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In a potentiometer, taper refers to how the resistance varies as the pot's armature is rotated (or, for a slide pot, as its wiper slides; or for a solid state pot like the DS1802, as its input voltage is varied).
For a pot with a linear taper, the resistance varies linearly as the wiper moves.
For a pot with a logarithmic (log) taper, the resistance varies logarithmically with the wiper's motion. When used in an amplifier circuit, the output varies slowly as the pot is operated at the low end and varies more and more rapidly as the pot is operated toward the high end.
This is also called an audio taper because it is most commonly used for audio volume controls. The ear responds logarithmically (each doubling in signal is perceived as an equal step in volume). The ear is more sensitive to changes at lower volumes, so an audio volume control varies the signal slowly at lower settings and more rapidly at higher settings. The net effect is that the sound seems to vary smoothly through the pot's range.
source: Electrical Engineering Glossary
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