Pitch is perceived logarithmically so the keyboard maps log-frequency to linear distance

Evidence

Musical scales are by nature exponential. For example, going up by octaves increases the frequency exponentially: the frequency of the kth octave above f is 2kf. To stretch scales in a way that changes the octave, we had better use an exponential rather than a linear scaling. The approach is to rule the rubber strip logarithmically and then stretch it. Recall that musical notation and the keys on a piano are logarithmic: distance vertically on the musical scale and along the keyboard is the logarithm of the frequency. — Eric J. Heller, Why You Hear What You Hear- An…, 2410

Categorization

• DEFINE: Defines the logarithmic basis of musical scales — keyboard and staff positions encode log frequency, which is why exponential stretching changes intervals.
• XREF: Connects to the rubber-sheet stretching thought experiment in the prior paragraph (2409) and to prior discussion of equal temperament in earlier chapters.