About absolute hearing.

Originally published in Zeitschrift für Psychologie, 3, 257-79.

J. von Kries

Translated by Christopher Aruffo

The ability to recognize the absolute pitch of particular tones, freely from memory at any time, is known to be uncommon.  In musician's circles it is usually called "absolute pitch"; although some object to this term, I will maintain this designation, since it might be difficult to substitute a completely different term of similar brevity.  The ability is also abbreviated as "AP".  AP is rarely found even in well-trained musicians, and does not represent (as Valentin had believed) an exceptional musical ability.  As far as I know, this has been presented in the psychophysical literature only by Stumpf [1] and by a number of special reports, although it has probably long been known within musical circles.  Numerous competent or even outstanding musicians can be found who do not possess AP.  "Nature," says Stockhausen [2], "gives only a few singers absolute hearing.  Whether relative hearing can be trained to an absolute, I do not know.  I have not yet learned it despite all diligence.  There are composers who have become famous without possessing absolute hearing.  Remember, for example, Meyerbeer, who always carried a small tuning fork or whistle with him which he used as a pitch reference."

Because little material has been presented before now on the subject of absolute pitch, and because I believe that there are various reasons why it is of interest to the sensory-physiological community, then I would like communicate here my observations about it.  I must thereby ask for forgiveness if I talk predominantly about myself; however, by whatever circumstance, it happens that I possess a measure of AP (although by no means to the highest level of competence which has been observed) and my attention has been trained on this phenomenon for some time, and have only had limited opportunity to attempt some experiments with other such people, who are difficult to find.  The scarcity of suitable test subjects and the tremendous individual differences in their AP abilities, should they possess even a slight sense of it, creates great obstacles for such investigations.  The present report will, I hope, catalyze larger studies in this area to generate richer factual data.

Of all the people who supported me in my report of their experiences, and participated in my experiments, my most obligatory thanks to Concert-master Röngen in Liepzig, whose very detailed reports were extremely valuable for many different reasons.

AP exists, to make a somewhat precise determination and demarcation of the object of our study, to aid judgment of the pitch of particular sounds.  It is thus differentiated from the interval memory, or "relative hearing", which permits the same judgment only if a pitch has been heard and named directly beforehand.  One might mean from this distinction that the AP pitch recognition is simply made with greater confidence and precision, but actually there is a sharp boundary between them, for in the latter category the memory for tones disappears extraordinarily fast.  This is in complete agreement with the experiences of Wolfe [3].  Personally, I can establish the pitch of unknown sounds through such strategies; those sounds which I do not recognize by AP, I can recognize after hearing other sounds whose pitches I recognize and making an interval comparison between them.  In each case, I am able to accomplish this only over the span of a few minutes.  However, AP functions completely independently of such circumstances; for those sounds which I recognize absolutely, it is irrelevant whether minutes, hours, or days have passed.  AP represents a persistent ability which is in no way dependent on any tones which have been previously heard.

Furthermore, AP is able to differentiate the memory for types of sound combinations.  When a particular chord has been recognized as a major triad, fifth, or seventh chord, it can be further recognized to have an E-major root.  This is a more specific ability than that ability which allows us to detect tones as either "high" or "low", which everyone possesses in certain measure; persons of the least musical experience and education call certain tones high and others low, and probably can recognize on different instruments whether pitches are higher, lower, distant from or near to each other.  This is, no doubt, a kind of absolute pitch, but if one nevertheless denies that this is AP, this may be explained by the following.  Along the pitch scale, the same names are periodically repeated, and the tones all stand in certain special relationships to each other due to the interaction of their overtones.  This observation is undoubtedly related to the fact that I find clearly and distinctly, as do others who also possess absolute hearing, that all equivalent tones share a common character.  To me, all A's possess a special characteristic which differentiates them from all C's, E's, etc.  When I recognize a C, it is a completely different task than recognizing the distance between C and D [4].  We may speculate that the recognition of pitch is merely a different degree of accuracy in measuring its height; if this should be so, then the ability in question would be completely nullified if the listener could not judge distances of smaller than a fourth, because then there would be no possibility of recognizing any particular pitch.  Rather, the designation of AP ability should be possible if the height judgment is accurate to no more than 2 or 3 semitones.  The habit of imagining sounds immediately and always at particular heights will presumably occur only when the discriminative ability is narrowed to a mere half-tone.

