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Absolute Pitch and Tone Identification

  Gilead Bar-Elli

Absolute pitch (AP), besides the psychological and neurological interests it has, raises some conceptual difficulties that can teach us about the richness of our notion of musical tone and various aspects of its identification. It is argued that when AP is conceived under a slim notion of identifying the pitch of a crude sound, it is hardly meaningful and has no significance in music comprehension. The rich notion, which is the meaningful and important one, involves knowing the position of a tone in a tone-space and its relations. This is presented as experiential: hearing and identifying tones under concepts and relations that are experienced rather than figured out or derived on the basis of crude identification of bare tones. Since many of these concepts and relations are musically meaningful, this rich notion of identification is thus connected to musical understanding and aesthetic appreciation of a musical work.  It may also be claimed to be vital in passing between different sense modalities, and can explain various aspects of AP and puzzles connected with it.

Key Words
experiential knowledge, identifying tones, music comprehension, perfect pitch, playing, sense modalities, singing


1.  Absolute pitch: some introductory remarks

Absolute pitch, or AP, sometimes called perfect pitch, is often characterized as the ability to immediately identify, without external aid, the pitch of a heard tone.[1] Sometimes this goes together with the ability to immediately identify the pitches of tones comprising a heard chord. I shall concentrate here on the former. Some researchers distinguish between an active and a passive AP. The above characterization applies to the latter. An active AP is the ability to immediately produce, for example, in singing or whistling, the exact pitch of a note identified by a name or sign.[2] AP is distinguished from relative pitch, which is the ability to identify the pitch of a tone relative to another, given one. Relative pitch, which can be learned and cultivated, is considered a central musical ability whose importance in music comprehension is unquestioned while that of AP is.

The ontological categorization of tones besets serious problems, on which there is recently a rapidly growing literature. Tones are often considered a subcategory of sounds and sounds have been argued to be objects, qualities, secondary qualities, events, event-sources, and more.[3] There are important issues involved here but I shall not delve into them, as they would detract from the main subject of this paper. Rather, I shall talk of identifying tones as a special instance of identifying objects, in the very general and loose sense of the term, in which it is whatever is the object of identification. This wide and general sense of identification is a key notion in our perception and thinking. We identify persons, places, colors, numbers, sounds, shapes, looks, and so on. Some are individuals, some are universals, some are particulars, some are properties, some are concrete, and some are abstract. In each of these it seems that different criteria are employed in ascribing the ability of correct identification.[4]

This variety and the general use of "identification" over it raise problems beyond the problems that pertain to each of its members. I shall leave these aside here, for my aim is not strictly ontological. There is, however, a feature that pertains to many of these cases that is relevant to the identification of tones and has a more general significance, which is that the criteria we employ in identifying objects often have to do with our surrounding knowledge about the object concerned. It seems as though we wish, and need, to keep the distinction between the very identifying of something and our knowledge about it. This may lead to minimizing the amount of knowledge we should require as a prerequisite for identification and, in the extreme, to reach a "crude identification" of a "bare object."

The theory of bare objects, or bare particulars, has come under heavy criticism, at least since the mid-twentieth century. Objects are always presented to us imbued with propositional knowledge, and their identification thus appears to be much more conceptual than the crude conception portrays. One important route for keeping the above distinction in a way that allows for understanding the relationship between its two sides is to regard identifying an object as always identifying it under a concept or in a system of concepts. This, though still not propositional knowledge, is yet conceptual and may pave a way to understanding the relationship between identifying an object and knowledge about it.[5]

I shall not delve here into these heavy waters but focus on one example of it, which seems to me neat and illuminating, the possession of absolute pitch and the identification of pitched tones involved in it. As a common conception of AP, it comes as close as any to the crude identification of an object, that is, the AP of a bare tone, irrespective of its properties and relations to other tones or to the musical context. I shall argue against this conception, and claim that the identification of tones involved in AP is a rich notion, in which a tone is identified in a system of concepts and relations. On the way to substantiating this and sharpening our intuitions regarding it, I shall briefly allude to some other cases of rich identification and present some puzzles of AP, in which the rich conception of identification seems crucial to their solutions. This, if correct, supports the general view that the notion of identifying tones involved in AP is a conceptually rich one, and from that we may learn more generally about other cases of identification.[6] Needless to say, hearing tones under concepts and the rich notion of identifying tones are essential to music comprehension and thus lie at the basis of understanding music and its aesthetic appreciation.

