The cochlea’s logarithmic place analysis explains why musical intervals sound the same across registers.

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

Categorization

  • DEFINE: Lays out exactly how frequency multiplication maps to perceived interval on the log place-analysis scale.
  • ADDENDUM: Relevant to the ‘Grafting & Growth’ article only in the loose sense of structures as infrastructure; more centrally it grounds the reader’s core psychoacoustics goal.
  • corroborated: 2 independent passages support this claim — David Howard, Jamie Angus, coustics and Psychoacoustics, 823
  • XREF: connects to: Logarithmic hearing means equal decibel steps need larger absolute pressure differences; The cent divides the octave into equal logarithmic frequency steps; Musical scales are exponential, so changing the octave needs logarithmic scaling (+8 more)

Broader Connections