I took the linked sound of the Cuban cricket and slowed it down a couple of ways.
Mainly, in SoundHack, I changed the sample header, so that it simply plays back very slow. Then I recorded that Systems audio.
https://app.box.com/s/2oeu3ym5q97hcz2brlmv6d675oezaynw
I imported the sound into the sampler instrument that goes with my sequencer, and played back the sound progressively lower, to give a feel for how it changes.
https://app.box.com/s/2v83j89mva6pkhnsilosw1twsvld3lvy
comments: Different chirps have different shapes overall. This one has a sort of 3-part structure.
0-40 sec quietest (2-part structure sometimes, longer-short, warble) Part 1
40-1:20 tiny bit louder (less warble, more even, moving to upward rise2) Part 2
1:30-2:25 louder (warble up by minor third max occasionally) (-2cnd down) Part 3
2:25-4:00 loudest plateau (also pitch up overall by maj 2cnd max)
eta: The "warble" is a little minor-3rd trill, mostly.
A slowed-down clean recording would show that a sound is made by an animal so it's more likely to have these kinds of small variations in structure than a machine (old-school machine, that is) would.