those moderately loud because the former had more overtones and accompanying noise. He believed that the louder of two tones of the same pitch would be judged the higher because (1) of the greater number of overtones in the louder tones, (2) singers when their breath gives out usually let the tone fall both in intensity and in pitch, (3) a high tone with stimulus intensity equal to that of a lower tone has a greater physical intensity than that of the lower tone. However, he thought the amount of illusion due to the above causes would be too small to affect judgments of absolute pitch appreciably. The experimental work of Guttmann (25) , Hancock (28), and Stewart (93) shows some evidence of the subjective effects of intensity on pitch, but in all cases the effect was quite well within the half tone step.

As has been mentioned above, the duration of the stimulus tone in absolute pitch experiments has rarely been controlled. Abraham (1) is the only writer to mention its effect. By experimenting with a siren he found that for the range of pitches used in music two successive vibrations were sufficient for a sound sensation and also, with practice, for an absolute pitch judgment. The accessory noise of the siren was, of course, a disturbing factor. Very likely the greater the duration of a note, the easier it is to judge, except for those reactors of greatest proficiency, but no experimental evidence is at hand.

The greatest uniformity in the results of experiments on the subject is found in regard to the effect of position within the tonal range on accuracy of judgment. Practically always, notes of the middle range are judged the best, high and low notes less well. Individual deviations correspond with the familiarity of the reactor with certain regions of the scale. For example, Stumpf's (95) double-bass player reactor was superior to the rest in the lower range, the first violinist in the upper range, and Stumpf himself, who had been practicing in the middle range of the piano, was superior to the other two in the middle range. Abraham (1) was accurate over a very wide range, and noted that variations in accuracy did not parallel difference sensitivity. Whipple, Baird, Gough, and Weinert all report the once-accented octave (from middle c upward) as being the most accurately and quickly judged. The other octaves decreased in accuracy as their distance from the once-accented octave increased. Weinert found a very regular alternation in this between octaves above and below the central octave. Baird's and Gough's order for accuracy in the five central octaves is the same as Weinert's.

Boggs (13) reports of some of her reactors that their accuracy was not affected by the region of the scale. Revesz (81) reports the same for the boy prodigy he studied, as does Gebhardt (23). Gebhardt's reactor was accurate for seventy notes of the piano (in a series test), and there is no reason why complete accuracy for all notes of the piano should not exist or be achieved. As Abraham says, the limits of absolute pitch sensitivity may not be far from those of difference sensitivity.

The difference between the sure accurate judgments that are frequently made in the middle range and the approximate, guessing judgments made in the more extreme ranges was one factor that led Revesz (78, 79) to postulate that there were two sorts of absolute pitch judgments, one made by Qualitat and the other by Hate. This theory will be taken up later.

The obvious and adequate explanation for the range effects mentioned above is that the region which is most often used and heard by the reactor is the one which will be the most definitely and elaborately associated in his mind with letter names.

It has been generally assumed that absolute pitch judgments are or at least can be independent of the interval since music or tones have been last heard. Stumpf (95) was not convinced of this before experimenting, but after experimenting he concluded from the introspections of his reactors that interval judgments could be excluded in a series of tones. Every subsequent experimenter has tacitly accepted this assumption. Rupp (87) was the first to point out that the difference between absolute pitch and relative pitch when learning to call notes by their names was mainly a matter of the time since a standard note was heard. He recommended a pause of at least half an hour between threshold work on different notes. Seashore (88) and Dunlap (21) within the past twelve years have strongly recommended that for a crucial test of absolute pitch ability stimulus tones be given in the morning before other music is heard. An experiment by Gough (24) on herself with differential forks is the only one in the literature meeting this requirement. Of the investigators who have given series of notes to their reactors, none has evaluated judgments on the first note separately from the rest, nor have the investigators presented their data in such a form that it would be possible for anyone else to do this.

2. Factors dependent on the reactor's condition and general training

The general psychological factors involved in making judgments of absolute pitch may be divided into (1) specifically localized conditions, and (2) the more diffuse conditions affecting the organism more as a whole. Of the first, larynx sensations are practically the only example of importance for the problem, and of the second some mention should be made of distraction, fatigue, and emotional effects. Within and between these two classes there are also a number of so-called "secondary criteria" to be discussed.

Older psychologists, if represented by Lotze (54), seem to have held that tone perception was curiously limited by the abilities of the singing voice. A similar view was evidently held as late as 1915 by Köhler (44), who was taken to task for it by Watt (106). Stumpf (95) and Abraham (1) have enumerated the fallacies in this view. But there is no doubt that the larynx sensations might be used with some accuracy in making judgments of absolute pitch. Ladd and Woodworth (52) think that an innervation of the larynx is ordinarily present, at least in an inchoate and impartial way, when one is trying carefully to judge the pitch of a note. Abraham (1) thinks that this may be helpful for unusual timbres or uncertain judgments. Only two experiments seem to have been done on the specific problem. The director of the school of music at the University of Illinois was presented certain piano tones within his voice range by Baird (9), and he (the director) judged their pitch consciously by throat sensations. While it would be impossible to say that the usual sort of absolute and relative pitch did not influence his judgments, yet his accuracy with this method was above sixty-three per cent (actual per cent not given). Gough (24) used an apparatus designed for the study of silent thinking to measure tongue and throat movements of two observers while judging the pitch of thirty-one violin notes. She found no evidence of specific larynx movements and concluded that kinaesthesis was a negligible factor in identifying notes. She does not state how proficient these reactors had become at the time of this experiment; an important point, since it might be expected that less expert reactors would make more use of such secondary criteria as larynx sensations than would the more expert.

Baird (9) is the only author to give the voice ranges of his reactors. He states in this connection: " Whether there is any definite correlation between the position and extent of the region of least difficulty and the position and extent of the observer's vocal range, is problematic. There is, of course, a general correlation in that those pitches which the observer can sing are most accurately identified; but there is far from being a perfect coincidence between that region of the tonal scale which can be sung and that region of the tonal scale within which pitch identification is most accurate." The general correlation could be explained by saving that, other things being equal, the observer would likely be generally interested in and pay attention to notes he could sing.

In the system of Dalcroze eurythmics (36) the student "learns to differentiate vocal sounds from (i.e., by means of) vocal chord sensations and by localization of sound vibrations. His hand, laid on his chest, neck, jaw, nose, or brow enables him, by means of the different forms of resonance of vibrations, to realize the pitch of, the notes emitted". Experimental studies of the pitch-naming ability of children so trained should be interesting.