By refraining from theoretical considerations and limiting myself to the purely actual, I may first state the fact that, just as Stumpf observed, I and a number of well-known persons possess this asset.  It allows me to identify any given individual pitch and the root of any given chord (although only partially, under certain conditions, which can be discussed further).  Because I have mentioned here that this is an individual peculiarity, then we can raise the question of the circumstances upon which the presence or absence of the ability may depend.  It is clear that a certain degree of musical learning is necessary so that the memory for pitch would become prominent and noticeable; additionally, the names of the different tones must be learned.  It is not impossible that recognition could take place in another manner, such as recognizing pitches not as "B" or "D" but as the pitch of a certain familiar bell or whistle; nevertheless, learning the systematic names for the pitches would lend strong support to the development of the ability, and a recognition of all the different pitches would hardly be possible without being able to name them.  It is a completely different question, however, whether AP is a result either of learning music or of musical experience over time.  "Everything rests," says Stumpf, "on practice and on memory; therefore, on an individual coefficient."  I mention this point mainly because my observations disagree with the widely propagated opinion that exercise plays a substantial role.  It seems to me that an individual factor is of crucial importance; this speaks to the fact that only a small proportion of musicians within the profession possess AP.  It could be objected that learning musical scale degrees is not substantially directed toward the recognition of absolute pitch; nevertheless, some musicians have taken great pains to aquire the ability and remained unsuccessful (Stockhausen's comments have already been mentioned).  Furthermore, it also seems that most musicians who have AP already had it in their early youth, the ability showing itself as soon as the names of the tones were learned.  This is well-known to be true of Mozart [5].  Mr. Röntgen informs me that his son (no a concert master in Amsterdam) at 5 years of age could not recognize the A-pitch of a tuning fork, but would be able to name any A that he heard from a piano.  most persons with absolute hearing report something similar.  The minimal significance of practice shows even more clearly in those with poorer hearing such as my own.  I can remember that as an eight-year-old boy I recognized piano tones with utter certainty; at that time I had barely any musical instruction (certainly not more than 2 years) nor much opportunity to hear music; currently, my AP is not so exact in that I recognize not all sounds but only certain timbres reliably.  Although I continued to practice music for many years, this experience extended my AP ability only very slightly.  I am therefore inclined to believe that (as one of my test subjects expressed) that the individual pitch memory is practically all, and practice is as nothing [6].  My investigations revealed no case in which it was proved that AP was acquired by practice.  Naturally, I may advance my dim view of practice only as a supposition; it may be confirmed or contradicted by the experiences of other observers.

It is also questionable, and necessary to address, whether the pitch memory is associated with a particularly keen sense of hearing.  Neither my auditory acuity nor my sense of interval are very strong.  I usually find violinists to be most superior regarding the recognition of small differences of pitch.  I would speculate that, contrary to AP, the refinement of the sense of interval is achieved by the manipulation of musical intervals (especially by playing bowed instruments), and that my poor accomplishment at this ability can be attributed to the fact that I never played a bowed instrument.  I must disagree completely with those musicians I have recently heard to claim that violinists would be more likely to possess AP and pianists less likely.  I and several other well-known musicians have a good AP without ever having played a bowed instrument, and I also know splendid violinists whose pitch ability goes completely off [7].

