Control of a continuous response dimension by a continuous stimulus dimension.

Researchers taught pigeons to peck a rod that could move left or right.

Each position matched a different tone pitch.

They then tested if birds would peck halfway for tones they had never heard.

The pigeons only matched the exact tones used in training.

When new, in-between tones played, the birds did not move the rod halfway.

Simple generalization did not create smooth control across the pitch range.

Neuringer (1973) showed the same flat control after presence-absence training with click rates.

Together, the two papers warn that reinforcing only one end of a sound dimension is not enough.

SLOANE (1964) had already found that adding extra S- stimuli along a flicker continuum can shift gradients, hinting that intermediate training points may be required.

Crowley (1979) later argued that gradients are really blends of separate, reinforced response classes, giving a mechanical reason for the gaps G et al. saw.

If you want a learner to respond smoothly across a range—say, matching voice volume to room noise—train several points in the middle, not just the extremes.

Without those intermediate teaching steps, expect flat or bumpy performance, not the neat slope you pictured.