The few mentions of distraction effects are contradictory. Boggs (13), whose conditions were not at all well controlled, reported that interruptions and outside noises were very disturbing to her reactors and prejudicial to accuracy. Gough's (24) and Mull's (65) reactors who were trying to acquire absolute pitch found outside noises very distracting. Weinert (107) on the other hand evidently had considerable outside noise distraction in his experimental work, but this apparently did not bother his reactors nor affect their scores. The explanation of the discrepancy is that Boggs' reactors were young students, while Weinert's were mostly highly trained professional musicians with more firmly set habits of pitch identification.

Evidence on fatigue is also slight. Stumpf (95) attributes the unusual number of errors in certain tests on his reactors to fatigue from previous activity, and Boggs (13) reports that eight of the possessors of absolute pitch whom she interviewed " must not be fatigued in order to do well ". Gough's (24) reactors trying to acquire absolute pitch often reported fatigue. Weinert (107), who gave all the notes of the piano a total of five times to his reactors, found no fatigue effects to speak of, in that there was hardly ever an increase in number of errors from the first series to the last. Evidently those with whom the identification is most habitual and automatic experience the least fatigue.

Abraham (1) tells of a musician who reports that after great tension or depression music seemed half a tone lower to him than it really was. There has been no experimental check on any case of this sort.

Naturally, the accuracy with which a given note can be sung on demand is dependent on the accuracy with which a pitch can be intoned at unison with or immediately after a heard tone. The studies of Miles (62), Sokolowsky (92), Kerppola and Walle (40), and Guttmann (25) all indicate that the accuracy of professionals in singing at unison with a tuning fork or organ pipe is usually within one per cent, and amateur singers are on the whole less accurate. Guttmann concluded from another study (26) on a violinist and a cellist that for women's voices and instruments of corresponding range variations from the correct pitch up to one per cent may be considered correct, and for men's voices and corresponding instruments variations up to one and a half per cent.

Introspections of reactors from Stumpf down agree rather closely on certain points. Reactors who are the most highly trained and accurate give the name of a heard tone immediately and usually cannot explain how they do it. For instance, Weinert's reactors (107) reported in the main that no more concentration nor attention was necessary than for the naming of seen objects. Usually these reactors report that associations of the note with letters, position on the staff, etc., sometimes enter in but are of no special help. With more inaccurate observers, however, and in certain cases with the more accurate, there is much uncertainty and "feeling around". Stumpf (95) says of such cases: " One reacts to the tone whose pitch cannot be determined... as to a quite new, strange phenomenon; even the timbre of my own piano seemed often unknown to me... One hears the tone almost as one hears it before all experience." He also mentions that in the interval between the tone and the judgment the memory for it decreases while the attention increases; the two processes thus working in contrary directions. Revesz (78), evidently in speaking for himself, says that uncertain tones are accompanied by a good deal of testing, verifying, comparing; first, the possible range of the note is limited, then more productions of the tone are wished for, so that the choice may be narrowed down still more. Gough (24) gives very interesting and complete reports of her reactors' introspections and these show some quite individual attitudes towards tones and a diversity of methods of judgment.

A brief list may be made here of the associations with tones which reactors report; some of which may be used as indirect criteria in locating pitch.

(1) Keyboard associations. Stumpf (95) and one of his reactors always had the touch of the piano key ideationally present when making a judgment. Whipple's reactor (111), one of Boggs' (13), and forty-five of Gough's (24) reported ideas of spatial position on a keyboard. Gough's reactors were tested in pitch estimation with a keyboard chart before them. Some of them felt that spatial position was the main or only guide in identification.

(2) Other executive associations. These include for violinists the hand position on the violin string; for singers, larynx positions.

(3) Musical associations. The heard tone may be recognized as the first or other prominent note of a certain song or composition. The sound of triads built on the tone may be thought of. Reactors may tend to call high notes because the symbol raises a tone.

(4) Non-musical associations, such as pain with high notes, and colored hearing. Here also belong such associations as "f seems split open " (Köhler) and of certain tones as "woody" or "muffled" (one of Gough's reactors) .

It is indicated that these secondary helps bring in their own sources of error and never admit of the accuracy of the immediate judgments without conscious association that experts are able to give. But as Abraham (1) states, if there are those who cannot name tones but who can produce them on demand, they must do so with the aid of these secondary criteria.

3. Practice Effects

Under the effects of training on judgments of absolute pitch there may be distinguished general musical training in the various branches of the art, and practice specifically designed for the acquisition of absolute pitch.

Judgments of absolute pitch can of course be gotten only from those in whom the basic associations have been formed, and practically all these are musicians of more than average competency. Bartholomew (11) found that as a general rule the proficiency of a reactor in pitch identification increased with the number of ear training and harmony courses reported. But many authors make the remark, probably based on personal opinion, that the majority of musicians do not possess absolute pitch. No one has found whether or not special training in pitch discrimination would have any influence on absolute pitch; the assumption is that it would not, since accuracy in judgment of the pitches of notes in different parts of the scale does not appear to vary with variations in pitch discrimination. This applies of course to pitch naming judgments in the ordinary chromatic scale where the difference between named pitches is a semitone.

It is generally assumed but not proved that string instrument players are more accurate in naming the pitches of the open strings than in naming other pitches. The effect of voice range on absolute pitch range has been mentioned. Harris (29) affirms that "a vocal student is often able to pitch a sound with remarkable accuracy if he can sing it, but guesses wide of the mark when asked to name a note sounded on an instrument".

