Why Human Hearing Is Logarithmic: From Hz to Perception
Human hearing exhibits a nonlinear response to both frequency and amplitude. While physical signals are measured on linear scales, our perception operates approximately on logarithmic scales.
This distinction is critical in engineering fields such as
- Audio signal processing
- Acoustic measurement (NVH)
- Speech recognition
- Audio compression
Understanding how humans perceive sound allows engineers to design systems that align with perception rather than raw physical quantities.
Frequency Perception: Linear in Physics, Logarithmic in Perception
Although frequency is measured in Hertz (Hz), human perception of pitch follows a logarithmic pattern.
This means
- Equal ratios in frequency are perceived as equal pitch intervals
- Not equal differences
For example
- 100 Hz → 200 Hz (×2)
- 1000 Hz → 2000 Hz (×2)
Both are perceived as similar pitch steps, even though the absolute difference is very different.
Why This Happens
The human auditory system, particularly the cochlea, processes frequency in a nonlinear way.
- Lower frequencies are resolved with higher precision
- Higher frequencies are compressed perceptually
This leads to perception being based on frequency ratios rather than absolute differences
Perceptual Frequency Scales
To model human perception, several perceptual scales are used
| Band | Description | Application |
|---|
| Octave band | Based on doubling of frequency | Music, acoustics |
| Mel band | Perceptually uniform pitch scale | Speech processing |
| Bark band | Based on critical bands of hearing | Psychoacoustics |
Mathematical Insight
1-Octave scale: based on double of frequency
Amplitude Perception: Loudness is Logarithmic
Just like frequency, amplitude perception is also logarithmic.
Loudness is approximately proportional to
This is why sound levels are measured in decibels (dB), not linear amplitude.
Practical Meaning
- Doubling amplitude does not double perceived loudness
- A 10× increase in power corresponds to a fixed increase in dB
This makes logarithmic scaling far more suitable for representing human hearing.
Practical Implications in Engineering
This logarithmic perception directly affects system design.
Audio Compression (MP3, AAC)
- High-frequency components can be compressed more aggressively
- Based on reduced perceptual sensitivity
Speech Processing
- Mel-Frequency Cepstral Coefficients (MFCC) rely on Mel scaling
Equalization and Mixing
- EQ bands are spaced logarithmically
- Matching perceptual resolution
NVH and Acoustic Analysis
- Human perception must be considered alongside physical measurements
MALMIJAL Example: Octave Band Analysis
Linear vs Logarithmic Scale in 1-Octave Band
PSD (Linear frequency scale)
PSD (Power Spectral Density) of white noise in dB/Hz
1/3-octave Band (Logarithmic frequency scale)
A-weighted 1/3-octave band level in dBA
1-octave Band (Logarithmic frequency scale)
A-weighted 1-octave band level in dBA
Comparison of 1-Octave and 1/3-Octave Band Analysis
1-octave band level is higher than 1/3-octave
Key Insight
Engineering systems that interact with human perception must not rely solely on linear physical measurements.
Instead, they should incorporate perceptual models such as
- Logarithmic scaling
- Mel or Bark transformations
- Decibel representation
Bridging this gap is essential for creating systems that sound correct, not just measure correctly.
Suggested Further Reading
You may also find these topics helpful:
Why Human Hearing Is Logarithmic: From Hz to Perception
Human hearing exhibits a nonlinear response to both frequency and amplitude. While physical signals are measured on linear scales, our perception operates approximately on logarithmic scales.
This distinction is critical in engineering fields such as
Understanding how humans perceive sound allows engineers to design systems that align with perception rather than raw physical quantities.
Frequency Perception: Linear in Physics, Logarithmic in Perception
Although frequency is measured in Hertz (Hz), human perception of pitch follows a logarithmic pattern.
This means
For example
Both are perceived as similar pitch steps, even though the absolute difference is very different.
Why This Happens
The human auditory system, particularly the cochlea, processes frequency in a nonlinear way.
This leads to perception being based on frequency ratios rather than absolute differences
Perceptual Frequency Scales
To model human perception, several perceptual scales are used
Mathematical Insight
1-Octave scale: based on double of frequency
Amplitude Perception: Loudness is Logarithmic
Just like frequency, amplitude perception is also logarithmic.
Loudness is approximately proportional to
This is why sound levels are measured in decibels (dB), not linear amplitude.
Practical Meaning
This makes logarithmic scaling far more suitable for representing human hearing.
Practical Implications in Engineering
This logarithmic perception directly affects system design.
Audio Compression (MP3, AAC)
Speech Processing
Equalization and Mixing
NVH and Acoustic Analysis
MALMIJAL Example: Octave Band Analysis
Linear vs Logarithmic Scale in 1-Octave Band
PSD (Linear frequency scale)
PSD (Power Spectral Density) of white noise in dB/Hz
1/3-octave Band (Logarithmic frequency scale)
1-octave Band (Logarithmic frequency scale)
Comparison of 1-Octave and 1/3-Octave Band Analysis
1-octave band level is higher than 1/3-octave
Key Insight
Engineering systems that interact with human perception must not rely solely on linear physical measurements.
Instead, they should incorporate perceptual models such as
Bridging this gap is essential for creating systems that sound correct, not just measure correctly.
Suggested Further Reading
You may also find these topics helpful: