The Rakahangan Intercalation

Both the native recorders, Haumata-tua and Aporo-ariki, in endeavoring to reconcile the Rakahangan 13-month cycle with the 12 European calendar months, wrote that though the old people (to tahito) stated that the long season consisted of 7 months, the meaning was 6 months and a part, and the short season of 6 months meant 5 months and a part. They then divided the calendar month of May between the two months Pipiri and Whakaau, giving each 15 days. In the use of the term May it may be inferred that the lunar month of May-June was meant. If, however, a full month of 30 days was divided regularly between two of a series of 13, and the remaining 11 were lunar months, the result would be a regular cycle of 12 lunar months with no system of intercalation. Such an interpretation is untenable.

As the short month, Pipiri, precedes Whakaau, it must commence with the new moon after the previous regular lunar month of Te Rehu, in which the Pleiades are descending. In Pipiri the Pleiades either sink below the western horizon or have disappeared. The following Whakaau month is indicated by the rising of the Pleiades, and as Pipiri is a short month, Whakaau cannot very well wait for the next new moon on all occasions. The problem is the division between Pipiri and Whakaau so that a system of intercalation may be possible. An indication is obtained from a statement by Best (2, p. 12) which shows that a similar system was known in New Zealand in addition to the one more widely used:

Tutakangahau, of Tuhoe, clearly explained the fact that in the Mataatua district the appearance of the Pleiades on the eastern horizon before sunrise was the sign awaited as a token of the new year. He made a peculiar statement that looks as though the year in that district commenced, or sometimes commenced, in the middle of the lunar month. If this was so it was a very singular procedure. He remembered that each month had thirty nights, but that the first month, Pipiri, had fifteen nights only “of its own,” its other fifteen nights formed half of the second month, Hongonoi. Hongonoi was composed of these fifteen nights and fifteen others “of its own.” The third and following months were made up in a similar manner. Unfortunately, I lost the oppor- page 228 tunity of obtaining further light on the subject, and so am still in the dark as to what the old man meant. He was a man of much knowledge, and the most trustworthy of authorities on old-time lore.

These remarks support the Rakahangan statements. Though Pipiri was the 1st month in the Maori calendar and the 13th month in the Rakahangan, they were both months evidently in the lunar month of May-June. In the Rakahangan calendar the rising of the Pleiades ended in the Pipiri month, and in the Mataatua calendar of New Zealand it commenced the Pipiri. It is significant that the Maori 13th month was also known as Te tahi-o-Pipiri.

As a working hypothesis based on the Rakahangan observations concerning the Pleiades, it is held that the morning rising of that constellation ended the Pipiri month and commenced the Whakaau. The Pleiades descend from the western sky on about May 7, which is in the month of Te Rehu. This is borne out by Table 22, except in the intercalated years. The next new moon after Te Rehu is taken as the commencement of Pipiri, which continues to June 4, whereas Whakaau commences with the morning rising of the Pleiades on approximately June 5 and finishes out the lunar month. In Table 22 the new moon commencements of the lunar months are given and, in parentheses, the number of days in Whakaau and Pipiri.

In the cycle 1927–28 the last month, Pipiri, commenced with the new moon on May 19, 1928, and ran to June 4, making a month of 17 days. The 1928–29 cycle commenced with Whakaau on the rising of the Pleiades on June 5, 1928, and finished out the lunar month to June 16, thus giving Whakaau 12 days. Thus the Pipiri of the previous cycle and Whakaau divided a lunar month of 29 days between them in respective proportions of 17 and 12, and not 15 and 15. The last month of the 1928–29 cycle commenced with the new moon of May 9, 1929, and ran for the long period of 27 days before the Pleiades rose. The Whakaau of the following cycle, 1929–30, thus had only 2 days before the next new moon rose to usher in page 229 Unuunu on June 7. The short Whakaau in 1929 led to the early commencement of the last month of the cycle on April 28, 1930, and Pipiri ran a full lunar month of 30 days without being stopped by the rising of the Pleiades. Nothing now remained but to commence the next cycle of 1930–31 with Whakaau on the following new moon on May 28, 1930. In this month the Pleiades rose on the 9th night, but the Whakaau month ran on the orthodox manner after the rising of the Pleiades to the end of the lunar month of 29 days. The intercalation thus consisted of bringing the two short months of Pipiri and Whakaau up to the value of two lunar months, when the Pleiades did not rise in the lunar month commenced by Pipiri. The principle is similar to the New Zealand method of adding a 13th month when the Pleiades do not rise in the 12th month of the cycle. The intercalation restored the balance between the lunar months and the seasons. At the close of the 1930–31 cycle, Pipiri and Whakaau again divided a lunar month between them. Pipiri closed the cycle with a month of 19 days, whereas Whakaau commenced the 1931–32 cycle with the remaining 11 days.

