This is kind of fun for me because it as one of the first bits of physics I distinctly figured out for myself. The doppler shift of sound is detectable to the ear because the emitter of the sound; i.e., a horn, emits only a narrow band of the frequencies that we can perceive, while the red and blue shifting of light is not detectable because the emitter of light; i.e. a star, emits a much wider band than the eye can perceive. As a bit of blue light moves toward the violet, and beyond our perception, a bit of green moves toward the blue. This same fill in effect applies all the way down the line where red moving to orange is replaced by infrared moving to red, and into our perception. A horn emitting a range of frequencies between 500-750 Hz can shift a long way in either direction before it moves beyond the ears normal range of 20-20,000 Hz.
Hey, thanks lyx2no, I'd never thought about that. I'm happy to have learned a little something.