Absolute pitch is the ability to identify the pitch value of a musical note played without any context. Because it is strongly associated with learning and playing music, it tends to be regarded as a musical phenomenon, and the thought follows that maybe if we could understand why some people have the amazing capacity for absolute pitch and most people don't, then we could learn something new about music.
The first thing to notice is that learning to perform music is one situation where a person is typically exposed to particular pitch values and names for those pitch values. So if some people have an ability to develop absolute pitch, learning music is one place where it is going to happen. But this does not imply that absolute pitch perception has anything in particular to do with music perception.
Pitch Translation Invariance
Music has the property that the musical quality of an item of music is essentially unchanged under a pitch translation, which means adding a fixed interval to all the notes in the music. In traditional musical terminology, we would say that a tune transposed into a different key is essentially the "same" tune. I use the expression "pitch translation invariance" to describe this property of music, to emphasise the fact that it is an abstract mathematical symmetry, one of five or maybe six that apply to different components of music perception.
In contrast, and more or less by definition, absolute pitch perception is not pitch translation invariant. So although a capability for absolute pitch is associated with music, because absolute pitch is often learned when learning to play music, actually it has exactly the opposite property of music perception, and therefore the perception of absolute pitch is not part of music perception.
If the mechanisms of absolute pitch are substantially independent of the mechanisms of music perception, then we would predict that the musical tastes of people with absolute pitch would not be significantly different from the musical tastes of anyone else.
As far as I know, this is the case, although I have not verified it by systematically interrogating individuals with absolute pitch. I have certainly never heard of musicians with absolute pitch preferring or performing music that only they like, and that no one else likes. Nor have I heard of musicians without absolute pitch performing music which they like and which musicians with absolute pitch do not like.
The How and Why of Pitch Translation Invariance
When information about sound is received by receptor cells in the ear, it is definitely not pitch translation invariant, because different receptor cells respond differently to different frequencies. (Strictly speaking it is meaningless to talk about "pitch" at this point, because pitch is a value derived from the frequencies of raw sounds as an estimate of the fundamental frequency of a sound that has harmonic frequency components, and this derivation occurs within the brain. However, given the approximate equivalence between "pitch" and "frequency", we can regard "pitch translation" as being equivalent to "frequency translation", or, to be more precise, "log frequency translation".)
Somewhere in the chain of information processing that leads from the ear to those parts of the brain that perceive the musical quality of music, the information being processed must become pitch translation invariant, or to put it another way, information about absolute pitch is "forgotten". If a person has an ability to perceive absolute pitch, that information must be extracted from the processing chain and made available to conscious awareness before those processing steps that produce pitch translation invariant results.
Exactly how pitch translation invariance is achieved is a non-trivial question to answer, and some detailed speculations are contained in Chapter 9 of my book What is Music? Solving a Scientific Mystery.
Whatever the details of the calculations that perform pitch translation invariant perception of music, pitch translation invariance implies the existence of a calibration process, for example to determine that the interval between one pair of pitch values X1 and Y1 is the same as the interval between another pair of pitch values X2 and Y2. In Chapter 12 of my book I develop the hypothesis that this calibration is determined by the perception of consonant intervals, and that the main reason that our brains perceive consonance is to achieve this calibration. This is related to the analysis by Schwartz, Howe and Purves as described in The Statistical Structure of Human Speech Sounds Predicts Musical Universals, although their analysis implicitly presupposes the existence of pitch translation invariant interval perception, thus missing the possibility that the classification of intervals into consonant and dissonant may be how pitch translation invariant interval perception is achieved in the first place.
To answer the "why" question, we must name some biological purpose that is satisfied by the pitch translation invariance of melody perception. The most obvious candidate is that the identification of speech melodies be pitch translation invariant, perhaps to allow for variation in the pitch range of people's voices.
Pitch translation invariance can be regarded as an example of perceptual constancy, where a given perception is robustly invariant, even when subject to varying factors that substantially alter the raw sensory inputs.
An example that has been heavily studied is the constancy of colour perception, where colour perception refers to the colour of objects, in contrast to the colour of light, which is what the raw sensory input consists of.
It turns out that our brains devote substantial machinery to factoring out the effect of ambient light conditions, in order to reliably perceive the colour of objects. This machinery is so effective, that it took scientists a while to realise just what was going on, and how much variation in light conditions the visual system was capable of ignoring.
There is a useful analogy to absolute and "relative" pitch perception, because the perception of object colours depends quite a lot on the "relative" perception of the colours of light, where the overall colours of objects in a region provide an implicit estimate of the colour of ambient light, which in turn enables accurate calculation of the colours of individual objects from the relationship between the perceived colour of light from each object to the perceived colour of light from surrounding objects and surfaces. Relative pitch perception seems to involve a similar "frame of reference", where the set of pitch values in a melody provide a background against which individual pitch values are located by the perceptual machinery. In my book I develop the theory that specific features of music such as scales, chords and home chords are a consequence of the machinery that the brain uses to define this frame of reference and locate individual pitch values within it.
Because almost everyone experiences the pitch translation invariance of musical perception, we simply take it for granted, and we regard absolute pitch perception as being more interesting because it isn't pitch translation invariant.
But a more thorough analysis shows that explaining absolute pitch perception is not particularly hard, whereas explaining pitch translation invariance of musical perception is quite non-trivial.
The implication is that we may learn more about the mechanics of music perception if we investigate pitch translation invariance in more detail, and we should not expect to learn a whole lot about music perception from studying absolute pitch perception, because music perception and absolute pitch perception must necessarily involve distinct processing pathways, and most likely they share only the very earliest stages of auditory processing that occur in the brain.