The question whether or not absolute pitch can be acquired by anyone was in former time usually answered in the negative. This was perhaps due to two causes: first, the fact that musical talent used to be generally considered a mysterious and unitary entity, and, second, the striking contrast between some isolated examples of phenomenal absolute pitch (as that of Mozart) and a few statements of musicians such as the famous voice teacher Stockhausen (94) to the effect that they had not been able to acquire absolute pitch after long and arduous endeavors. Nevertheless, as excellent an authority as Jadassohn (35) stated before 1899 that the faculty was easily acquired. Neutral evidence is that given by Boggs' (13) and Weinert's (107) reactors who reported that the faculty appeared in them without any special practice. The first actual experiment on acquisition was that of Meyer (58) with himself and another observer, who learned to name sixteen tuning forks from 100 to 4000 v.s. by their vibration numbers, and thirty-nine notes of the piano with a rather high degree of accuracy, but both men evidently had a fair share of the ability to begin with. Baird (9) rejects their conclusion and states that the ability is very difficult to acquire, but there is absolutely nothing in his experiments or data on which he could base such a statement. Boggs (13) improved her pitch naming ability by paying especial attention to overtones, and Köhler (44) his by concentrating on "tone-body". Copp (17) states very dogmatically from her experience as a school music supervisor that eighty per cent of all children can acquire absolute pitch, but gives no statistical data. The studies of Katz (39) and Bennedik (12), who worked with children taught by the Tonzcorti ethode of Eitz (82), substantiate Copp's general conclusion though not her high percentage. But the studies of Gough (24) and Mull (65), very much different in technique but alike in aim and general results, show that a certain amount of pitch naming ability can be acquired by musical and unmusical college and graduate students. The first trained a group of over ninety Smith College students in naming piano tones given in series, and found a general though not large increase in accuracy. The range of the original and acquired pitch identifying abilities within the group was large and the individual practice curves very irregular. Neither the original nor the acquired pitch naming ability seemed to have much relation to musical training nor to frequency of hearing piano tones. She found evidence of some retention of the acquired ability after a year's time. Mull (65) trained observers more intensively to single notes of the Appunn Tonniesser and found that they could learn to recognize the learned note as different from pitches less than a half tone away. These two studies, supplementing each other, indicate that systematic practice in pitch identification is effective, even though carried on for short periods of time.

Those who have outlined plans for the acquisition of absolute pitch usually recommend beginning with intensive attention to one note. The next step advised is practice either on the octaves of that note or on other notes in the same octave. Gough's (24) experimental results indicate that this advice is not entirely well founded. Observers become bored with the piecemeal method and find that it gives little scope for variety in practice. She concludes: " 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."

In the system of Dalcroze eurythmics (36) the students are taught to sing all twelve scales starting with middle c. The author of this system states that " this so impresses c on the memory that a student can sing it without an instrument, also he can by means of this c determine the key and individual notes of any piece he hears ".

The difficulty inherent in acquisition of absolute pitch is explained by Watt (106) and others by pointing out that relativity in pitches is more important for music and hearing than is any absolute value. Abraham (1) adds that we pay attention to timbres as such more frequently than to pitches as such, and also that tones affect one modality and hence are less likely to acquire specific names than objects that affect two or more modalities.

A great deal of stress has been rightly put on the contention that one should attend closely to the individuality of the various pitches if absolute pitch is to be acquired. As Kfilpe (51) has pointed out, " there is nothing in the whole construction of the musical scale to call attention to the absolute significance of the separate qualities " (meaning pitches). And Warren (105) adds that since tones cannot be recognized by most people as the same after a period of time they do not acquire names, as colors do. Hence it is necessary to pay special attention to tones as individuals and unusual concentration is required, since tones do not ordinarily have associations with other modalities, as the taste of a strawberry may with red. Boggs (13) lays stress on the desirability of attending to each tone and its overtones as distinct from other tones. Köhler (44) says that to him c is closed, fast; g is satisfied and restful; f is split open. One wonders how well together the strings for f on his piano were tuned. If individualization consists in developing associations with other features of a tone than the pitch feature not a great deal of transfer of pitch naming ability to tones of other timbres and intensities would be expected. It is not surprising, then, that Köhler, who acquired his absolute pitch on the basis of " tone-body ", would not be able to find the closed, satisfied, or split qualities in pure tones. Revesz (78, 79) states that for the fortunate individuals with qualitative absolute pitch tones stand out as distinct identities, while for others there is no differentiation between adjacent tones. This difference he likens to that between perception of colors and perception of grays. Perhaps he gets the cart before the horse as does Wellek (108) who says that "to assert that tones have no characteristics, no character peculiar to themselves and distinguishing them from others" is to reduce them from the psychological level to the physical. No doubt tones have pronounced characteristics for Wellek and others now, but that does not mean that these characteristics are inherent and not built up.

Experimental studies confirm the advantage of individualizing tones. Children taught by the Tonwortrnethode, in which c, d, e, etc., have always the same name, have been shown by Katz (39) and others to acquire a measure of absolute pitch, and both Gough (24) and Mull (65) are convinced from their reactors' introspections that individualizing of tones is of prime importance in acquiring absolute pitch. Gough had each of eighty observers concentrate on a specific piano note in the learning, and found that each observer named her own note correctly about two and a half times as often as the average of correct namings for the other notes.

The influence of the tuning to which the reactor is accustomed is an important though not much noticed topic. Braine (14) remarks pertinently that a violinist must keep his instrument strictly in tune if he is to acquire absolute pitch. Planck (75) tells how as a boy he developed a pronounced Tongefuhl for his own piano and felt confused when playing on pianos of different tunings. When older he could with sufficient effort raise his a half a tone up or down. Abraham's experience (1) was almost identical. Three of Weinert's reactors (107) present significant examples of this. (1) Nerong, a fourteen year old boy, had studied piano for four years; his teacher's piano and the test piano at the university were tuned to international pitch but the one in his home was one and a quarter tones lower, being old and weak. Weinert tested him on both pianos and concluded that he evidently had absolute pitch memory independently for both tunings. It is unfortunate that the test was to name notes given in a series, since this makes it impossible to tell how far these pitch memories were really absolute and not relative. (2) Sager's piano was a quarter tone too low, and with him there was not the distinct separation of tunings that Nerong was supposed to have had; this resulted in Sager's uncertainty with both tunings. Both he and Nerong judged notes from their own pianos better than those of the university piano. (3) Lindenborg at the time of his first test had a cold and was also concert-master in an orchestra that for two weeks was being tuned a half-tone low; most of his errors were a half-tone too low. Several months later, after these influences had ceased, he named tones accurately.

Triepel (99) reports that his father, who owned a French piano tuned about one-fifth of a half-tone higher than the German standard, always named notes from a German piano a half-tone too high. Since he always tuned his piano himself it is possible that the real discrepancy in tuning became higher than the theoretical. Perhaps also the first time he named tones from a German piano their (to him) unfamiliar pitch was confusing and he gave them half a tone too high, and the tendency persisted.

4. Factors belonging to the field of "tone psychology".

Of the factors that may be said to fall within the domain of "tone psychology", the following have been thought to have influence on absolute pitch judgments: (1) periodic qualities supposed to be inherent in the pitch scheme and repeating themselves from octave to octave, (2) what Stumpf calls the "Octave Töuschung ", best translated not as illusion but as confusion of a note with its octave, (3) interval judgments, conscious or not, based on preceding tones, (4) auditory images of tones, (5) attributes of the auditory sensations, such as brightness, vocality, tone-body, and volumic outline, which are assumed by some English, German, and American psychologists to inhere in tones in addition to the universally accepted attributes of pitch, timbre, intensity, and duration.

