The 24 hour day is named by the Major and Minor scales of the circle of fifths. AM is major #scale. PM is minor scale. 60 minutes of each hour are broken into the 7 parts. The first part is 12 minutes long and represents the note of the scale, the notes are broken into 8 minute segments, for a total of 7 segments per hour. These represent the 7 notes in every scale. For example, right now the time is "Hour of B Flat Major - note of A" Which correlates to 10:54 AM with familiar 24 hour time keeping. Time to advance your mind children of Earth, time to use more than 1 clock.
One issue when designing this clock is how to deal with #enharmonic notes.
Code for The #CircleOfFifths Music #Clock at Github:
https://github.com/chromalendar/ChromaCelestialCalendar/blob/master/music-clock.js