Pitch recognition is dependent on some conditions which, although they may not be concisely explained, can at least be described with a reasonable analogy.  First of all, there is the a certain intensity and duration necessary for accurate recognition.  These factors are, for me, very clearly pronounced with sounds whose recognition is difficult and uncertain and which I cannot immediately identify.  Such sounds are not impossible to identify; if I heard a brief tone (e.g. a train whistle), after sufficient repetition of the whistle a confident judgment will form [8].  For easily recognizable sounds such as piano tones, a light intensity and short duration are enough to render an immediate judgment.  Even so, it can be said that extreme brevity and minimal intensity, especially accompanied by background noises, will impair recognition of any type of sound.  A more noteworthy fact is how I find, as do Stumpf and his test subjects, that middle pitches provide the easiest and most secure judgments, while very high and very deep tones are more difficult.  I find an evident reduction of security if the pitch ranges above the fourth octave or into the contra-octave.  This observation is undoubtedly connected to the fact that music uses these extreme tones far less frequently than those in the middle positions.  So it is already difficult to precisely assess the lowest sounds of the piano, with which the interval sense requires a much narrower refinement than those in the more commonly used central positions.  Something similar probably applies to the highest tones as well.

For me, the most remarkable dependence seems to be that of timbre.  I would like to first report on my own insight which I was able to observe closely, and then on the experiences which I was able to track down from others.  I will speak here of different timbres, including those which possess no distinct pitch and can therefore not be readily sung, such as bells which have numerous and discordant overtones; however, it is not true that the pitch of a sound can always be determined instantly and accurately by singing.  It is generally expected that the AP possessor is able to name the pitch of any sound they hear, but this is not at all the case.  I noticed this myself in my youth and was quite surprised by it.  At the time, I did not divide the sounds into recognizable and unrecognizable.  To the former would belong the tones of the piano and most musical instruments (both categories of wind instruments); to the latter singing tones of the human voice, tuning fork tones, and most whistles including those from the lips.  The greates contrast between the two was that I could recognize the piano tones with such certainty that I would almost never make errors (and then, a semitone at most), while I could not recognize singing tones at all.  In these conditions, the pitch must be recognized by the method mentioned previously of comparing two particular tones or comparing one tone with another that had been heard previously, since the timbre does not play a substantial role in this comparison.  It must therefore be held, first and foremost, that it is fundamentally correct to say that the identification of tones is not occurring through comparison with a tone held in memory, independent of the particular tone to be judged, or from a mental image based on a certain pitch.  If possessed such a mechanism and recognized tones based on their relationship to my memorized images, then it would be inconceivable that I would fail to recognize pitches because of their timbre.  With respect to the task of freely imagining a particular sound and singing its pitch in order to identify it, I am highly unsteady, and if I try it I succeed only in exceptional cases.  The entire ability of sound recognition, at least with me, has nothing to do with making a comparative judgment; however, opinions still diverge substantially regarding the exact view of these processes.

To form a more complete view of the process, we may try to tie it in to the process of association.  As one of the simplest and purest examples of this kind, we may describe pitch recognition as Lehmann does [9], as recognizing by name.

Whether this is a pure association or a recollection of similar sensations from the past is not of substantial importance.  Either type would evince the effect of associating a perceived sound with its designated name.  We could say, accordingly, that certain sounds will evoke certain names and others will not.  That a sound suffices to evoke a name is not sufficient to generate the image of the pitch concerned; one could find various interesting examples for the general statement that the two types of association are not always equally facilitated in both directions.  Thus it occurs, e.g. in learning a foreign language, that we frequently understand a word when we hear it but, when we wish to express the same meaning, the same word will not appear in our imagination.  The association is thus produced by the word, and not the other way around.

