Whether or not someone has “perfect pitch” (sometimes called “absolute pitch”) is a debatable issue as this talent has to be tested in a number of ways. By definition, perfect pitch means being able to recognize a tone instantaneously simply by hearing it (without any reference such as a pitch pipe or a particular note on a piano or other instrument). In other words, if you play a note on the piano, someone with perfect pitch will be able to identify that note (be it an F, G#, Bb, etc.) without being told it’s name. Further, they should be able to identify that note without hearing (or knowing the name of) any other note. It is also assumed that someone with perfect pitch also has the ability to recognize the tone (note in music) of door bells, the ringing of a telephone, or the beeping of a microwave. Other ways someone can display perfect pitch are naming the key of a certain piece of music or identifying a particular chord and all the notes in that chord.
Studies of this phenomena are still being carried out but most feel that perfect pitch comes from both musical training and a genetic predisposition as it seems to run in families (though not as prominently as facial features or height and weight).
There are those that profess the ability to teach perfect pitch to anyone but the prevailing opinion is this is not true. Further, there is debate about the purpose and importance of having (and applying) the skill. Even for a working musician, perfect pitch is not a great aid to their performance.
Relative pitch is the difference between two notes (pitches) with one note (the first note played) being the reference. With a certain amount of musical training, some will be able to accurately sing a note compared to a reference note. For example, the note E is a whole step above the note D. If one is told the note being played is a D, they may be able to sing an E (the note one “step” above a D).
Some that show this skill admit to thinking of relative pitch as based on the mathematics of music. In other words, as above, the note E is one step above D, where F# is one step above E (making F# two steps above D). Using an octave as a reference point is also thought as part of the mathematics of music and can help find a pitch.
Relative pitch is very important when it comes to forming chords. The notes in a chord are relative to each other (as intervals) and its this relation that gives the chord its unique sound. For example, if the musician hears the root (note) of a chord, they can play or sing the other notes in the chord.
Sight reading can also be aided by understanding relative pitches. Many musicians, when seeing a group (or series) of notes on sheet music can (in their head) sing or play the notes. A good sight reader typically learns a piece much faster than some without the skill.