Frequency perception requires logarithmic measure because octaves multiply by factors of two.

Evidence

Of course, the subject of frequency will come up again and again in connection with dissonance and temperament. Absolute frequencies and frequency differences are self-evident quantities, but frequencies go up exponentially on the linear musical scale since going up N octaves above a fundamental is a factor of 2N higher in frequency. We need logarithmic measures of frequency or frequency deviations. The measure used universally is cents (defined in section 23.18). — Eric J. Heller, Why You Hear What You Hear- An…, 2318

Categorization

• DEFINE: Explains why cents (logarithmic frequency units) are the universal measure in music - because frequencies double per octave, perception is logarithmic.
• XREF: Relates to psychoacoustic principle that pitch perception is roughly logarithmic (Weber-Fechner style scaling), as seen in previous chapters on the soundscape.