Equal frequency ratios occupy equal perceptual distances regardless of starting pitch

Evidence

The use of a logarithmic representation of frequency in perception has the effect of giving equal weight to the frequencies of components analyzed by the hearing system that are in the same ratio. Figure 3.5 shows a number of musical intervals plotted on a logarithmic scale, and in each case they continue up to around the upper useful frequency limit of the hearing system. In this case, they are all related to A1 (f0 = 55 Hz) for convenience. Such a plot could be produced relative to an f0 value for any note, and it is important to notice that the intervals themselves would remain at a constant distance on a given logarithmic scale. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 816

Categorization

Category: Causal Relationships

• XREF: Grounds why the octave (a 2:1 ratio) is perceived as the same interval at any register — connects to how the ear’s log mapping makes musical intervals invariant across pitch.

Related

• Perceived pitch intervals match log-frequency ratios regardless of register (similarity 0.89)
• A fixed frequency ratio always yields equal logarithmic distance at any pitch (similarity 0.88)
• Frequency perception requires logarithmic measure because octaves multiply by factors of two. (similarity 0.85)
• Ratio pitch curve shape matches other psychoacoustic frequency-dependence curves (similarity 0.84)
• Perceived pitch compresses against frequency above roughly 500 Hz (similarity 0.83)
• Pitch is perceived logarithmically so the keyboard maps log-frequency to linear distance (similarity 0.83)
• Logarithmic hearing means equal decibel steps need larger absolute pressure differences (similarity 0.82)
• Perceived frequency differences scale logarithmically, not linearly with Hz (similarity 0.82)
• The same musical interval’s dissonance changes with pitch register (similarity 0.82)
• The cochlea’s logarithmic place analysis explains why musical intervals sound the same across registers. (similarity 0.81)
• The mel scale appears discredited but its underlying effects still hold (similarity 0.81)
• Tonotopic frequency ordering persists from cochlea to auditory cortex (similarity 0.81)
• Semitones are logarithmically equal steps, not linear ones (similarity 0.81)
• Musical scales universally favor intervals with small integer frequency ratios (similarity 0.80)
• Loudness perception is essentially logarithmic (similarity 0.80)