Continuous change of delay time causes a pitch shift

The way we commonly avoid clicks when changing the amplitude of a sound is to interpolate smoothly sample-by-sample from one gain factor to another, using an object such as line~. Does that same technique work well for making a smooth change from one delay time to another? As it turns out, that's not the best way to get a seamless unnoticeable change from one delay time to another, because changing the delay time gradually will actually cause a pitch shift in the sound.