Much in the above characterization of AP is obscure and raises a host of problems. Some of them concern empirical issues, on which much research has been carried out and some important findings obtained.[7] We shall leave these aside and concentrate on one of a conceptual character, which is what is meant by "identifying" a tone in these formulations?

There seem to be three main criteria for correct identification of tones: labeling, memory judgments, and ability to reproduce. Each raises problems of its own, but in relation to all three I argue below that when conceived under a slim notion of the ability to label a heard tone, or perform some memory-tasks with it, or reproduce it, detached from some basic knowledge regarding it, they all are inapt for identification as involved in AP and, in fact, are hardly intelligible. On the other hand, all three do fine when conceived under a rich notion fused with concepts and relations pertaining to the tone identified.

2.  The singing/playing discrepancy (SPD)

We shall start with a little puzzle about the third and most common criterion. A common criterion for AP, that is, for identifying the pitch of a tone, is the ability to immediately match or reproduce the pitch of a heard tone, say, on an instrument one knows how to play. However, in showing this ability, there is a great difference between the means of reproduction. Most people can easily repeat a heard tone, or even a short melodic phrase, by singing or whistling in the correct pitch. This ability is very common and is not considered evidence for AP. However, many of them will be unable to do it on an instrument they know how to play. An ability to do this, even when they don't know the names of the notes they are playing, is considered evidence for AP. Why? What is the root of the difference? If the ability to repeat a heard tone or phrase on a flute or violin is a sign of its identification and evidence for AP, why is repeating it by singing not regarded as manifesting such identification? It seems to me that any serious account of AP, and of the identification involved in it, must address this problem and also related ones, some of which will be mentioned below, which we shall call the singing/playing discrepancy (SPD).[8]

It should be noted that we don't seem to have a similar discrepancy with regard to speaking and writing. It seems that a proficient writer or typist can write or type a heard word or phrase, even when perceived phonetically, without understanding it, with more or less the same ease in which he or she can repeat it in speaking. Rhythm also does not beset such a discrepancy. We can easily repeat a heard rhythm with our mouth or hands or an instrument. The discrepancy, however, is vast as it relates to the ability to repeat, in the correct pitch, a heard tone or short melody in singing as compared to playing. Why? To this problem we can add a small addendum. In reading music notes, the relation seems to be the opposite. An experienced player can play seen notes on an instrument quite easily, directly, and naturally, while singing them requires a special skill (solfeggio), and singing them in the correct pitch requires AP. Why is that so?

It seems that the answer surely has to do with our experience, perhaps in early childhood, and with our learning to speak, which surely involves imitations of various sorts. But this is too general. It should be noticed that we usually have very little experience in matching, imitating, or reproducing pitch. Neither are we normally required or encouraged to do so. Further, even assuming that sometimes we do imitate or match pitch, as in singing, this must involve identifying what is thus imitated or matched. Hence,  some notion of identification is involved in matching or imitating the pitch of a heard sound also in singing. Why, then, isn't that considered evidence for AP? So, if experience can account for SPD, it must be in a very complicated and roundabout way. We still need to be more specific on what is involved.

Roughly, the answer we shall propose is rooted in the notion of identification alluded to above, which, as exemplified in AP, I shall argue, is a conceptually rich one. The tone is identified as belonging to a tonal space, bearing specific relations, including metrical ones, to other tones. Repeating a tone or phrase by singing or whistling seems to us natural and direct in a way that does not require the mediation of such rich identification of the tones concerned. To the extent it involves identifying the tones, in this respect it is what we shall call slim identification. Doing it on an instrument, on the other hand, does require such identifying mediation. What the nature and role of such mediatory identification is, and what "natural" means here, are not easy questions, to some aspects of which we shall return later. If correct, even in its general line, this answer supports the view that identifying tones, as exercised in manifestations of AP, is conceptually rich; it is identifying them under a rich network of concepts.

