I guess taka-rua means two (rua) cycles (taka):

Taka, takataka = Circle; to form circles, to gather, to get together (of people). Rua = 1. Two; second; other (precedes the noun); te rua paiga, the other side. 2. Hole, grave; holes in the rocks or between the rocks of the coastal lagoons; he keri i te rua, to dig a hole. 3. To vomit.

Which with a minor change could be altered into Taku-rua:

... At the risk of invoking the criticism, 'Astronomers rush in where philologists fear to tread', I should like to suggest that Taku-rua corresponds with the two-headed Roman god Janus who, on the first of January, looks back upon the old year with one head and forward to the new year with the other, and who is god of the threshold of the home as well as of the year ... There is probably a play on words in takurua - it has been said that Polynesian phrases usually invoke a double meaning, a common and an esoteric one. Taku means 'slow', the 'back' of anything, 'rim' and 'command'. Rua is a 'pit', 'two' or 'double'. Hence takurua has been translated 'double command', 'double rim', and 'rim of the pit', by different authorities. Taku-pae is the Maori word for 'threshold'... Several Tuamotuan and Society Islands planet names begin with the word Takurua or Ta'urua which Henry translated Great Festivity and which is the name for the bright star Sirius in both New Zealand and Hawaii. The planet names, therefore, represent the final stage in the evolution of takurua which was probably first applied to the winter solstice, then to Sirius which is the most conspicious object in the evening sky of December and January, and was then finally employed for the brilliant and conspicious planets which outshone even the brightest star Sirius. From its association with the ceremonies of the new year and the winter solstice, takurua also aquired the meaning 'holiday' or 'festivity' ...

Could these two cycles then not be the same as those great 'circles' (mata) we have seen earlier - in Keiti's 1:st period for the year - where I tried to translate these two mata + maro into: 'Winter has reached its end.'

*258
Eb2-1 (326 + 43 = 369) Eb8-40 (628 → 2 * 314)
Nov 18 (*242, 322) 322 + 259 = 365 + 216 (Aug 4)
SCHEDIR (Breast) α Cassiopeiae DRAMASA (*320.0 20 * 29 - 180)
hia → count!

... It was 4 August 1968, and it was the feast day of Saint Dominic, patron of Santo Domingo Pueblo, southwest of Santa Fe. At one end of the hot, dusty plaza, a Dominican priest watched nervously as several hundred dancers arranged in two long rows pounded the earth with their moccasined feet as a mighty, collective prayer for rain, accompanied by the powerful baritone singing of a chorus and the beat of drums. As my family and I viewed this, the largest and in some ways the most impressive Native American public ceremony, a tiny cloud over the Jémez Mountains to the northwest got larger and larger, eventually filling up the sky; at last the storm broke, and the sky was crisscrossed by lightning and the pueblo resounded with peals of rolling thunder ...

Possibly the culmination of the pair of Cassiopeia breasts inspired the design of Eb2-1.

I have also tried to explain a pair of great rhombs as the two seasons of the year - as dictated by the Moon, in contrast to how two great circles might mean the two seasons of the year as dictated by the rays from the Sun.

Now we have found in the text on the Q tablet two great mata again, this time in 4b and 6b (the Q glyphs in 5b are obliterated):

1b   2b   3b
113 Hb3-14 Hb3-38 Hb3-39 Hb4-13 Hb4-14
4b 5b 6b
188 Hb4-42 Hb5-50 Hb5-51 Hb6-23 Hb6-24
...
Qb7-31 294 Qb9-4 Qb9-5

When drawing a map for the sun year / the seasons / the cardinal points, we should ideally start with winter solstice = new year = north. Next would then come spring spring equinox east - we are going clockwise = the course of the Sun during the day if we are living north of the equator. But perhaps on Easter Island - south of the equator - they went counterclockwise (withershins), obeying the Sun rather than their wristwatches.

At spring equinox the summer half-year should begin and we should abandon the winter half-year we are in between two great cycles. When we talk about a year we could start at winter solstice, but when we talk about a 'year' (half-year) we should start at spring equinox. Where then should this pair of great cycles be located?

The pair at 4b in the Q text might be motivated because they were intended to refer to the southern spring equinox (possibly around half a year after Hb3-14 → March 14). On the other hand: 294 + 60 = 354 (→ 314 + 40).

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