I have started a project to describe and share my analog electronic circuits designs so that people can better understand my electronic practice. My project, located on Hackaday.io, is called “Hacking Nature’s Musicians.” You can find it here: https://hackaday.io/project/161443-hacking-natures-musicians
In a recent project log, I describe how I create chirping crickets using discrete transistors. Check it out: https://hackaday.io/project/161443-hacking-natures-musicians/log/153312-crickets-natures-favorite-astable-multivibrator
This video is designed to show you the elements of a cricket's song. In the beginning, you will hear a steady, unbroken ringing. This is created by a transistor astable multivibrator with relatively small capacitor values (both are 2.2 uF in this example). The resulting oscillation goes through a simple high-pass filter and transistor amplifier to a custom 2.8KHz piezo electric speaker (in the background - details available on Hackaday under my project "Hacking Nature's Musicians").
Next, I unplug the base resistor of a transistor in the astable multivibrator (==silence) and connect the base to a signal incoming from another, slower astable multivibrator. The cricket starts to chirp. It's that simple: an astable multivibrator that generates timber connected to an astable multivibrator that controls tempo.
Finally, I add a pull-up resistor on the same transistor base just to show you how it affects the sound. Minor adjustments to this design will give you many variations on the theme (crickets with personality).