Crickets chirp (mostly a single kind of chirp) while Cicadas grind. The grinding lasts for half a minute or so, and they rhythmically pulsate the frequency, ending in a descending slowing of the grinding. Like a long WEEEEhoooWEEEEhoooWEEEEEeeee...
I enjoy the sound of crickets and cicadas (which are much louder) except for the one particular kind of cicadas we get occasionally in Texas that make a singular unwavering high pitched ambient buzzing sound, like the whine of an old tv cranked to 11, coming from everywhere. It's a horribly unpleasant sound, but thankfully they don't stick around long. The other cicada sounds are nice.