During a study of the question of periodic qualities in the pitch series the whole matter seems vexing and fruitless, but on further thought the question resolves itself into two simpler forms: (1) are periodic qualities inherent, and if so, (2) is perception of them the inborn gift of a limited number?

The use of the term quality in this connection tends towards confusion, as about three meanings have been given to it. The terms to be used here in speaking of the three meanings are (1) individuality, not necessarily respective of timbre or position in a scale but including extraneous associations, (2) timbre, the tonal characteristic dependent on wave form, (3) periodic quality, that which all a's, b's, or c's are said to have in common and by which all a's differ from all as's, etc. Musicians that Boggs (13) interviewed reported making use of the first type. Von Kries says that tones have for him a characteristic which is evidently a combination of the first and third. It is difficult to be sure of Kulpe's meaning (51): it perhaps includes all three. Meyer (59) , after rejecting independent variability as a criterion for an attribute of sensation and championing as more fertile for science a more naive attitude towards sensations as they are, concludes that besides intensity and duration the attributes of auditory sensations are pitch, which he conceives as being inherently periodic, and quality, which is equivalent to Stumpf's Tonfarbe and Klangfarbe. "Absolute memory for pitch " is explained as much less a memory for pitch than a memory for quality, and thus he would seem to argue that wave-form rather than a local sign factor (which does not appear in his theory of hearing) is important for absolute pitch. In 1929 he states his position thus (61) , using the term vocality in place of quality: " For me it is a tremendous achievement when, by listening to the relative shrillness, that is, the voicing of a piano tone coming to my ear, I can tell that it is neither below the middle c nor above the d next to the right. With tuning that has nothing to do, for we do not say that the tone d is mistuned when it is heard instead of c." Revesz (78, 79) is outspokenly committed to the existence of an inherent periodic quality (Qualitat) in tones existing alongside of a feature called tone-height (1-1-Otte). This is not dependent on common overtones, as Helmholtz thought, because the periodic quality appears in pure tones. But Revesz does not demonstrate that perception of the periodic quality is naive and not built up by association. He argues that in a case of pathological hearing that he investigated all tones from c" ' to 4" ' had the quality (periodic) of 4, yet playing them in a scale gave a sensation of change of height (Mille). He thinks it possible that in other pathological cases two different qualities, say e and f, may have the same height, as g. Also, as Meyer (59) remarked, with very high tones change of height may be perceived but periodic quality is lacking. Since a quality such as a appears many times in the scale, and a certain height, as that of a, only once, the height of a tone is never so exactly individualized as its periodic quality. Baird (9) agrees with Revesz that certain " quales " of c-ness, d-ness, etc., are inherent in tones, but there is absolutely nothing in his published data to necessitate such a view.
Riemann (84) rather ridicules Revesz' pitch dualism. He says that in his own experience he can not find the difference between Qualität and Höhe by any of Revesz' criteria. He can give names to the pitches of König's cylinders, and an octave interval on them does not seem to him like a ninth. This would contradict Revesz' assertion that the Qualität feature exists or functions only in the middle ranges. Riemann mentions that Aristoxenos 2200 years ago pointed out these attributes as merely two ways of treating the same thing. Finally he states that Revesz does not specify how many qualities there are or should be, nor whether or not these should enable one to notice comma differences. Ogden (71) argues that the difficulties in the case of pathological hearing that Revesz investigated were not peripheral but central, and hence a matter of association. Redfield (77) quite emphatically states that "nothing perhaps is more subversive of effective harmonic practice, nor of consistent harmonic theory, than the gratuitous assumption, now so universal as to be almost the corner-stone of harmony, that tones an octave apart are harmonically identical".

Weinert (107) explained Revesz' dualism to his expert reactors after testing them and they all reacted negatively to it. They never reported judging separately according to periodic quality and height. If they thought of e or f at the height of g" the result had the "quality" of g, not of e or f. No sharp divisions were found between ranges in which errors were scarce and in which they were plentiful, hence notes were not judged by quality in the middle and height at the extreme ranges. Tones of the same "quality" (as f) in different octaves were frequently given different letter names; this alone would indicate that "quality" was not independent of "height". Of course, Revesz' loophole in answering these objections would be to say that the errors made by Weinert's reactors may be attributed to a momentary lapse of the Qualität criterion and a use of the less dependable Höhe alone. Bartholomew (11) states that the great majority of his reactors said there was no characteristic quality for each of the twelve notes. Gough (24) reports that for many of her observers the tone series was evidently unidimensional without distinctive recurrences from octave to octave. Those who did report such recurrences found them usually in the middle range. Mull (65) found little evidence of judgment by periodic quality in her reactors, but most of her work was done with notes from a range of less than two octaves.

It is obvious that any audible pitch belongs to a family of pitches whose vibration frequencies are to each other as the powers of two are to each other. As far as is known, the cochleae and nervous systems of all with normal hearing respond to all these pitches individually. In so far there may be said to be inherent periodic qualities. But the evidence above points to no special adaptation of the organism for perceiving periodic qualities nor to any group of people who have exclusive use of such an adaptation and can use it separately from their perception of pitch height. Rather it indicates that people may build up strong associations with individual tones (perhaps often from their functions as tonic, dominant, leading-tone, etc., in certain familiar scales) and these associations may come to function almost without fail when the tone is heard. Associations of this type would naturally not be so rich or strong with extremely high or low tones, since these are less often heard and used, and are less interesting than more centrally located tones.

The fact that musicians sometimes make an error of exactly an octave in judging the pitch of a tone, especially one of unfamiliar timbre, has been given a rather undue importance. Stumpf (95) explains this octave Tauschung or confusion by saying that except for pure tones each simple clang is the same in pitch as the first over-tone of the simple clang an octave below. Therefore two such tones become associated with each other and tend to become confused, especially as they have the same letter names in music. The fusion of two simultaneous tones an octave or a fifth apart he called fundamental, but the similarity in periodic quality of two successive tones an octave apart he would lay to a habit of perception (60). In his experimental work on absolute pitch he did not have his reactors give the octave locations of the notes, as he thought most octave errors would be due to the reactor's unfamiliarity with the octave designations.

