Absolute tone consciousness.

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

Otto Abraham, Berlin, Germany

Translated by Christopher Aruffo
www.acousticlearning.com

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.

1)  How long have you possessed absolute tone consciousness?

2)  Do you play an instrument?  Which?  For how long?  Do you sing?  For how long?

3)  Do you compose?  Do you use the piano (or other instrument) to compose?  Do you have difficulty finding the correct pitches to well-known melodies?

4a) Do you exhibit absolute tone consciousness in that that you correctly name a specified sound?
4b) Do you exhibit absolute tone consciousness in that you can correctly produce a desired sound through singing or whistling?
4c) Do you have both these abilities?

5)  Do you have a specific way or arriving at a correct pitch judgment?
a)  As soon as you hear the sound, do you know its letter name from memory?
b)  Do you compare the sound to another sound in your memory?
c)  Do you sing the tone?  Is this necessary for your judgment?
d)  Do you have the ability to imagine a specified sound without singing or otherwise hearing it?  In what timbre do you imagine the sound (such as violin, sung tone, etc).
e)  Do you compare the specified pitch with your highest or lowest singing tone, and judge the pitch from that?
f)  Do you employ any other psychological process?

6a)  Is it easier for you to recognize the key of a melody than a single sound?
6b)  Is it easier for you to recognize the root of a chord than a single sound?

7a)  Is it easier for you to sing a pitch from memory if you see its printed note?
7b)  Is it easier for you to sing a pitch from memory if you imagine a familiar melody which begins with that pitch?

8a)  Are there upper and lower limits to your absolute tone consciousness?
8b)  Can you judge any particular octaves better than others?  Which?

9.  Must a pitch have a longer duration for you to accurately judge it?  Does it matter whether the sound is higher or lower?
a)  Does the sound have to be loud for you to judge it correctly, or can you also identify weak sounds?

10)  Do you make errors occasionally?
a)  Octave errors?
b)  Fifth errors?
c)  Semitone errors?

11a)  Would you say that all pitches of each category possess something similar-- a thing which distinguishes all B's, C's, etc?
b)  Do you also perceive this resemblance, if more slightly, between A and E?

12)  Do you notice when an instrument is tuned a quarter-tone or eighth-tone deeper than another (Naturally, this comparison must be made after sufficient delay to avoid relative judgment.)

13)  If a song is transposed by the accompanist, can you sing it easily, or do you need to be given the same transposition?

14)  Is there a difference in your ability to judge different timbres?  Can you judge equally well among violins, pianos, singing, wind instruments?  Which is better?

15)  Do you have an especially good memory for melody?  Do you have to produce the melody in its original key, or can you imagine it in a different key?

16)  Did you attain or improve your absolute tone consciousness through deliberate practice?  How did you practice?
a)  Do your parents, grandparents, or siblings have absolute tone consciousness also-- or any other outstanding musical characteristics?

17.  Do you perceive any colors when you hear certain pitches or timbres?  Which?

18.  What do you call your absolute tone consciousness?  (absolute tone consciousness, absolute hearing, absolute sound memory, sound sense, sound feeling, or otherwise?)

19)  Do you know other people with absolute tone consciousness, and would you be willing to provide their name and address?

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.

First of all I will speak only about the judgment of absolute pitches.

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".]

Stumpf [5] declared this "octave-deceit":

This is partly based on the similarity which exists between compound sounds, as a whole, when the overtones are included. Since the fundamental tone is most obvious component, we name it after that known sound with which it possesses the greatest similarity. This similarity is evident when a different compound tone is introduced, causing the transmission of the appropriate name from the presence of the fundamental pitch. Each tone also possesses a similarity with its neighboring pitches, but as simple tones these are clearly different; therefore, mistaking them is less likely than with the compound deeper octave. "Octave deceit" is based partly on tonal fusion. That is, in the cases where a simple sound (pitch) is to be identified in a concretely presented complex sound, we imagine the sound and identify with which pitch the given sound merges most strongly, and name it thusly. Due to this process, the simple sound could probably become too highly or too deeply estimated around one or more octaves.  The possibility always existed, from the reasons already stated, that a tone could be mis-identified; here I meant to explain only why this would happen with octaves rather than neighboring pitches. Thus is explained the paradox that, when making errors in absolute height judgment, musicians more easily make errors of larger distances than smaller ones.

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.

We must distinguish:

1)  Physical sounds.  These consist of regular vibrations following a disruption of the air; the circumference of the physical sound is endlessly large, at least theoretically, although there are natural mechanical boundaries.

2)  Sounds which can be perceived by a human.  According to the newest investigations by Stumpf, Meyer, and Karl L. Schäfer, this range is approximately between 16Hz and 20,000 Hz.

3)  Musical sounds.  This area amounts to approximately 7 octaves, between 50 and 4000 Hz.

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:

1.  What is the minimal duration of a sound at which it can be perceived?

2.  What is the minimal duration of a sound for which an absolute pitch judgment may be made?

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:

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:

1.  How quickly can two sounds follow each other (i.e. such as trill or tremelo) yet seem temporally separate and recognizable according to their absolute pitches?

2.  How quickly can absolute pitch judgments be made following the multiple sounds of a musical structure?

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

The melody was

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

2nd trial

The melody was

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

3rd trial

The melody was

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

4th trial

The melody was

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

5th trial

The melody was

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

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:

1.  The sound characteristic which results from associated concepts and feelings,

2.  The tone color of simple sounds,

3.  The timbre defined by the overtone series,

4.  Accompanying background noises,

5.  Variations of strength, height, and dynamic intensity.

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:

Generally, if chords containing rich single sounds are more easily analyzed, then it can be concluded that very soft sounds are comparatively weak.  Regular overtones are present only when accompanying a specific fundamental pitch of adequate intensity, and they will grow proportionally with the strength of the fundamental pitch.  Reversing this observation, sounds without overtones may be identified only by a single, relatively weak signal, and excluding the highest octave this type of sound would therefore be more difficult to identify.

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:

1.  The generation of the physical sound,
2.  The time required to perceive the sound,
3.  The duration of absolute judgment,
4.  The time of the subject's hand movement,
5.  The time to depress the key far enough to break the circuit.

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:

1.  The duration of absolute judgment
2.  The time to physically locate the relevant key.

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

In the 2nd octave, C + u2 = 440
In the 3rd octave, C + u3  = 487
In the 1st octave, C + u1 = 562
In the 0th octave, C + u0 = 606

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 colo