Perfect pitch is the ability to identify a note or key without any other musical reference. Only about 1 in 10,000 people have perfect pitch although that number is higher among musicians. In my classes it was something like 1 in 60-100. It is generally associated with musical skill but it does not seem to be a result of training, at least not exclusively, and turns up in people with little or no musical experience as well as musicians. It does make some aspects of music easier (such as writing down music by ear) but it can get in the way of others (such as when a group plays a piece in a different tuning or key than a person with perfect pitch is used to hearing). Some people speculate that it is inherited and some that it is a result of an early musical environment. It is more common for children raised with tonal languages (languages were the pitch changes have meaning) to have perfect pitch but only if they are raised speaking the language. In "The Singing Neanderthals", Steven Mithen mentions a study that suggests all humans are in fact born with perfect pitch but most of us lose the ability as we age. Also when people sing, they usually sing within a whole-step of the key they originally learned the song, with or without musical training. The suggestion he makes is that perfect pitch actually gets in the way of learning languages (all of them, but less for tonal languages) so most of us become more flexible and switch to using some form of relative pitch with a few hanging onto the perfect pitch ability for some reason.
Relative pitch is not the same thing as perfect pitch but at its most refined levels can seem similar. It is the ability to take one note as a starting point and identify or play other notes accurately related to it. This CAN be learned to varying degrees and is part of the focus of ear training classes. One student in a theory class I assisted with had almost never sung in his life, just played instruments. When he began the class, he had a terrible time sight singing and was in danger of failing the class but he could hear that he wasn’t singing things right. He spent a great deal of time practicing, studying and improving his relative pitch sense. By the end of the year, he was almost at the same level as the top 5 students in terms of accuracy which was the point. People with perfect pitch may have good relative pitch without trying but also may have to struggle to learn relative pitch. A friend of mine from college with perfect pitch said that identifying notes on the slightly out of tune piano used in our ear training class was incredibly difficult and showed him that he needed to develop his relative pitch more.
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