Revesz, as has been shown, considers a similarity between notes lying an octave apart as absolutely fundamental, whether the notes are simultaneous or not. To account for the fact that those who have what he calls qualitative absolute pitch do not in naming notes make more octave errors than they do, he says that they judge tones by both Qualität and Höhe, getting the letter name from the first criterion and the octave position from the second. Lapses in attention to the Hate criterion, as well as unfamiliarity with the names of the octaves, cause the octave errors and these are reduced by practice. Köhler (44) says that neither he nor his reactors made octave errors because the brightness difference between the two notes of an octave on a familiar instrument is too great for confusion. However, this difference is not great enough to prevent tones a fourth or a fifth apart being confused by their similarity in tone-body.

Whipple's reactor (111) made no octave errors, but she was tested within a range of only two octaves. Baird's (9) supposedly expert reactors frequently made octave errors though getting the name of the note correctly, and this tendency was less pronounced with the organ than with the piano. Baird thought that this indicated an effect of timbre on the octave illusion but it must be remembered that the range of the organ was sixty-one notes, while the piano has eighty-eight; hence it is quite possible that if octave errors made in the outer octaves of the piano were excluded there would not be so much difference in the results between the piano and organ. Gough (24) found a conspicuous rise in the error curve at the octave in only nine cases out of eighty-nine; in the others there was little change at this point. It is inadvisable to draw conclusions as to the nature and effect of octave confusions from such contradictory reports, inasmuch as techniques of experimentation and proficiency of reactors vary so much in these investigations.

It is the consensus of opinion that a facile auditory imagery for tones is in no way essential to absolute pitch ability, but that it may be helpful. Whipple's (111) reactor could image and produce tones with accuracy, but no extensive tests were made of this. Some of Weinert's reactors (107) reported that they sometimes judged the presented tones by comparison with a memory tone, but the effect of this on accuracy was not ascertained. One of his reactors audilized a major triad over doubtful tones and this usually led to accuracy. Gough (24) found that reactors possessing a predominance of auditory imagery, as indicated by a questionnaire, ranked from the middle to near the top in ability to identify notes. She concludes that good auditory imagery is more important than kinaesthesis for recognition of tones.

If a series of notes is given in a test for absolute pitch, the question immediately arises, would not the reactor be bound to compare consciously or unconsciously all the tones after the first with a previous tone or tones in the series and estimate the present tone as a fourth above, ninth below, etc., a preceding tone? Stumpf (95) at first thought that interval comparison could not possibly be avoided in such a test, but after some work of this sort decided it could be eliminated if long enough pauses filled with other activities were introduced. He states that interval comparison always bothered him when pauses between notes were long enough only for the response to be given. All observers who have used a series of notes in testing for absolute pitch give rather specious reasons for their belief that interval comparison may be excluded. Stumpf says interval comparison is possible only when the preceding tone and the interval between it and the tone to be judged are clear in the mind; also that concentration on the latest heard tone will exclude comparison with earlier tones. Abraham (1) cites Wolfe's work (116) as showing that memory for a tone vanishes rapidly. As a matter of fact, Wolfe's work was with pitch intervals which, except for lower tones, are much finer than those in the musical scale, and he also found evidence of a periodic recurrence of the memory image. His time intervals also were never greater than sixty seconds. Abraham also mentions that an eb given after a correctly judged b is always named as eb, never as d, as would be expected from interval comparison. But that does not in the least exclude the possibility of interval comparison. Köhler (44) thought absolute pitch judgments were too quickly given to allow time for interval comparison, since with the same reactors interval comparison might be slow and poor. These generalizations are based on no actual data or tests, and no specific relation was worked out between the two methods of judgment for the same people. As a third reason he states that some people can judge intervals in regions in which they cannot judge absolute pitch, but this proves nothing about judgments at ordinary ranges. Baird (9) mentions some unsuccessful attempts to trap his reactors into interval judgments during a test series; this made him feel that the interval judgment did not affect the results. None of these investigators seem to have considered that interval judgments may be incorrect as well as correct and that the former sort may have as certain an effect as the latter, and that even though there may be no trace of correct interval judgments in the results of a series test for absolute pitch, yet incorrect interval judgments may be there in numbers. Failure to consider this is curious, since it is often mentioned that absolute pitch and good relative pitch are not necessarily found in the same person.

On the other hand, Bartholomew (11) and Weinert (107) frankly give evidence of interval judgments when the stimulus tones are given in series. The first reports that the majority of observers noticed at least some degree of influence of the preceding tone on the tone being judged. One reactor, who said she did not consciously use relative pitch, evidently did anyway as in sixteen successive judgments her errors were +1 fourteen times, +13 once, and -11 once. Here all the names were being given a semitone too high. Weinert also says that reactors frequently reported making judgments by intervals, usually with immediately preceding tones. One reactor judged intentionally by interval in the first three series and not in the last two; this resulted in a shorter reaction time and more errors for the last two series. He concludes that while in many cases absolute pitch and relative pitch are in close connection, yet there are plenty of cases in which a faulty Intervallgehor exists alongside of good absolute pitch ability (as measured by his method). Also with seven reactors there was some spontaneous correction of previous tones due to interval comparison with the just given tone, sometimes over wide distances. Falsely judged tones sometimes caused preceding ones to be falsely corrected. Evidently, then, there is no sure way of eliminating relative pitch judgments in a series of pitch estimations.

It is hardly necessary to discuss in detail here the so-called attributes of brightness, vocality, volumic outline, and tone-body which have been asserted by some writers to be fundamental in tone perception. Abraham discovered brightness by comparing the tone produced near the center of a siren with a tone of the same frequency produced near the periphery. The tone from the periphery had a harder, brighter sound. Hence Abraham assumed that brightness was independent of pitch but varied with it to a certain extent, higher tones being generally brighter than lower. Meanings of the term brightness vary among the writers, but Ortmann (72) has shown that it can be logically explained as a secondary quality integrated from pitch and intensity. Köhler was led to postulate a vocality attribute to tone sensations in which reactors reported that low tuning forks had the sound of oo, higher ones o, ah, ay, and the highest ee and i. He asserts that he can easily name tuning fork tones by attending to their vocality, but piano notes require a different method since they do not have much vocality. Volumic pattern is the volume characteristic of tones, by which some tones appear larger than others. Rich (71) claims to have found a differential limen for this not coincident with the difference limen for pitch. Tone-body seems to be either a complex of all the attributes or an integration of volume and brightness. Köhler, for instance, says that a student who always names piano notes perfectly may call an a tuning fork d and feel no discrepancy, and this is because the tuning fork a is more similar in tone-body to the piano d than to the piano a. He concluded that pitch recognition based on tone-body alone would be helpless when strange tone-bodies are judged, but this is merely a repetition of the old statement that differences in timbre affect pitch judgment. He explains the difficulty of judging human voice tones by saying that while the voice maintains the same pitch its vocality and brightness can be varied. Watt (106) thinks that most of Köhler's conclusions are unwarranted and refutes them in detail.