In Table 23 the range of the Rakahangan lunar months has been worked out in sequence over a cycle of 19 solar years. The range is estimated from the earliest new moon to the end of the lunation commencing with the latest new moon. The exceptions are in the 1st and 13th months.

It is apparent that with the exception of split months and the intercalated 13th month, the month names in any Polynesian calendar have a range of 57 or 58 days in a cycle of 19 years. Some names, such as Takaonga, extend into three calendar months, as from October 30 to December 26. As, however, the month can only occupy two days of October at the most, October may be eliminated and the general grouping of Takaonga may be considered as November-December. The fallacy of attempting to identify page 230 the Polynesian lunar months with one calendar month is evident. They must be correlated with double calendar month names as given in the “Calendar Correlation” column of Table 23, except perhaps in the split 1st and 13th months which extend only 9 and 10 days over a full lunar month. In the “Native Attribution” column it is seen that Haumata-tua was correct as to his sequence of calendar months in so far as they agree with the first calendar months of the calendar range occupied by the native lunar months. The mistake in Whakaau is due to splitting the calendar month of May, when it was the lunar month range of May-June that should have been divided, May going to the 13th month, Pipiri, and June to the 1st month, Whakaau, of the next cycle.

It will be observed that at different periods in a 19-year cycle the second calendar month of one lunar month will become the first calendar month of the succeeding lunar month. Thus Paroro-mua (August to September) will at one period be in the calendar month of September and at another period the next lunar month of Paroro-muri (September to October) will also be in September. The coming of the tomore fish is associated with Paroro-mua; but if the fish comes regularly in the calendar month of September, the result will be, from a native point of view, that the tomore arrives in some years in Paroro-mua and in others in Paroro-muri. Such occurrences may have constituted one of the factors which led to variation in the sequence of similar lunar month names in different localities.

The Rakahangan information establishes a hitherto unrecorded method of correlating the lunar cycle with the Pleiades year. It is known from various writings that the lunar cycle was used throughout Polynesia and that in most areas the appearance of the Pleiades in the morning or evening sky gave the sign for the commencement of the new year. None of the early writers who had the opportunity of obtaining information from Polynesian astronomers have recorded how the Polynesians corrected their annual lunar cycle to prevent a dislocation of the seasons. Best (2) has recorded that the Maori year commenced with the first new moon after the morning rising of the Pleiades. He recorded lists of cycles of 12 months and some of 13 months. Though he did not follow the matter up, it may be inferred from his work that when the Pleiades did not rise in the 12th lunar month of the cycle, the Maoris had to delay the commencement of the next cycle for a whole lunar month. This meant the addition of an extra lunar month to the 12-month cycle. The intercalation of a 13th month was decided not by mathematical calculations but by the simple rule that the new year could not start until the first new moon after the morning rising of the Pleiades. The rule of not commencing the new year until the first new moon after the astronomical sign applies equally well if the evening page 231 appearance of the Pleiades is taken as the sign. The strict observation of the rule would automatically lead to the intercalation of a 13th month in some cycles. Under this system, the usual year of 12 lunar months would consist of 354 days and at intervals a 13-month year of 383 or 384 days would prevent the dissassociation of the lunar month names with the seasons. The range of variation in the year was one lunar month.

The Rakahanga system, if I have analyzed the evidence correctly, differs in that the new year commenced on the actual morning rising of the Pleiades. This led to the splitting of a lunar month with the result that the calendar was a constant 13-month cycle though the lengths of the two split months varied. Though the two months were contiguous and split one lunar month between them, they did not belong to the same cycle, one being the last of one cycle and the other being the first of a new cycle. The total of the two split months in the same cycle amounts to more than a lunar month. The total taken over a period of 19 years ranged from 31 to 49 days. Thus in the Rakahangan system a correction was made every year and the number of days in a year ranged from 356 to 372. The Rakahangan year was never more than 9 days longer or shorter than the solar year, whereas the New Zealand year varied from 11 days shorter to 19 days longer. Rakahanga resembles New Zealand in observing the morning rising of the Pleiades. The Rakahangan system of the constant split 13th month is more accurate than the intercalated 13th month attributed to New Zealand, but there are indications that the split 13th month was also known in New Zealand.