Research Article on Perfect Pitch

Originally published in Collections of the International Music Company, pages 1-86, 1901.

I. Description of the ability -- Literature -- Working plan.

That is, for example, someone gifted with absolute tone consciousness may hear a piano tone and, without looking at the keys or hearing any other sounds, correctly designate the tone as an F; also, they may upon request freely sing an F from memory. It's not always necessary for the letter name to be applied to achieve recognition, nor must the singing skill be connected to the printed note or the piano key. It's certainly not necessary that the observer gifted with absolute tone consciousness must first see the note or the key, or think of the letter name, in order to imagine the tone. More frequently, the note and key are directly connected to the imagined sound, so that all three sound signs are to be regarded, whether optically or acoustically, as equivalent. We must, however, differentiate between the abilities to correctly name and to correctly produce a designated sound.

It is unfortunate that the same label is applied to two different abilities, but the semantics have already been set in place. This usage developed from the belief that the ability is based on having an available memory for pitch sounds. I would like to comment that this is not necessarily the case, and that the label is incorrect in some instances of apparent absolute ability.

I was not able to determine who invented the name "absolute tone consciousness." I presume it was a composer, for until recently only the musicians bothered themselves, and only occasionally in biographical notices, with comments on the ability. Psychology entered this arena only recently, and it is Stumpf [1] who touched the most pertinent questions in his Tonpsychologie. After Stumpf, von Kries [2] in his work "Über das absolute Gehör" noted different aspects of the ability. To both works, which gave me the motivation for my treatise, I will have to return repeatedly, either to refute their observations or illustrate them in greater detail. Besides these two, a little treatise of Meyer has just been published. I will report on Meyer (with whom I worked) in a later chapter, and I will also discuss the works of Wallaschek, Planck and Naubert, which address individual questions about this ability.

Part of the reason such an interesting ability has so little scientific inquiry is that it is difficult to find subjects. In other studies of sound psychology, usually slight musical knowledge will suffice, but here one must first search at length in order to find potential subjects with absolute tone consciousness. Furthermore, these people are frequently musicians who, if they are older, have no time to sacrifice for psychological experiments, and if they are younger, their musicianship is more pedantic than artistic, and the observation of their ability leaves much to be desired.

I ran my experiments with only a few musicians gifted with this ability. Many of the results are similar to my own, because I possess a very good sound consciousness; but overall, there are so many individual dissimilarities of this ability that I printed a questionnaire and sent it to every musician I knew who possessed absolute tone consciousness. Because, in this form, I asked for additional addresses, which were often amiably supplied by the respondents, I am proud to now be in possession of hundreds of completed questionnaires, which provided m with extremely valuable material. I express my warmest thanks to the musicians, violinists, pianists, and singers who participated in the experiments and questionnaires.

The questions, which I arrived at in an empirical way, and, which are organized in a specific logical order, read as follows:

Questionnaire about absolute tone consciousness.

You can see that of these 19 questions, some can be answered quite simply while others require some self-study. The answers must be taken, especially those regarding limits and the influence of different sound qualities, with some reservation, and serve mainly to support the results shown by precise experimentation. My psychological experiments were carried out exclusively in the Berlin Psychological Institute, whose director Dr. Stumpf was most helpful and friendly, and to whom I express my most binding thanks.

II. Association method I: Letter name evokes tone sound -- judgment of absolute pitches -- limits of the interval-sense.

The main postulate, which one must acknowledge to be definitive of absolute tone consciousness, is that pitches are recognized and named without interval-comparison with other sounds.

Certainly, people with very little musical development can recognize tones as "high" or "low" without comparing them to other sounds. This ability to recognize high and low, demonstrated by von Kries, is different from what is commonly understood to be "absolute tone consciousness" or "absolute hearing." But even though people call the ability by different names, everyone agrees that someone with the ability will correctly name any tone of the musical scale. When a person can discriminate tones within a semitone, we can begin to talk about absolute pitch; in my opinion, it is the naming ability which is definitive. A pitch and its name are so frequently sounded together that, if a tone is played and attention given to its pitch, its name is impressed into consciousness. A firm association between word-image and pitch-image is therefore demonstrated by musicians with absolute tone consciousness, and so we make a separation between the distinct abilities of absolute tone consciousness and ability to detect "high" or "low".

People with absolute tone consciousness are usually not sure how they engage it to arrive at the correct pitch judgment; as soon as the sound is played, the word label is there. To be sure, there are many who have special strategies with which they make their judgment, or who use indirect criteria; there are others who have absolute consciousness for only one or two sounds, and must recognize all other sounds by means of partial absolute tone consciousness combined with interval consciousness.

This interval consciousness, which is much more frequently found, may be contrasted with absolute consciousness; with this skill, a person may determine a pitch through interval estimation versus another sound. One can immediately see that this is a different strategy than absolute tone consciousness. If a musician gifted only with relative sound consciousness hears a tone and is told it is C, he will recognize a new tone as a "third above" by means of his interval sense. Because the first tone is named C and the third above is E, he will name this new tone E. We have here an entirely different type of reasoning, a logical process with premises and conclusions, while absolute tone consciousness takes no time at all and no deliberate thought process; rather, simply in hearing the pitch, its name is known. The term "relative sound consciousness" seems illogical; we will be content with the label "interval sense."

Overlapping between interval sense and absolute tone consciousness is the memory for sound combinations, with which a chord is recognized as a triad, or seventh, etc. These labels inherently imply interval judgments, but if the judgment "E major triad" is rendered without earlier comparison sounds, it falls into the realm of absolute tone consciousness; at least, the "E" judgment belongs there, while the "major" and "triad" labels may be determined by either absolute tone consciousness or interval sense.

It was previously believed that absolute tone consciousness could not be adequately separated from interval sense, because there would always be memory of other pitches available for comparison. However, this is not the case; in Wolfe's experimental assessment, it was shown that pitch memory disappears unusually quickly [3]. As an apparent proof that perhaps interval sense plays somehow into absolute consciousness, it has been suggested that when two sounds are played following each other (e.g. B and E-flat), the second sound is named because its label represents a familiar interval. The second sound is named E-flat, and not D-sharp, even though it is the same tone as D-sharp. Because the B is still in memory, it is said, the E-flat must be named by interval comparison. I would challenge this assertion. I would say that the judgment is given by the most frequent occurrence of the note's label (E-flat is probably more frequently featured in music than is D-sharp), and that it is more frequently associated with that name. Further, the explanation does not hold up to large leaps of more than one octave, even between the same pitch classes; the delay of reducing into the same octave would reveal the strategy.

If a person wanted to confound interval sense in conducting a pitch-naming test, they could leave large pauses between the tones, and fill those pauses with conversation or oddball piano notes which a subject could not follow with interval sense. Then one would recognize that absolute tone consciousness is a lasting ability which does not depend on reference pitches.

III. Peculiarities in pitch judgments -- octave deceit -- similarity.

Further explanation is required for the statement that, with absolute tone consciousness, a pitch name automatically appears when the sound is heard. Suppose the D3 pitch is played on an instrument. The absolute listener knows immediately that this notes is D, not C or E, but which D he may only tell after some meditation. He considers the tone and sings it, and then decides that the tone is either D2 or D3, whichever is the more familiar octave designation. This process may occur very quickly, or there may be an enormous time difference between when the judgment "D" or "D3" is expressed.

One could think that the reason for this is simply a lack of musical knowledge or training. Certainly this is a consideration; I myself was initially slow when I answered these acoustic questions, and now I need considerably less time than before to deliver a perfect height judgment. But this doesn't sufficiently explain why the delay occurs; it is not merely the octave label, but the octave height itself, which is unclear to the listener. This usually happens in the middle octaves. Semitone errors are not unusual (for a musician, who through too many different tunings over their lifetime may be driven a little crazy), but octave recognition errors are common. This was shown by Engel [4] in his publication on timbre. He produced a D2 by whistling, and this was compared to a tenor singing an equally strong D1. Most listeners with and without absolute tone consciousness judged the sung sound to be higher than the whistled. Even with absolute tone consciousness, a gifted musician would be in doubt whether the whistled sound is D0, D1, or D2, but they would never confuse the "D" with another pitch. I attempted this experiment with 10 subjects, who reacted without exception in this described manner. I know that for myself, the whistled D2 always seems higher than a D1, or even a D0. [Editor's note: the German designations appear to be the reverse of the English designations, so that "D0" is higher on the scale than "D2".]

This explanation suggests that a musician has absolute tone consciousness not merely for simple tones, but with overtone-rich sounds. To make these kinds of errors, the feeling for the relationship between octaves must be strongly perceived. We talk about the octave similarity as though it were the same as comparing two simple tones. But the similarity of a complex tone can be explained by similar characteristics and equivalent components, while simple tones in different octaves have no equivalent parts. But we call these tones "high" or "low", recognizing that some similarity exists and is also felt. I believe that there is a fundamental difference between the musicians who have absolute tone consciousness and those who judge only by intervals. The latter group claim the similarity between G and C# to be more important than C and F#. But those with absolute tone consciousness have no or only a low-grade feeling for the similarity of these sounds; a C# is just as dissimilar to G as it is F# or B-flat. On the other hand, they may have unusually strong perceptions of complex tones. Octave errors stand out most prominently, but fifths and major thirds are also indicated as common errors. I found several respondents to my questionnaire who said they very easily mistake fifths and octaves, and one who often makes errors of major thirds. All of these observers almost never make half-step errors.

This octave similarity is based on the equality of its parts, not its characteristics. If each tone had the same characteristics, then all tones with the same tone quality would seem to be the same tone. The equal parts being discussed here are the overtones which are collapsed into the fundamental tone. To recognize the similarity between a complex tone and a simple pitch sound, an absolute listener must have a strong ability to interpret a complex tone. Someone could object that you only need to reduce the distance between two tones to force a similarity judgment; you don't need to compare C and C#, but any two tones which differ in only a few oscillations, and even a casual listener will be forced to recognize these as more similar to each other than, for instance, C and F#. But the absolute tone consciousness is a function of memory, not of perceptual sensation. In memory, we know that over time, tones which deviate by only a few oscillations will be remembered as identical; and for the absolute listener, where equality stops, similarity ends. I therefore believe that the nature of absolute similarity judgments is of great importance; but whether they are a cause or a consequence of absolute listening, I cannot answer. Perhaps originally, with certain people, a tone appears to them as an individual identity, and the person focuses their attention on that tone while neglecting its relationship to other tones. Thus, on the one hand, they strengthen their understanding of the tone, but on the other hand, they lose the ability to recognize its similarity with neighboring tones. This can lead them to an acquisition of absolute tone consciousness.

In addition to absolute tone consciousness, it's clear that there are other capacities which render pitch judgments. The judgment depends on the qualities of the sounds and the qualities of the individual; that is, the same sound can be differently judged by different listeners. One musician judges by height, another not, and a third needs some indirect method to arrive at their judgment. An absolute listener has many choices to select among the sound qualities, to identify the tone either directly or indirectly. For the absolute listener, all sound qualities are important and distinct: pitch, intensity, duration, and timbre.

IV. Effects of pitch on absolute pitch judgment.

Of all the sound qualities, pitch naturally plays the largest role in absolute listening. But even if a person is capable of correctly identifying the absolute position of many sounds, it does not necessarily follow that he can identify all the sounds he hears.

Which area of sound provides the best conditions to deliver absolute pitch judgments? This area should be compared to these different boundary zones, in order to determine whether absolute listening is more connected to generalized perception or to musical practice.

Obviously, between different individuals there are great dissimilarities in absolute judgment ability. One may be able to name only a single sound correctly; a second may be able to name tones within a few octaves; a third may be able to recognize the entire musical range and beyond.

We do not include here those whose absolute ability is limited to only one or two tones, e.g. the standard tuning tone A1, or A and C. As will be discussed afterwards, these listeners' absolute recognition is usually accomplished by indirect criteria; spontaneous labeling of the tone does not come naturally to them and is not dependent solely on the association between name and pitch. The dissimilarities in these listeners' abilities are significant, and it would probably serve no purpose to include them in a large time-consuming trial. On the other hand, it is interesting to test such a person to determine who can show, after short tests, the limits of their judgment zone and the maximum circumference of their recognized sound area. I am fortunate to be able to function as a test subject; I recognized my judgment area as larger than other observers whom I have examined. Although there are probably musicians in this study whose abilities exceed mine, I believe I am nevertheless entitled to publish my attempts, as they give an interesting picture of the sources of error. I employed these attempts together with Mr Giering, which he has used for another paper. For the lower areas we used Edelmann's tuning forks, and for the higher areas we used small bellows-driven organ pipes. We solicited judgments of every tone. The pitches are indicated in the following table. The size of the error is indicated by the column heading, and the percentage of selections is indicated within the table.

Low tones boundary.

High tones boundary.

With a quick glance, it is immediately noticeable that judgment is more secure within the range of familiar musical sound, and the number of correct answers constantly increases while approaching the middle tones. In both tables, however, some accompanying circumstances should be considered: the low tuning fork pitch, like the pipe, normally oscillates at 435Hz. As is shown in later tables, in my consciousness I have an A1 which is far higher, i.e. approximately 446Hz. A1 = 435 seems too low to me, and I have to adjust myself to the different standard. This may have caused many half-tone errors. But it's not just the low-tone errors which result from this tendency; to adapt to it, I often shoot beyond the high tones and judge them to be higher than they are. I therefore believe that the half-tone errors (up or down) should not be counted as errors, but that "correct" judgment should incorporate a tone and its neighboring semitones. With this adjustment, the pattern shown by these tables becomes even more pronounced.

Looking at the lowest sounds, it seems remarkable that in all the lower regions, at the boundaries of perception, tones are judged with greater accuracy than higher tones. If we include the neighboring semitones, the lowest test sound (D#) was correctly identified in 100% of the cases, while the middle of the highest octave shows only 70-90% correct. However, this apparently paradoxical fact can be easily explained: the lowest tones are intermittent. Lower tones seem to be humming, and still lower tones seem to be fluttering. The individual oscillations can practically be counted and estimated. After sufficient time, the speed of a tone's fluttering can be estimated to correctly identify the tone. It's possible that a tone could thus be determined by absolute position without actually having absolute tone consciousness, but this is only indirect recognition. Even if the pulses are considered qualities of the low tones and no sense other than hearing is used, the indirect criterion of time would be employed to facilitate judgment. Although I'm not very good at evaluating the vibratory speed, I can examine and verify my existing pitch judgment based on this additional criterion. This factor explains why the lowest tones were so well judged.

We must not exclude the potential effect of overtones with the lowest fork tones; the tones seemed to be overtoneless, but since for those depths no resonators exist, it is not entirely certain.

At the upper boundary of sound, we have no indirect criteria as we do with the lower sounds, so the number of incorrect answers increases constantly with height. The curve describing the correct judgments of absolute tone consciousness, over both tables, would be illustrated by the following graph.

From the octave below middle to the third octave above middle, judgments were correct without exception. One sees that the lower tones are judged more precisely than the higher ones, for the reason previously described. Starting in the middle of the fifth octave above, correct judgments are to be regarded as coincidence. From that place onward, the tones appear to me to be sharp and pointed, and they all sound much the same. I particularly wanted to think of them as always F# or G# because the "pointed" character of the highest tones evoke an association with these pitches that have a "pointed" quality. In any case, the upper limit of my pitch recognition ability lies in the center of that fifth octave. Perhaps I could raise this boundary through practice, but in any case my attempts to guess in this region were all equally ineffective. I can't easily determine the lower limit of my absolute perception, since I cannot eliminate the indirect criteria. Taking this into consideration, however, the lower limit of my absolute perception seems coincident with the perceptual limit, while there is a gap between my perception and the upper limit of hearing. On the other hand, my absolute tone consciousness goes beyond the border of the range of musical tones in both directions.

One can see from this, as was already indicated by Stumpf, that absolute sound memory is not parallel with discrimination ability. Stumpf [6] found that judgments of low tones were far worse than high tones. If I found the opposite, this is only an apparent contrast; I experiment from the sub-octave to the fifth octave above, while Stumpf only used C1 to F#4; that high tone is where my judgments begin to fail and get worse, while security in judgment increases by continuing further down on the lower side of C1.

V. Effects of intensity on absolute pitch judgments.

We now want to examine the second sound quality, intensity, and its influence on absolute pitch judgments. This is a precarious thing because, unfortunately, no sufficient apparatuses exist with which one can measure the physical intensity of a sound.

We must distinguish between stimulus strength (intensity of the physical sound) and perception strength. It makes sense that there may be a strength in the stimulus which does not equate to strength of perception. Very weak sound stimuli which encounter the eardrum are overcome by the natural resistance of the physical ear and thus do not excite the auditory nerves at all. But even if the auditory nerves were slightly stimulated, the stimulation could yet go unperceived. One must suppose that, just as the sound is weakened by its propagation in the ear, it will also be in other media-- here the nerve mass-- and may be totally extinguished. If one had internal apparatuses with which one could precisely measure the stimulus strength and calculate the resistance of the nerves, it would still not be clear what stimuli are necessary to breach the minimal perceptual threshold. For as soon as we deliver a judgment of a perception, we must have already perceived it, and perceptions which enter above or below our natural thresholds are not perceived. It is possible and conceivable that an existing, perceived feeling nonetheless goes unnoticed because of weak signal, lack of attention, fatigue or other outside circumstances. Both thresholds-- of feeling and of perception-- would be most giving under favorable conditions of great attentiveness and extreme silence. In general, however, the perception threshold sways significantly.

Further, one can perceive an extremely weak sound without being able to identify its pitch. The pitch judgment occurs after a type analysis of the perception; only after perceiving a sound can a person focus on its individual qualities such as height, intensity, timbre, or duration. One can say, therefore, that at a minimum intensity it may only be possible for a listener to acknowledge the existence of a sound, but at another intensity they may determine its pitch. We must therefore must make a psychological distinction between the threshold of perception, the perception itself, and the pitch judgment, all of which may be different for absolute and relative pitch judgments.

The numeric values for the perceptual threshold, which are calculated by individual examiners, refer partly to noises, partly to tones. Conta [8] has measured tuning-fork tones. Boltzmann and Töpler computed the amplitude of an air particle to determine the just-audible threshold of a 181Hz pipe sound, which they calculated to be 0.00004, and the mechanical energy delivered to the ear to be 1/3 trillion of a Kg. Rayleigh is investigating even smaller values [9].

If these investigations already have great difficulties, the obstacles grow yet larger in calculating the stimulus strength required for an absolute pitch judgment. As mentioned above, a type analysis of the individual sound characteristics is part of the perceptual judgment. Every sound has its background noises, and only if the intensity of these noises is infinitesimally small-- or at least so small that the listener's attention can be taken from them-- is a pitch judgment possible. If we used the Boltzmann-Töpler experimental assembly to address this question, we would have to tacitly accept that the tone and background noises are proportionally weakened by the distance of the acoustic source. This, however, is not proven by any means, and in fact it would seem that, with distance, the perceived strength of the noises would decrease more rapidly than those of the tones. This is why Stumpf [10] indicates that military music in a room is different from that heard on the street; the noises from the street obstruct the musical sound, but these noises are weakened by passing through distance and the walls of a room.

