At IKEA there is the VÄCKIS clock. Cheap enough to try some hacks.
I don’t know why all clocks have a 12 hours face while each day has 24. So let’s make a clock with 24 hours. Firs attempt was to manipulate the gears, after removing every second teeth at the minutes to hours gear the clock was stuck. The clock has a quartz crystal “XTAL” as precise timing element. As usual the Frequency is 32768 Hz which is a power of two and gets divided down to 1 second to drive little stepper motor. If we replace the XTAL with a 16 kHz one, the clock would run half speed thus one turn per 24 hours. But typically watch crystals are fabricated in the 32.768 kHz standard frequency only. Let’s make an extra circuit to generate half the frequency and feed the clock with it to let it run half speed.
For the circuit a low power consumption and component count is best. Logic chips can also be used for low power analog functions like oscillators, see Claudio synthesizer. The 74HC14 hex inverter is used. Inverter oscillator circuits normally need loading capacitors and resistors to work, but with the 74HC14’s clamping diodes and parasitic capacitances it works simply without anything beside the crystal. After having the 32.768 kHz signal we need to divide it by two. This can be done by a T flip flop but its construction with the left over inverters far from easy. A second oscillator synced to every second pulse of the XTAL frequency should work. It’s a RC-oscillator where the diode controls the oscillation. The oscillator now runs on half the XTAL frequency. By feeding this signal to the clock, it will now tick only after two seconds, so the hour’s indicator will do a full turn in 24 hours. The clocks alarm will activate only once each day and its sound is now one octave below.