The ideas in this post largely come from Nicolas Collins' excellent book 'Handmade Electronic Music', which I would highly recommend.
The 4017 decade counter takes a clock input, and has 10 outputs labelled O0 - O9. Each output will, in turn, output a pulse in time with the clock pulse. If the reset (RES) pin is briefly held high, and then brought back low, the count is restarted and the process can begin again. The chip also has a carry count (CR) pin, which outputs a pulse if the clock is counted beyond the tenth output with being reset.
A 40106 oscillator is used as a clock source, which is feed into pin14 of the 4017 decade counter. The 10 counting outputs of the 4017 will begin to pulse in turn with the clock input. By connecting the signal from one of the outputs of the 4017 to the reset pin of the 4017, the 4017 will reset at a clock pulse count below 10. For example, if clock output number 2 of the 4017 is connected back to the reset, then when the second pulse of the input clock is mirrored to output 2, the 4017 is reset.
For example, consider that output 3 of the 4017 is fed to the reset. Now, the clock frequency - which had a frequency of, say, 440 Hz - now has a frequency of 146.67 Hz (which is 1/3 of the original) and a duty cycle that is only 16.67 %. This is because only every third clock pulse actually becomes part of the final signal.