From the earliest records the AE had a 'idealized' calendar based on solar / lunar / stellar / agricultural cycles.
The year (rnpt) had three seasons (tr) - each season divided into four idealized months (Abd) of thirty days each = 360 days + five days which were 'those over the year' (Hr (j)w-rnpt). Their year was actually 365 1/4 days, but the extra 1/4 day was not taken into account, so their calendar 'wandered'.
The 5 Hr(i)w-rnpt are mentioned in a list from a festival offerings calendar for the Dyn 5 Sun Temple of Niuserre at Abu Gurob, and also in Neferkare's Dyn 6 'pyramid texts: "He whom the great heat foretold has come forth from the interior Akhet and has seen the arrangement of the festival calendar and the making of braziers on the birth of the gods on the five days added to the year (5 Hriw-rnpt) on your arms, Great Breasted One in front of the inductees..." (Sethe Vol 2: 472; §1961c)
A year with 3 seasons / 12 months / 360 + 5 days, is attested in the OK.
A typical example of a date (from the reign of Sneferu): Year of the 15th occasion 2 Peret 14.The 15th occasion refers to the year when the count of all the cattle and herds of Lower and Upper Egypt in the reign of Sneferu took place. 2 Peret 14 is the 14th day of the 2nd month of the season Peret.
Lunar phases regulated their sacred festivals - New Moon festival, monthly festival, half-monthly festival, sixth-day festival etc. (PT §861) ".....you ascend to the sky on the Sixth-day festival (CT 47) etc.
'the coming forth of Spdt' (prt spdt) - heliacal rising of Sirius on new year's day:
In northern Egypt, the heliacal rising of Sirius (spdt), the second brightest star in their sky after the sun, took place around June 26th +- 2 days during the OK, and roughly coincided with when the ancient Egyptians expected the beginning of the annual flooding of the Nile at Abu in southern Egypt. The exact timing of the flooding varied, as it depended on when the monsoon rains fell on the Abyssinian plateau, but it normally began around the time of the summer solstice at the end of June. (summer solstice c.2570 BC, about the 26th of June; heliacal rising of Sirius, also around 26-27 June)OK reference linking spdt to the year and the beginning of the year:
This Pepi has come to you, lord of the sky. This Pepi has come to you, Osiris. This Pepi will wipe your face and clothe you with a god's clothing, having become clean for you in Djedit (Ddt, necropolis of Iunu). Sothis (spdt), your daughter whom you have desired, [who makes] your [fresh vegetables (rnpwt) in] her identity of the year (rnpt), is the one who led this Pepi when this Pepi came to you. (Sethe Vol 2: 39; §964-5) ('year' = D21 (r) N35 (n) Q3 (p) X1 (t) + ideo. M4 (rnpt))
(note: a possible play on words between 'fresh vegetables' (rnpwt.k) and 'year' (rnpt))
MK reference linking spdt to the year and the beginning of the year:
Sah (Orion) speaks: 'He is my son, older than I (sic)' - so says Sah (Orion) '....N, who is pure and young, and Sopdet (Sirius) bore him, (even) she the young (rnpii), she of the year (rnpt), a goddess from her birth who is at the start of the year... (CT 689)
(note: a possible play on words between 'young' (rnpii), and 'year' (rnpt))
Sirius may have been associated with the inundation as far back as the first dynasty. An ivory plate from the reign of king Djer shows a cow with a feather (H6) between the horns, and above the 'feather', a dark disk. Below the cow are three plants on a horizontal base similar to M8, ideogram for the Akhet season (Axt. 'inundation (season)').
CT