I was wondering if there is/are any aural exercise('s), analogous to how playing scales can develop your muscle memory, that can help to develop "Perfect Pitch"?
I think a more realistic goal is to aim for relative pitch; then when you have that, perhaps try for perfect pitch.
Relative pitch is essentially being able to recognise and identify intervals, relative to the root note. Gaining relative pitch is fairly easy, a good way to do it is to pick a simple Major scale ditty, play it, and identify the intervals in it. A good song for this is the Wedding march, R 4 4 4 R 5 4 5 etc.
Then each time you need to figure relative pitch, refer back to the one or more ditties you have stored up. Gradually over time this will become automatic, when it has become automatic, perfect pitch is the next stop.
Perfect pitch is the holy grail for a musician; and is not easily obtainable without a lot of training. It is doable though and I think some of the best training you can do for it is to learn how chords sound and the intervals within those chords; and each time you play/listen to something, think about how it sounds and what is actually going on.
I use David Lucas Burge's method for learning perfect pitch. I know many people who think that perfect pitch is something that cannot be learned, but within a few months of working with this method I have made tremendous progress: I can often recognize certain tones (for example F# and B), without using any kind of reference (i.e., without playing any note on an instrument). I can also sing an A whenever I want (apparently this skill is called Tonal Memory or Aural Recall). The exercises proposed mostly consist in listening and singing the tones.
Pitching in here as someone that does have perfect pitch - however, I'm one of these people who has just always had it rather than sat down and learning it. It's as clear to me that the note being played is say an Ab than the folder currently to my right is green, and always has been. I don't profess to know this from some superhuman effort in training, it's just a trait I have. Nevertheless, a few thoughts.
Firstly, having perfect pitch / absolute pitch isn't something that's required to make you a good musician. Far from it, there are many excellent musicians around with far from a perfect sense of pitch. They all have a good sense of relative pitch in general, which is much more important - but not necessarily perfect.
However, there are things that it can really help with. Dictation is the classic example, especially if you're trying to dictate atonal and experimental pieces by ear, at a pace. Being able to just hear the note and write it down rather than work it out is incredibly useful in this respect. But with that said, there's also situations where it's incredibly detrimental to have perfect pitch. Tuning down to an A at 415Hz to play "authentic" Baroque music is quite frankly awful, on the violin I end up playing everything out unless I'm careful as I naturally try and overreach about a semitone to get out what my ear expects to hear. In similar situations, tuning down to the pitch of a particular organ that didn't sit at 440Hz brings similar nightmares.
So regardless of its usefulness, can it be developed? Or is it just something that you have or don't have? Research in this area is shady and there isn't one definitive way to "learn" it that's agreed on and shouted about by the masses. I don't know anyone who has learnt perfect pitch in this sense either, however I do know someone who, through shear determination of listening to the same note over and over again, was able to identify and produce this note at a whim. Whether this is a "true" definition is up for debate, but in this sense he had perfect pitch - he could produce this note from no relative standpoint, and could then relatively identify other notes from that one. It clearly wasn't as quick or necessarily reliable a process as someone who had the ability naturally, but was above the traditional definition of relative pitch.
So my advice would be that the answer is a definite "maybe" if you're willing to spend long hours listening and practising to get the sort of ability defined above - but I'd carefully consider whether the time you'd need to spend is worth it, when (let's face it) you could be doing something much more interesting!
There is no way that I personally have perfect pitch, but I can offer some suggestions:
Hope this helps in some way
Like most people answering, I don't have perfect pitch but I'm "pitching in" anyway.
There are various interpretations of perfect pitch, one of which could be considered a curse -- to know when a pitch is sharp or flat of a reference pitch you're accustomed to, by an amount that's not a whole number of semitones. Some people would hear a Jimi Hendrix recording -- where everybody's in tune with each other, but nobody used a tuning fork, and wince.
Another interpretation is to be able to name the note when you hear it, without breaking into too much of a sweat if it's a fraction sharp or flat. I'm sure that could be useful.
Other answers have referred to relative pitch. I believe that perception of relative pitches is an essential skill for any musician. You should be able to answer "if this note is C, what note is this" questions. This is a standard aspect of music training, and you can find many answers about it on this site.
Now, if you have a good sense of relative pitch, perfect pitch is simply a matter of having at least one reference pitch in your memory. Consider that if you perpetually hummed an "A" to yourself (and didn't wander off pitch), and had relative pitch skills, you would be able to fake perfect pitch. In fact, I'm not sure it would be fake.