I believe that the process I have just described requires some modification.  We could probably imagine that certain sounds will always produce a pitch name and others will not, maybe adding that the latter group would do so occasionally under particularly favorable conditions.  But this view would not be adequate to encompass the variety of processes employed in the actual recognition.  In addition, we must consider the distinction of whether the naming process represents a mere co-existence of both concepts (the ear's perception and the sound's name) or whether it is a sequence of association.  This is a point which I believe is not sufficiently differentiated in the theories and discussions of association.  Obviously, in making the judgment "this pitch is C", I do not arbitrarily imagine the label "C" simultaneously with hearing the relevant sound.  Thus, although the specific concepts (feeling and name) are both part of the naming process, this process is more involved than their simple co-existence, although exactly how remains unknown.  The first part of the process is a set of characteristics within the sound which (to me) reveal its identity.  I may immediately recall a certain name, perhaps "C", upon hearing a sound, even if I am still somewhat uncertain whether I have heard C or D.  On the other hand, it is also possible that I hear the pitch clearly but cannot match it to its name.  Then, recognition becomes a deliberate effort.  I therefore try (completely arbitarily) to imagine the sound as a C and determine (I know no better word for this) whether the "C" designation is appropriate.  I often then feel clearly that this is not the case, and continue to search; after some searching, I come across a name that fits, and arrive at a secure judgment which is almost never wrong.  One would undoubtedly assume that the reverse association would impose itself; e.g. that I would spontaneously imagine different pitches, independent of the sound in question, in order to compare.  I believe this is rarely the case.  I am very familiar with the task of imagining particular pitches, and I have already mentioned that I find it very difficult; as well-known as that behavior is to me, no trace of it is apparent to me in this particular process.  Thus it also never occurs that an arbitrarily presented name would prompt a different pitch concept, whose distance from the questionable pitch could be assessed, and which therefore could help identify the unknown sound via the interval sense.  Some people may use this indirect method of tone identification, but I do not.  Rather, it seems that the judgment's formation is favored and facilitated by the random application of the appropriate name.  This same phenomenon occurs in other areas of memory.  If, for example, a person has a very common first name, then the whole concept of their personality appears the moment we imagine only their first name, as soon as we direct our attention toward it.  If we can't remember the first name, even if we do remember the surname, we will sort through a series of first names associated with that gender, recognizing each one as wrong until we finally reach the one which is obviously right, at which point we immediately recognize it to be the correct appellation.  Or, if we try to remember the year of a historical event, we will probably imagine a number of different possible connections which facilitate its identification.

I may describe sounds as having a degree of recognizability; I can measure this attribute not simply by whether or not they cause me to recall a name, but more specifically by the quality and accuracy of the judgments which may be obtained.  If I were to rank different sounds by their recognizability, then piano tones would be at the top of the list.  With these, pitch recognition is totally direct; the correct name immediately appears in my mind; I am not aware of any time delay necessary for comprehending the sound, and the process does not require even the smallest amount of mental effort.  I would like to believe that these judgments are also unusually precise, perhaps more specific than a half-tone range; however, this has not been the case on different occasions.  From time to time, a pitch initially appears to me to be a C, but then I become uncertain about whether perhaps it is a C-sharp, from which I draw the correct conclusion that I have heard a C that is sharper than what I consider normal.  The fact that small differences in pitch are noticed in this way undoubtedly owes its existence to the fact that our naming system does not account for categories smaller than semitones.  This circumstance naturally makes it more difficult to be sure of judging pitches which are somewhat out of tune, and is also an unfortunate inconvenience given that we do not have an innate disposition which allows us to recognize and memorize only certain and exact pitch frequencies as A, C, etc.  Thus for many years I had my own piano tuned noticeably lower than most orchestral music.  The different pianos I have played are always tuned differently, sometimes by as much as a whole tone, and it is understandable that this would work against the exact training of pitch memory.

