Electronic musical instrument with portamento function

An electronic musical instrument having portamento function comprises playing keys, a musical tone signal generating device, a key depression detection device, and a control device. The key depression detection device detects a displacement of a depressed key. The control device, when a new key depression occurs following a previous key depression, controls, a tone pitch of the musical tone signal generated by the musical tone generation device to change continuously from a tone pitch of the previously depressed key to a tone pitch of the new depressed key in response to displacement of the new depressed key.