Exponents differ across sensory modalities

What it is

The exponent in Stevens' power law is not a constant. Brightness, loudness, length, area, and weight have different subjective-to-physical mappings, so an exponent from one sensory modality cannot predict perceived multiples in another.

Why it happens

Receptor coding, dynamic range, and central integration differ by sense. The same physical ratio can be compressed in one modality and expanded in another. Within vision, length, area, colour, and motion do not share one subjective scale.

Stevens split sensory continua into two classes to explain this systematic pattern. Prothetic continua (loudness, brightness, electric shock) encode intensity by summing neural response, which saturates and compresses, pushing exponents well away from one. Metathetic continua (pitch, spatial position) instead encode by substitution across different neural channels rather than summed intensity; their subjective scales run closer to linear, ratio judgments ("twice as much") fit them poorly, and interval rather than ratio scaling is used to describe them. A handful of prothetic exponents are still cited as reference points: loudness around 0.6, brightness around 0.33, electric shock around 3.5, apparent length around 1.0 — the spread itself shows that modality does not just loosely correlate with exponent, it predicts it systematically once continua are sorted by type.

Studying it

Measure each target channel independently over its real presentation range using magnitude estimation, pair comparison, or matching. Control reference and background, and prevent co-varying cues from supplying another dimension. State modality, device, and range, otherwise an exponent is not reusable.

Cross-modality matching gives a more direct check: observers adjust the intensity of one channel (say, hand grip force) to match a given intensity on another (say, a tone's loudness), with no number ever entering as an intermediary. If exponents obtained separately for each channel predict the matching results consistently, both measurements are likely sound; a mismatch points to a problem with instructions or stimulus range on one side, rather than to some special property of the channel itself.

Where it stops holding

Modalities are not isolated: colour changes brightness judgments and sound and image can interact. Semantic goals can override low-level differences. Validate actual identification and comparison tasks rather than inferring experience from a published exponent.

Metathetic dimensions such as pitch or spatial position resist a clean exponent description in the first place — their subjective scales were never built from ratio judgments, so forcing a Stevens exponent onto them and comparing its compression to loudness or brightness applies the wrong framework. Interface dimensions like position or rank order behave more like metathetic continua; encoding decisions for them should follow ordering and discriminability, not the compression logic that governs intensity-type channels.

Related

• Same group: B1.09.1 Subjective intensity follows a power function of physical intensity · B1.09.3 Data encoded by area and volume can be systematically underestimated
• Nearby: B1.08 Weber's law · B1.07 Power law of practice
• Search terms: Stevens' power law · sensory modality · psychophysical exponent