The Super Noisy Regen(erative) radio circuit.

The reason for the 5:1 turns, tuning coil to pickup coil ratio is to protect the tuned circuit from the low base input impedance of Q2 and the variable capacitance of the  junctions of Q1 and Q2 with voltage change. For example transistor datasheets often show the variation of the collector base capacitance with voltage. Such capacitance shifts cause phase noise that can make SSB and CW reception difficult.

The tap on the tuning inductor is primarily there to project against changes in the Q4 base emitter junction capacitor with voltage changes.  Q4's input impedance as the tiny base current (approx. 3 nA) it operates at is very high.