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I have heard that it is a resonance effect stimulating sensory nerves.It occurs when the frequency of the sound vibrations is the same as the inherent frequency of impulses in the nerves.http://en.wikipedia.org/wiki/Resonance
It seems likely that the response would be a result of preventing physical damage. If it was a response in the nerves of the fingertips, it would affect only the person making the noise, but as most everyone has experienced, the sound of fingernails scraping a chalkboard is painful to everyone within earshot. The response probably comes because the frequency of the sound is similar to the sound created by damage to the human body. Perhaps the chalkboard sound is like the sound of bones breaking, specifically the type of break that would come from jumping off of something too high to safely jump off of. Moreover, the slip and stick motion is similar to the feeling of teeth scraping together, or teeth being scraped by something too hard to chew. Perhaps the reaction comes from the need to preserve one's teeth for eating meat.
So why do sounds with frequencies between 1-2 kHz cause the effect? My guess is that the effect is produced by activation of various myogenic reflex responses including the stapedius response, the post-auricular response and responses of other muscles innervated by the facial nerve (and possibly the trigeminal nerve). It so happens that the tuning curves of stapedius motorneurons have their best frequencies between 1-2 kHz with a threshold of about 75 dB in the cat (see Kobler et al. (1992), J. Neurophysiol. 68, 807-817).