In its regular use, identifying a tone does not mean only being able to repeat it or to attach a name or a label to it. These are not only not necessary, but also not sufficient. Identifying a tone involves also knowing its position and role in a certain system or space of tones, their properties and relations, such as, some intervals, scales, basic chords, and harmonic functions. This, as we shall see below, is true of many other cases of identification, even those involved in manifesting AP.  For example, where pianists are concerned, it applies also to knowing special places and spatial relations on the keyboard, or, for violinists, on strings. Such knowledge may be regarded as part of what identifying a note-key on the piano, or a position on the string, means.

3.  Examples of rich and slim Identification

In order to clarify this, let us think of the following example. Imagine someone who, when seeing a box of matches spread on the table and asked how many they are, says immediately fifty-seven, and, with another box, sixty-five. Suppose both are correct, and that this is also the case in many other instances. However, when asked which box contains more matches, or which of the numbers is bigger, our savant hasn't an idea of what is asked for, or gives correct and wrong answers at random. Would we say the savant identified the numbers of matches? I think we would not, as knowing that the first box contained less matches than the second seems a necessary condition for ascribing him such identification; or, at least we should distinguish between a slim and a rich notion of identification, where in its regular use identification is fairly rich.

I leave "fairly rich" in its vagueness, for it is obviously hard to tell, in advance, which of the infinitely many mathematical relations between these two numbers he or she should know. This is something we would usually determine according to specific aims and other pragmatic factors of the situation. But for our regular notion of identifying numbers, one should evidently know some, like that sixty-five is bigger than fifty-seven, that it is the following natural number of sixty-four, and so on. Slim or crude identification is identification with minimal conceptualization, where "minimal" is again left rather vague. It can be manifested, for example, in pointing at "the object out there," or in mere labeling, as in uttering "fifty-seven" in the above example. With regard to tones, it can be manifested by uttering a name or a label like "middle D," "F," or even in specifying a wave length like "245 Herz." According to a common, and by now perhaps outmoded, conception, any identification is based on a crude identification to which a concept may be attached. I find this wrong and try to demonstrate it with the case of AP.

Likewise, we should distinguish between a slim and a rich notion of identification in many other cases, including that involved in AP. In spite of the fact that we can think of criteria for a crude identification of the pitch of a sound as an acoustic phenomenon, for example, in uttering a label, or in matching it or repeating it in singing or whistling, when such identification is slim and detached from knowing the relevant space of relations, it is very doubtful whether we would regard it as identifying a tone in the fairly rich sense required. On the other hand, it is evident that knowing this space, with its properties and relations, is not sufficient for the identification concerned. It is nevertheless important to bear in mind that these conditions, not being sufficient, are still relevant and perhaps necessary for the identification concerned. It should be noted that rich identification, involving as it does knowledge of various concepts and relations, is still identification of a particular, a tone, a number, and so on. It is rich in that what is identified is not a bare sound, not even a particular pitch, but is conceived under these concepts and relations. This is what slim identification lacks.[9]

These considerations about the nature of the identification concerned are connected with a central problem in the philosophy of music and its ontology, namely, what is the nature of (musical) tones. We shall not discuss this here but point out that a musical tone, to be distinguished from mere sound, is conceptually rich. It is not a crude acoustic event but an acoustic event, under a particular description that expresses the concepts in which the tone is conceived and relegates it to a tonal space in which it is conceived. By this I mean that the concepts and relations concerned, which may vary from one musical culture to another, do not form a super-structure imposed on a given array of bare tones but are, rather, constitutive of the tones and their identity.

Some philosophers might express this by saying it is an intensional entity.[10] The claim made here about the conceptual richness of the identification of tones squares with this intensional conception of tones. This notion of rich identification of tones is very important, in fact, crucial, for music comprehension, understanding, and evaluating musical pieces. These always involve concepts and hearing under concepts, even when people are unaware of it and don't know the customary names for these concepts. Some are technical, like phrase, period, tonic, dominant, inverse, stretto, and so on, while some are more general, like tension and relaxation, movement, peak, and so on.