Moving into other sound types, my recognition of bowed violin sounds is almost as strong.  My accuracy is somewhat less than the piano, which is made evident as I mark the strings with my fingers; here it is not unusual (either at the grand piano or in the central positions of the violin) for me to make errors of a semitone; the pizzicato sounds of the violin I do not even try to recognize.  I can identify the tones of most wind instruments within about a semitone, but with the pipe instruments with their weak overtones I may fluctuate by as much as one and a half steps.  With all these sounds, however, a pitch name will come to mind as soon as I pay attention to the sound, although frequently in an indefinite way so that I vacillate between two neighboring pitches.  At the lowest end of the recognizability scale are those which do not cause a name to appear automatically, and with which the strategy of trying different names proves completely fruitless.  I had once believed that there was a sharp border between the sounds which could or could not be recognized, but recently it has seemed very probable that this is not the case.  Firstly, some sounds may occasionally but not consistently evoke their pitch name; and at those times when it does, the judgment will exhibit varying degrees of accuracy.  Because there are sounds I may recognize but only with extreme inaccuracy, it seems reasonable to suppose that this is explained by the previously mentioned circumstance, of how musical sounds bear specific and consistent relationships to each other (shown in part by the repetition of pitch names from octave to octave).  For this reason, as soon as the recognition drops below a certain precision, it can seem to be completely absent.

I should additionally mention here that I can limit the error range of these uncertain sounds by a certain amount through practice, and the results do persist.  Thus I am now able to recognize tuning fork tones with reasonable security [10], although I still find difficult the sounds of high whistles like those of locomotives and high-pitched pipe instruments.  But even then, the recall of the pitch name is often not direct, and I am not only dependent on the previously-described method but usually uncertain by at least a semitone.  Therefore I am recognizing these sounds better than I used to, but still not with the ease and confidence with which I recognize piano or bowed violin tones.  I nearly always require some time to consider.  The tones of bells and chimes, even though they may be easily repeated by singing with the human voice, I nearly never recognize; but I can "sing" along with them by whistling.  Bells and whistles have a similar effect, and are often unrecognizable for the same reasons.  A young musician (Mr. W) finds that he has exactly the same response.  The reason for this is not entirely certain, and I don't think it is always because of general conditions of the mental state (fatigue and so forth); rather, I would prefer to believe that there are slight but noticeable differences in the timbres which affect their recognizability.  Perhaps it also depends on whether the particular pitch coincides exactly with other internalized pitches that are entirely familiar [11].  Accordingly, I now recognize from time to time the pitch of a singing voice with total reliability and accuracy (i.e. with an error of at most one semitone).  I tend to recognize soprano sounds sooner than men's voices, and the tones of the human voice are generally more recognizable to me in that area.  But tones I sing or whistle, I never recognize [12].

Finally, some consideration must be given to the recognition of tonal masses.  In this regard, I find that entirely atonal masses are less easy to decipher than inharmonious combinations of 4 or 5 piano tones.  I frequently know the individual elements, but may not be completely certain in my identification of them, if they are too low or too close together.  This is a remarkable contrast to the ease with which I recognize harmonious chords.  This has always been especially noticeable to me in choral singing (without accompanying instruments) which would give me immediate and specific impressions of pitch, particularly if the most consonant intervals were produced (fourths, fifths, or thirds).  Thus it often also occurs that when I hear a voice and do not recognize its pitch, if it is joined by another voice singing a second or third harmonically below it, this is sufficient to allow me to judge the pitch.  This fact does not seem so strange when you consider that, in recognizing any chord, all its pitches (or at least several) are implicitly determined.  With orchestral music produced by different instruments, I almost always recognize the key signature and thereby recognize, if not every tone, at least the most prominent of them.

Regarding the nature of others' AP, I found at least some cases which show that the influence of timbre on recognizability, as I feel it, is not unusual.  The experience most similar to mine is that of Mr. P, a competent piano player who wrote to me the following:  "I find only the piano tones to be directly recognizable, such that the pitch is recognized immediately and certainly without possibility of error, and without assistance of the deductive faculty.  I do not have this direct impression for any other kind of tone, such as strings and wind instruments, singing, whistling, bells, etc."  Mr. P. says he may succeed in identifying these tones by imagining a particular pitch and comparing it to the one he hears; but this procedure is not completely effective, because his recalled pitch may not be accurate.  Direct recognition is therefore, with Mr. P., even more limited than my own; on the other hand, his association between name and pitch memory is more developed, even if it is not infallible.

