Just copy V5A in this schematic. It doesn't get much simpler than this...http://www.schematicheaven.com/bargainbin/gretsch_6160.pdf
V5A is a phase shift oscillator (sine wave) just like most of the tube tremolo circuits, except the timing resistors and caps are much smaller. It's used as a guitar tuner so the freq is audible. Don't have a clue how wide the range is but that would only be a minor challenge.
You could run the output through another gain stage and then use back to back diodes to clip the sine into a reasonable square wave.