Many people ascribe to AP much significance in musical activity and music comprehension and education. Many musicians possess it, and the rate of people with AP among musicians is much higher than in the general population, which is about 1:10,000. It is quite certain that up to a certain, and good, degree, AP is an acquirable ability, and the likelihood of acquiring it, with moderate training, up to the age of about nine is good and much higher than later on. Currently, there are courses and books devoted to teaching and bringing music students to acquire AP.  Many of the great composers had AP, and many professional performers and musicians have it.[11] From all this it seems that there is a strong connection between AP and musical talent. On the other hand, besides the fact that many excellent musicians don’t posses AP, it is claimed that the rate of people having AP among speakers of tone-language, such as Mandarin Chinese and some others, in which the pitch of a spoken word or phoneme is semantically significant, is especially high.[12] This has nothing to do with musicality, but the linguistic phenomenon, not less than the musical one, is a case of rich identification, in which the identified particulars are conceived in a system of concepts and relations.

4.  AP and experiencing concepts and relations

My central claim in this connection is that AP, when conceived with a slim notion of identification of a crude tone, detached from the tone-space and its relations, if meaningful at all, is insignificant for music comprehension and may even be a hindrance to it.[13] In order to see this and the significance of “in itself” in the above formulation, let us sharpen and enhance the above consideration about slim identification. Consider someone having slim AP but being interval deaf. Upon hearing the notes C-E and G-B, he or she is unable to hear and to experience it as the same interval. He or she might say it is the same interval and respond appropriately to various tasks but will not hear it. He or she can perhaps figure it out or derive it on the basis of identifying the four tones and knowing some elementary theory, and then figuring out that these must have been two instances of a major third, but will not hear it. His or her responses to it will differ, perhaps being slower, from responses to things he or she hears.[14] But evidently, such hearing and experiencing are what is important for music comprehension and understanding: to hear and to experience the identity of the interval, not to calculate it or derive it from other things one hears.

This might be likened to someone having an absolute sense of length or height. On seeing an object, such as a person, tree, house, and so on, a person can immediately say its height. We can imagine, however, that such a savant will not see height or length relations. He or she will not be able to see that A is higher or longer than B. He will see A, and B, know immediately their heights, and then derive or figure out that the one is higher than the other by knowing that A is, say, 1.87 meters and B is 1.76, and knowing that the first number is bigger than the second. I think we would all agree that something is defective in his or her sight – he or she doesn't see what we do – though he or she can respond correctly and behave generally like us.

We can likewise imagine something similar with respect to colors. Most of us seem to have an "absolute sight" of some colors. Imagine someone who identifies colors well but cannot see, for example, that yellow is brighter than blue. He or she can figure it out by identifying the colors and knowing some theory about colors but cannot see and feel it. I think we should say that such a person’s visual perception is different from ours and doubt whether he or she sees, for example, a Kandinsky's picture as we do.[15]

Likewise, our interval deaf person can hardly be said to hear music; definitely not like us. In fact, he or she will also not hear, upon our playing twice C-E, that this is the same interval. He or she won't even understand our question whether he or she hears the same interval. Again, such a person may figure it out by identifying, in a slim way, the four notes separately but not hear the intervals. He or she can hardly, therefore, be said to have our notion of an interval. More than that, we can imagine this person not being able to identify a tone; he or she may not hear the tonal identity of two tokens of the same tone. Upon hearing middle C twice, he or she will not hear it as the same tone but derive it or figure it out by identifying each as middle C.

This difference between experiencing, for example, tone-intervals, color relations, height relations, and so on, and calculating them is an instance of the above distinction between identifying-under-concepts and knowing about. Tones are conceived and identified under concepts and relations as involved in hearing, for example, intervals. They are not crudely identified as bare objects, which is then somehow attached to knowledge about them. And what we have said about intervals is true of actually most musical concepts. We can imagine someone with AP who is unable to hear tonality, though he or she may figure it out or derive it on the basis of some theoretical knowledge from identifying the tones. He or she would not hear harmonic relations like the one between tonic and dominant, would not hear the difference between a consonance and a dissonance and various kinds of musical tension, and would not hear modulations, cadences, sequences, transpositions, and so on.[16] All these he or she may figure out or calculate by identifying tones but not hear them or experience them.[17]

But, to repeat, such hearing and experiencing is what hearing music is all about. One who is deprived of this does not hear music, in the normal sense, and does not experience it, though he or she may know, by way of figuring out and deriving, much of what we know. Having said all that, we must re-emphasize that when AP involves rich identification, this is not confined to perceiving relations like the above but is identifying the tones themselves under some concepts and relations. So, with such AP one does not only hear, for example, a major third but identifies the tones comprising it.

