A single op amp--one of four contained in the popular LM324-- is operating in a variable pulsewidth, free-running squarewave oscillator circuit, with its timed output driving two transistors that control the on/off cycle of the tape-drive motor. The oscillator's positive feedback path holds the secret to the successful operation of the variable on/off timing signal. The two diodes and pulsewidth potentiometer R8 allows the setting of the on and off time, without affecting the oscillator's operating frequency. One diode allows only the discharge current to flow through it and the section of R8 that it's connected to.
The other diode, and its portion of R8, sets the charge time for the timing capacitor, C3. Since the recorder's speed is controlled by the precise off/on timing of the oscillator, a simple voltage-regulator circuit (Q1, R3, and D4) is included. Connecting the speed control to most cassette recorders is a simple matter of digging into the recorder and disconnecting either of the motor's power leads, the ground or common side might be best, and connecting the recorder through a length of small, shielded cable to the control circuit. In some recorders, a remote input jack is furnished to remotely turn on and off the recorder. Before going in and modifying a recorder with a remote jack, try connecting the circuit to the external remote input.