Now take breaks from the humming, but remember the note so you can resume the hum. The longer the breaks, without you resuming at the wrong pitch, the closer you are to having perfect pitch.
But, I don't think it's necessary to do this in order to have something that's as useful as perfect pitch, in a musical context.
In a musical environment -- for example in the middle of a band practice -- there are loads of reference points. The notes you played while tuning up. The notes you played in the last piece. The quiet sounds your instrument makes when you handle it. So you don't need to remember what a note sounds like for very long. With those notes, and your sense of relative pitch, you can again "fake" perfect pitch.
Take a well known tune that's usually played in a specific key.Just sing the first note. I use ( 'cos the wife watches and it's played 4 times in each episode )the theme from Coronation Street (U.K.) .It's a C over an Ab chord .Sing the note just before it's played, and soon you'll (hopefully) be very close. Every time I go past a piano, I sing the C, then check it.There's little point in recognising all notes, as that, or the one you choose, will give you others as they're relative.
I think it is possible. But now I will explain what I mean by 'it'. I also think that most of the research done that points to the contrary has been misguided. Identifying pitches is the same as learning the colors. Yet, very often the two are not approached in the same way. We learn (the names of) colors by first learning to group visible light frequencies in a small set of big groups: the reds, oranges, yellows, greens, blues, those close to indigo, violets. Yet with pitches we struggle from the beginning with a much finer subdivision and in addition a cyclic naming (instead of a linear one) of A,B,C,D,E,F,G plus the sharps. The analogous with colors would be to be trying to learn around 88 colors from the beginning with a naming that is cyclic, in which you would call the same name simultaneously to some reds, oranges, ... according to the ratio of the frequencies. This cyclic naming is particularly hard for learning compared to the linear naming of colors, in which nearby frequencies are called reds until the linear distance is big enough that then you call it the next color (orange).
I am convinced the reason learning PP is hard is more related to the naming of pitches than to the actual nature of the task. It would be equally hard to try to learn, from the beginning (even more if you don't have a young brain) a finer list of names of colors, for example The Wikipedia List of Colors. Even more if the naming is non-linear with respect to the frequencies but in some other ordering that is convenient for other purposes than learning them, for example in the Wikipedia list the names are alphabetized. Alphabetized names is good for searching the name sequentially, when written in English, but as it can be seen it ignores how the color looks like and alphabetically nearby names can be given to colors that don't look alike.
The naming of pitches has been designed to make it convenient for harmonization. This is, such that all sounds that we call A sound good together, and likewise with any sounds we call A with anyone we call C and any we call E. Now, what is useful for harmony is not necessarily ideal for learning.
I believe that if the goal is to learn PP we should try to learn to identify pitches in the same way we learn colors. First by learning a naming convention that is not very fine and gradually improving the subdivision. In addition, a naming convention that is monotonic (in the mathematical sense) in the frequencies i.e. nearby frequencies get nearby names, instead of cyclic would help too. For example divide the piano keyboard in a few big groups of keys. The groups should consist of keys that are one next to each other. For example, the octaves. Then aim first to identify without reference given a sound in which of these groups the sound is. If it is very low you would try to chose the group that is more to the left of the keyboard, etc. You are considered to have given the right answer in that initial level of difficulty if the sound is actually in that group of keys, even if you didn't select the exact right key of the keyboard. Then gradually refine the division of the keyboard into smaller groups and repeat. Of course, there are going to be people that will manage to get further ahead and be able to work with finer division than others and go ahead in the levels of difficulty faster than others.
I don't have perfect pitch, but without reference given a sound I can find a key in a piano that is like that sound not more than three keys apart from what the sound actually is. This means that my ability to identify pitches is, compared to perfect pitches, as what my ability to name colors is compared to naming them in the Wikipedia List of colors scale. I definitely know far less colors than in that list, but I do know more colors than the seven colors we learn at young age.
I think that research that points to the incapacity of learning perfect pitch for older individuals has been misguided because they are asking the wrong question about a skill that is improperly trained, in my opinion, in addition to using a naming convention that is improperly adapted to learning pitch identification.
I have often heard that technique of practicing relative pitch and combining it with the recollection of a reference sound that the person managed to remember. I find this method really awkward. Imagine learning colors that way.
Edit: For completeness let me repeat something that many others have said. For music relative pitch is more useful than perfect pitch. Being in harmony is more important than being able to hit rather exactly a pith without reference. That is why the nomenclature, the naming A,B,C,D,... is well adapted to express being in harmony and not being able to name a particular pitch without reference.