We therefore cannot investigate the threshold value of the sound intensity required for absolute judgment. We would only be able to produce a clear answer to that problem in conditions that allowed us to arbitrarily produce stimulus strengths to the smallest possible degree and to physically calculate those intensities.

We also cannot answer whether a sound, having been identified, requires additional intensity in order to trigger the naming process. In all my attempts, each of which was with very short and very weak sounds, I discovered that where my colleagues-- who had musical experience, but did not possess absolute tone consciousness-- were able to recognize the tone well enough to repeat it by singing, I would always be able to recognize and name it. The boundary was so sharp that we all recognized it instantly and simultaneously. All this would seem to prove is that the psychological procedure in the brain which analyzes the sound and that which manages the absolute pitch judgment require the same minimal intensity in the sound stimulus.

The difference between the perceptual threshold and the judgment threshold depends on the listener's ability, practice at making such judgments, and level of fatigue. With very practiced observers and favorable conditions, the two thresholds lie may be very close to one another.

Another notable influence on the intensity threshold is the strength of the sound. A very strong sound, for example a strong trombone, carries more absolute information than a softer sound; with a louder sound, not only are there are more overtones present, but more background noises are detected and drawn into the listener's perception of the tone. This is particularly noticeable with sounds that have distinct overtones, such as bells or glass tones; the more quietly one strikes a glass, the more easily one will be able to distinguish the sound of the glass from the environment and thus identify the pitch. It can sometimes be impossible for a listener to identify the pitch of a loud bell sound, while they can easily identify a similar sound of weak intensity; the optimal strength for the absolute judgment lies somewhere between maximum and minimum, considerably favoring the latter side.

A further influence of strength on pitch judgment exists in that stronger sounds are usually perceived as higher than weak sounds of the same frequency. It seems unlikely that this illusion is a function of perception. Stumpf, in Tonpsychologie (I S. 238 f.), mentions several arguments of his own and other researchers. Stumpf recalls how a singer's pitch may seem to drop as their breath runs out, even though the singer does not physically lower the pitch. The illusion is also fostered by the fact that higher sounds are perceived to be stronger than lower sounds of the same intensity. Pitch judgments may involuntarily fluctuate because of a tone's perceived strength. Third, fewer overtones are produced by a weak sound; adding more overtones gives a higher feeling to each tone, because the sensation thereby becomes more similar to the higher tones. In general, however, the influence of sound strength is hardly a consideration to the absolute listener. The slight distances by which the stronger tones seem higher than the weaker usually amount to only a fraction of the pitch category, and the sound is therefore identified by the same musical name (in the middle octaves, each category may span 40-100Hz). The strength illusion is a greater concern for interval comparison. Nevertheless, it would be interesting to discover the effects of this illusion if it were possible to measure its influence numerically; we would have to have apparatuses to measure the intensity and the stimulus strength, but if we had the means to measure it we could know the ratio of stimulus strength to perception strength for various pitches.

VI. Effects of sound duration on absolute pitch judgment.

Another sound quality whose relationship to absolute listening should be examined, and which joins with intensity in its relation to threshold values, is the sound duration. We must differentiate here between the necessary duration of a single sound and that of a sound which forms only one member of an arpeggio. Also the perceptual judgment must be regarded separately from the absolute pitch judgment. To first address only the duration of an individual tone, we may use the following questions:

I pursued detailed investigations of both questions in partnership with L.I. Brühl, which are published in Zeitschrift für Psychologie v. 18. I therefore will refer you to this treatise and will indicate here only a brief representation of the procedure and its results.

We gave ourselves the task of producing the shortest possible sounds whose frequency and duration could be easily calculated, to examine their effects on perception and pitch judgment. The most appropriate device for this purpose was air blown through a siren-disk. Using a circular aluminum disk, with a diameter of 80 cm, we punched two concentric circles of holes so that the size of the holes and the distance between each hole was equidistant (2mm). The larger circle contained approximately 500 holes and the smaller 300. The disk was turned from its center at different speeds either by hand or by means of a gas motor. We blew through these holes via a 1 cm thick glass tube whose mouth tapered to a 2mm aperture; the production of air was first accomplished by a bellows, but we discovered that our lungs yielded the necessary quantity and pressure of air. We affixed the glass to a movable tube and directed by hand the mouth of the glass toward the holes in row I or II. While one of us blew and turned the siren, the other (Abraham) determined the pitch, registered the judgments, and sometimes compared the judgments to the harmonic sounds. The rows of holes bore the ratio of 300 to 500, i.e. 3:5, which produced the interval of a major sixth between the sounds. To test sounds with short duration, we covered up a quantity of the holes in Row I, leaving row II as a control sound with all its holes uncovered. We made attempts with 20, 10, 5, 3, and 2 holes, which means that we were experimenting with sounds of 20, 10, etc. oscillating cycles. In this manner, we arrived at the result that for the sounds between the lowest octave to the middle of the fourth octave, two oscillations were sufficient to generate a sound perception. Above that point, the higher the sound, the more oscillations we had to produce:

Oscillations (cycles)	Frequency (Hz)
2	3168
3	3960
4	5020
5	6000
10	7040

We can see that the number of cycles increases with frequency, and let us now consider the absolute time which these express. A pitch at 3168 cycles per second therefore requires for two cycles 2/3168 = 1/1584 seconds or, if one uses the symbol σ for 1/1000 of a second, .63σ. A tone of three cycles therefore needs .76σ; four cycles require .79σ, five cycles .83σ, ten cycles 1.42σ. One could say that for generating a tone, a minimum time is necessary which decreases with increasing pitch to .63σ before growing again with higher tones.

After we had assessed in this manner the minimum time required to perceive the sound, we sought to answer the second question: how many cycles are necessary for absolute pitch judgment? We had noticed that we usually had to repeat the short sound in order to make a definite judgment. The sound pulses are the same, but they are accompanied by background noises which probably consist of reflection waves and irregular after-oscillations. These background noises were very disruptive to the pitch judgment, and they persisted, joined by the noises of the air blowing and the disc turning. However, when I applied strict attention I did succeed in recognizing the pitch at its briefest duration, which identification became more certain after a repetition of the sound. The time which elapsed between my feeling the sound and making a judgment was significant, approximately 1/2 to 1 minute, and became proportionally smaller with each repetition of the sound. I was highly conscious of my analysis process. I separated all background noises from the target noise and very suddenly, after about half a minute, the pitch name came to me. I compared this to my mental image of the sound in my memory, and examined whether the designation fit; sometimes I also whistled the pitch and compared this to the feeling I had received from the sound, which was easier than comparing the received feeling to my internal memory of a pitch. I made very few mistakes, and those mistakes I made were nonetheless correct within a semitone.

It appears that the same duration threshold is decisive for absolute judgment and perception. For determining the pitch, however, a repetition of the sound was very valuable, and the number of repetitions depended on disposition, expectation, fatigue, and practice. Under normal circumstances, if the attention is not trained just on the pitch, a certain duration will be required to be able to determine the pitch, and this is surely affected by the timbre, intensity, and pitch height of the sound. Thus v.Kries (1st c.) says that, if he hears the tone of a locomotive ring out briefly, he is often unable to make a judgment of its pitch height, only succeeding when it sounds for a longer duration or when the short sound is repeated.

VII. Effects of temporal distance in sounds following each other.

Another essential influence on absolute pitch determination is the temporal distance of sounds following each other. This may seem to contradict what I have already said, that absolute tone consciousness has nothing to do with interval comparison, so that it wouldn't matter whether a minute or a day passes between the perception of two sound events. Certainly this is correct, in that large temporal intervals have no influence on absolute pitch judgment (provided that absolute tone consciousness is not diminished through years of neglect). However, smaller temporal intervals between sound events are significant to the judgment of pitch, and I have conducted a more exact experimental test of this effect in partnership with Dr. K.I. Schaefer [12]. We had given ourselves two tasks:

Both tasks simultaneously demonstrate how arpeggioed tones may influence perception and judgment.

Our first experiment was similar to the investigation of short sounds. The sounds were produced by blowing through a siren disk on which several concentric holes had been punched; for the higher octaves, we used the aluminum disk described above, and for the lower tones we manufactured a similar disk of wood whose holes had larger diameter. We blew through each row by means of small tubes whose opening was exactly the same size as the holes. The air was blown either through a compression apparatus or from the mouth. The disk's rotation was provided either by a motor of uniform speed or by one of us who had practiced turning it by hand. The interval of the alternating sounds in a tremelo is independent of the rotational speed. If the one circle passes through 8n holes while the other circle passes through 9n, this will always produce a major-second interval. By combining a circle of 8n holes with another of 10n we produced sounds that stood a major third apart from each other, and in the same manner we were able to produce tremeloes of fourths and fifths. We did not alternate blowing at each of the circles; instead, we taped over or clogged the holes for alternating stretches along each circle. So the first half of one circle and the second half of the other was sometimes covered in thick paper. In other cases, the first and third quadrant of one circle and the second and fourth of the other was sealed with cork-stopper. Whether the circles were divided into semicircles, quadrants, sextants or octants, depending on whether we wanted to obtain higher or lower sounds, we were generally mindful to include both higher and lower sound trials in order to prevent unexpected influences of sound area.

The siren was prepared in the indicated manner, and the attempt began: we first turned the disk very slowly and heard low yet clearly-separated sounds. Then the speed was gradually increased so that the sounds became higher and shorter, until we arrived at a rather sharply-defined boundary at which the sounds could only just be perceived individually, or began to fuse with each other into a chord. Following this moment, which could perhaps be called a trill threshold, both sounds formed an interrupted chord, which became increasingly smooth as rotation was increasingly accelerated. We also observed the effect in the reverse direction, looking for the point where the two sounds separated and ceased to be a chord, and this proved in general to be the more appropriate method. In any case, both types of experiment were repeated often enough to come to a clear judgment of the trill threshold and the corresponding pitch values. Then, a simple calculation was sufficient to find the accompanying duration (d) of the sounds. If the number of cycles is s, and the number of holes in the circle sector is n, then d must be n/s. The frequencies were measured with the standard A1 = 440Hz. The results of our attempts can be compared in the tables below. In general it appeared that, apart from the highest and lowest sound trials, in which the time necessary to identify the trill threshold is larger, the threshold is almost identical for the middle octaves, namely 1/35 second per sound up to the fourth octave above the middle. Trills may therefore be detected in all octaves with equal speed, or tremeloed to produce separate sound perceptions, and the exact interval makes no remarkable difference.

It should be highlighted that in the high region, the duration threshold of a trill is considerably longer than the perception of a single pitch sound (0.63σ). I have provided an explanation of this incidental fact in my referenced paper [13]. In that publication I clearly described the reasons which may account for this perception; discussion of that topic might prove to be too much of a digression for this paper. What does belong here, however, is the description of circumstances which influence the perception of absolute tone consciousness (fading away, etc) and special ratios which influence and interfere with each other in arpeggioed sounds.

In the section dealing with short sounds, it was demonstrated that a comparatively large time was necessary to render a judgment, during which the sound is psychologically analyzed. This analyzing, we had said, became easier through the repetition of a sound. In this case, repetition makes judgment more difficult. Attention is continually drawn from one tone to the other, and cannot linger on either in order to extract its basic pitch information from the background noises and timbre. This explanation was supported by the fact that, at maximum trill speed where the two tones were already merged into chords, pitch determination was far easier than the speed at which the tones were perceived separately. Despite the far greater speed and the shorter physical duration of the sound, it was much easier to recognize the pitches of a chord.

We can say therefore that, if a separate perception of trilled or tremeloed pitches is not yet present because of its speed, the absolute pitch determination of the sound becomes easier as it moves away from the trill threshold.

The second part of our work is far more practical to music, in which we took into consideration the maximal speed of musical structures for perception and pitch judgment. We made these investigations in partnership with the late prof Oscar Raif of the Royal University for Music, and we kindly thank his valued part in these experiments. The trial proceeded as in the previous investigations, except that the quantity of arpeggioed tones was increased, and now attention could be paid to the melody as well as the absolute sequence. We have listed all five attempts here. In the first four, the melody was four tones, and the fifth attempt had five. When the disk was spinning quickly, we heard only that it had a series of not completely simultaneous tones; however, the observers could therefore recognize the pitches correctly, to a large extent (in particular the highest and lowest tones), even though they could not recognize the melody. The melody was first recognized at an average duration of about 1/10 second per tone. A reproduction of the five trial protocols will illustrate these ratios best:

1st trial

2nd trial

3rd trial

4th trial

5th trial

Both test subjects were remarkably congruent in their replies, nearly agreeing either correctly or wrongly. It is also remarkable that the irregular sound combinations were judged incorrectly to be more regular musical structures. So the observers believed, for example, that in the first attempt they were hearing the pitches of a familiar minor seventh chord rather than the actual tones. As with the trill attempts, it was more difficult to detect pitches which occurred in rapid sequence than those of a broken chord. Some individual tones (see 5th trial) were not heard at all. Those which were noticed were recognized far more quickly than at the medium speed; the judgment time at medium speed was larger. These trials demonstrate how the pitch judgment for sounds following each other is influenced by the temporal interval; in addition, the judgment is influenced by the musical structure. If a pitch within the structure is recognized, then someone with absolute tone consciousness can name it; it is not the pitch-recognition ability which is affected, but the ability to hear the pitches clearly and correctly.

VIII. Effects of timbre (tone color).

Timbre has an important influence on the judgment of absolute pitches. Timbre can be so powerful that many musicians of instruments that produce that timbre can name those tones with total confidence, while other timbres leave them groping in the dark; when listening to other timbres they can easily hear an E and call it A or B. In my experience, the ability to recognize tones is more frequently restricted to single timbres than it is expanded to all sounds. We must use the term "timbre" in a very specific way: usually, timbre is differentiated from the general ambience of sound. Stumpf describes all of the following as components of timbre:

The first component, of associated concepts and feelings, need not be discussed here, because we cannot possibly regulate them in an experiment. It is possible that a flute sound can evoke the name "C" or be thought "idyllic" by the listener, but neither concept has a significant influence on the timbre itself. Furthermore, the second component is not relevant to our investigation; rarely does one find overtone-free sounds. Also, any sound character emerging from variations of pitch and intensity cannot be measured, because it influences associated feelings, not pitch judgment.

For our purposes, we place importance on the timbre which results from the addition of overtone sound and background noise, produced mainly by a type of instrument.

Of all the instrumental sounds which are most easily recognized, the piano is the prime leader. Piano sounds are most easily determined, followed by violins, woodwind, sheet-metal instruments, tuning fork, sung tones, and finally the sounds of bells and glasses. Superficially, one could conclude that the instruments most easily identified are the ones which are most frequently heard. But this is not the case, because even though piano sounds are most easily recognized, the sounds produced by the human larynx can easily compete in frequency of occurrence-- and those are at the lower end of the recognizability scale. Therefore, although practice may have an influence on pitch recognition, there must nevertheless be a further reason which explains the difficulty in recognizing sung tones. The reason must lie in the sounds themselves, and in the sounds, the principal difference is in the heterogeneity of the overtones. It appears that simple (or overtone-poor) sounds such as tuning forks are not the easiest to identify, rather, the more overtone-rich, sharper instrumental sounds are more easily recognized. And yet, to be sure, the fundamental pitch is more important than the overtone sound in determining the overall pitch of the tone.

This is clearly evident in the easily recognized sounds of bells, glasses, and human voice. In the bells and glasses, the pitch sound is so strongly reinforced by the overtones that it often disappears behind the overtones, so that only through attention and practice can its pitch be detected and identified. In singing tones, the inharmonious sounds of the vowels may obscure the pitch sounds, which makes pitch identification difficult for most observers; thus J. v. Kries in particular complains that he can only recognize the tones of the human voice in exceptional cases of high soprano voices. The reason that higher vocal sounds should be more easily recognized-- whose partials do not obscure the sound, which supercede the inharmonious vowels, and which are strongly connected to a key signature-- should be self-evident.

It is more difficult to prove why sounds with richer overtones are more easily recognized than those whose overtones are weak. There are several entirely different possibilities to consider. If it is correct that the primary condition for judging pitch is hearing the fundamental pitch, then it would seem logical that sounds without overtones, such as tuning forks, would be more easily judged-- but in reality, these are usually more difficult. Stumpf found in his experiments, which were focused on the judgment of intervals, that stronger timbres facilitated identification, and he offered the following explanation:

Stumpf thereby explains that the easy recognizability of sharp sounds is that when the fundamental pitch is strengthened, so too are all its partials, which in turn increases the strength of the relationship between the fundamental pitch and its partials. Although Stumpf was describing the analysis of chords, the same logic is true of recognizing tones which also consist of partials. It is necessary to analyze whether this is different for pitch judgment, and I will examine that question in greater detail in a moment.

Secondly, practice can also be a great influence; one hears overtone-rich sounds more frequently then overtone-poor sounds, and they are therefore more easily identified.

As these explanations indicate that hearing the fundamental pitch is easier with overtone-rich sounds than with mild, it is possible to reject the idea that hearing the fundamental pitch is necessary for identifying the tone height. One can defend the opinion that the fundamental pitch is not what is analyzed; the fundamental pitch has no label associated with it, but the entire complex tone is wholly identified, including partials exclusive to the timbre. What we call "A0" is not in fact A0, but A0 + A1+ E2 + A2 and so on. This would make self-explanatory why tuning fork tones are recognized only with greater difficulty. J. v. Kries advances a similar explanation for the easy recognizability of chords. He says that generally, if associations are made between related effects a and A, also with effects b and B, where a cannot be caused by A alone but only by A and b together, then a will become associated with b. J. v. Kries does not ignore the arguments against this opinion, but holds this as the most satisfying explanation. I believe that this explanation is inadequate-- otherwise, one would have to assume that a sound would become easier to recognize by adding more overtones, while in truth there is a limit to the overtones which can be layered on before they obscure judgment. Sounds with moderate overtones are most easily recognized.

I imagine that, through practice with piano sound, one learns to interpret the complex sounds which correspond to each piano key; another process occurs to analyze the sounds of a violin. Sounds that are overtone-rich are equipped with the same features as the piano sound; overtoneless sounds are not recognizable until they are presented with the necessary overtones to correspond to the piano's timbre. This does not occur through the physical adding of overtone sounds, but rather a mental comparison of the existing overtoneless sound with the memorized piano tone. Therefore, only observers who can correctly imagine a tone will be able to judge the pitch of unfamiliar timbres, given appropriate conditions. We can therefore now explain why very strong and very mild sounds are more difficult to judge than moderate sounds.

