When using the Kronometer plugin, Alternis Kerbol Rekerjiggered takes advantage of the functionality and implements a new clock.
Joys: Orbital Period of Jool. (15.23 weeks, roughly one stock Kerbin year.) Rotes: Rotational Period and Orbital Period of Kerbin. (58.86 hours) Sours: 1/60 of a Rote, 0.98 real hours. (Etymology: Sixtieth + Hour = Sour) Minutes: 1/60 of a Sour, 0.98 real minutes. Ticks: 1/60 of a Minute, 0.98 real seconds.
The replacement for the year is the Joy, or JOolean Year. It is equal to about 15.23 weeks, exactly 9,211,018.76215 seconds, and is about equal to a stock Kerbin year.
The replacement for the day is the Rote, or Rotational pEriod. It is equal to the Sidereal period of Kerbin. (I was too lazy to calculate the solar period, oops.) It is about 59 hours long, or exactly 211,926.35802 seconds long. There are 43.46 Rotes in a Joy.
The replacement for the hour is the Sour, or Sixtieth hOUR. It is equal to 1/60th of a Rote. It is about 98% of an hour, or exactly 3532.105967 seconds long.
The replacement for the minute is also called a Minute, and is 1/60th of a Sour. It is about 98% of a real-Minute.
The replacement for the second is the Tick, and is 1/60th of a Minute. It is exactly 0.98114054638 seconds long.
To recap: 60 ticks in a minute, 60 minutes in a sour, 60 sours in a rote, and 43.5 rotes in a joy.