While it must be emphasized that absolute pitch associations may fully as well be bound up with the whole impression of a tone as with its pitch characteristic alone, still it is hard to see the advantage in multiplying entities of tonal attributes, especially since these new entities can be readily explained as compounds of timbre, pitch, and intensity, and as built up by association with other fields of perception.

5. Relation of the Naming and Intoning Abilities

All investigators have noted that the ability to sing tones correctly on demand is much more rare than the ability to name them. Von Hornbostel (32) observed that many persons when trying to sing a tone immediately after it is heard will make large errors. He thought the cause of this was that they tried to match the heard tone in their voice not by pitch but by timbre. Köhler (44) says that the idea of a certain frequency (pitch) would not tend to bring up the idea of any certain tone-body, and thinks that this explains the difficulty of intoning specific notes on demand.

Bennedik (12) trained three children to sing by the Eitz method described above and found that the naming and intoning abilities developed at different tempi in different children, but that the naming ability developed first. Katz (39) tested twenty-four. eleven year old children who had had a month's training in this method. He had each of them intone four certain notes on one day, and on a subsequent day write down the names of the notes when presented. He found them slightly more correct with intonation than with naming. Gough (24) had nine reactors sing a' and c' from memory into a tonoscope and found that those who could do this most accurately were those who were best at naming notes. Three violinists had the best results of the group for a', but on the whole c' was the more accurately intoned. Weinert (107) found two-thirds of his reactors able to name and reproduce tones quite correctly, and these seemed to be more independent of timbre in pitch naming than the others.

6. Colored Hearing

The relation of colored hearing to absolute pitch is mentioned occasionally, but only one case in which both were present has been thoroughly investigated. Abraham (1) stated that a few of those who answered his questionnaire reported both phenomena. These did not derive their pitch judgments from the associated colors but report that the latter came into consciousness coordinately with the former. Of Weinert's twenty-two reactors only one reported color associations with tones. Anschutz (6) investigated a musically proficient man who had become blind twenty years before at the age of thirty. He had pronounced and constant associations of colors with tones and heard no tones or music without photism. He was given all the tones of the piano to judge by letter name only, and the correspondence between the associated colors and the reaction times and errors was worked out without regard to the effect of the pitch judgment itself on the reaction time. There were more errors on tones for which the photism was " thickest " than on the others, and it seemed that tones associated with yellow (a) and blue (c, eb) were more often correctly judged than those associated with orange (a#) or red (f, d, b). Perhaps yellow and blue were preferred colors.

Wellek (108) states that those who assert that individual tones and keys have no peculiar distinguishing character are analogous to the color-blind, who see nothing but a series of grays of various brightnesses. Revesz (78) makes a similar assertion about those who perceive no periodic quality in the scale. This simile is too far-fetched to be useful. First, neither author is able to demonstrate that there is any basic physiological difference between those who perceive " quality " and those who do not. Second, neither can show satisfactorily that perception of " quality " in the tone series is not built up by association. Third, Revesz at least intimates that perception of " quality " is rare, but forgets that its so-called analogue, color vision, is the rule, not the exception.
Kramer (41) describes a somewhat visionary method (Marco-tone) by which absolute pitch might be taught. In this system school children were taught to associate each note of the scale with a certain color; then when a tone was heard the child could tell the name of it from the color sensation aroused. There seems to be no report available as to how successful the method was.

F.  The basis of absolute pitch judgments.

Since pure tones are relatively seldom found in musical practice it must be assumed, with von Kries (48), Abraham (1), and Schafer (89), that letter names become associated originally not with isolated tonal elements but with tonal complexes. or patterns. This view differs from Köhler's (44) and agrees with Watt's (106) in that the predominant emphasis is placed upon the pitch of the fundamental as a criterion, since it is mainly in this that the middle c's (or any other specific notes) of all instruments and timbres are alike. Since the fundamental seems to be practically always dominant in a complex of fundamental and overtones, and since the number and intensity of overtones varies so widely from one timbre to another, there should be no reason for not basing absolute pitch judgments on the most constant and dominant portion of all the F's (or Bb's) in music—the pitch of their fundamentals. Confusion in naming tuning fork tones, especially if this timbre has never been heard before, would hardly qualify as an objection, as there is little reason for believing that people with absolute pitch for piano tones could not learn to name tuning fork tones with a little practice.

But this view in no way denies that attention to the overtones in a clang may not help to fix the name of the fundamental, as Boggs (13) and others have reported. The more concentration there is applied to any bit of sense data and the more its details are attended to, the more likely it is to be remembered in specific connections.

Ogden (71), following Rich, and Watt (106), emphasize the importance of attention to volumic outline or pattern in a tone for judgments of absolute pitch. That volume is a primary characteristic of auditory sensations has not been conclusively demonstrated, but at all events those who claim to have found it say that it varies directly with the pitch, but not as finely. If such is the case, it would have to take a secondary place as a criterion for absolute pitch or pitch sensitivity of any kind.

Older writers, like Wundt (117), thought an inherited Anlage as well as practice were prerequisite to absolute pitch. Some musicians (i.e., 91, 114), who as a rule are uncritical, are quite positive that absolute pitch ability is inherited and cannot be acquired. Revesz (78) is positive also that qualitative absolute pitch is inborn, while judgment by pitch height can be acquired with difficulty and may be quickly lost. Recent work (Gough, 24, and Mull, 65) has shown that absolute pitch can be acquired, but with rather wide individual differences. Hein (30) analyzed mathematically the errors made by two reactors in judging piano notes in series, and developed curves which seemed to be symmetrical with respect to a central note having few or no errors. From this he concluded that mathematical features of the scale are bound up with these errors, and that this pointed to a latent absolute pitch underlying all tone perception. While his mathematics may not be pertinent, his conclusion is very possibly well taken.