The explanation would not contradict the above view, which describes how individual partial tones obscure the fundamental pitch of glass and bell tones. We must, however, assume that when we speak of "hearing the pitch" we are not speaking of the simple sound but of the entire complex tone. Whether this tone is actually analyzed is doubtful. A complete analysis of a sound, such that the fundamental pitch is heard separately and its remaining partials used individually for recognition and evaluation, does not occur in normal pitch judgments. But it is possible that the fundamental pitch is heard, along with a certain sum of overtones, and that the latter is ignored in forming the pitch judgment. Or perhaps the judgment concerns solely the mental image of the complete sound unit which a musician has formed through practice; tones which greatly resemble this image, the musician may immediately identify, but others which do not so closely resemble the image require more time and attention to compare and recognize the essential pitch component.

It is not easy to tell whether the judgment therefore concerns an analysis of the sound or a reproduction of the sound image-- but this would only be a theoretical difference, because in practice we can only be certain that timbre is of great importance in making pitch judgments. The sounds are categorized into the same basic units, and whether this categorization is accomplished via piano tones or other instruments does not interest us as much as the fact that large fluctuations of ability exist between different kinds of instruments. The fact that we hear a complex tone, consisting of several tones, as a single unit seems also to prove the "octave deceit" previously discussed.

All persons with absolute tone consciousness evidence some effect of timbre upon their judgment. To be sure, many of them will be able to identify tones regardless of their timbres, but the accuracy of their judgment-- especially in the length of time required to render their judgment-- is highly variable. I myself believed that, for me, timbre would be an insignificant factor, but when I tested my times for pitch recognition I found powerful differences between timbres.

IX. Duration of judgment in determination of absolute pitches.

The duration of an absolute pitch judgment is the time which elapses from the moment the tone is perceived to the moment the tone is identified, whether that identification is accomplished by association with a word, an image, or the key of an instrument. Yes, there is a period of time between the instant the sound is generated and when the sound waves reach the ear; but there is also a period of time between when the sound is perceived and when it is recognized. Auerbach and Kries [14] had found experimentally that recognizing low tones took longer, and thus the duration of judgment was longer for lower tones than higher tones. I cannot agree with this opinion; in our investigations on the maximum speed of pitch sequences, Dr. Schaefer and I [15] found that the trill threshold for all tones is similar, as was the intensity threshold. We achieved these results using the non-resonant tones of a siren disc. As soon as we began using tones from a piano or stringed instrument, the time judgment immediately changed because the physical strings take longer to vibrate than do the smaller strings. High tones are therefore perceived more quickly than low tones, but the difference is physical, not psychological. Thus a conclusion about judgment duration related to high and low tones cannot be made from v. Kries and Auerbach's experiment. If our opinion is correct, that the judgment duration is the same for high or low tones, then we could expect that the calculation of judgment duration would be accomplished by maintaining the moment of the physical event as constant. We have had the opportunity already to observe the duration of absolute judgment. We saw that tones in the middle octaves are judged far more quickly than the highest and lowest tones, perhaps because the extreme octaves are unfamiliar and must be compared to the more familiar tones; we found that very brief tones have a very short judgment time once they are sifted out of the background noise; furthermore, we saw that tones possessing unusual tone qualities require a longer judgment time than well-known sound types, either because they must be mentally compared to known sounds or because one must extract the pitch information from the convolution of overtones. Thus the judgment time is predicated on the height, duration, and tone quality of the tones. Of course, individualized circumstances are possible beyond the physical differences; perhaps different physical circumstances are judged differently by different listeners. An average judgment time would therefore be worth calculating only as a curiosity; it is more important to determine the most favorable physical and individual circumstances. Solving this task, however, presents substantial challenges.

The first important question is how the judgment is to be rendered. It can be accomplished by speaking a name, writing a letter, drawing musical notation, indicating the appropriate key on a keyboard, or demonstrating the fingering on another instrument. I tried first to determine, in cooperation with Dr. Max Meyer, the time spent in expressing the judgment. Our experimental assembly was as follows: because harmonium tones were judged easily and quickly, we used that instrument in our trials, and could thereby measure the time between the production of the harmonium sound and the expression of the pitch designation. The harmonium keys were fastened to wood clips whose ends were fitted with metal plates connected to an electrical circuit. When the key with the clip is depressed, and the metal plates are pressed together, the current is closed; the current is broken by a contact placed between the lips of the observer which, when speaking, moves through a flexible spring. To measure the time of the event, a chronometer is connected to the circuit, where the chronometer is accurate to 1/1000 of a second. We believed that this apparatus would make it possible to determine the judgment time. The keyboard contact functioned very well, but the lip contact less so; first of all, the mouth was sometimes opened before speaking the note name, and secondly, different letters are formed differently, especially vowels versus consonants, in the lips, tongue, and palate areas. Since we would not have been able to change this problem even with practice, we abandoned the entire method. A written judgment would not be useful because in each case we would receive an indirect judgment, where the tonal recognition would have to be further transformed into a pictorial association.

Pressing a piano key corresponding to a test sound is probably a direct judgment. The keyboard is so well-known to a piano player that, if he hears an E tone, he will be able to press the E key without first having to remember the name or pictorial symbol associated with E. Even if this were the case, the process takes considerably less time than writing the letter, and perhaps even less time than speaking it. We therefore structured a new kind of trial. Again, we used harmonium tones, fastened the harmonium with the clip contact that closed the electric current; to open the current we created a new apparatus. We provided a small piano, resembling a children's toy piano, and fitted its keys with metal plates which rested on a metal rung connected to the circuit; the keys therefore maintained the circuit when they were not being depressed. When a key was pressed down, then the plate was disconnected from the rung, and so the electric circuit was broken.

So first, a tone is played on the harmonium with the clamp-contact (e.g. F), and the test subject responds by pressing the F key on the toy piano; the chronometer records the time between each event. This time interval is not the actual judgment time, but includes all of the following events:

With a harmonium, the time between the circuit's closure and the production of the physical sound is constant. Furthermore, because we did not use great variations of height but restricted ourselves to the middle octave, any difference in generative time is slight and insignificant. For the same reason, the perception time for all trial sounds is essentially the same. The time to physically press the toy piano key is also a minimal constant in our calculations, which means that there are only two significantly variable quantities:

The time required to locate the physical key can be considerable and varied, depending on the direction and position of the trial sounds. On our little piano, we had only an octave of tones. When I was a test subject, I endeavored at the start of each trial to fix myself in the middle of the keyboard so as to be physically equidistant from all available keys.

At the beginning of our investigations, Dr. Meyer played tones from diverse octaves subsequent to each other; this, however, proved highly inappropriate. Because if I had just heard a D3 and was then asked to judge a B2, I would automatically seek to the left of the D-key, because I am accustomed to looking for lower tones on the left of the keyboard-- but then I would remember that my keyboard was only one octave long. This created unusually long seek times and was consequently not helpful in answering our question.

Therefore, we examined each octave independently. Depending on which octave was being tested, I imagined myself at the piano sitting directly before the middle of that particular octave. Dr. Meyer monitored the accuracy of my responses, and there were no errors in any of the trials. The results are as follows:

This table shows the interesting result that for different octaves, there is an unequal time between making the judgment and striking the key. I would refrain from referring to this as the actual judgment time, because locating the key certainly takes a considerable part of the calculated time. Because of our procedure, however, which treated each octave independently, I believe that the influence is not the respective octave height but the result of constant factors. The judgment time for the different pitches within each octave is the same, varying on average between 499 and 563 for a difference of 64, which can probably be explained by the time used in hand movement. In any case, it cannot be argued from this table that one sound may be judged especially easily compared to the others, or that there was a linear relationship between the times to judge these sounds. One might have supposed beforehand that A, which is usually used for tuning, would be the fastest judged, but remarkably the fastest tone was B instead. If we imagine that the variation between pitches within an octave is due to the seeking time, we may conclude that the judgment time is different for absolute pitches in different octaves. I judge most quickly in the second octave; the further from this octave, the longer I take. The fixed time for each octave, then, where C is the constant of seek time and u us the judgment time, is therefore

It would now be very convenient if one could calculate the constant C to deduce a pure judgment time. Unfortunately, we were unable to accomplish this-- however, our attempts led to such interesting results that they are worth describing. We wanted to compute the time between the moment the name is mentally conceived and the moment the test subject presses the appropriate key. For example, Dr. Meyer spoke the letter C and simultaneously pressed the C key on the harmonium, and I reacted the same way as before, i.e. by depressing C on the toy piano. The times required for the individual letters were as follows:

These numbers are just as large as those in the previous table. The times are even larger than those for the second and third octave. Therefore, we can not regard these figures as we had hoped, and deduce the judgment time by subtracting the constant time; if we were to do this, we would find negative times for two of the octaves. But this has provided an unexpected result: the discovery that when hearing a letter sound, an image of the letter is produced, which is only afterward connected to the piano key. This letter image is not produced when responding directly to a tone sound. The connection of the tone to its key is more intimate and direct than the connection of the key to its letter name.

The seek time could not, therefore, be isolated and determined in this manner. Seek time is a considerable factor in our figures, so we are unable to determine the exact judgment time-- that is, the time between hearing the sound and producing the sound label (either as a keypress or a letter name)-- with any exactitude. However, we have determined that my composite judgment time is recognizably swiftest in the second and third octaves. This is important because I practice both piano and violin, that is, instruments in which the second and third octaves are used most frequently; perhaps if this same experiment were conducted with a cellist or bass player, they would identify the lower octaves more quickly. I do not, however, believe that I recognize only the second and third octaves and unconsciously compare all the other octaves to my memory of those octaves. The differences between octaves are too slight, and progress too uniformly, to suspect that that should be the case.

X. Pitch determination through indirect criteria: sound type and characteristic.

We have now seen how different physical sound qualities exercise their influence on pitch judgment. Height, strength, tone quality, and duration are important to any observer. There are still great individual differences, so that under similar circumstances one observer will easily recognize tones while another will struggle; however, in all trials there was one constant factor. Whenever the fundamental pitch was perceived, the absolute judgment could be given. The judgments were a direct evaluation of the perceived sensory content. If a tone is named F, an observer will call it F without having to "figure it out". He is unaware of any analysis in his judgment.

But this is not the only way to arrive at a correct pitch judgment. As with other senses, there are also indirect methods. If, namely (Stumpf I, S. 87), a stimulus is presented regularly along with another, so that a is associated with A, b with B and so on, then the listener will use these associations to infer further judgments. These become indirect criteria. We know, for example, that very high sounds may evoke a pain in the ear. If we tested in our trials to determine which pitches caused this pain, we can logically infer the pitch of a sound which causes the same pain. Also, there are people who perceive colors when they hear sounds (or certain timbres). They may determine the pitch from the color they are experiencing. Still others will, when hearing sounds, make mental comparisons to the tension of their larynx when producing the same sounds and judge pitch from that; the muscle movement for such a judgment may be reflexive or deliberate. We have, therefore, entirely different types of indirect criteria which can be used for pitch determination. There is direct sensory association, reflexive muscular response, and conscious physical judgment. I would like to examine the last of these.

One often hears the opinion that absolute judgments are produced by "feeling" the pitch. In layman's circles, the word "feeling" is used in many different nonsensical ways; if we take the word literally we can understand its application to pitch sound. Each perception of sound is accompanied by a characteristic feeling; we can hear a sound and describe it as "comfortable" or "unpleasant". This effect is to a large extent a function of its timbre, which is based on its overtone sounds and background noises; so we can produce the same tone (a tone with the same fundamental pitch) on different instruments and one will be comfortable while another is unpleasant. If we separate the timbre from the pitch, however, the difference in the feeling of each pitch is weak. If one compares the feeling of middle C to middle G, one will hardly be able to detect any difference at all. I could not even say whether the tones would feel differently if they were in different octaves. In any case, I believe that musicians who have very fine tone discrimination would find it impossible to internally measure this feeling to render an exact absolute judgment of it for each semitonal category.

To be sure, the nearer a pitch is to the boundary of musical sound, the more its characteristic feeling will change (without changing the timbre derived from overtone sounds), purely because of the way the quality of its vibration interacts with the physiological arrangement of our ear apparatus; the highest sounds are accompanied by a perception of pain, as though the ear were being pricked by a fine needle [16]. If this boundary at which the pain began were always the same pitch, this could of course be used as a definite criterion for absolute pitch recognition, at least for the pitch which sat upon the boundary. But this effect does not occur in all musical sounds, and in fact occurs in very few; fortunately, the boundary for painful perception lies far past the limit of sounds which are within reasonable limits of musical use. I would maintain that the "feeling" of a pitch is insignificant to the recognition of absolute pitch. In the same vein, the "roughness" of lower pitches, in which the pulsing oscillations of the pitch are individually perceptible, gives each pitch a rough feeling; as the pitch lowers this roughness becomes a humming and finally a shimmering character [17]. Sounds which are audible in the area of 16-30 oscillations per second, for which one can literally count the pulses, can be judged comparatively well by this criterion; I have been able to accomplish this myself with great accuracy. This skill is arguably unmusical, however, and is only of theoretical interest. Additionally, the criterion of pulse-calculation would not be included in the category of "feeling", for the perception of roughness is not a feeling as much as it is detecting a specific quality of the tone, and perceiving the pulses would seem to be a mechanical function of the ear.

A third case should not go unmentioned: our eardrum itself has a characteristic resonance. It varies between people, but is usually an F#2. When an F#2 is sounded, the eardrum is in greatest resonance, and the pitch can be recognized in that manner. This would be a derivation of pitch judgment based on the perception of intensity.

All these indirect criteria-- sound feeling, pain perception, roughness, and intensity-- are used for pitch judgment only in exceptional cases. They are, nonetheless, all provided by the hearing apparatus. Usually, indirect criteria are drawn from other senses in order to render an absolute pitch judgment.

Indirect criteria can have consistent effects, so that a certain sense is excited by a stimulus which then automatically evokes a related perception. I have found numerous examples of these kinds of effects, and they are often used to help form a pitch judgment. If the A pitch is played, some people may imagine the musical notation of A, others may think of pressing the A key on their instrument, and still others may remember the alphabetical letter A. This kind of association is comparable to the much-discussed phenomenon of synesthesia. We have known for some time that excitement of a particular sensory nerve can stimulate a different nerve which is part of a different sense modality. Just as a sensitive nerve may be responsive to nearby activity, a strong nerve may stimulate other nerves which would otherwise not receive a direct signal. In this manner, a sound stimulus can evoke optical perceptions. Bleurer and Lehmann in 1881 studied these associations, describing them as "compulsory light perceptions through sound."

True synesthetes, who actually see colors when they hear sounds, are quite thinly sown among the population. There are a greater proportion of people who, when hearing sounds, obtain the sense of a color; whether this is a weaker form of synesthesia as Hennig [18] asserts, or a non-perceptual process, I would not be able to determine; whichever it may be, Hennig differentiates between a physiological and psychological effect. In the first scenario, the color perception is evoked by physiological processes and are, in the truest sense of the word, "compulsory", so that they would arise unbidden and with no regard for the listener's conscious preference. In the psychological scenario, the sensory input receives a mental judgment and is thereby linked to a color concept rather than with a visual experience.

I would prefer to consider most of these effects as belonging to the psychological category, including the color concepts associated with vowels. Hennig says that these colors are a direct function of the sound type (overtones, etc); I find it even more complicated than that. I make the following color-vowel associations:

It is possible that the colors I associate with a and u are drawn directly from the timbre of those sounds; the others are undoubtedly because the vowel sounds are in fact present in the words which describe the colors "gelb" [yellow], "rot" [red], and "grün" [green]). Perhaps my association with black can be explained by the presence of u in the word "dunkel" [darkly]. There are certainly complicated sensory associations being made here, but this is obviously not a function of perception.

It may happen that a person receives a perception of color, or a very intense visual sensation of colors, in hearing certain sounds, and in the appearance of the color he could recognize the sound. Unfortunately, the literature describing such individuals is not only sparse, but unclear and contradictory. Flournoy describes the color perception of Prof. Cart Letzterer thusly:

But later, Prof. Cart explains that he cannot identify the sounds by their associated colors, out of his own lack of musical development.

Hennig describes a very interesting case in which a lady experienced no phantom perceptions at all, except in D-flat major. When she heard a piece of music in D-flat major, she received a general impression of redness, and identified D-flat major in this manner. Unfortunately, Hennig was not able to conduct extensive tests of this observer.

In my questionnaire, I asked about color associations, but I did not ask about whether the color was a concept or a feeling. Most respondents would describe pitches as shaded brightly or darkly, and only a few described actual color perceptions. These cases are shown in the following table.

The color perceptions are created sometimes by hearing musical compositions, sometimes by hearing musical sound; sometimes it is not automatically heard but is perceived only with deliberate attention. All possible factors should be considered. Almost everyone named "C-major" as white, probably because of the white keys which are used in that key signature. One observer named C-major "yellow", possibly because his piano is rather old, so that the ivory of the keys had gradually turned a yellow color. I do not have enough information to explain all these color assignments, but I believe that for many the color association was similarly of extramusical origin.

For those with absolute tone consciousness, no color perception was used in making judgments. Even if listening to a sound or composition evoked a color perception, none of the observers identified the pitch based on the color; rather, the pitch judgment was already present and the colors occurred as an incidental adjunct of the experience. To my knowledge, synesthetic color associations are not used as an indirect criterion for pitch judgment.

When considering indirect criteria, we have to ask the question of where there is a kind of absolute tone consciousness which is not actually based on absolute tone consciousness. This matter has been discussed extensively in the past decades. A gifted musician with absolute tone consciousness can immediately name the key signature of a piece of music, provided that he hears enough of it, obviously. This ability seems dissimilar to others who have partial tone consciousness, who can recognize only certain sounds. It is significantly easier to recognize scale degrees than pitch sounds, for in a chord or scale it is far more probable that the familiar sounds will occur and be more prominently heard than the individual tone qualities. The familiar sounds serve as a base from which relative judgments may be made. Of the 100 respondents to my questionnaire, 18 explained that it is far easier to recognize a musical structure than a single tone; everyone who said this, however, had only partial absolute tone consciousness.

Is it conceivable that a person who possesses no trace of absolute tone consciousness would, nevertheless, possess absolute tone consciousness?

This question has been previously discussed in conjunction with the characteristics of musical key, and has been distorted through opinionated and subjective views. The problem was therefore solved neither theoretically nor practically. It is surely impossible to entirely separate a key signature from its characteristic sound; the only way to accomplish it would be to strictly segregate the individual parts. Hennig wrote exhaustively of the characteristic of the key signature in 1897; I will address Hennig's treatise after making some establishing statements.

It is a fact that a composer selects for each work a musical key which seems appropriate for that work. I am intentionally being vague, because the choice of key signature can have any number of possible causes, and is not necessarily due to the character of the key signature.

