Good question! There is a great deal of debate around this question. In the research, the term Absolute Pitch (AP) is used for the more common term of perfect pitch. This recent study points to a stronger genetic link than previously thought.
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“Keith Schneider and colleagues compared auditory cortex structure and activity of three groups of 20 participants, including AP musicians, non-AP musicians of similar musical expertise, and a control group of individuals with minimal musical training. The AP musicians had a significantly larger auditory cortex capable of representing distinct tones without a reference note.
AP is rare, even among expert musicians, and the relative contribution of genetics and experience to this ability is debated. These findings suggest AP may be more strongly under genetic control than previously thought, given that nearly one-quarter of the AP musicians did not begin musical training until adolescence.”
Check out the article here