Haecker and Ziehen (27) found some evidence that absolute pitch was inherited through the father more often than through the mother, but this and all their other conclusions, being based on questionnaires, are quite open to question.

Weinert (107) suggests as prerequisites (1) an individual Anlage, perhaps based on finer differentiation of fibres in the labyrinth, and (2) practice with an instrument standing always in normal tuning.

There has been some discussion as to whether the naming of a heard tone by comparison with a memory tone is essential to absolute pitch. Seashore (88) is quite certain that all absolute pitch judgments are made by this method, but gives no proofs. Rupp (87) is quite as certain with more right that absolute pitch in its true sense is dependent on a whole scale of tones imprinted in the memory, and judgments made by comparison with one memory tone are something else than absolute pitch. Chiloff (16) thinks that most absolute pitch judgments were done by comparison with a memory tone, but his data neither clearly supports nor denies this.

Abraham (1) raises the question whether or not an "absolute key consciousness" may not precede absolute pitch genetically, but disposes of it by saying that he knows of no musician who has acquired absolute pitch in this way.

Two other statements as to the basis of absolute pitch should be given because of their divergence from the general assumptions. Von Kries (49) observed that although a memory tone might be fresh in his mind yet he could not sing it, nor could he judge a note of strange timbre by comparing it with a memory tone. Since so psychological a matter as a memory tone failed him, he concludes "we must seek the basis of recognition in a physiological process, whose entrance can depend accordingly on many sorts of physiological conditions".

Auerbach (7) remarks that absolute pitch is a product of such factors as the dissimilarities and faults in the tonal scale and its production. Some of the latter are: faults and critical points of instruments, the inability of the larynx to make other than certain tensions, differences between the black and white keys. Most authors would call these secondary criteria.

G.  Comparative aspects of absolute pitch.

1. Distribution

There are no reliable data as to what proportion of musicians or of the total population has come to acquire absolute pitch without practice specifically designed at obtaining it. Baird (9) states that most reported cases of absolute pitch turn out to be relative pitch: that is, most such people feel around with their voices or hum in order to judge a note. Slonimsky (91) states that the number of " absolute pitchers " is much fewer than generally supposed, especially among Wunderkinder. Riemann's Musiklexicon (85) states that orchestral musicians usually have absolute pitch because of their frequent tuning of their instruments; Wilson (114) agrees and adds that many organists do not have it—they often cannot find the note on which the priest is intoning. Such data as are given below are merely suggestive because the methods of testing were inadequate and unstandardized, and groups were not well selected.

Haecker and Ziehen (27) made a study of the inheritance of musical talent from 295 replies to questionnaires, giving information on about 5000 persons. Of all the cases reported, 64 (50 men, 14 women) were mentioned as having absolute pitch, and if the number was restricted to those who filled out the ques. tionnaires it becomes 35, or 12 per cent of 295. This percentage is probably much too high for the general population, since questionnaires were sent mainly to musically inclined people, were probably the more often filled out by the more musically inclined, and the material came mostly from the music-loving people of north Thuringia.

Mjøen (63) and Koch and Mjøen (43) made similar studies. Eleven per cent of the 2452 people reported on in the former study had absolute pitch, and of these 51 per cent were classified (by the rest of the questionnaire data) as very musical, 42 per cent as musical, 6 per cent as somewhat musical, and 1 per cent as unmusical.

Harris (29) mentions a test for absolute pitch given at the Royal Academy of Music in London in which only one out of seven students could name correctly any note named or sung. He knew of three such people in a town of 3000, and five in a town of 5000.

Weinert (107) gathered from his reactors the following data on distribution of absolute pitch in musical communities:

Stumpf (95) and others held the opinion that the ability was less frequently found in women than in men. Weinert's and Bartholomew's investigations, however, showed no significant sex differences. All the reactors in both Baird's and Gough's experiments were women; Baird's were experts, and some of Gough's acquired something like an expert status. Koch and Mj~en's study (43) (based on questionnaires) found no sex differences.

There have been the usual attempts to classify the possessors of this ability into types. Revesz' dual classification has already been discussed. Wellek (109) suggests three types: first, those who usually err by only a whole or half tone; second, those who usually err by a fourth or fifth; and third, those for whom associated colors help the judgment of certain tones. There is no evidence in any of the experimental work for a sharp differentiation between the first and second types, and Wellek (109a) is the only investigator to have found a predominance of the second type. Eighteen out of the twenty reactors he tested with seventy-three octaves, major chords, and minor chords each throughout the piano range made errors mainly of a third, fourth, or fifth. The description of the procedure and the statistical statement of the results are both quite inadequate. Most other investigators would have been slow to admit that reactors making such consistently large errors had any absolute pitch worthy the name. Wellek states (109) that there are two sub-types of the third, synoptic type: one resembles the first type in that its exponents make in the main half or whole tone errors, supposedly from confusion of the color aroused by the stimulus tone with closely neighboring colors in the spectrum, and exponents of this type are frequently found; the other resembles the second type in making larger errors due to confusion of the colors aroused with related colors at a spectral distance corresponding to the interval of a fourth or fifth. He cites Scriabin as a master example of this sub-type, which is seldom found.

Weinert's terminology is: unipolar for those who can name tones but not reproduce them, and bipolar for those who can do both. Seven of his reactors fell into the former class and fourteen into the latter, thus reversing the usually estimated distribution. Gough, Mull, and Bartholomew describe individual differences in speed and sureness, but attempt no classifications.

Anschutz, quoted by Weinert (107), advances the interesting hypothesis that people with absolute pitch belong to an analytic type which tends to notice individual things in the environment. They would represent Spranger's " aesthetic man ".

2. Absolute Pitch in Animals

Abraham (1) taught a parrot to sing a phrase of four notes, and the parrot always sang this phrase at the same pitch level. The same experiment succeeded likewise with a starling. All subsequent references to absolute pitch in birds (Hornbostel, 32, Myers, 67, and others) seem to be based on Abraham's two pets. But the author, following Stumpf (97), would hazard the statement that orioles, wrens, bluejays, and perhaps the great majority of songbirds repeat their songs at approximately the same pitches,. or in the same " key ". If birds have not acquired the concept of transposability in song their sense of absolute pitch can hardly be compared with that of human beings.

Kalischer, quoted by Johnson (38), thought that his dogs had absolute pitch because the animals learned to expect to be fed after one note of a pitchpipe and not at another. But Johnson's own work shows conclusively that it is almost impossible to learn much about the pitch perception of animals even when conditions are very rigidly controlled, and conclusions drawn otherwise are quite unreliable.