1. The selected sound type may be especially familiar and comfortable to the composer, either technically or harmonically. A composer may be able to improvise extremely well on the piano in G and D-major. These keys may be easily modulated into others, but if the same composer continued to improvise in F# or C# he might soon trip himself up and break off, partly because of difficulty in handling the instrument but also because of his lack of training in the harmonies of this key. The choice of key signature has in this example subjective reasons which do not correspond to the character of the key signature. It may be possible that this occurs only with second-rate composers, but no music master was born with his skill fully articulated, and probably experienced these difficulties in his youthful attempts before selecting familiar musical keys for his compositions. Even if over the years he trains himself to overcome these problems, he may retain his established preferences for certain musical keys.

2. Perhaps a composer wants to write a difficult masterpiece and wants to increase its complexity through the choice of musical key. Fortunately, this reason, which might be given by an ambitious student, is laughably impractical. This reason is of no great importance, and I mention it only because Hennig cited it prominently several times. I did not find this reason discussed anywhere else.

3. The composer selects the key signature because it seems the most agreeable to the disposition of the piece. This is why one frequently hears the cheerful C-major or G-major, or minor keys for gloomier pieces. I want to say immediately that I will not launch into a psychological investigation of the major and minor qualities of key signatures, because they have nothing at all to do with our subject. I do not understand why Hennig would claim that some major keys have a stronger minor character than other major keys. For me, all major keys have the same character of major-ness which does not fluctuate in the slightest. For our purposes, the major and minor keys are to be considered entirely separate and are to be compared only to each other.

So now we may ask the question: for what psychological reasons might a composer select certain key signatures?

A. The reasons may be purely convention. The composer may want to express something powerful, and selects D-minor because he knows that many powerful musical works have been written in D-minor. That would indicate an intellectual connection between D-minor and the "powerful" quality. This kind of influence is even stronger with themed music. A composer who wants to musically describe the feelings of a clear moon might choose F#-minor because other moonlight compositions also use this key: Mendelsohn's Komposition, von Lenau's Schilflied, Schumann's Mondnacht. The last of these is written in E-major, but features many sections of F#-minor. Anotehr composer may select C#-minor for moonlight because of Beethoven's C#-minor sonata, the so-called Moonlight Sonata (a name which Beethoven never used) which creates the association between C#-minor and moonlight. The musical work that provides the choice of key signature is given by a composer, not by the consciousness. The association is already so established that any decision making is dispensed with. The reasoning behind choosing a key signature is usually forgotten, which accounts for the many fantastic explanations offered for key-signature choices. However, many composers can, with some introspection, name from which pieces they formulated current conceptions of key characteristics, which itself is proof of what powerful influence may be ascribed to convention. Even Hennig, who only briefly describes the influence of convention, gives in the second part of his treatise examples of test subjects whose judgments were arrived at through convention (Dr. Michaelis, Prof. v. Kries, Prof. Cart).

It is possible that the convention may have not only ontogenetic but also phylogenetic sequences, so that an evoked association causes anatomical vibrations which can be inherited; this is the explanation of Billroth [19] for the entire development of harmony.

Someone could object to this explanation of convention by saying that the entire question is merely shifted, not solved. What could have originally influenced a composer to write a moon song in F#-minor? If Schumann's is effective, and is evidence of the convention, why did he choose F#-minor? What caused a composer to use F#-minor for a moon song in the first place? A potential answer is that if convention is not the exclusive reason for choosing key signature, it may be that there had been technical reasons due to imperfections in earlier instruments which demanded a specific key signature. The original cause of the convention is difficult to determine, but convention may nonetheless be mentioned as an external reason for key choice. It applies the established pattern of a designated key signature.

B. It is not to be denied that a difference exists between F#-major and G-flat-major; even on the piano, where both pitches are identical, they seem to have a different character. The difference in character could be due only to the symbols or names assigned to the pitch; the effect of the signs would derive from the symbolism of the sounds. We may call a tone "sharp" and describe it with a symbol of sharp crosses (we also call high tones "sharp"). Conversely, flats have the opposite character of being soft and mild and, since one associates lower tones more easily with darkness, darker than the kinds of tones named with sharps. Galley writes in his musical encyclopedia:

The magnitude of this association's influence (sad-flat and cheery-sharp) cannot be easily determined, but it certainly does exist, just as the name of a key may have an effect on the character of its key-signature or even on the characterization of the pitch itself. The words "F-sharp", "C-sharp", "D-sharp" have a pointed sound, which automatically transfers to the tonal characteristics of their related pitches. This may be why F#-major and minor are often described as sharp and pointed sounding. I am even affected by the names myself. When I began my investigations in the highest sound regions, in which I could no longer identify the pitch sounds, all the sounds sounded to me like F#, C#, or G#. As each tone rang out, they made me think of the word "sharp"; I wondered if perhaps this was because the tones were actually the sharps of the scale, but I soon discovered that it was a deception resulting from the "pointed" quality of the tone and the name "sharp".

The character of a key signature may be judged by the character of the tones being played. The white keys may communicate "brightness" and the black keys may seem "dark", so that a key signature in which many white keys occur (C-, G-, or F-major) may seem bright, while those with many accidentals (a-flat minor, d-flat minor, etc) will seem dark.

As we can see, the characterization of key signatures resulting either from convention or association are, nonetheless, individually subjective. They are not a natural consequence of the "sound character". Also, such judgments are usually only revealed when a listener is explicitly requested to produce one, and an observer's judgments usually fail if they cannot see the piano and know the name of the key signature or the chords they are hearing. Yet there are still more influences to consider, separate from subjective tonal characteristics, which can affect judgment.

C. The reasons may be physical, generated by the mechanics of the instrument being played.

1) We know that the piano's white keys give a purer, lighter sound than the black keys. As Helmholtz [20] indicated, this is partly because the white keys produce a stronger lever effect; but also, because the white keys are played significantly more often, the hammers become disproportionately worn and do not dampen as effectively. Accordingly, the key signatures which use more white keys-- especially those signatures which feature a white key as their tonic-- sound more brightly than other key signatures.

2) The empty strings of the bowed instruments, G, D, A, and E, produce more overtones and sound more brightly than other tones. Therefore they provide a brighter character to the key signatures in which they are frequently used, especially when they are the tonic.

3) The natural sounds of wind instruments are also brighter than those produced by valves and plugs.

From this perspective, C-major would sound brightest on the piano; G-, D-, A-, and E-major on the stringed instruments, and E-flat major on the wind instruments (especially the brasses). This would indicate that a brass orchestra playing E-flat major would seem unusually brighter and sharper than the E-major of an orchestra composed of strings or piano sounds. The physical differences of instrumentation therefore have a great influence on judgment of sound character; it can be so strongly impressed on a listener's memory that it is the principal determinant in the judgment of key signature, even if it is not explicitly recognized.

It is possible that any of these may be a listener's primary criterion. One person may judge key character solely from the instrumentation, another entirely from convention, and a third may form their conclusions from the mental associations previously discussed.

D. Most likely, however, a listener will not use one exclusive strategy, but will employ any and all of them at different times while listening to a composition. This cannot be properly investigated, because each individual case is different and depends entirely on the immediate disposition of the observer. Sometimes the components of a judgment will reinforce each other; other times they will conflict. Thus, for example, a C-major chord can create a light, fresh, joyful impression

Of course, one may wonder how "mild" and "pointed" may be combined. Hennig, for one, refers to F-sharp minor as "remarkably pointed" or "unpleasantly shrill" and compares it to a pallidly flickering light.

I believe, therefore, that one must refrain from making key-character judgments based on a feeling-memory. Judgments should be made from direct perception of the individual sounds, a practice which will at least avoid the criterion of conventional association. To obtain the sense of a key signature's character, one may select not a single musical piece, or even different musical pieces in the same key, but only chords-- because the character of a musical piece affects the key characteristic far more than the other way around. If one proceeds in this manner, one will perhaps discover that, sometimes, an observer who pays strict attention to the physically separate tones will create such a solid image of the key character that he may be able to recognize its individual pitches. If an observer hears a great deal of piano music, he will soon learn to distinguish between the white and black key sounds; and if he hears several chords which contain only white keys, he will become able to recognize C-major. Another person may learn G-major, D-major, A-major, and E-major from their stringed instrument, and a third may learn E-flat major from a brass instrument.

However, we cannot say that this ability represents absolute recognition of a key signature. Absolute recognition should be an effect of the pitch quality, not the physical tone qualities of an individual instrument. If there is such a skill as absolute key-signature recognition, it could only be established by eliminating physical differences as completely as possible. This has not yet been done anywhere. Hennig, who in his book discusses almost all possible physical and subjective reasons for recognizing key signature, unfortunately does not draw the logical and practical conclusion from his remarks. He maintains that a listener who possesses no trace of absolute tone consciousness may nonetheless, under certain conditions, recognize a key signature purely by its character, unaffected by subjective influences or factors of the physical instrumentation. He offers many examples of when he recognized the key signature of piano pieces, or orchestral pieces, and few specific examples which demonstrate recognition of chords.

I believe I have found a method which one may use to eliminate the influence of the disturbing factors. If a chord is recorded to phonograph, the exact same chord can be played at different pitch heights by varying the speed of the phonograph. When the speed is changed, so too is the pitch. By the charity of the Louise Bose Foundation for Acoustic Investigations, an Edison's phonograph of the best quality was put at my disposal. The machine's rotation is driven by an electro-motor and can be turned quickly or slowly, as desired, by a brake-arrangement. If, for example, I have A1 = 440Hz on my phonograph recording, but use only half the rotation speed, then the record will not produce A1 because it is now playing only 220 oscillations per second-- which is A0, the deeper octave. Now, with my phonograph, I have the ability to lower or raise the pitch sound at will, within a range of one and a half octaves. So if the recorded tone is an A, which on a violin has a particularly bright character that can be recognized as the quality of an A, that same quality would not be diminished by playing it at a different speed. For the timbre is created, to a large degree, by the overtone sounds, whose frequencies are geometrically related to the fundamental pitch; consequently they will remain in the same ratio whether the fundamental tone is raised or lowered by any value. Therefore, we would hear the light character of A1 from the phonograph whether the pitch itself was heard as G, A, F, or any other pitch. In this manner we remove the difficulty of assessing physical sound differences in favor of producing a pure judgment of pitch.

This system cannot be expanded to all instruments, by the way, because in some instances the timbre is created by sounds other than the overtone series. We know, for example, that the human larynx may produce musical pitches and overtones related to each pitch, but there are also absolute vowel-frequencies present which are unrelated to the musical pitch. These vowel sounds are also changed by the phonograph speed so that if, for instance, an "A" vowel was produced at an F pitch, the transposed vocal sound would no longer be recognizable as an "A".

Dr. Hennig graciously allowed me to test his memory for key signature, first indicating that he is significantly out of practice. At his request, I began with the sounds of his own piano. Because he recognizes only minor keys, I played minor triads, sometimes adjusting to the kinds of sevenths and triads included in a specific key signature. Later we experimented at a harmonium, and then at an unfamiliar piano; in every case, however, we did not yet involve phonographic recordings.

It appears that only the F#-minor of Dr. Hennig's own piano is definitely recognized; the judgments rendered in other keys and timbres do not statistically demonstrate a recognition better than chance. It is possible that a larger set of data, and more practice by the subject, would produce different results; but provisionally, I would prefer to conclude that Dr. Hennig possesses good timbre consciousness (within which the F#-minor is particularly recognizable) rather than an ability to judge key signatures. This would explain why he was occasionally able to recognize F#-minor on my piano, whose sounds are somewhat muted.

In any case, if the ability of absolute key judgment exists without absolute pitch judgment, it is extremely unsteady. It seems most likely that the ability can be explained either in the observer possessing a partial ability of absolute tone consciousness-- i.e. he may receive an impression of key characteristic through repetition of familiar tones-- or through the aid of indirect criteria, such as unconscious color perception (association) or feeling-perception (association), so that the F-sharp minor sound first creates the association "moonlit night" followed by the label "F-sharp minor".

It is nevertheless possible that a certain feeling-impression is evoked by a key signature which, being characteristic of that key, may lead to recognition and accurate identification. Wherever the character of a key signature originates, be it the mechanics of an instrument or conventional reasons, it cannot be denied that any musician will have a different feeling-impression of C-major than of A-flat major. These feelings cannot all be verbalized, nor can those which can be verbalized all be expressed as simply as "comfortable" and "unpleasant", but they are substantially different. These feelings can be, theoretically, the probable indirect method by which judgments of key signature can be made. Individuals who have a sense for these key-qualities may not have absolute tone consciousness, but may find it easy to obtain if the characteristic sound of the tonic is transmitted along with the name of the key. In this way, absolute tone consciousness would develop from absolute recognition of key. It is possible that absolute tone consciousness develops in this manner, where pitch recognition arises from the characteristic feeling of a tonic note; but unless musicians can be found and tested while in this developmental stage, where they can correctly judge key signatures but not individual pitches, there will be no factual proof of this hypothesis. Even so, it does not seem likely that absolute tone consciousness develops from the ability to recognize key signature.

XI. Association method II: Letter name evokes tone image-- Absolute sound association ability.

I have previously only discussed one type of absolute pitch recognition: where a tone is correctly designated, i.e., the tone image evokes a verbal label. It was mentioned in the introduction, however, that the psychological reverse may occur, so that a verbal label evokes the tone image. This type of absolute tone consciousness can be observed separately from the reverse ability, because the two processes do not necessarily occur together. There are a category of persons who can name a tone that has been played, and for brevity we will call this "Ability A", but this person cannot produce the musical sound when prompted by the name of the tone ("Ability B"). Others can do both A and B, and finally there are a number of musicians who have Ability B without possessing Ability A. I'd like to speak now of this last category.

At first, it seems unthinkable that a person would have absolute tone consciousness without being able to correctly recognize pitch sounds. This apparent paradox is eliminated, however, by acknowledging that sounds can be imagined via indirect criteria. In my questionnaire, I found this to be true without exception, although of course I cannot say whether auxiliary constructions are theoretically necessary. In correctly judging tones, the method of Association I goes from tone-image to word-image whereby the spoken name is produced; if we imagine and reproduce a desired sound, Association II is reversed, becoming word-image to tone-image. The first way is possible without the second, and numerous examples exist of this; on the other hand, there are no examples to be found in which the second ability exists without the first. Although there may be exceptions to this apparent rule, it is possible that Association II is the more difficult, and can be learned through practice once Association I is present.

The indirect criteria used to help imagine the pitch sounds are the same as those employed in pitch judgment, only here they are used with conscious awareness. A violinist often imagines a pitch by picturing their hand and finger position on the instrument. In my experience, I found two musicians who, to recall "concert A", would imagine holding their violins and pressing the D-string with their second finger in the third position; this made it easy for them to recall an A. This criterion can be realized as both visual and kinesthetic association.

Other musicians tend to use specific visual images. One person may imagine the printed note corresponding to the pitch; another may picture the associated piano key. A third may imagine himself sitting at the piano and playing a certain key. Singers use entirely different associative complexes but are usually centered around concert A. Some will imagine the desired sound as the beginning of a well-known melody, and if they sing the entire song and it feels right they can often produce the correct pitch. Others may create entire pictorial scenes; one musician indicated that he would create the A-tone in the following manner: he thinks of the final scene of "Don Juan", where the melody proceeds A0, D1, D0, Db0, F0, D0, A0, A0. By imagining this melody along with all its associated scenery, he creates the conditions to know with almost absolute security that he has produced an A-- but without these indirect criteria, recognition is impossible.

Of the hundred respondents to my questionnaire, three must have a key signature, seven a printed note, and two a scenic picture in order to produce a pitch sound.

It was once commonly held that it would be impossible to mentally recognize or produce a sound without first singing it, or making the necessary muscular movements in the larynx, or at least to imagine singing the sound thus exciting the nerves necessary to produce the muscle movements. We could theoretically imagine, therefore, that a sound is recognized purely from the feeling of muscular contraction, provided the observer knows from earlier attempts that this muscular awareness corresponds to a certain sound. Following this, it is possible that a person may, through "absolute larynx", be able to sing desired pitches without a trace of absolute tone consciousness. The criterion of muscle sense can support and supplement a deficient absolute tone consciousness.

Lotze [21] notes: "No memory of sounds and arpeggios can be created without being accompanied by the subtle feeling of speaking or singing. Thus each pitch is not associated with a weak memory, but with a strong excitation of muscular feeling, which we would experience when producing the pitch."

G.E. Müller [22] agrees with Lotze: "Just try to imagine a particular sound, or a number of sounds, without simultaneously imagining yourself producing corresponding movements with your vocal tract. In our observations, you will never succeed, or only sometimes directly after the sensual perception of the relevant sound, in which case you are responding only to your immediate memory."

Stumpf speaks against this view in the introduction to his Tonpsychologie [23]. From his and other experiences, mental singing is not necessary for imagining a tone. He also makes these arguments against the above-mentioned views:

Stumpf's first argument proves that judgments of discrimination have nothing to do with muscle perception. A follower of muscle-perception theory could say, against the third argument, that a person does not imagine a tonal mass but the feeling produced by a chord; but I believe that these are essentially the same, depending on whether one pays attention to the absolute pitches or the interval effects (fusion, harmony).

1. First of all, I am able to imagine sounds that lie far outside my vocal area, and even outside my entire range of musical production; I am just as able to imagine a C5 as a contra-C, although I can sing only as low as F and play pipes as high as G4. Moreover, for the high sounds I would have to have muscle perceptions in my lips which I could observe as clearly as my laryngeal muscles.

2. I can sing a sound and simultaneously imagine another sound. This is, in my opinion, striking proof that no muscle perception is necessary for imagining a sound. And yet Stricker [24] rejected a similar objection by Paulhan. Paulhan describes how he could loudly sustain the letter A while thinking to himself "E, I, O, U," and even an entire verse. Stricker is not convinced: "If one speaks the A loudly, one must begin by bringing the mouth into the A position; however, once the position is set, the A is extended only by means of the outgoing air flow. The internal muscular articulation may now effectively produce the O and E. This type of experiment does not satisfy me," Stricker closes, "for I must emphasize once again, my requirement is to imagine the A and O simultaneously while speaking. If someone should be able to do this, that can be used as an argument against me." But I do not believe that Stricker would accept this argument; either he would not believe the subjective observation or he would assume that the subject is alternating between A and O. Even so, this could validate the previous objection that we do not imagine a tonal mass, but rather only a feeling-impression of it.

Here I would like to relate an observation which sheds light on the subject, as it shows how imagined tones are separate from muscular perception, via a musical difficulty that I cannot seem to overcome.