We have brought these various thought-experiments of deafness in order to sharpen and emphasize important factors of our musical hearing, of which the deaf concerned is deprived. AP, in the slim sense of identifying a crude tone, is compatible with these kinds of deafness. In fact, it is not very different from the ability to identify music notes on paper. And here, as there, we can imagine such an ability to be detached from solfeggio ability, from any ability to fancy or know how the notes concerned would sound. Such crude identifying ability is possessed at a certain stage, by any kid beginning to read notes. He or she sees a note, a sign on a stave, and says C, sees another note and says E, and so on. We can imagine him or her at this stage to know nothing about how the notes would sound, how would the interval between them sound, which one would sound higher, and so on. Such a kid, supposing him or her to be especially bright and knowledgeable, may figure out these things, may figure out which tone is higher, how is the interval between them called, when such intervals are equal, and so on. But by our supposition, he or she will not experience these, will not have an "inner hearing" of them, and will not know how they should sound.[18] In principle, AP, in the slim, crude sense of identification, is no different from such identification of notes except that instead of the eyes one uses the ears.

Let me emphasize again that these things are not meant to be true of persons with AP and of their musical experiences. Their aim is, rather, conceptual: to reduce the slim, crude sense of identification and a notion of AP based on this to the point of absurdity, in which it looks inappropriate and hardly intelligible, in order to sharpen and bring to the fore essential elements of our notion of a musical tone and of musical hearing and music comprehension. Chief among them are the following: 1) The recognition that a musical tone and its identification are rich concepts involving experiential knowledge of its location and status in a tone-space with its properties and relations; and 2) The recognition that hearing and comprehending music consist in hearing and experiencing, as opposed to figuring out, calculating, and deriving, the musical concepts and relations concerned. AP, under the rich notion of identification, can accompany and even enhance this but is not necessary for it. Under a slim notion of identification, if intelligible at all, AP is neither necessary nor sufficient for it, and hardly relevant.

These considerations support the general philosophical view that it is a mistake to conceive of perceptual identification as crude identification of a particular plus derived knowledge about it. It is, rather, identification of the particular under or in a system of concepts experienced by the identifier. I cannot indulge here in a detailed discussion of what identifying something under a concept is but will just express my hope that the above considerations show that it need not be identifying a bare “it” plus applying the concept to it. Therefore, I don't think that the rich concept is necessarily built on the slim one. Moreover, the rich notion of identification, with the experiencing and feeling of the concepts and relations involved, whether technical musical ones or more general, common ones, as explained above, is directly connected to the expressiveness of music and to the aesthetic appreciation of a piece of music as a piece of art.

5.  SPD and sense modalities

On the basis of the above considerations, we may come back to the SPD problem posed above, why singing, or whistling, a heard tone is easy and not considered evidence of AP while repeating it on an instrument is. I suggested, in brief, that the latter involves and depends on a rich identification of the tone that the former does not. As noted above, one may still protest that the former also involves some kind of identification, exactly that which is expressed by matching or repeating the tone in singing. One may go even further and ask what does identification have to do with the difficulty at question? In response, let me emphasize again that the gist of the above considerations is that our regular notions of a musical tone and of identifying tones are rich concepts that involve perceiving tones in a system of properties and relations, including even sort of a metrics over the tones, for example the regular diatonic system. The difficulty in repeating a tone or phrase in another system, in another medium, such as the spatial dimensions of the piano keyboard, is therefore a difficulty in mapping this system into the new medium. This is why the rich notion of identification is required here, and this is why passing between them may be difficult. In singing, on the other hand, it is doubtful whether there is such mapping, and even if there is, the relevant system is so close to the one involved in hearing, and the congruence between them is so readily accessible, that we hardly feel a difficulty in passing from one to the other, and identification in the rich sense is therefore not required.

