This calendar uses the balanced base twenty-four number system, with the Pitman (↊, ↋) digits for ten and eleven, and (for the time being, until augmented system fonts are developed) the alchemical symbol U{1f718} for the digit twelve. (U{1f718} is an approximation of the corresponding Argam numeral, created by Micheal de Vlieger of the Dozenal Society of America). This project is primarily inspired by the Dozenal Solstice Calendar (with which it shares its epoch and season day distribution concept) and the traditional Chinese calendar (from which it borrows the fifteen-day solar term, and the calibration of these terms to the solar longitude as observed by the earth). The calendar can be reproduced from the following constraints:
- The zeroth hour of the day is the one centred at noon. Times are then described by the positional balanced base twenty-four division of the day.
- The days of the solar terms (of approximately fifteen days each), are numbered from negative seven to seven.
- The zeroth day of each solar term is the day, beginning and ending at midnight Barycentric Dynamical Time (TDB), during which the solar longitude of the sun (as observed from the centre of the earth) passes through an exact multiple of fifteen degrees. The 0-degree longitude mark is taken to be the traditional March equinox and the longitude increases as time increases.
- The solar terms themselves are numbered from negative twelve to positive twelve. The positive and negative twelfth terms are only half terms: the negative twelfth term begins with the positive half of the zeroth day, and the positive twelfth term ends with the negative half of the negative zeroth day.
- The traditional June solstice as measured in TDB falls on the zeroth day of the zeroth solar term.
- The fifteen days of each solar term are split into three five consecutive day pentads, the zeroth of which contains the zeroth day of the term.
- When the number of days between zero-days (as required by the solar longitude constraint) is not fifteen, days are added or subtracted between solar terms as necessary. These extra days are called "season days" or "S-days". Season days are evenly split between the two terms: the first term takes the negative half of the S-day as day eight and the second term takes the positive half as its day negative eight. If a day needs to be subtracted, the seventh and negative seventh days of each term, respectively, are shared. (In the first 1000c years of the calendar, there is at most one and at least negative one season day between consecutive terms.)
- The distribution of season days within the calendar year is completely determined by the solar longitude in ecliptic coordinates as observed by the centre of the earth, and the definition of TDB. Due to the eccentricity of the earth's orbit, and the unsolvability of the n-body problem, this means there is no predictable S-day pattern for any given year.
- The epoch of the calendar is defined as noon TDB of the zeroth day of the zeroth solar term of the year corresponding to 9564 BCE in the Gregorian calendar. This is the most recent time that the perihelion occurred on the June solstice, or the zeroth day of the year in our calendar.
- The zeroth year of the calendar begins on the epoch. No negative term in year zero, nor any term in any negative year, is required to conform to the definition of the solar terms given above. This means that there are no season days before the zeroth term of the zeroth year, and that no exact date is required to be expressible in the calendar if it predates the epoch. However, in order to keep negative years meaningful for large-scale timekeeping, the solstice is still required to fall within the zeroth term of each year.
- The calendar year rolls over at the transition between the positive twelfth term and the negative twelfth term; that is, at noon on the December solstice.
Equinox and Solstice Predictions