I sang a G with a strong voice, and sustained it as long as possible, during which I imagined familiar melodies. When the sounds of the song formed large intervals with the tone I was singing, I experienced no trouble; if, however, the sounds of the imagined melody ranged within a tone or semitone of the sung tone it became considerably more difficult. If I attempted to imagine, for example, an A-flat, my sung tone was pulled up not by a semitone but a distance closer to a fourth. If I attempted to remedy this by singing the G more strongly, the reverse occurred, as the imagined tone was pulled downward. While they lay close together, there was constant interference between the sung and imagined tones. My explanation for this is that I have a physical association with the imagined tone, and likewise the physical tone evokes a mental image. As the images converge, they disturb each other, but when they are very different then no interference takes place. I also noticed that, while I can imagine sounds of any timbre (such as violin, clarinet, or wind instrument), when the sound I imagined was a semitone away from the sung tone it would always have the timbre of my voice. I tried the same experiment with several very talented vocal musicians, and I was able to determine each time their imagined song approached the sung tone by the variations of the sung tone. From this, it would seem that imagined sounds are more important for absolute pitch recognition than are muscle perceptions; whether the imagined sounds are necessary, and whether we can separate our ability from these imagined sounds, is yet to be determined. However, our imagined song is far from a physical excitation, as was described by different researchers; it concerns rather a simple memory image of a sung tone without muscular involvement.

The "absolute larynx" ability of which I have spoken is not actually proven to exist. Probably, one can imagine that a well-practiced singer has the ability to adjust the muscles of their larynx so exactly that a certain intended sound emerges, and yet does not have the mental skill of absolute tone consciousness. In reality, however, I have learned of not a single singer who is capable of this, neither in my questionnaire nor in any published experiment. I used to believe that I had the ability, because I seemed able to sing any tone (such as C) immediately on command; but with sufficient observation, I noticed that the aural image of the C always appeared first and the larynx was adjusted to match this image. I find thus that the muscle feeling is always controlled by the sense of hearing (in contrast to the above view which stated the ear sense could be controlled by the muscle sense). I now wanted to discover whether one could avoid imagining the tone sound, and whether one cannot indicate the appropriate pitch solely from a certain contraction of the laryngeal muscles. Muscle contractions produced in the normal way proved useless because, as soon as a letter sound was evident, it activated the corresponding mental image of that letter and its corresponding muscular contraction. I thought I might succeed by attempting to isolate my larynx muscle [musculus cricothyreoideus], the tension adjuster of the vocal cords, and determine the sound by feeling its tension before releasing the sound with a simple exhalation. Unfortunately, several laryngeal physicians with whom I discussed this issue assured me that the muscle could not be isolated; it only activates through the agency of the nervus laryngeus superior.

We see therefore, on the one hand, that the indirect criterion of singing is unnecessary to imagining or producing a particular pitch; and on the other hand, it seems that an absolute larynx ability does not exist without absolute tone consciousness.

This is not to say, however, that singing is not used as an aid to pitch recall. Quite the opposite; we frequently see that a musician will, when attempting to identify a pitch, first sing a test sound before delivering judgment. Usually this is done with tones of unusual timbre, such as bells and glass sounds. The purpose of this is the same as that which was described in the section on key characteristic: one may recognize pitch information first by recognizing a sound mass which one has (through practice and habit) associated with the name-label of the pitch. We mentioned piano sound units, and so on; if a musician has a great talent for identifying sung tones, and can sing particular tones, he can easily relate other sounds to those of his own voice; he can then make easy comparisons by singing a sound after hearing it.

In a similar way, this can help with very low or very high tones which one is not able to directly determine, because one may sing octaves of each tone which are easily recognized, since the interval-sense is better than the absolute-sense at high and low extremes. A person may thereby employ relative and absolute abilities to facilitate judgment.

Finally, the sung repetition of a sound is used in yet another manner for the pitch judgment. Many musicians are aware of the highest and lowest pitches that they are able to sing; they may compare the unknown pitch to their lowest or highest tone and determine its identity from interval estimation. This, however, has nothing to do with absolute tone consciousness; it is only a logical conclusion arrived at through interval judgment and knowledge of vocal limitations. Moreover, it is a highly unstable and usually defective manner of judgment, for the lowest or highest singing tone we can produce is highly variable; it is affected by mornings, evenings, weather, and diet. Damp air lowers vocal pitch as surely as smoking and drinking beer. Anyhow, I do not believe that pitch can be deduced from the muscle feeling of the larynx alone, but an uncertain judgment can be strengthened with the help of this feeling.

It seems therefore that the indirect criteria are more useful for producing tones than for identifying them, and because they are consciously and willfully applied, they are subject to influences which do not affect automatic perception and reflex judgment. If these criteria are used in addition to reflexive judgment, then a finer differentiation of pitch may be achieved, and the absolute pitch may be clarified in memory, so that through practice of this indirect approach a direct approach may be developed.

XII. Both association methods are jointly available.

Having now discussed the second type, and having seen that indirect criteria are an indispensable condition for this type (at least according to my experiences), it yet remains to discuss the third group.

Of all those who claim to have absolute tone consciousness, my statistics show that 35% have the ability to correctly name and to correctly imagine and produce a desired pitch. In the use of these abilities, absolute tone consciousness is strongly pronounced-- fast functioning, and useful for fine tonal discrimination.

This latter use is easily explained: a musician who can only name sounds (Ability A) may have formed categorical pitch boundaries of one quarter-tone. He may judge the A-tone to be "A" because the tone image evokes the name, and likewise recognizes a B-flat to be "B-flat". A sound that differs only slightly from standard A will also be recognized as an A; however, if the tone is somewhere in the middle of A and B-flat, or when A and B-flat are played together, both names "A" and "B-flat" will be evoked, and the musician will conclude that the tone lies between A and B-flat. A quarter-tone interval is still rather large, and Ability A may not lead to finer discriminations.

This is very different from a musician who can also imagine a sound separately from hearing it. Such a musician can compare the unknown sound to the imagined sound of the same pitch designation, and can so note finer differences. These cases are, as mentioned, rarely found; however, in the past, such hearing was attributed to prodigies and held in great critical acclaim. An especially famous anecdote is the composer Schachtner's description of the 7-year-old Mozart. The same kind of ability has since been reported elsewhere; nevertheless, I find it worth repeating as it appears in Jahn's biography of Mozart:

Schatchtner says: "You must remember that I have a very good violin, which Wolfgang always called the 'butter violin' because of its soft and full sound. One he played on my violin and couldn't praise it enough; after one or two days I came to visit him again, and when he played his own violin he immediately asked, 'What makes yours a butter violin?' Then he played his violin again, thought about it, and said to me: 'Mr. Schachtner, your violin is tuned a half-quarter tone lower than mine, that is, it was when I played it last.' I laughed at this, but his father, who knew the extraordinary tone feeling and memory of this child, asked me to get my violin and see whether this was true. I did, and he was correct."

This little scene is very interesting, although unfortunately it cannot be used for evaluating Mozart's hearing ability. First, the comparison instrument is a violin, which easily goes out of tune and might account for the results. Temperature, moisture, and tension cause new strings to relax considerably in a day or two. Secondly, Mozart's "a half quarter tone" seems very precise, but experience has shown that the perception of 1/8 tone is very unsteady and defective, as is the estimation of intervals smaller than a quarter tone. Even if the violin had held its tuning exactly, and the difference between each violin had amounted to precisely 1/8 tone, Mozart's achievement is not as astonishing as it seems. The following tables of Prof. Raif's and my absolute pitch abilities will show that this refinement of absolute pitch recognition is not exceptional. To be sure, Mozart was at the time only 7 years old, but we frequently find a precise absolute tone consciousness already present in young children (age 5-7); in the 100 cases I surveyed, 24 indicated that they already possessed absolute tone consciousness before their 8th birthday.

However, one of the consequences of Mozart's ability being so emphasized and praised is that Hennig, in his repeatedly-cited book The Characteristics of Key Signatures, comments that such refinement of absolute tone consciousness would be totally unthinkable if one did not suppose that Mozart used his sense of hearing and sight in conjunction, i.e. with each pitch (1/8 tone and smaller) he had some feeling of color. But since there is no evidence in any of the literature that Mozart associated colors with pitches, and an equivalent refinement of visual color perception occurs with equal rarity, I see nothing to support this view.

Both Prof. Raif and I experimented with the refinement of our absolute tone consciousness, but used no trace of any visual associations to assist ourselves. Most musicians who answered my questionnaire also possess no "color hearing"; the few who do imagine colors when they see sounds do not make their pitch judgments based on those colors. The pitch judgment is immediately there in addition to the imagined color, not subordinated to it.

XIII. Refinement and accuracy of the sound image.

I measured the accuracy of our absolute pitch judgments in two ways. By means of a "tone meter" we are able to produce a continuous series of tones which differ only by a few oscillations. Our two methods were that of selection and of correct/incorrect assessments.

In the selection method, I was first kindly supported by Dr. M. Meyer. He produced a pitch in the proximity of the standard concert A; I said whether or not this was a correct A. If I rejected it, then he went higher or lower along the series until I announced that the particular A correctly matched my memory of the A-pitch. It was evident that, to make more exact pitch judgments, I deliberately compared the tone to a sound which was present in my memory. These trials cannot be explained a la Kries [27], trying to judge from oscillation to oscillation which is the correct A is impossible without comparison to a specific memorized tone. Not only do I know that I consciously make this comparison, but since my memory was often too weak versus the loud sounds of the tone meter, I would often sing my memorized A and could thus easily compare it. The results achieved by means of the selection method are shown in the following table:

Table I.

I would like to undertake the discussion of this table after presenting the tables of the second method, that of correct and incorrect cases: an A is played between the range of 435-460Hz, and the observer notes the judgment "correct", "too high", or "too low". With Meyer, I attempted 24 trials for each of the indicated frequencies. The results are in the following tables.

Table IIa.

Because the trial series was so short, in 1899 I attempted new trials in which Prof. Raif and I served as subjects.

Table IIb.

[The numbers on the left are the figures noted on our "tone meter". Because the metal prongs of the apparatus are not entirely steady and exact, in the autumn of 1900, Dr. K. L. Schaefer and Cand. Pfungst determined its exact absolute pitches; this happened with the use of a normal tuning fork and also measuring the distance between neighboring prongs. It was determined that the true range of this device was 403-807Hz, rather than 400-800. Whether my trials from three years ago match this last session is doubtful, but that effort depended less on an entirely precise absolute pitch value than on the range of A-sounds. Whichever the case, in discussion of these tables, I will include the old numbers next to the new using parentheses.]

Looking at the results of the selection method (Table 1), it appears that my memory of the A varies between 434 (437) and 460 (463) and, apart from the device which provided these limits, between the means 442.8 (445) and 451.3 (454). According to the correct/incorrect method (table IIa), the A varies between 442 (445) and 454 (457), and according to table IIb between 436 (439.5) and 452 (455). The results agree very well with each other. The high tendency of my absolute tone consciousness is remarkable; my recalled A varies between 434 (437) and, after excluding the exceptional cases, between 443 (446) and 451 (454) in method A and between 440 (443) and 448 (451) in method B. While I was consistent within this range, Professor Raif's recalled A lay between 420 (423) and 450 (453) and, after excluding exceptions, 432 (435) and 444 (447). I designated 442-446 in all trials as good.

What explains the difference between the A-pitch in each observer? The answer may be found in the fact that the instrument one plays most will impress its disposition most strongly on the memory. I tested the frequency of my piano and found its A to be 438 Hz; this did not surprise me, because I have long been aware that my internal A is higher than that of my piano. I looked a different cause to explain the high nature of my absolute pitch memory and I believe I have found it: the piano on which I studied from ages 5 to 13 was tuned unusually low, more than a quarter tone flatter than normal tuning; because of this, I frequently had to tune my violin higher to the accompaniment of a another piano. Therefore, I became accustomed to tuning my violin after my piano lesson and, although it was tuned to my memory of other pianos, I tended to adjust it even higher. It is now a well known phenomenon that one exaggerates small distances in music, so I and my violin gradually pushed the A higher than it should have been. So the too-high disposition of my absolute tone consciousness is probably explained by the too-low disposition of my piano. With Prof. Raif, the cause of his recall was easily investigated; his piano was tuned to A = 435 and this agreed with his memory for A (437-443). Professor Raif additionally reported that he returned from each summer vacation with his absolute tone consciousness lower than normal because in his summer location, he regularly played a piano which was about a semitone lower than normal tuning.

That these pitch memories are not entirely steady, but are instead subject to many variations, is clearly shown in our tables. In table I, the date of the trial is noted in each case, and a quick look shows that the data was different depending on my mood each day; also, the tables reflect the influence of practice. During the summer of 1898, my recalled A was between 442 (445) and 454 (457), and ranged between 446 (449) and 452 (455), but after I was able to practice with the normal pitch (a = 440), my indications dropped to 438 (441) - 452 (455), and the narrower range of 442 (445) to 446 (449.5).

Concerning the accuracy of the judgment, i.e. the range of the recalled A, this amounted to 8 oscillations between 440 (443) and 448 (451); at the same time, between the end values 440 (443) and 448 (451), the judgment "good" was made in only 50% of the trials; within this, 10% of the cases between 442 (445) and 446 (449) were so judged. I am therefore able to compare sounds which differ by 4 Hz. If one accepts A = 440, then the next higher pitch is B = 495 Hz. The difference of 55 Hz implies my discrimination ability to be 4/55 = 1/11.25 of a whole step. I only calculate this to show that the previously cited anecdote from Mozart's life is not so exceptional as a representation of absolute tone consciousness, but can be achieved through practice if absolute tone consciousness is available. Prof. Raif, who has less practice in acoustic trials than I, was not as able on the first trial day to specify such slight differences in frequency; but after some days' trial provided practice in judging, he narrowed the boundaries of his A-category from 26 Hz to 8.

It would now be very interesting to compare the refinement of absolute tone consciousness with the ability to discriminate pitch sounds; it could be described analogously as a yardstick in which the exactness of memory deviates from the exactness of perception. I have not yet conducted experiments to test my discrimination skills, but I do know from earlier attempts that I recognized two tones in the A1 range which differed from the standard in less than 0.5 Hz, yet I correctly identified the higher as too high and the lower as too low. If this were the range of my discrimination ability, then the memory image which spans 4 Hz is 4/0.5 or 8 times more indistinct than the perceived image, where one tone follows on the heels of the other. In any case, it would be profitable to pursue this point still further as regards pitch memory in general (not just absolute pitch memory).

After the A, I also examined the E and B-flat of my tonal memory, with a very similar result; a highly consistent judgment was obtained for all trials.

Particularly interesting is the different results for C-sharp and D-flat on the one hand, and of G-sharp and A-flat on the other. As you know, these sounds are identical on the piano; although theoretically F-sharp is lower than G-sharp and C-sharp is lower than D-flat, in my memory this is reversed. My mental image of C-sharp ranges between 574 (579.5) and 580 (586), and D-flat is between 548 (553) and 566 (571); the G-sharp between 426 (429) and 427 (430) [the boundary does expand to 422-434] and the A-flat between 417 (420) and 426 (429) [with a boundary of 414 (417) to 432 (435)]. This remarkable difference may be explained by their musical uses; I often think of C-sharp as the major seventh of D-minor which resolves upward to D, while with D-flat I feel no such bias. Maybe the "sharp" designation also causes me to think of the tone as higher.

Despite practice, absolute pitch recognition still seems to depend on physical and mental disposition. So, on different trial days, I could notice completely different tendencies in my judgment. Perhaps relevant to this is an observation which Professor Gernsheim wrote in one of his questionnaire responses. It often happened to Prof. Gernsheim, after mental overexertion or psychological depression, that he would perceive a familiar orchestral piece as exactly a semitone lower. Since this observation is purely subjective, where an A-pitched tuning fork is also heard to be too low, it is difficult to know whether this is an error in perception or an error in judgment. It is perhaps possible that fatigued perceptual nerves provide defective reactions, although this does not support Helmholtz' resonator theory. It seems more likely to be a judgment error, but this is also problematic; because the A-pitch is absolutely associated with the letter A, and the A-flat sound is associated with the term A-flat, there would have to be a completely different association to connect the A-pitch with the term A-flat; the psychological depression would thus have caused one's hearing sense to be depressed by a semitone. Also, absolute tone consciousness may be affected by conscious will; with some effort, one can adjust absolute perception as much as a semitone higher or lower and can maintain that perception for a short time (1-3 hours). I will give examples of this later.

We have seen that there is also a direct connection between word image and tone image, just as we initially found it in the opposite direction during the pitch judgment. Because this ability is not found without the presence of the first type of absolute-pitch ability, it requires indirect criteria; mainly for this reason, we assumed that producing a pitch based on its name is a more difficult association than that of a tone image to its name. This is supported by another fact: in the passage which described the judgment time for pitch recognition, we saw that only a minimal time is necessary for the tone image to evoke its name; if we calculated the time for the reversed process, we would find it to be disproportionately long. I did not conduct exact trials because no sufficient apparatuses exist for it. We would have to try again to use the electric clock and the lips-key, whose errors I have already discussed above, and which would for this purpose be equally useless. A contact piano or analogous instrument would also not be useful for this purpose. But one can clearly observe without exact trials that the time is greater for the production of a named sound, perhaps by a factor of hundreds, than for the naming of a tone. The explanation may be found in the following: A pitch is a specific sound which we learn to associate with a certain letter name. The F-tone is associated with the letter F and with nothing else. Reversed, the letter F corresponds to a certain F-pitch, but this is only one among the letter's many associations; the letter F begins many words, including the musical terms forte, fine, etc. In short, the letter F sparks a host of associations, only one of which is the musical tone F. So it may be that the extra time is required to select the correct association between the letter F and the F-tone.

XIV. About the learning of absolute tone consciousness.

The theoretically and practically most important question which one can ask concerning absolute tone consciousness is: where does it come from, that individual humans with the ability are talented, but most are not? From this question arises two sub-questions:

Most musicians whom one asks about the origin of their absolute tone consciousness would maintain that the skill is innate; this must be incorrect, for no child in the world could be born with the ability to name any sound as "A" (a child born in Italy must then be born with the ability to name the same sound "la"). In order to label a tone with its common designation, one must necessarily learn the sound and name in connection with each other. Whether this is sufficient, and how often such listening is necessary, is quite another question and surely depends on individual abilities; but we know that generally the ability must be learned.

If one shows a child a bell, for example, and calls it by the name "bell", after frequent repetitions the child will form an association between the object and its name. The object must be shown 10 times in connection with its name, then seen 50 times more, before a continuing association is made; some children will not learn the name despite multiple repetitions, especially if they are idiots, imbeciles, or sufferers of sensory aphasia following brain injuries.

To make this example analogous to absolute tone consciousness, the idiocy or aphasia in this sensory category would have to be quite widespread. Therefore we want to observe what differences exist that should make the label of a tangible object learned by most persons, but the label of a sound only by a few.