Perceptual or sense modality is also important here, especially the difference between hearing and seeing. When the two systems, the origin and the target, are both seen, the congruence between them may be readily accessible. Therefore, assuming that passing between the two involves some sort of mapping, it is relatively easy. This can explain why, for a trained pianist, playing on the piano from a score, that is, repeating on the piano what is seen in the score, is relatively easy in comparison with playing what is heard, and does not require AP. The score and the piano keyboard are both spatial systems, and the congruence between them is easily mastered. Passing between them does not require AP. A kid beginning to learn to play the piano learns to map the visual notational system to the visual spatial system of the keyboard.  Although this evidently involves some sort of identification, as he may even know the names of the notes, it has nothing to do with AP and with the identification involved in it.

On the other hand, hearing a tone or a melody is a different perceptual modality, and heard tones form a system whose congruence with the spatial one of the keyboard is much harder to grasp and less accessible. Since such passing, say, between heard tones and the piano keyboard or the notational system involves the mapping of systems, it requires a rich notion of identification and the corresponding AP. Likewise, this can explain why singing from a score in the correct pitch is difficult and may require AP. For whatever the sense modality of sung tones is, it is probably very different from the seen notational system. By the same token, repeating in singing a heard tone or phrase need not require AP, for it involves mapping closely congruent systems in the same or in very close perceptual modalities.[19]

SPD and its related problems indicated above, and the distinction between the slim and the rich notions of identification of tones alluded to above, are apparently different issues, each calling for explanation in any serious treatment of AP. They both stand on their own merits independent of our speculation about the sense-modalities and their relative congruence, even if this speculation is rejected. This speculation, however, has the merit of connecting them in suggesting that the latter is a clue to the former.      

6.  Conclusion

We may conclude our discussion by saying that the tone-identification involved in AP has two characteristic facets. 1) It is not crude identification of the pitch of a tone as an acoustic phenomenon but a rich concept in which a tone is perceived in a tone-space with its properties and relations. 2) It is manifested in the ability to pass between different sense modalities, in particular, seeing and hearing, that is, in the ability to map, in an easily accessible way, the heard tone-system into the visual spatial one. Identification in the same sense modality, or in close ones, may not depend on such rich identification and is therefore not evidence of AP. But let it be noticed again that, be the case with SPD and its explanation what it may, the main point about AP involving a rich notion of identification remains. The hypothesis about SPD gives it support but it is not dependent on this hypothesis.


Gilead Bar-Elli

Prof. (emeritus) of Philosophy, The Hebrew University, Jerusalem

Main fields of research: Classical analytic philosophy (Frege, Russell, Wittgenstein), logic, classical music, Judaism. Recent relevant article: "On the Aesthetic Value of Performing Music," forthcoming in Journal of Aesthetic Education, Spring 2017. For other publications see: http://Bar-Elli.co.il  and  http://pluto.huji.ac.il/~barelli/

Published on November 1, 2016.

End Notes

[1] I shall use "tone" for a heard sound and "note" for a customary sign for it.

[2] Pitch, along with volume, timbre and duration, is often presented as a property of tones. This may be misleading in many ways, but even if one chooses to talk this way, it should be noticed that pitch is an essential property of tones, or that tones supervene on their pitches, in a way that timbre, volume, and duration do not. Change of pitch, unless very slight, is change of tone, while change of volume, even when significant, is not. I shall therefore not be strict on distinguishing identifying tones from identifying their pitch. This also accords with the way musicians usually talk of tone-identification.

[3] A very useful compilation on this, with a helpful introduction, is M. Nudds and C. O'Callaghan, Sounds & Perception (Oxford, 2009).

[4] Readers familiar with P. Strawson's Individuals (Methuen, 1959) should notice that I am not concerned with identifying, or re-identifying,  tones as particulars in his sense. Tones in my use are closer to his universals or "thin particulars" (see, for example, p. 70, and the whole of chapter 2); and even more so to Scruton's "secondary objects;" see chapters 1 and 2 of his The Aesthetics of Music (Oxford, 1997).

[5] I personally like to think of it in the context of a Fregean theory of sense, and prefer talking there of "identifying under a sense," for, evidently "concept" is not used here in the Fregean sense. But I shall not pursue this here.