With a well-known musician from Berlin, renowned because of his pitch sense with which he could recognize piano tones even in inharmonious masses, I had the curious opportunity to notice that he had mis-identified the pitch of a man's voice-- a trained and resonant voice-- by a fourth.  Unfortunately, it was not possible for me to make any further observations in this case.

A young lady with good (but not outstanding) AP, and who has trained as a singer rather than a piano player, also showed a decided preference for piano tones before piano tones.  The piano tones were easier to detect and recognize more quickly and certainly, whereby sung pitches could be recognized only hesitantly and after some thought in which the tones were "mentally sung".

The young violinist mentioned above, Mr. W., possesses a very precise AP for piano and bowed violin tones, but has the same relationship to pipe tones as I do, so he recognizes them only occasionally.

Furthermore, there are certain people who recognize chords or the key signature of an entire piece, but cannot recognize individual tones.  Stumpf reports such a case in R. Franz.  He was always uncertain of individual tones, but he would always recognize chord roots and the keys of piano and orchestral pieces (but not those of organ music).

In contrast to these, there are also numerous persons whose AP is not limited to special kinds of sound.  Mozart is an obvious example of this, for whom his father claimed, "He recognizes all tones, individually or in a chord, on the piano or any conceivable insturment; bells, chimes, clocks, etc.  No matter what the conditions, he will recognize it."

And within the population that has AP, the expression of the ability which is able to detect the pitch of all sounds does not seem to be too rare.

Concert-master Röntgen finds all "purely musical sounds (i.e. those which are free from inharmonious overtones or irrelevant noises) equally recognizable, in particular those of the human voice.  Also, I convinced myself that two local musicians were able to immediately and directly identify the tones of tuning forks; both said that, like most of the people who have this particular form of the ability, that they had never noticed a difference in recognizability between any types of sound.

It should probably be noted that, even if all sounds can be correctly identified without the person involved noticing any difference between the timbres, this does not necessarily reflect a tendency toward more precise judgments.  Only a specific and systematic investigation-- which would, unfortunately, be very difficult to execute-- could show this.

The people in this category represent the highest level of AP.  The least degree of the ability which may still be called AP is, I think, best described as an uncertain recognition:  sometimes it works, sometimes it doesn't, and when it doesn't specific reasons can be identified.  People who have this ability often feel that they are "guessing" at the pitch.

After the facts communicated here, it might be worth attempting a more detailed discussion of the dependence of pitch judgment on the timbre.  It is not obvious why, for pitch judgment, the pitch alone is not sufficient; it is even less obvious if one considers that when one hears two sounds in quick succession, only an impression of their combined sound is possible.  If one further considers that all possible sounds which possess the same fundamental pitch all bear the same name, then one should expect that only the basic feeling of pitch would be linked with the name; the accompanying overtones would be irrelevant, as they are at the furthest borders of musical sound.  But we find that, in contrast to this, in many cases the association and judgment is only formed if a complete timbre is present.  For this reason alone we may conclude that the pure pitch is not the sole deciding factor.