We return again to our bell. The child initially receives a visual perception of the bell; secondly, a sound is presented simultaneously with the visual image. Thirdly, the child may generate a touch sensation by palpating or tasting the bell; fourth, the child may receive a sensation of temperature. Even absent the two latter, less significant senses, there are nevertheless at least two senses employed; the perceptions create conceptions for which an association is created, in this case between the visual image of the bell and the word "bell". The difference in labeling absolute pitches is thus revealed: during the concept formation of a tangible article several senses are coordinated, but with an absolute pitch only one sense, its sound, may be noticed (with the exception of the lowest sounds, which may also be felt). If the child is shown a new bell which deviates from the first in its shape, the crucial factor for the child will be whether the thing produces a bell sound; i.e. the hearing sense helps the visual sense in forming the general concept. With absolute pitch, this assistance is completely missing.

There are, however, qualities of sound which are easily impressed into memory. For example, timbre is remembered by most persons not only in relation to other timbres, but as itself. If a person hears different instruments-- piano, violin, cello, etc.-- they will easily retain the timbre in their memory. Because I can produce the same timbre using many pitches, it is easy to abstract all the other sound qualities as separate from height and intensity; above all, however, because we have far greater practice in detecting timbre we are more able to remember a timbre. We hear one evening of piano music and therefore have an entire hour to experience the piano sound; a pitch, on the other hand, appears for only a moment within the music and people don't usually practice hearing only single tones. Another factor which may be relevant is that we use descriptions of timbre which arise from a different sensory category; we call a piano sound "sudden", the cello "twanging". Of course we don't need this label to remember the timbre, but it's possible that the subconscious compares the timbre to other sensory impressions which makes it easier to recognize and remember a timbre.

I believe this particular because I encountered similar conditions when comparing absolute tone consciousness to absolute color consciousness. Absolute color seems more common than absolute pitch; very fine color differences are recognized and shades of the same color are represented by different names. How fine the color differences must be in order to be analogous to the half-steps in music has not yet been investigated, although one might approach the problem by identifying the sensitivity of color discrimination and compares it to pitch sensitivity. I have observed in myself and others that, if a color is to be recalled, a person must recall an object of that color. I find it impossible, for example, to imagine the colors light green, brown, red, or light blue purely as colors; I must think of them as colored boards. For a yellowish green I must imagine a spring lawn; brownish-red is a Portiere in my room, and light blue is the Gynecology textbook which has a light blue cover.

In this way I recall color concepts extremely well. Therefore, I believe that this imaging of objects helps significantly in the development of an absolute color ability, and in that alone it is already going to be found more frequently than absolute tone consciousness. Additionally, as with timbre, the longer duration of sensory perception and greater amount of practice make recognizing colors a more obvious skill. The indirect criteria that can be requisitioned for absolute pitch judgments are, as has been described, usually unsteady and always aural in nature; therefore they cannot be compared to the multimodal criteria of color recognition. We can therefore see that absolute pitch judgments must be developed only in brief moments, and that the single task is that of fixing the pitch in memory; if absolute tone consciousness is already rarely found, its prevention can be further reinforced by moments which disrupt the development of absolute tone consciousness.

We can imagine how a child actually receives its musical training. In the first years of life, the mother is a great influence, and later the father and siblings. The mother sings the child to sleep with a lullaby; if this is successful it is repeated daily. If the mother does not have absolute tone consciousness and does not pay special attention to always using the same key signature, she will sing the song first in C-major, then in B-major, etc, depending entirely on how she may feel that day; the father and siblings, who all have different larynxes, may sing the same lullaby in accordance with the different lengths of their vocal cords and thus again in different keys. In this way a child may learn interval sense, but not absolute tone consciousness. When a child attends kindergarten, they learn songs with piano and violin accompaniment. If they have trouble remembering a song, it is expected that the mother will help at home, but she may produce it in a completely arbitrary key. Finally, the pianos and other instruments differ so substantially from each other that they may prevent the development of absolute tone consciousness in favor of interval perception. This was so indicated to me by Professor Dessoir; he said that he once had very good absolute tone consciousness, but through playing different violins the ability deteriorated. If such a reason can worsen an existing absolute tone consciousness, many more like it could prevent its development altogether!

Finally, there are song-instruction methods in which the student names each sound after its position in the scale. They either use numbers (1, 2, 3, 4) or the syllables do, re, mi, etc. If do means C in C-major, and E in E-major, it is obvious that the absolute personality of the sound is thereby cancelled.

Thus, in the normal musical training of a child, there are many factors which restrain the development of absolute tone consciousness, and nothing which operates to instill it.

Individual music teachers have certainly tried to teach their students to have absolute tone consciousness. Unfortunately, no one has generated statistical details about the results, as it is usually attempted in the manner of an apprenticeship. To my knowledge, only Naubert [28] has published a curriculum, unfortunately however without any description of the successes; nevertheless, Naubert's writings are very valuable. Naubert proposes to let a student play and repeat the A pitch as often as possible with a correctly-tuned piano. Then the student should, if possible, frequently try to reproduce the A-sound and compare that sound to the piano's A. So this sound would be impressed on the memory after practice. As soon as this is the case, Naubert selects another sound which is easily recognized independent of its relationship to A, such as C; once this learned tone is "steadfast and certain" he moves on to E-flat. Naubert works only in a single octave and maintains that, as soon as these three sounds have been learned, a student possesses absolute tone consciousness for an entire octave. Then Naubert teaches his student to practicing recognizing chords and key signatures, and to pay particular attention to the sound character of individual pitches. Even if Naubert's remarks here can be contested, they do have some merit, indicating as they do a method which, although unfortunately not scientifically conducted, occasionally leads to the desired goal.

In a more scientific form and with exact statistical materials, M. Meyer examined the training of absolute tone consciousness in his work "Is the memory of absolute pitch capable of development by training?" [29]. Meyer places the theoretically important question at the forefront of his work: are humans divided into two classes, where one has the memory for absolute pitch sounds, and the other lacks it, or do we all possess a graduated perception of pitch? If this were the case, we would have to suppose certain physiological characteristics, to which the ability of absolute pitch recognition is attached; but if the second is the case then one must call the ability to recognize that violin tones are "high" and bass tones are "low" a form of absolute pitch recognition. J. v. Kries, in his work "Über das absolute Gehör" [30], considers this high/low discernment as separate from absolute tone consciousness, and refers to it as absolute pitch regulation. He asserts that one may only speak of absolute tone consciousness when the error range does not exceed 2-3 semitones. Meyer, in partnership with Dr. Heyfelder, conducted trials which showed that, by systematic and continuous practice, a moderate pitch memory can be improved so that no mistakes larger than 3 semitones would occur, as Kries insists. Meyer's trials were undertaken with tuning fork and piano sounds which were not named after a musical pitch but rather their vibratory frequencies. At first, they used only a few tones at large intervals from each other; first 10 tones a sixth apart, then 20 tones at a major third, and finally 39 which were separated only by a whole tone. In their final trials, the observers indicated judgments which were 60% correct and mistakes that were rarely greater than a whole tone. From these attempts, Meyer concludes that the memory for absolute pitch can be improved, and that the difference between individuals is not qualitative but quantitative.

However, the ability which v. Kries names "absolute hearing", and which corresponds to our absolute tone consciousness, is a special type of sound memory. We have seen that the essential matter is the association between a tone and its name (in my opinion, the error limit is at most a semitone in either direction). This association is what makes absolute sound memory a lasting ability; if missing, the pitch memory will disappear after a short time without practice. Meyer and Heyfelder indicate in their report that their learned ability to name pitches totally disappeared; because he did not bring the name and pitch to his ear simultaneously, he was not able to instruct himself in the association between them. In any case, Meyer's attempts are very interesting and form, together with Naubert's recommendations, some support for the view that absolute tone consciousness may improve through practice. From my experience I would accept the proposition, because it concerns not a hypothetical question but rather a materially important pedagogical issue for the practical production of music.

In the question of training absolute tone consciousness, both associations must be recognized as distinctly separate, i.e. (I) producing a pitch name from a heard tone versus (II) producing a sung tone from a specified pitch name.

In order to recognize a thing, one must perceive it frequently and focus one's attention upon it. One may concentrate attention on an object more easily if there are few distractions; therefore, in order to recognize a certain pitch (A), one must present the sound to the ear as isolated, not in connection with other sounds. Yet the A-tone has additional qualities besides the pitch, including duration, intensity, and timbre. Under normal circumstances, duration is not a significant consideration, but intensity and timbre frequently capture the attention and overtake pitch as the prominent characteristic of a tone. Therefore, if one wants to retain a pitch in memory, the sound qualities of each tone should remain homogeneous, i.e. always using the same timbre. The optimal intensity must be carefully determined. Too strong a sound can cause physical problems (such as background noise); too weak a sound and the listener cannot hear well enough to make a decision. The optimum therefore lies between them. An intensity at which the sound is just clearly perceived seems best suited to the task, as it does not distract attention.

It is far more important to turn the attention away from the timbre and to the pitch sound. We have previously seen how, to make an absolute height judgment, one must analyze the timbre, either by isolating the pitch or by isolating the tone, depending on the observer's primary musical instrument (e.g. a piano tone). For myself, when I still had very little musical instruction, I made frequent acoustic investigations with tuning forks, which are nearly overtoneless, and thus do not draw attention to the timbre, away from the pitch. However, if a musician has been trained for many years as a pianist, then to him the piano tone is the simplest, and all other sounds would seem to have strange timbres; that is, their timbre would call attention to itself. Therefore, such a pupil must be trained by using piano tones, at least to begin with, until he can judge these sounds. First of all one plays the sound A, listening attentively, while simultaneously speaking or thinking the letter "A". Through frequent repetition, the association will be created; afterwards, one may attend to other qualities of the tone, but always using the same fundamental A-pitch. Of the 100 respondents to my questionnaire, no fewer than 9 achieved their absolute tone consciousness in this manner. Six had listened to tuning forks and pitch pipes and, if possible, would sing the sound to match it; three learned from their experience at the piano. A little 6-year-old boy who was very musically gifted, but who did not have absolute tone consciousness, I presented with a set of pitch pipes, and I taught him how to use them correctly; to my delight, after 1/2 year he was able to not only sing an A consistently, but other pitches on demand. He was less confident in his pitch recognition. When a student has only an A firmly in memory, and can recognize it repeatedly, he can use this absolute pitch memory combined with interval sense to recognize other pitches; with practice, he may acquire absolute tone consciousness, as the interval sense is gradually "turned off" or he begins to practice other sounds directly such as A0, A1, A2, A3, etc.

In this manner the attention is immediately directed toward the octave relationship. This is the best start because the octave is the strongest relationship even in overtoneless sounds. Then, once the A2, A3, etc. are consistently recognized by their relationship to A (but without judging intervals), they may also be recognized absolutely. I consider the octave especially suitable for this exercise, and I am further convinced by my questionnaire that with most instances of absolute tone consciousness "the tone quality of the octave forces itself upon talented persons, and we should probably see this feeling of similarity as an important factor in the development of absolute tone consciousness." I refer again to the section on "octave deceit"; also, among other researchers, this was emphasized by Kries in particular.

Then, when the A's are all recognized absolutely, I would begin with chord practices, using the A-major, F-major, and D-major triads. If we assume that within these triads the A is absolutely recognized, then from the position of the A within it the chord will be analyzed and judged by the interval sense. Through this process, the students' interest is strongly excited, and their attention will be directed on the other sounds of the triad so that soon these too will no longer need to be recognized through interval sense, but rather can be recognized by absolute position. After these three chords, other chords could be practiced if the student has not yet achieved a general absolute tone consciousness.

These practices require much time and diligence from both the teacher and student. Success will differ depending on the aptitude of the individual. One may take a short time, another a long time, and some may never learn it or other musical abilities; however-- and this I regard as the main issue-- I would not abandon this last type of student, but rather attempt a second method of instruction.

This second method attempts to teach the second type of absolute association, which is recalling a tone from its letter name. We have seen that this production does not occur without the reverse association, except with the aid or indirect criteria; the aim of this second method is therefore to enable a student who fails the first method to use indirect criteria to produce the sounds. If this ability is present, then the ability to recognize the same sounds may develop through continued practice.

One would first need to evaluate how the student responds to each type of criterion. Of the different senses that may be employed, vision and muscle awareness are the most obvious. We related how different musicians may imagine pitches as a printed note, a piano key, or an entire scene. These would all be methods of associating the visual and aural senses; the muscular sense is, however, equally important, especially that of the laryngeal muscle. We have already discussed the contraction of this muscle in detail; it is as useful to the singer as finger-position is to the violinist (when depressing a string). Many musicians explicitly declare that this physical imagery makes it substantially easier to recall a melody; fewer will suggest that it might be useful to their absolute tone consciousness.

If the pupil shows no inclination to use indirect criteria, then the teacher must try to steer him toward imagery. So that time and trouble are not uselessly wasted, it is good to recognize which types of images are most vivid to the student-- whether they are predominantly acoustic, visual, or motor. To test this question, one cannot make a precise examination with a suitable apparatus; instead, a raw psychological trial may be conducted. The teacher prompts the student to think of any well-known poem, or to mentally count numbers, and to describe the psychological process. Some will see the written words of the poem; others will hear the words before speaking; still others will mentally write the words before reciting them. Similarly, the numbers can be mentally written, heard, or read before being spoken. Through different trial series, one may assess the pupil's favorite type of imagery, and use this knowledge in practical application to the child's tone imagery. The proven value of this could be demonstrated only by a lengthy investigation involving numerous students; let them picture their image while hearing the tone (either a printed note, key, or scene). How these pictorial selections are chosen, it's difficult to say; a teacher may objectively coach only the physical action and the printed note.

Advise the pupil simply to play the A-pitch for himself as often as possible, and to pay equal attention to the aural sensation and visual image, always trying to connect the mental image of the physical key to the sensory image received by the ear. If this doesn't help, give the student a piece of sheet music to learn which begins with the A-pitch. The teacher may indicate the A-pitch on the piano as the first tone of this musical piece and let him again try to make a visual connection between key and tone. I know different musicians who reputedly can produce requested tones on demand, but who do not use this technique; still, the examples of my questionnaire might be considered evidence of the appropriateness of this method.

If a pupil is brought to the point where the visual image evokes the tone, then the teacher may further attempt to introduce the printed note to be associated with the tone sound, but this should be given up if the pupil always visualizes the keys which he used to practice the sound. In this way, a teacher may enable many students who prefer visual imagery to correctly recall and produce tones. If a pupil can do this, he may not yet be able to recognize an A when he hears it; this will only occur after much practice, until the visual association is no longer necessary for recalling the pitch (at least not consciously).

For the students whose imagery is more tied to their motor skills, a different approach must be used. For these, one must try to associate the tone image with a muscle memory. To teach a violinist to recall an A, a student may be encouraged to imagine how they would produce the A on their instrument, picturing the movements of both hands simultaneously. Because the empty A string requires no movement, it may be more appropriate to use the A-pitch achieved by placing the second finger on the 3rd position of the D-string. Similarly, one may coach singers to recognize the feelings of their larynx as their instrument. In the data provided by my questionnaire, 5 observers reported that they recalled musical tones by imagining them as the first tone of a familiar song.

A students whose imagery is purely acoustic will probably not respond to method B, and should be instructed in method A. Therefore, if this mental-imagery approach is correct, then it may be most appropriate to begin absolute tone consciousness instruction by first determining which type of mental image the student prefers, from which the selection of method A or B, and corresponding subdivisions, would follow.

It is much easier to teach children to recognize pitches than it is to teach adults. I have mentioned that the main obstacle to developing absolute tone consciousness is that childhood musical instruction considers only the structures of interval sense. If a teacher would instead train a child to hear a sound or melody always in the same musical key, the child would be much more able to gain absolute tone consciousness; currently, all methods seem to work towards the suppression of absolute tone consciousness. Stumpf reports in Tonpsychologie that an 18 month old boy was trained to correctly sing a C on command; I have not personally seen absolute tone consciousness demonstrated at such a young age, but I know of many (myself included) who were able to name all the piano tones by age 5. I have made some practical attempts to train little children in absolute tone consciousness. The students were three girls, two aged 4 and one aged 3. The four year old had already learned some songs in kindergarten; the other two had not received any exposuer to music, and all came from working families where the mother had little time to raise them, much less to teach them. These three children always visited me together, so I always instructed them as a group. I sang them the word "Ade" using the pitches A0 and D0; the children immediately repeated the singing, of course transposing the sounds into their own vocal range (A1 and D1). I repeated this for six consecutive days; each day I repeated the sounds ten times and let them sing it in immediate response. On the 7th day, I took each girl individually and said only the word "Ade". Two of the children repeated the precise pitches A1 and D1. The third sang an accurate fourth, but as C2 and F1; further repetitions, with breaks in between, produced B1 and Eb1 or even Eb2 and Ab1. This child was the one who had already learned some songs in kindergarten. The other two had retained their memory for A1 and D1. After breaks of 14 days to a quarter year, they were still able to produce the same pitches (30 attempts with 100% accuracy), while the third child only achieved 9 correct (i.e 30%); with all three children, the association was supplemented by a piece of chocolate. I accidentally encountered one of the girls a short while ago on the street, nearly 1 3/4 years after our previous pitch trials, and as soon as I gave the "ade" cue she promptly sang the correct pitches A1, D1. I am currently teaching a fourth little student via the first method. In any case, absolute tone consciousness seems to be awakened much more easily in a child than an adult, but substantial data would have to be gathered in order to draw effective conclusions. It would be very appropriate to engage these attempts in homes for the blind, because congenitally blind persons naturally pay greater attention to acoustical input than those with sight.

Even with animals, I have been able to develop some absolute tone consciousness. I had a parrot to whom I always whistled songs in the same key signature; it was thus trained to be able to repeat the melodies, and always in the same key signature. Thus it learned the beginning of the C-minor symphony as G G G Eb. Only once did the bird begin to whistle these sounds too highly, but only as A-flat, and in repetition reverted to the correct G-pitch. Whether the bird accomplishes this accurate reproduction by the muscular perceptions of its thick tongue, or through other indirect criteria, naturally cannot be determined. I bought another bird, shortly after the untimely death of the promising parrot, which always used the correct absolute pitch when repeating the songs whistled to it.

My results therefore can probably be added to Naubert's and Meyer's, and to other musical educators as well, such as Prof. Jadassohn in Liepzig who has recognized that absolute tone consciousness is a normal tendency which can be taught to many people. Such an ability is not normally attained without practice specifically dedicated to learning it; but one need not presume that certain physiological conditions are necessary. The time and method used in practicing are what matters. However, it can be recognized that certain individuals may achieve the ability without special practice, and others with practice, while others cannot achieve any ability to name or recall tones [31].

