lesson
Updated 6 days ago
If you plotted an audio equalizer on a standard linear ruler from 20 Hz to 20,000 Hz, the entire bass range would be crushed into a microscopic 1-millimeter sliver on the left edge.
To give equal visual weight to every musical octave, audio engineers and exam boards use a logarithmic frequency axis paired with a linear decibel grid.
Why does human hearing require this special mathematical grid in the first place?
The Logarithmic Frequency Axis (X-Axis)
The human ear detects sounds from 20 Hz to 20 kHz across ten octaves, where each octave represents a doubling of frequency (20 Hz→40 Hz→80 Hz).
In 1860, psychologist Gustav Fechner formulated the Weber-Fechner Law, proving that human pitch and loudness perception scales proportionally with ratios rather than arithmetic addition.
📊Interactive diagram
How do we divide this axis into clear, standardized sections on an exam paper?
Spacing Decades and Intermediate Gridlines
A decade is a ten-fold multiplication of frequency (10 Hz→100 Hz→1 kHz→10 kHz). Each decade takes up an equal width on the page.
The geometric distance of any frequency f within a decade spanning fstart to fend=10⋅fstart is proportional to log10(fstartf).
For example, the distance from 100 Hz to 200 Hz covers log10(2)≈30.1% of the decade's width, while the step from 800 Hz to 900 Hz occupies only log10(9/8)≈5.1%.
This causes intermediate division lines to compress toward the upper end of each decade. For example, moving from 100 Hz to 200 Hz occupies log10(2)≈30.1% of the decade width, while 800 Hz to 900 Hz takes up only log10(9/8)≈5.1%.