If we look for an explanation, the most obvious is that it is a consequence of the listener's experience of auditory learning.  One may imagine that anyone will hear certain kinds of sounds with unusual frequency, and thereby link the pitch names with these special sounds, and it does not seem inconceivable that they learn to identify these sounds more easily than others.  In that respect, it may come as no surprise that an associated idea (in this case, a pitch name) always occurs only with an entire complex of feeling, so that to evoke recall the entire complex must necessarily be present, as an individual part of the sensation is not sufficient.  All the same, I do not believe that this perspective completely explains the facts.  For me, it would only account for the dominant sound of the piano and perhaps some of the other instruments; it would not explain the special difficulty I have with the human voice.  There must be additional, coincidental conditions, because I have been singing regularly without accompaniment since I was 12 years old.  It does not seem that anything would be more suitable to practice than harmonizing, because one must always attend to the principal singers and follow their movement.  Nevertheless, singing tones are still the most difficult for me to recognize.  When I hear a singer singing along with violins, I may later recall the music and say with great confidence that I recognized the violin tones without any substantial recognition of what she was singing.  Also, one can hardly that violin tones are at all similar to piano tones [13].  And if the explanation is improbable, it becomes untenable when considering one's aggregate experience of sound.  One hears individual singers far more frequently than multi-part singing; if the latter is easier to recognize, as in other cases where a chord can be recognized but not individual pitches, then this certainly cannot be attributed to different levels of practice.

These facts suggest another explanation.  One may be inclined to accept a connection here between the kind of psychological effects we find in other areas.  This would be in regards to processes of association, and can be generally expressed as:  effect a is connected to b when it occurs with c, but a cannot occur by itself; therefore, b can only be produced when a and c occur together.  There are well-known examples of pathological handicaps produced by this association; this is how someone may not be able to speak the words of a song, but only sing them [14].  Another example is the case mentioned by Ehrenfels [15] in which someone was able to imagine certain pitches only by recalling a particular piece of music; there are probably many other examples that can be found in entirely mundane conditions.

If a person may recognize individual pitches only within a chord, an analogue of this ability can undoubtedly be found in other areas.  One could further assume that, with individual sounds, a certain richness of overtones makes them more similar to chords, and thus recognition of these tones is favored versus sounds which are nearly or completely overtone-free.

This explanation seems more satisfactory, but is not without its flaws.  For one, the higher sounds of the piano have relatively weak overtones.  If I were to hear a brief, weak single piano tone through several closed doors, I could still identify it instantly; it is difficult to imagine that this is due to the pattern of overtones, as hearing them is completely impossible under such conditions.  I can also point out that the human voice is full of overtones where the tuning fork has none, and yet I find the recognition of the former far more difficult.

Is it possible that the pitch recognition of a sung tone is made more difficult by the recognition of the vowel which accompanies it?  I did not find that it made much difference to recognizability on which vowel a pitch is sun.  Also, the humming tones, which are created by a closed mouth and do not have a vowel character, are still just as difficult (if not more difficult) than recognizing a vowel-sung tone.  If, as demonstrated by Hermanns' investigations, there is only a very small difference between the actual pitches of the U and O (U is C3-D2, while O is D3-E2), then the confidence with which the two vowels are differentiated by all humans is surely very strange when compared with other achievements of pitch recognition [16].

The discovery of a completely satisfying and justified explanation of these facts, I must leave to the future.  A systematic experimental treatment of the question would probably be the swiftest route to its answer.  It has not been possible for me to construct such an experiment because I am not in possession of the extensive apparatuses necessary to produce a systematic variation of both tone qualities and pitches.

Aside from whatever that explanation might teach us, I find the peculiarity of the absolute ear interesting in many respects.  To have two tones, one of which is recognized by absolute height and the other not; this could be a psychological failure of some kind of logic.  Perhaps this occurrence is analogous to those about which Fleischl [17] sagely wrote: "logical laws, in particular the set of contradictions, are only valid for thoughts and ideas, and not for direct feelings."  Although the statement itself is surely debatable, it is nonetheless useful toward expressing important theoretical aspects of this discussion.  The meaning is the same, it seems to me, as how the immediate and reflexive response of judgment is so rarely attached to the physiological process of sound reception, producing only "feelings" in the strictest sense of the word.  But the more exact pursuit of this viewpoint is too far outside the framework of the present report, and will have to be reserved for another time.

[1] Stumpf, Tonpsychologie, Bd. I, S. 305 f.

[2] Stockhausen, Gesangsmethode S.1.

[3] Wundts, Philosophische Studien, Bd. III, S. 534 ff.