XV. The individual factor.

We must now regard what could possibly account for this individual factor. We may suppose that our ability is connected with a special refinement of our sensory apparatus, so that a musician gifted with absolute tone consciousness may distinguish the sound qualities of a pitch better than other people. Their recognition of pitch would not be affected by a sound's intensity or duration, and would be secure at the highest and lowest limits of musical sound. Most of these points were discussed in previous sections. I was not able to find that a special sensitivity exists for intensity, either absolute or relative, which bears any relationship to absolute tone consciousness; such a thing would hardly be likely because, as I demonstrated above, to train absolute tone consciousness it is necessary to use an intensity which does not violate certain thresholds. Also, the threshold of duration is not an issue. In the work jointly completed with Dr. Brühl [32] regarding brief tones and noises, we did not have identical duration thresholds although we possess the same absolute tone consciousness. Also, in the experimental trials conducted Dr. Shaefer, the trill threshold occurred for each of us at the same time even though Dr. Shaefer does not have absolute tone consciousness. Concering the pitch, the high and low boundaries of competent judgment are nearer to each other than the boundaries for simply perceiving the sound. It is therefore unlikely that the perceptual boundary is relevant to pitch judgment; additionally, the perceptual boundary is highly dependent on physiological variations in age, and absolute tone consciousness seems to be unaffected by these variations. Also, the ability to discriminate tones seems unrelated to absolute tone consciousness, because this would require a memory for many distances between tones instead of directly perceiving each tone.

The individual coefficient, which causes the predisposition to acquire absolute tone consciousness, could originate from anatomical conditions. We can imagine how, in certain individuals, sections of the brain may be present by whose functions absolute tone consciousness comes to exist, while in other individuals these sections are either absent or nonfunctioning. This theory would shift the question of absolute tone consciousness to be possibly a skill inherited from the prior generation; but my questionnaires did not provide convincing evidence to support this. More than half of the respondents to my questionnaire indicated that there was no evidence in their family for absolute tone consciousness or any other special musical characteristic.

Unfortunately, we know very little about the sense of hearing. We know that there is an acoustic center to receive the sound, which Munk, Vernicke, Thaller, and Pick believe can be found in the temporal lobes. In animal trials, Munk [33] believed he found special centers for high and low sounds, where the high sounds were located near the cerebellum and the lower sounds in the vicinity of the Sylvian fissure. It is difficult to make conclusive observations in animal trials, principally because of the often defective interpretations of the reactions, so these results should be observed with great caution; and it does not seem particularly applicable to absolute tone consciousness anyway, as none of the physiological research relates to the neural centers which judge absolute pitches but merely the neural centers involved in perceiving sound. If there were such a thing, however, we would have to suppose that this memory center for absolute pitch was also divided further into other memory centers, not only one for absolute pitch but one for intervals, one for melody, and so on; the hearing sense would have to be broken into numerous little centers. Unfortunately, we lack both the physiological and pathological research, and it is useless to waste time speculating when there is no supporting evidence. Whether we will eventually be able to discover a brain center for absolute tone consciousness is doubtful, but rejecting this idea is in no way a priori.

Although we have only scant knowledge of the brain's centers, we nonetheless work with them psychologically. So it contributes substantially to our understanding of the psychological process of absolute tone consciousness if we draw ourselves the schematic diagram that must exist by analogy to other senses.

XVI. Examination of common names for the ability.

Following this discussion we are now well able to undertake a critical examination of the names commonly given to absolute tone consciousness. Through my questionnaire, I learned these names:

The expressions hearing, tone hearing, and musical hearing should be rejected because they are too generic. For the same reason, we can throw out tone sense. Actual tone sense is a psychological function of our entire ear-apparatus and contains both perception as well as a memory and feeling for all sound qualities; absolute pitch perception is therefore only a subset of tone sense.

A characteristic feeling accompanies each pitch [34]. According to its qualities, a sound can be described as comfortable or unpleasant; the highest sounds may be accompanied by a perception of pain and therefore may be quite unpleasant indeed. If we supposed that this feeling were the sole criterion of absolute pitch judgment, it seems impossible to imagine that even the finest musician could exhibit such a fine sensitivity of discrimination to deduce the name of a tone from its level of comfort or unpleasantness [35]. The intensity of a tone contributes more significantly to this perception than does pitch, and timbre is even more influential still in determining the pleasant quality of a tone; whether a mild C sounds more pleasant than a mild G, I do not believe I am any more qualified to determine than any other observer. I don't think it is possible to tell. If the tones are thus not judged by their feeling, we may reject such terms as tone feeling and absolute tone feeling.

Previously, however, we have occasionally discussed the characteristic of a key signature as evoking feelings in other senses. The feeling caused by A-flat major is different from that of C-major; whether it is developed from conventional or physical causes, these qualities can be transferred from the feeling-character of the key signature to the tonic tone of the same; these feelings are qualitatively different and do not rank the simple category of pleasant-to-unpleasant. What type of feelings these are, however, cannot be explained conceptually and are highly individualized. The feelings may have emerged through complicated paths of association which no longer exist; we have already discussed the possibility that this process may contribute to the origins of absolute tone consciousness. But even if this could be proven as the ultimate origin of absolute tone consciousness (which I do not believe), it would not help us identify the process which led to its development. Because we have defined absolute tone consciousness as the ability to execute the association between word image and tone image, the expression "absolute sound feeling" is therefore under all circumstances inexpedient and illogical.

J. v. Kris has, in his repeatedly-quoted work, named the ability "absolute hearing". If one knows the background information presumed by this term, the term appears quite suitable especially because of its brevity; but the term is not adequately complete in itself and thus requires further explanation. v. Kries recognizes this, and used the name only because of its brevity and because of its popular usage.

I have used the term "absolute tone consciousness" because I have encountered this term most frequently in my experience; but I have already described its insufficiency. "Consciousness" is ill-defined, and there is no consensus over its meaning [36]. One generally understands the psychological concept of "consciousness", and absolute tone consciousness as an ability certainly belongs in the realm of psychology, but then the label "consciousness" is again too generic. If one considers consciousness to be only the psychological awareness of the contents of a sound, then on the one hand the name is too general (one would have to say pitch), and on the other hand the expression is too specific, because it includes neither the ability to correctly name these sounds nor the ability to recall them to memory. We could therefore call the ability "absolute tone consciousness" only if the ability to freely imagine any pitch is considered part of that consciousness, although then it remains a problem in calling this ability "consciousness".

All these difficulties disappear, however, if we apply a concept under which recognition, association, and production all fall: memory. I believe that we would not then need to designate the different types of the ability, but can rather be summarized logically and psychologically under the label "memory for absolute pitches." Well, admittedly, this expression is also too general, for certainly a pitch can be held in short-term memory without having absolute tone consciousness. One would have to bring permanence of memory into the expression of the concept; and yet the ability may fade with lack of musical practice. I believe that "memory for absolute pitches" is the best name, or perhaps "absolute tone memory" with the tacit prerequisite that there is another kind of pitch recognition, in which people associate characteristics, which has nothing to do with this other type.

XVII. The value of absolute tone consciousness in relation to music.

As with most things concerning absolute tone consciousness, this topic has been discussed in many ways, yet still no clarity or unity prevails in the discussion. Specifically, it has not yet been decided whether absolute tone consciousness is a necessary component of musical ability or if it is merely a musical curiosity. Most musicians, especially those who do not possess the ability, hold to the view that it is unnecessary for musical practice and is not a criterion for outstanding musical performance. Stumpf presents the completely opposite view in his Tonpsychologie [37], which I quote here:

I completely agree with Stumpf. Yes, it is possible that a well-trained interval sense can replace absolute tone consciousness for many purposes. So, for example, a singer who can judge only intervals may sight-sing a piece of music, but these are exceptional cases. It is much more difficult to retain a sense of pitch when hearing similar music.

A well-known, outstanding musical singer tried, at my suggestion, to sing a quartet in a chosen key signature and then modulate it. Although he does not possess a trace of absolute tone consciousness, he was able to modulate all four phrases of a Haydn quartet, identify all the modulations, and at the conclusion of each phrase to return to the original key. In a subsequent quartet of Brahms, however, he had to throw in the towel after 8-10 measures; he said that even the Haydn quartet had been a terrible exertion, accomplished without any enjoyment of the music. The enjoyment of music does not exist in analyzing relationships but in the elementary effects of scales and harmony, the recognition and execution of themes, etc. Both the elementary feelings and the more complicated involvement cannot be had if one pays desperate attention to the sole factors of tonic and dominant. That is, therefore, the most important utility of absolute tone consciousness; that one can experience the beauty of music and yet, in each moment, retain the sense of the fixed key and easily participate within it.

Therefore, absolute tone consciousness cannot be replaced even by the most perfect interval memory. Many musicians always carry a tuning fork in their pocket to help them stabilize their sense of pitch and key, but obviously this cannot be used in a concert situation, and so much time is lost by striking the fork (or blowing on a pitch pipe) and comparing its interval to another pitch that the next chords and measures completely escape the attention; this strategy may be a remedy for recognizing pitches, but is in no way a replacement for absolute tone consciousness.

The value of absolute tone consciousness is to be recognize even more clearly in the production of music. I do not believe that it can possibly affect the purity of an instrumental tone, but it is of great importance for singing. A singer with absolute tone consciousness will only ever have technical difficulties. The problems that other singers encounter with unfamiliar scales and intervals does not exist. For this singer, singing F-A is no different from singing F-C#, because she is singing neither a "third" nor an "augmented fifth" but rather the absolute pitches F, A, and C-sharp. The harmonic relationship is entirely irrelevant to the singer's accuracy.

Also, in my opinion, a composer cannot do without absolute tone consciousness. Each key signature has some characteristic quality, and many a composer would be insulted if he had to listen to the usual transpositions which occur in modern times, either by convention or for other causes which I have previously indicated. The composer, either consciously or unconsciously, composes with the key characteristic in mind; if he does not have absolute tone consciousness he must either have a piano at his disposal or avail himself of a tuning fork. Although absolute tone consciousness is not an unconditional requirement for composition, it is nonetheless indispensable. There are well-known exceptions; Meyerbeer always carried a pitch pipe to reassure himself of the pitch of the sounds he imagined.

Composers with absolute tone consciousness also differ in one other way from those who have only interval memory. Their compositions are a function of the imagination, where images and memories are arranged by value and importance (in contrast to memory, where temporal sequence is predominant). The smaller the units of memory, the more imaginatively they can be organized, and the more original the composition becomes. A musician who composes several measures which resemble those of a well-known piece may be consciously or unconsciously plagiarizing, and many phrases are, naturally, a result of such borrowing; but one cannot get by in music without some repetition, because composition takes place within the constraints of music theory (rhythm, harmonic relationships, etc). If these are set aside, the most original composer would be the one who mixes the smallest memory images; for the composer with only interval sense, his smallest unit is the interval, but the absolute musician also has access to the single tone. Because an interval is always composed of two sounds, then such a musician composes within even greater constraints than those who compose with pitches, even within the boundaries of music theory which apply to everyone. Consequently, the composer with absolute tone consciousness would be the more original composer. Whether this consideration is only of theoretical interest, or has practical importance, would be subject to a test of the composition and absolute abilities of the better-known composers.

In any case, it is clear that absolute tone consciousness contributes both to a penetrating understanding and a quick grasp of musical beauty, which are important both to the practicing and the composing musician. It is, however, also conceivable that an absolute tone consciousness may exist without any worthwhile musical characteristics; this view is of course maintained by musicians who have no absolute tone consciousness, for reasons which may be best sought among those without absolute tone consciousness.

I consider the imagination to be a yardstick for outstanding musical aptitude. This is not necessarily documented in expert compositions, or so-called daydreaming at the piano; the ability to immediately find the correct modulation is a sign of the productive talent. My questionnaires gave me extremely valuable information regarding the relationship between absolute tone consciousness and musical productivity. All respondents to my questionnaire, with the exclusion of those who recognize sounds through indirect criteria, all 87 of them indicated that they felt particularly free to improvise. The question of whether they would be able to play the correct accompaniment to well-known melodies was affirmed by many as obvious. This answer appeared so regularly together with the existence of absolute tone consciousness that the ability must be even more coordinated with absolute tone consciousness than it appears to be. I believe there is a causal connection; although we cannot indicate the cause, we can observe the consequence. It is possible that absolute tone consciousness can, because the musician becomes free to explore memory images, make a musician predisposed to musical activity. On the other hand, it could be possible that by musical activity the attention is turned especially to the pitches, from which absolute tone consciousness results. For the latter view, one could say, if necessary, that anyone with absolute tone consciousness has productive musical talent, but not all those with productive musical talent will have absolute tone consciousness.

It seems to follow from my data that, if one regards productive musical talent as a measure of outstanding musical talent, and if absolute tone consciousness is paired with this, then absolute tone consciousness should be generally regarded as a sign or a predictor of an outstanding musical talent.

It is also interesting to examine the relationship of absolute tone consciousness to other musical abilities. I have already described how the interval sense can affect one's entire musical perception. We also saw how absolute tone consciousness and interval sense are totally different from one another, such that musicians gifted only with interval sense differ substantially from those with absolute tone consciousness; but the musician with absolute tone consciousness does nonetheless have interval sense, and we must examine how he uses it. Can a person who would otherwise interpret a musical piece by its absolute pitches re-interpret it only with intervals, which is the prevailing preference?

It seems that generally, even in musicians who possess absolute tone consciousness, interval sense is more strongly pronounced. But cases do occur where the sense of interval diminishes completely in favor of absolute listening. On can find proof of this in the following. Many musicians who have absolute tone consciousness may find it very difficult to sing a song that is transposed into a key that does not match what is printed on the page. If a singer is to sing C, E, A, and for whatever reason the accompanist transposes it a step higher, the singer would have to sing D, F#, B instead. The printed notes C, E, and A are firmly associated with specific tones, and the singer must now calculate the new tones. If a song is written in fast tempo, the singer would have no time to figure out each new note, and would end up singing the incorrect note in spite of their good ear and tone perception. I can offer an example from my own experience; I am a member of the local chorale, whose conductor (professor Schnöpf) for technical reasons frequently allows a song to be sung either a tone or semitone higher or lower than is printed on the page. All the other singers proceed without difficulty, not even being aware that the song has been transposed, because they are singing intervals-- but for me it is a torment. While I never make an error in singing the correct tone, I must transpose each single note as I go through the song, and I often fall out of rhythm.

The distance of transposition often makes an interesting difference. For a distance greater than a whole tone I must always manually calculate the sounds. But if the transposition is only a half-tone, I begin by calculating the transposition, but then after some measures I persuade myself to adjust my absolute pitch by a semitone, forming a new association between the printed note and the sounds in my head. There are probably two circumstances which make this possible. Practically, in music we hear various tunings; normally we have A = 435, but many tuning forks deviate from this standard, whether deliberately or through poor manufacture. So it happens that we may hear piano and orchestra concerts which deviate from each other by nearly 1/3 tone. Thus, the pitch name becomes more flexible; a musician who has absolute tone consciousness may find that listening to different sources of music will make their ability somewhat elastic.

The second important factor is the conscious will. Stumpf wrote in his Tonpsychologie I, 244 that, if a tuning fork is swung next to the ear, it is possible to interpret the alternating strong and weak ones as an increase or decrease in pitch. I am not sure how this can be explained psychologically, but it seems possible that the will is part of the equation; for it is not possible that the arbitrary detuning is explained by the flexibility of the sound category alone, especially since (as I have just explained) my pitch terms are very precise. A semitone is the extreme boundary, around which I can adjust my memory-image up or down and manage to get through a choral piece where I am forced to continue using the new associations. Then I gradually backslide into my normal use of the notes. I once conducted an experiment relating to this under rather unpleasant circumstances: I sang a quartet in an a cappella performance with three other gentlemen. All four of us began in B-flat major, but during the song the other three gradually dropped to A-major, while I continued to maintain my B-flat orientation. It was supposed to have been a soothing song, but I found it thoroughly maddening. Stumpf [39] speaks of a similar occurrence:

With the piano and similar instruments, transposing is not quite as disturbing as it is to singing and bowed instruments, although the ear must also become accustomed to the strange voice. A Miss P.C. informed me of her experience:

This illustrates how one may deliberately confuse the ear to form new associations. This process does not always succeed; the ability varies between individuals. Professor Rudorff explains how his mother got "a new piano that was tuned lower than the one we used to have; so she played Beethoven's C-sharp minor Sonata in D-minor, because it made her uncomfortable to play the C-sharp minor keys and hear C-minor instead." An explanation of this phenomenon is not easy. The lady in question has very strongly developed absolute tone consciousness; with it, the term "c-sharp minor" is, by name, printed note, and keypress, firmly associated with the absolute pitches of C-sharp minor. Because it is now unpleasant for the lady to hear the song, that is, because she cannot form a new association between the C-sharp minor keys and the C-minor sounds they produce, she plays the D-minor keys in order to hear C-sharp minor. Because it is such a small shift between C-sharp and C, and since the off-tuning is the same as between D and C-sharp, one must assume that there is a specific C-sharp concept which is predominant over any other. It is entirely possible that the concept is suffused throughout the piece and is evoked by the piece in its normal tuning. The C-sharp minor sonata, when played in tune, evokes a feeling in this lady which is not obtained from the transposed piece. It is easier to overcome the technological obstacle by playing the D-minor keys than it is to eliminate the psychological feeling of disturbance.

In my questionnaire I asked: if a song is transposed by the accompanist, can you sing it without difficulty, or must you manually transpose the pitches? The majority of the respondents were not aware of any conscious transposition, so for them apparently the interval sense is stronger than absolute tone consciousness; yet about one-third of the respondents had to calculate their transpositions in the manner that has been described, and they unanimously described this process as unpleasant.

Max Planck [41] says that he played piano when he was younger, at which he possessed a very strong absolute tone consciousness. When he was asked to play a well-known march on a strange, somewhat more deeply-tuned piano, he had to stop after playing only a few sounds, because he was completely confused and did not possess the mental dexterity to accomplish the double transposition of mentally adjusting the sounds but then pressing the keys associated with the original key signature [42].

It is conceivable that a musician who has absolute tone consciousness would have no interval sense. I once believed this to be true of myself. I would hear the interval A-F, and I would determine the interval; even if I correctly judged this to be a sixth, this was not an original perception but rather a calculation. Now I know that the interval A-F is called a sixth, so I call it that; I can therefore deliver a correct interval judgment without possessing a trace of interval memory. Historically, it seems as if the existing absolute tone consciousness prevents the development of interval sense in a similar manner to how, in the bulk of practicing musicians, the development and nurturing of the interval sense does not allow the development of absolute tone consciousness. With larger intervals, this is how I will naturally judge them; however, this year I noticed that I recognize smaller intervals (seconds and thirds) by interval sense. Professor Stumpf conducted several trial series to produce judgments of briefly-played intervals; the subjects wrote down the interval name and, in a different column, the absolute pitches of the interval. I know from this that I deduce the intervals of a fourth or larger only from their absolute pitches; only with the smaller intervals was I consciously aware of using interval judgment. The judgment "third" jumped out regardless of the absolute pitches. I had to turn myself away from the absolute pitch sounds and give myself over more completely to the feeling of the interval.