[6] In recent researches it has been found that super-recognizers, who show fantastic abilities in identifying faces, do about normal when shown faces in inverted positions. See R. Russell, B. Duchaine, K. Nakayama, "Super-recognizers: People with Extraordinary Face Recognition Ability," Psychonomic Bulletin & Review,2009, 16 (2) 252-257. This is not strictly relevant to our case of AP, but in a remote way it may support the claim that the pertinent notions of identification are imbued with a conceptual framework. Super-recognizers identify faces given as such, as faces in their normal position, and when inverted or distorted they lose this face-aspect.

[7] On some of the empirical findings and speculations, see: D.J. Levitin & W.E. Rogers, "Absolute Pitch: Perception, Coding and Controversies," Trends in Cognitive Science, vol, 9 no. 1, (January, 2005). On some aspects of the relationship between AP and memory, see also, Judy Plantinga and Laurel J. Trainor, "Infants' Memory for Isolated Tones and the Effects of Interference," Music Perception, Vol. 26, No. 2, (December, 2008), 121-127.

[8] I hope SPD doesn't sound like asking why skiing is harder than walking. But there is no analogy. SPD is about the easiness of repeating a heard tone in singing in comparison to repeating it on, say, the violin, even by a proficient player. The difficulty it asks about is somewhat analogous to one we would have faced if a proficient typist would find it much harder to repeat a heard word in typing than in speaking, "somewhat" because there are differences that even make SPD more acute).

[9] I shall not delve on the question of whether the talk of absolute pitch is meaningful at all. It certainly may irritate holistic and relativistic ears. I assume it is clear enough for our purposes, for which the fact that it changed in the last 150 years is also indecisive.

[10] See G. Bar-Elli: "A Note on the Substitutivity of Notes," Analysis, vol. 41 (1981), 27-32; R. Scruton: The Aesthetics of Music (Oxford, 1982), chs. 1-2.

[11] The data here is inconclusive. Recently there seems to be a vogue of discovering great musicians who lacked AP. For example, in an internet article, E. Gold, admitting himself to lack it, remains indecisive about Bach and Handel but relates, (on personal acquaintance), that Bernstein and Stravinsky lacked it, and says that Schumann Wagner and  Horowitz very probably lacked it, and that it is doubtful whether Haydn, Brahms, Ravel, and Mahler possessed it.

[12] Though some experiments may cast doubt on that. See, "Is There an Asian Advantage for Pitch Memory?" Music Perception, Vol. 25, No. 3 (February, 2008), 241-252.

[13] As is well known, AP can be a hindrance in transpositions or when performing on an out of tune instrument, but this is not my point here.

[14] This is not entirely speculative. For some related experimental data, see Ken'ichi Miyazaki, "Absolute Pitch as an Inability: Identification of Musical Intervals in a Tonal Context," Music Perception, Vol. 11, No. 1 (Fall, 1993),  55-71, where it is argued that some listeners possessing AP are relatively poor in identifying pitch relations in tonal contexts, and sometimes tend to stick to absolute pitch even in a task that needs relative pitch, resulting in poor performance in perceiving musical pitch relations. Miyazaki evidently assumes AP with a slim notion of identification, whose appropriateness is questioned by our argument.

[15] See Part I of Wittgenstein's Remarks on Colour (University of California Press, 1978), where various deviations and failures in grasping the logic of color words, though not this one, are considered.

[16] These, though presented here as thought-experiments, are not entirely hypothetical. In the above paper, Levitin and Rogers cite researches according to which persons with AP did very poorly, in comparison to others, in recognizing sequences and transpositions of simple phrases. See also Myazaki's paper cited above.

[17] In various reports of savants, for example, Daniel Tammet, and about them the situation is almost the opposite; various exceptional mathematical and cognitive abilities are described by them as sense perceptions.

[18] For a philosophical background and elaboration of this difference between experiencing and figuring out, with reference to Wittgenstein's late writings, see G. Bar-Elli, "Wittgenstein on the Experience of Meaning and the Meaning of Music," Philosophical Investigations, vol. 29/3 (July, 2006), 217-249.

[19] I don't know how to define this and must leave it to the mercy of intuitive understanding. I assume that the sense modality involved in singing is much closer to the auditory than to the visual one, in somewhat like the way in which the tactual sense is closer to the visual than to other modalities.