How would you design a clock in order to play triplets?
6 has factors 2 and 3. So if you start with a clock that is 6&times; your quarter note rate, you can divide by 2 to get eighth-note triplets and by 3 to get eighth notes.

The MIDI system clock messages are transmitted at a rate of 24 per quarter note (2&times;2&times;2&times;3), which allows 64th-note triplets to be generated directly.


Every clock &rarr; 64th triplets
Every 2nd clock &rarr; 32nd triplets
Every 3rd clock &rarr; 32nd notes
Every 4th clock &rarr; 16th triplets
Every 6th clock &rarr; 16th notes
Every 8th clock &rarr; 8th triplets
Every 12th clock &rarr; 8th notes
Every 16th clock &rarr; quarter triplets
Every 24th clock &rarr; quarter notes


... and so on.