[4] I remained unfamiliar with this task for a long time; I did not know the names for the different octaves and was often confused.

[5] Vgl. Stumpf, Tonpsychologie, I, S. 280.

[6] Mr. Röntgen shares the same opinion. "It seems," he wrote to me, "that the ability to determine the pitch of a sound without all further aids is innate to some humans. Attempts were often made to acquire this ability through practice; the results are always weak, however, and are usually limited to relative pitch, i.e. determining the height of a pitch from another given tone."

[7]  To illustrate an effect of AP, Mr. Röntgen tells me that it is quite impossible for violinists who possess it, like he himself and Mr. Joachim, to play with a violin which has been tuned too highly by a half-tone or more, as Paganini prescribed for the performance of his Eb-major concerto.  The fact that Paganini gave this instruction, and that he and numerous other violinists could play in such a way, suggests that he probably did not possess AP.

[8] Mr. Röntgen also described how repeated hearing of the same sound makes it easier to distinguish.

[9] Lehmann, Wundts Philosophische Studien, 1889.

[10] To give a numerical description of this fact, I want to mention that in 20 attempts with tuning forks (I used the 12 tones of the chromatic scale, from A0 to A1) I produced 7 exact judgments, 8 semitone errors, 3 whole tone errors, and 1 error of two tones.  The comparison to piano tones is blatant, as with the piano I never make mistakes (at most I will occasionally err by a semitone).  The main difference, though, does not reveal itself by these numbers; the main difference is that the recognition of the tuning fork tones does not occur directly.  It must be achieved through careful consideration and delivers an uncertain judgment, if indeed a judgment can be delivered at all.

[11]  This fact speaks to the observation that sometimes, children are better able to recognize lower tones of the piano.  When playing the higher keys, errors of up to a fourth may appear, such as hearing an F-sharp as a C-sharp.  Stumpf reports such a case with an 8-year-old girl, and I remember making similar errors when I was a boy.

[12] The widely accepted opinion, that recognizing the pitch is based on feelings of the laryngeal muscle which accompany the sung pitch, is thereby undoubtedly nullified.  I have already asserted it to be untenable that sounds are recognized by completely indirect conditions or by singing for comparison.

[13] Also applicable is the argument of perceptual interference from noises or inharmonious overtones.  Both are often completely absent in the hard-to-recognize sounds.  An irrelevant mixture of noises, if not very strong, actually does not interfere very strongly with recognition.  For many years, paying attention to the recognizability of sounds, I often had the most remarkable experiences of perceiving pitch accurately even within with strong noises, e.g. in the sound of a circular saw or a creaking door.

[14] VgL über Fälle dieser Art Wallasohek, "Über die Bedeutung der Aphasie für den musikalischen Ausdruck. Vierteljahrsschrift für Musik-Wissenschaft, VII., 1891, S. 61.

[15]  Ober Gestaltqualitäten. Vierteljahrsschrift für wissenschaftliche Philosophie 1890.

[16] If one wants to find a more specific examination submitted in other sense areas with similar features, then for this I offer mainly the absolute estimation by sight, which is not only capable of recognition but of determining absolute sizes, some facts of which I have reported here and in other places.  Following the assumption that recognition is promoted by the synthesis of disparate elements, one could ask whether, for example, which is recognized more exactly:  the size of a whole circle or the distance between an individual pair of points.  I tested this question myself by manufacturing a number of pairs of points either  49.5mm or 50.5mm apart, and likewise a number of circles of 49.5mm or 50.5mm in diameter.  The trials extended over many days; to avoid each attempt being influenced by the previous one, I could only attempt a moderate number of trials each day.  The data, although not completely finalized, has already shown (by a percentage of correct judgments) that there does not appear to be a substantial difference between pairs of points and whole circles.

[17] v. Fleischl, Physiologisch-optische Notizen. Wiener Sitzungsberichte Math.-phys. Cl., Bd, 86. 1882.