Musical scales are exponential, so changing the octave needs logarithmic scaling

Evidence

A doubling (or halving) of a value anywhere on a logarithmic frequency scale is equivalent perceptually to a raising (or lowering) by a musical inter­ val of one octave, and multiplying by 32 (or by 23 ) is equivalent perceptu­ ally to a raising (or lowering) by a musical interval of a perfect fifth, and so on. We perceive a given musical interval (octave, perfect fifth, perfect fourth, major third, etc.) as being similar no matter where in the frequency range it occurs. For example, a two-note chord a major sixth apart whether played on two double basses or two flutes gives a similar perception of the musical interval. In this way, the logarithmic nature of the place analysis mechanism provides a basis for understanding the nature of our perception of musical intervals and of musical pitch. — David Howard, Jamie Angus, coustics and Psychoacoustics, 823 (#expands, via linked claim)

Categorization

• XREF: connects to: The cent divides the octave into equal logarithmic frequency steps; The mel scale conflicts with musical logarithmic scales but remains useful in technical applications; Whether combination tones are musical depends on the tuning system (+5 more)

Broader Connections

• The mel scale conflicts with musical logarithmic scales but remains useful in technical applications #complicates (0.80)
• The cochlea’s logarithmic place analysis explains why musical intervals sound the same across registers. #expands (0.80) — David Howard, Jamie Angus, coustics and Psychoacoustics, 823
• Whether combination tones are musical depends on the tuning system #complicates (0.72)