This is an analog circuit that plays a synthesized drum beat. It can be scaled in amount and the quality of the noises.

Step 1: What You Need

1 power source
3 breadboards
Wires (Yellow, Blue, Red, and Other) if you feel like following conventions
2 Speakers
6 OPA551 Op-Amps
2 TL081 Op-Amps
4 2N3904 NPN Transistors
2 10kOhm potentiometers
2 diodes
2 LEDs (optional)
Resistors:
3 200kOhm
6 1kOhm
2 4.4kOhm
1 3.7kOhm
3 1.7kOhm
2 160kOhm
3 5.8kOhm
Capacitors:
4 0.1uF
2 0.047uF

An Oscilloscope for debugging can come in quite useful.
Wire stripper/cutter

Step 2: The Circuit

It all goes together just like this. It's good to note that we only included a "bass" and a "snare". Prepare a circuit diagram of any other tones you wish to include in your circuit if you wish to add additional sounds on top of the basic ones we've included.

Step 3: Making the Beat

This circuit uses a hysteretic oscillator as origin of the "beat". The hysteretic oscillator in this circuit has a frequency of about 1 hertz. The oscillator outputs a capacitor voltage "shark wave" which is compared using a comparator circuit to a steady voltage of about 2.5 volts. The 2.5 volts is made simply from a power source and a series of resistors. When the shark wave exceeds with the steady voltage, the comparator outputs 12 volts, essentially turning the circuit "on". When the shark wave is below the steady voltage, the comparator outputs 0 volts, essentially turning the circuit "off". For the second part of the beat, another comparator is used but compares the shark wave to -2.5 volts is used and that triggers in a similar fashion to the previous.

Step 4: Making the Base

Using another hysteretic oscillator, the "bass" sound of the circuit is able to be made. The output of the operational amplifier in the hysteretic oscillator outputs a square wave that is then run through low pass filters. Without these two low pass filters, the sound from the oscillator will harsher than desired for a base sound. The two filters are made of 6k ohm resistors and .1 uF capacitors and provide a cut off frequency of approximate 265 hertz. This provides the low bass drum frequency in our beat box. To ensure that the sound is able to be heard through the speakers, a non-inverted amplifier is used and increases the amplitude of the filtered waves by a multiple of 2.

Step 5: Making the Snare

Unlike the bass, the "snare" sound in the beat box circuit originates from a white noise generator but is also then amplified by a multiple of 2 by a non inverting amplifier. The circuit making up the white noise generator is detailed in the above by Rick Andersen in his 1997 publication of a "White Noise" Generator using avalanche-mode biasing. Here's the link to that: A "White Noise" Generator using avalanche-mode biasing.

Step 6: Combining the Beat and the Sound

Now that the circuit has a distinctive "base" and "snare" sound, the signals from those are fed into two separate speakers. Each speaker is then connected the collector pin of their respective transistors. The base pin of the transistors are connected to the outputs of the "beats" that were made previously. By attaching the wave made by comparing the shark wave to positive 2.5 volts to the snare circuit and attaching the wave made by comparing the shark wave to negative 2.5 volts to the bass circuit, there are now two sounds are offset from each other. The beat box should produce a bass, pause, produce a snare, pause, and then repeat.

Step 7: The Completed Circuit

Congratulations! You've made the circuit! By taking more hysteretic oscillators and filtering out other frequencies, one is able to make new sounds and overlay them on the ones already made. Feel free to experiment with adding new layers and offsetting the times, the duration of the beat, or the values of resistors across the bread board.