3. Absolute Pitch and Primitive People

Myers (66) in 1907 suggests methods for testing for awareness of absolute pitch in primitive people. He includes aversion to transposing as one criterion of this, but such a criterion alone is quite unsafe. Later (68) he describes some Malu songs from Murray Island in Torres Strait which show after the end of each verse a return to an initial high note so as to start the next verse. His account is not clear as to the accuracy of this return. On this and other grounds he states that the sense of absolute pitch is probably strongly developed in primitive people. But Stumpf (97) states emphatically that primitive people readily transpose their songs, and so it is doubtful whether the phenomenon Myers describes is anything more than a rather well-developed relative pitch.

Von Hornbostel (33) advances the hypothesis that the presence in two or more races or culture groups of the same or similar scales containing a number of notes of the same pitch is a pretty sure indication of cultural connection. Four xylophones from Burma and two from Africa show a remarkably close correspondence between certain notes and also between the scales. The same is true for pan's-pipes found only in Western Polynesia and Peru. He argues that this correspondence was an auditory matter, not visual, because pan's-pipes and xylophones vary greatly in size, as do other primitive instruments. This close correspondence between instruments from widely separated regions is rather astounding, and if not due to chance could be explained only in three ways: first, by the travels of a primitive instrument maker with remarkably good absolute pitch; secondly, by travels of a certain instrument or succession of instruments now lost, to which others were tuned; or thirdly, by a combina tion of the two methods. Generally speaking, it would seem that the conditions of native life, which allow little means for standardizing the tunings of instruments, would be very unfavorable for the development of absolute pitch for a large number of notes or for an absolute pitch widely transferable; but on the other hand a xylophone player hearing constantly and attending to only eight or ten notes might easily develop a strong memory for those notes.

4. Absolute Pitch in Children

Though little study has been made of absolute pitch in children and much of it is defective, it seems rather clearly demonstrated that it is possible for normal children to learn to identify notes and to sing certain syllables at the same pitches, if they are not taught singing by the Tonic-sol-fa or other transposing method. Stumpf (95) found two children, an eight year old musically talented girl and his own seven year old son, to be quite accurate at naming pitches. Abraham (1) trained three four year old girls to sing " Ade " to the notes a'-d'; one of them had been to kindergarten where songs were transposed, and she sang the word at various pitches but with the correct interval; the other two were always correct even after three months, and one of them after one and three quarters years. Bennedik's (12) study of three children has been mentioned; all three acquired absolute pitch ability but in different measures. Of three other investigations, Schoen (90) gives no statistical data on absolute pitch, Katz (39) gives only a slight amount, and Revesz (80) used a method which measured not absolute pitch but ability to find by means of spatial or auditory cues what note the experimenter was striking on the piano.

Of children that could be called prodigies, three have been tested for absolute pitch, at the ages of five, six, and seven years respectively. All have shown rather astounding ability and freedom from the errors and limitations of older reactors. In all of them there has been from infancy an unusual interest in things musical. Rather full reports on them are given in the literature: (23), (81), (96). The story told of the seven year old Mozart, that he was able to tell when a violin was tuned a quarter of a half tone too low, was perhaps responsible for Stumpf's beginning the first psychological investigation of absolute pitch.

There are no reliable data as to the age of first appearance of absolute pitch in children. Following are the ages given for this by certain reactors in the literature: Popper (Stumpf, 95), 8 to 9; Whipple's (111) reactor, 12; some of Weinert's (107), 4 or 5; three of Haecker and Ziehen's (27) correspondents, 4; one, 14.

Twenty-four of the 100 musicians answering Abraham's questionnaire (1) reported absolute pitch before 8 years of age.

Preyer (76) and Meumann (56) both recommend that children be taught to name heard tones at any early age, and Copp (17) reports doing this rather extensively. However, it is an open question whether or not the time required for this might not be more profitably spent on other phases of music education.

H.  Musical relations of absolute pitch.

1. Memory for isolated tones.

The work on memory for isolated tones (Wolfe, 116, Whipple, 110, Angell and Harwood, 4, and Angell, 5) shows that the effects of relative clearness of memory image, of timbre differences, and of various sorts of distraction on the accuracy of the memory judgment are comparatively small and not uniform. The method used in all the experimental work above has been the method of right and wrong cases, and the time interval between standard and test tones ninety seconds or less.

Whipple (110) also did some work with tone recognition using the tone variator and method of average error. He found that expectation errors were present and in all cases increased with increase of the interval between the initial setting and the note to be judged. The mean variations were quite large.

Wissler (115) reports tests of Columbia freshmen with a sonometer on which the reactor was to try to set the bridge so as to produce the same tone as one previously sounded to him by the experimenter. They do not seem to have done very well on this test. Wissler's main interest was not in auditory memory and the data he gives are not sufficient for drawing conclusions. here. Hughes (34) suggests some substantial improvements on Wissler's method.

Chiloff (16) tested all his reactors with a pure tone and a complex tone separately. They named the tone when first presented; then reproduced it with their voices at the end of successive 2, 5, 5, 10, 15, 20, and 25 minute intervals. It is not clear how the accuracy of these reproductions was estimated nor what other controls were used. Chiloff concluded that length of memory span for a tone was proportional to the accuracy with which the tone was named in the first place.

2. Judgments of pitch in chords and melodies.

It is general opinion that it is easier to judge the absolute pitch of notes when presented in the more frequently used chords than when presented alone. It also seems to be generally true that more people can name intervals (such as a major third, augmented fourth) and the simpler chords (as a major triad) correctly and quickly than can name isolated notes. Stumpf (95) found the above to be true of his reactors. Von Kries states that he can name the individual notes in an unharmonious clang more easily in high register than in low, and if the notes are not too close together (48). He also mentions that if one voice is playing or singing alone it may be hard to recognize its pitches, but if another enters and moves a third below the two often can be named. Abraham (1) and Raif, experimenting with a siren, found that they tended to report unfamiliar combinations of tones as more familiar ones. They also found it more difficult to judge notes when these succeeded each other at a moderate speed than when the notes followed each other so quickly that they seemed united into a chord. Köhler's (44) reactors seemed to have as much difficulty recognizing tone variator chords as single notes, but such chords would doubtless have an unfamiliar sound. Weinert (107), sometimes after his reactors had made erroneous judgments, repeated the wrongly judged note as the highest note of a chord. This almost always brought forth a correction from the reactors, some of whom said that the s