Of the further areas of musical ability which are to be examined in relation to absolute tone consciousness, musical memory is of special importance. Musical memory can be segregated into memory for rhythm, harmony, and melody. To get more details about the rhythmic memory of musicians who also have absolute tone consciousness, one would have to engage in a long series of tests and compare these results with those of non-absolute musicians; this would be extremely tedious, and is probably not worthwhile because there is no obvious connection between memory for tones and memory for rhythm. I would not assert this as a conclusive fact, but would prefer to leave this question unanswered.

On the other hand, it is easier to assess the relationship to melody memory, because listeners pay more attention to melody memory than any other musical ability. Therefore, a subject can compare their melody memory to others and deliver a judgment of whether it is good or bad. Of course, the concepts of "good" and "bad" are highly elastic, and only the extremes of very good and very bad are useful for scientific results. It appeared in my questionnaire that some individuals who had strong absolute tone consciousness but who also had an extremely deficient memory for melody. I refer to "very strong" absolute tone consciousness as one which is stronger than the interval sense and which functions in both associations I and II. The possessors of just this absolute tone consciousness complain specifically about the fact that they find it more difficult to retain a melody than do people who are far less musical than they.

We must distinguish here between short-term and long-term melody memory. The first is especially deficient in the person who has absolute tone consciousness. However, once the melody is fixed in memory, it can be recalled for a long time afterwards. Many of these musicians have specific strategies for improving their memory for melody, such as spelling words out of the notes' letter names. I do this myself; for example, I would see the notes A, C, E and think of the word "ace", or the notes B, A, B, E as "babe", etc. Other solutions are suggested by the responses to my questionnaire, such as picturing the movement across piano keys or imagining the fingering of a violin; i.e. using the same indirect criteria for remembering melodies as is used for remembering pitches.

It also appears that people who have absolute tone consciousness show, to a large degree, a deficient memory for scales (melodic). This allows us to draw the conclusion that melody memory and absolute pitch memory are either different, involving different centers in the brain, or that in people who have absolute tone consciousness, ignoring the names of each pitch in favor of the melody is more difficult without using aids such as words, visual imagery, etc. This could explain why those with the strongest absolute pitch memory (stronger than their interval sense) also have the poorest melody memory. In those whose absolute tone consciousness and interval sense are equally well-developed, or for whom the interval sound predominates, we also find a better melody memory; my questionnaire shows this to be true throughout. One must therefore suppose that Mozart, who had a phenomenal melody memory in addition to a "sharp absolute ear", belonged to the latter category, so that his interval perception equalled his absolute pitch perception. Naturally, I would not say that the type of melody retention that I describe for musicians with strong absolute tone consciousness is the rule, in that they use words to recall the letter names of the notes from which they produce the sung tones. Analyzing exactly how a melody is fixed in the memory is certainly a very difficult task, if not an impossible one. But, at the same time, there are definitely at least two mental strategies. The melody may be perceived as single tones or intervals, so that the melody memory may consist of the memory for the single tones (absolute tone consciousness) and the interval memory. Thus the individual with absolute tone consciousness need not retain a melody exclusively by memory of the single tones. The opposite seems to be the more common occurrence; an individual can sing a folk song any requested key signature, and this would suggest interval memory. With more difficult songs, on the other hand, I would probably be able to sing it in the correct key by heart, but not in another key. A particular illustration of this is the ballad "Edward the Lion". I could sing it in the regular key from beginning to end; but if I chose a different key, I would get lost after a few measures, or I would fall back into the normal key. I would make this error particularly with larger intervals of sixths and sevenths. I can sing folk songs in all kinds of keys, but this is probably because I have often heard them in different keys to begin with, and also because I hear them so frequently their intervals are fixed in my otherwise poor interval memory. The observation that I failed to produce large intervals agrees quite nicely with the observation from the experiment in which I could recognize smaller intervals (such as a third) immediately by interval sense, but the larger intervals were inferred from their absolute pitches.

We can see how the absolute musician memorizes a melody from its individual tones, to a large extent; and if it is true that the stronger the absolute tone consciousness the weaker the melody memory, then one must assume that the interval memory is far more effective for remembering melodies than the absolute pitch memory. The essential matter for remembering a melody is to remember its first few tones. In reading, the first few letters of a word often prompt the remainder of the word, so that with a long word only the first few letters are actually read and understood while the rest are inferred; likewise, the first few words of a poem's verse cause the rest of the poem to be recalled. This same effect appears in music, so that the memory for melodies relies much on its first few sounds, by which the entire work is often reproduced. How often happens that a musician is asked for a melody, and cannot produce it, but as soon as he hears the initial tones he can produce the entire melody perfectly by heart! Each tone carries a reference to the next; like rings of a chain, the sounds of a melody are lined up with each other; tugging at one is enough to draw along the entire chain provided that the connections are strong enough to prevent the chain from breaking. I have deliberately selected this metaphor because it clearly depicts what I want to demonstrate. We have spoken of how a melody can be fixed in memory and recalled both by absolute pitch and by interval memory, so that absolute pitch keeps the individual tones in memory and interval sense the relationships between the tones; therefore, in order to reassemble the entire chain, the absolute memory knows only the single rings, while the interval sense knows the connections between them. The sequence A-C-F is known by absolute tone consciousness to be three sounds which are totally unrelated to each other, but the interval sense recognizes them as "minor third" and "fourth". Therefore there are no longer three but two units. The perceptions differ further in that the absolute A suggests no relationship to C, but the A that is part of a minor third implies the C which follows it. Bain, who has written a treatise on the type of image a melody forms in the memory [43], makes a similar statement: "the first note does nothing; three or four are necessary to determine the song." Since the melody memory depends principally on the beginning tones, it follows that interval memory must be far more effective for this than absolute pitch memory, which is confirmed by the data.

This is different from harmonic memory. To fix a chord in memory, it is firstly necessary to recognize its individual components. One cannot reproduce a chord of five tones if one hears and knows only three of them. We have already seen how absolute tone consciousness is extremely valuable in interpreting and analyzing chords. A musician who can judge absolute pitches can analyze unfamiliar sounds much more easily than the musician who relies on interval judgment. Also, Wallaschek says in his treatise "Das musikalische Gedächtnis" [The Musical Memory] [44], relative perception seems to facilitate melody just as absolute perception seems to facilitate harmony. It is clear that absolute musicians have an advantage in fixing harmonies in long-term memory, if only because they are better able to perceive them. This was not the case with melody memory because single sounds do not need to be analyzed and present no special perceptual difficulty.

We have also seen how anyone with absolute tone consciousness is also able to improvise, to compose, or at the very least to easily create a harmony appropriate to the melody. This ability to form harmonies is so easily accomplished by gifted absolute musicians that it may be difficult to tell where harmonic memory stops and harmonic imagination begins. If an imagined chord corresponds to one that was played earlier, it is impossible to tell whether or not this is memory; if it deviates from the earlier chord, one can suggest only that perhaps imagination is stronger than memory. Since both are of unknown strength, they can not be separated out of the equation. In all other respects, however, such complicated things are possible with memory research that I do not want to present myself as having analyzed the musical memory in my writings; there are still rhythmic feelings, feeling for harmony and fusion, memory for rhythm, etc, to be considered. I only took into account musical memory as it related to absolute tone consciousness, and drew logical conclusions from the available data.

XVIII. The musicians gifted with absolute tone consciousness form a unique musical type.

We saw in the last chapter that absolute tone consciousness has specific relationships with other musical characteristics, but it also functions as a sure criterion for musical aptitude. Despite being in common usage, the word "musical" is poorly defined, used liberally both in psychology and colloquial language. The word "musical" seems to encompass the concept, but much is falsely subsumed within it, and the determination is often arrived at via insufficient methods.

To call everyone who listens to music "musical", recognizing "musical nature" as defined by Schladebach-Befnsdorff in their universal lexicon of the art, would create many contradictions. It may not be linguistically incorrect, but it gives no insight toward what we call "musical" in humans. I do not prefer the word "musical", but rather the term "musical aptitude" which has a more specific and appropriate definition.

Frequently, one identifies the concept "to make music" with the phrase "is musical". Someone who plays an instrument is called musical; therefore, an artist who stops playing his instrument must be called unmusical, even if he stops playing for purely technical reasons. The musical ability, however, does not lie in the hands, lips, or larynx, but rather in the brain itself. It is that central organ which carries out the movements, turns perception into consciousness and memory and processes it freely, restricted only by conventional laws of sequential processing.

Different musical dictionaries attempted to define the "musical ear". Koch-Dommer (1865) defines it as the ability to judge tones for purity or impurity, recognizing the exactness of an interval and any slight deviations from the standard. Therefore it identifies the musical ear with judgment of purity and discrimination.

More recently, psychology and also M. Meyer have offered definitions of the concept "musical" [45]. Meyer specifically defines the concept of "unmusical", even though this is essentially a reversal of his explanation of "musical". He says:

Stumpf objected to Meyer's definition [46] by saying that the term "limited duration" is so vague that any person could be declared to be unmusical once the sounds are played too quickly for them to analyze. After Meyer subsequently made some additions to his definition in a supplement to his treatise, he finally acknowledged that he had not intended any general definition of the concept. Meyer's explanation would also only cover one specific area-- the analysis of harmonies-- even though this is an important area of music.

A very strange explanation of the musical ear is found in the music dictionary of Mendel-Reissmann: "The musical ear is the capacity of our soul which, through the agency of the ear, feed the nerves and brain the ideas, thoughts, perceptions, and feelings of others through representations of sound. The musical ear does not thus perceive isolated events, but seizes upon the single perceptions to merge tone images together and transfer the mental motions of the composer to our own psychological mechanism." This excludes the talents which are based on musical memory, such as absolute pitch memory, being able to recognize intervals and chords by ear, or being able to hold particular tones and chords in memory for later recall. This talent is surely of great use to the musician, although admittedly someone may possess it to a high degree without actually having a good musical ear. This definition further excludes the sensory images provided by the imagination, i.e. the ability to recall impressions of melodies, as well as all those susceptibilities which lie completely outside of the tonal art, e.g. the beautiful timbre of an instrument. By this definition musical hearing is, strictly speaking, the ability to receive the connected sounds and chords of a composition and determine how the composer intended it. This definition which excludes any sense of interval, memory, imagination, or joy in the beauty of sound, does not seem plausible to me.

I believe that one must observe all these abilities in a person in order to describe them as "musical". There is probably a measure of interest in music, a well-functioning perception-apparatus, a feeling for the beauty of sound, a good memory for pitches, interval, melody, rhythm, and finally imagination and productivity. What measure of any single factor is necessary for our concept of "musical" must first be determined before one could venture a definition.

General psychology has given us most of our questions for music psychology. Stumpf, in his famous Tonpsychologie, conducted investigations particularly regarding feeling, judgment, memory, feeling, and in this manner obtained very important psychological results. In order to further realize the term "musical", however, one would still need the methods of individual psychology devised by Binet and Kraeplin. What use is it in the analysis of musicality to know that the ability to discriminate pitches or to memorize them varies between this and that limit? We do not yet know what this has to do with music. For our purposes, it would make more sense to examine the psychology of general judgments of music. If we could include the stories of our great musicians' psychological contributions, then we would probably make further advances in understanding the relationships which exist between the individual factors of musical talent.

Yet it does seem to make sense to me to divide the general type of "musical" into separate sub-types. These would not be arbitrary and artificial lumps like the main category, but would be determined by observations in psychological research. The sub-types emerge through the specific abilities demonstrated by a series of exercises to be superior to the other factors of music ability. The different areas of memory, memory for absolute pitch, for intervals, for harmonies, for melody, and for rhythm would be the starting point for this kind of psychological typing.

One of these abilities, that of absolute tone consciousness, we have now seen to have a powerful influence on interval perception; it facilitates memory for harmonies and melody, and it bears a clear relation to musical imagination and aptitude for composition. Musicians gifted with absolute tone consciousness therefore have not merely the ability to recognize and recall pitches, but rather are a unique class of musician. A psychological examination would probably identify several such types among the universe of musicians; then the relationship between single factors of musical talent and the entire area of musicality would be revealed for examination.

11) Otto Abraham und Ludwig J. Brühl, Über kürzeste Töne und Geräusche (Zeitschrift für Psychologie, XVIII).

12) O.Abraham und K. L. Schaefer, Über die maximale Geschwindigkeit von Tonfolgen (Zeitschrift für Psychologie, XX).

13) Otto Abraham, Über das Abklingen von Tonempfindungen (Zeitschrift für Psychologie, XX).

14) v, Kries und Auerbach, über die Zeiten der einfachsten psychischen Prozesse (Arch. für Physiologie, 1877).

15) O. Abraham und Karl Schaefer, Über die maximale Geschwindigkeit von •Tonfolgen (Zeitschrift für Psychologie XX, S. 412).

17) Max Meyer, Über die Rauhigkeit tiefster Töne (Zeitschrift für Psychologie, Bd.XIII).

26) Unser Apparat umfaßt die Oktave von 400--800 Schwingungen und enthält 120 Zungen, die zwischen 400 und 480 um je 2 Schwingungen, zwischen 480 und 600 um je 3, zwischen 600 und 800 um je 5 Schwingungen differieren.

32) O. Abraham und L. J. Brühl, Wahrnehmung kürzester Töne und Ge räusche, a. a. O.

33) Munk, Monatsberichte der Berliner Akademie, 1881, S. 481. Siehe auch Stumpf, Tonpsychologie II, S. 289.

41) "Die natürliche Stimmung in der modernen Vokalmusik" in der Vierteljahrsschrift für Musikwissenschaft IX, S. 428.

42) Ich verstehe hierbei allerdings nicht die "doppelte Transposition". Meiner Ansicht nach handelt es sich um eine einfache Transposition, entweder auf dem Klavier in eine höhere Tonart, oder im Gedächtnis in eine tiefere.

45) Max Meyer, Über Tonverschmelzung und die Theorie der Konsonanz (Zeitschrift für Psychologie XVII, S. 413 und XVIII).

46) C. Stumpf, Die Unmusikalischen und die Tonverschmelzung (Zeitschrift für Psychologie, XIV, S. 425 und XVIII).

Our judgment:	where the duration of each individual tone was (in seconds)
	0.042
	0.065
	0.075
	0.111

Our judgment:	where the duration of each individual tone was (in seconds)
	0.037
	0.059
	0.091

Our judgment:	where the duration of each individual tone was (in seconds)
	0.055
	0.076
	0.111

Our judgment:	where the duration of each individual tone was (in seconds)
	0.028
	0.059
	0.095

Our judgment:	where the duration of each individual tone was (in seconds)
	0.023
	0.050
	0.076
	0.100

	-6/2	-5/2	-4/2	-3/2	-2/2	-1/2	0	1/2	2/2	3/2	4/2	5/2	6/2
D#2					5	15	35	35		5	5
E2					5	30	35	10	10	5	5
F2				15	-	20	25	25	10	-	5
F#2					10	15	30	30	10	5
G2				5	15	15	15	35	10	5
G#2				10	20	15	25	10	15	5
A2		5	5	5	20	40	15	10
Bb2				10	10	20	30	10	10	10
B2				5	30	20	30	-	15
C1			5	-	5	25	40	20	5
C#1					5	35	40	20
D1						35	60	-	5
D#1						15	40	15	15	15
E1					5	25	35	25	5	5
F1				10	5	30	20	15	15	5
F#1					5	25	45	10	5	10
G1					5	10	50	30	5
G#1				5	10	-	70	15
A1			5	10	5	10	70
A#1						10	90
B1						30	70
C0							100
C#0						10	90
D0						10	80	10
D#0							100
E0						10	80	10
F0						20	80
F#0							100
G0							100
G#0							100
A0							100
A#0							100

	Small octave	First octave	Second octave	Third octave	Average
C	576	571	445	441	516
D	645	598	453	529	563
E	544	590	458	507	538
F	499	559	486	527	521
G	655	565	399	477	538
A	714	591	426	463	515
B	606	457	412	468	499
Average	606	562	440	487

	Letter	Named
C	556	509
D	549	605
E	566	562
F	563	492
G	561	573
A	394	503
B	509	546
Average	528	541

	Own piano	Harmonium	Strange piano
C-minor	? C ? Eb D	C ? Eb	C# C ?
C-sharp minor	C# G# ? C C	? C C	F# C# ?
D-minor	Eb D C# A D	F ? ?	? B C
D-sharp minor	Eb ? ?	? ? ?	Ab Eb ?
E-minor	E B Eb E A D E A	B F ?	B F E
F-minor	F B F F#	? ? G	F# F# ?
F-sharp minor	F# F# F# F# F# F# F#	? ? ?	F# ? F
G-minor	A B F ? G ? A	? ? A	A F ?
G-sharp minor	F E A Eb	? ? ?	F Eb B B
A-minor	? C ? Eb A	? ? ?	Eb Ab E F
B-flat minor	F G B	? ? ?	Bb ? F
B-minor	B F B A	? ? ?	B ? B A

Pitch	Frequency	Date	Boundary values		Number of trials
A	451.3	23./3. vm.	448	458	8
	450.6	23./3. nm.	446	460	7
	442.8	26./6.	434	448	10
	444.4	28./6.	440	448	10
	447.8	30./6.	444	450	10
C	659.3	24./3.	645	670	15
B-flat	472.0	24./3.	466	478	3
	472.7	26./3.	470	476	3
	477.8	20./6.	474	486	6
C-sharp	574.2	20./6.	564	582	5
	580.2	21./6.	576	588	5
D-flat	566.0	III.	561	576	3
	548.0	III.	546	552	3
	559.8	20./6.	552	573	5
	553.8	23./6.	546	561	5
G-sharp	426.4	23./6.	422	434	5
	426.8	25./6.	424	432	5
A-flat	416.7	III.	414	410	3
	422.0	III.	420	424	3
	426.0	23./6.	422	432	5
	420.4	25./6.	418	424	5

	too low	good	too high
430	24
432	24
434	24
436	24
438	24
440	24
442	23	1
444	20	4
446	11	12	1
448	8	15	1
450		19	5
452		9	15
454		4	20
456			24
458
460

	Raif			Abraham
	too low	good	too high	too low	good	too high
420	5	1		6
422	6			6
424	5	1		6
428	4	2		6
430	4	2		6
432	3	3		6
434	2	4		6
436	1	5		5
438		4	2	5
440		4	2	3	3
442		3	3		6
444		3	3		6
446		2	4		6
448		1	5		3	3
450		1	5		1	5
452			6			6
454			6			6
456			6			6
458			6
460			6	6

Absolute tone consciousness.