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The earlier system had 10 months and then there was a reconstruction making it into a system with 12 months.

... Whare-patari, who is credited with introducing the year of twelve months into New Zealand, had a staff with twelve notches on it. He went on a visit to some people called Rua-roa (Long pit) who were famous round about for their extensive knowledge. They inquired of Whare how many months the year had according to his reckoning. He showed them the staff with its twelve notches, one for each month. They replied: 'We are in error since we have but ten months. Are we wrong in lifting our crop of kumara (sweet potato) in the eighth month?' Whare-patari answered: 'You are wrong. Leave them until the tenth month ...

January February March April May June September 8th month November December - -
January February March April May June July August September 10th month November December

It is therefore interesting to find a pair of 5-flame Suns in the C text. They were placed earlier in the text than the pair of 6-flame Suns:

325 55
Ca12-10 (326) Ca12-11 Ca12-12 *Ca14-21 (384)
179 172
Cb8-1 (564) Cb8-2 (173) Cb14-17 (346)
354 (= 12 * 29½)
Cb14-18 (739) Cb14-19 (348)

The Council of Nicaea was in the year 325 A.D. and the Pope changed the date for the equinox from the Julian 3-25 to the Gregorian 3-21, although the astronomical average was 3-20. The creator of the C text has put a reversed bird (manu) as glyph number 320, at ºJanuary 31 = February 4. A kava sign was placed as the preceding day 399:

Kava

1. Sour; salty: vai kava, saltwater, sea; te kava o te haíga, acrid underarm smell; tagata kava - tagata kakara i te kava, man with smelly armpits. 2. He-kava te haha, to be thirsty. 3. To turn sour, to become embittered, bad-tempered, exasperated (used with manava): tagata manava kava, bad-tempered, angry man. Vanaga.

Bitter, salt; vai kava, brackish water; hakakava, to embalm; kavakava, acid, sharp, bitter, salt, spiritous, vinegar, poisonous, disagreeable; akavakava, to make sharp; hakakavakava, to make acid. P Pau.: kava, disagreeable to the taste; kavakava, acid, sharp. Mgv.: kava, to be bitter, sour, acid, salt. Mq.: kava, bitter. Ta.: ava, bitter, acid, salt. Kavahia: 1. Comfort, comfortable, to feast; hakakavahia, comfort, comfortable. 2. Repulsive (of food), disgusted; hakakavahia, repulsion. Kavakava, rib; moi kavakava, a house god G. P Mgv.: vakavaka, the breast. Mq.: vakavaka, vaávaá, rib. Ma.: wakawaka, parallel ridges. We shall need all the available material in order to determine the germ sense of this word. Sa.: va'ava'a, the breast-bone of a bird; fa'ava'a, the frame as of a slate. To.: vakavaka, the side. Fu.: vakavaka, the side below the armpit. Ha.: hoowaa, to make furrows. In all these we may see the idea of ridge or depression, or of both, as primal (Rapanui, Samoa, Marquesas, Maori, Hawaii), and as secondary the part of the body where such appearances is common (Mangareva, Tonga, Futuna). Churchill.

Mgv.: kava, the pepper plant and the drink made therefrom. Ta.: ava, id. Mq.: kava, id. Sa.: 'ava, id. Ma.: kawa, a pepper. Kavakava, a fish. Sa.: 'ava'ava, id. Kavapui, a tree. Ta.: avapuhi, a fragrant plant. Mq.: kavapui, wild ginger. Sa.: 'avapui, id. Ha.: awapuhi, id. Churchill.

Mq.: ava, a small fish of sweet water. Sa.. 'ava'ava, a small fish. Ha.: awa, a fish. Kakava, burnt. Sa.: 'a'ava, very hot. Churchill.

Notably the creator of the C text seems to have made it easy for us, because the glyph numbers were probably corresponding to the heliacal positions of the stars.

For instance was Bunda close to the Full Moon in August 12 (*144) and half a year later Bunda would have risen heliacally in day *144 + 183 = *327 (February 11). Ca12-11 is glyph number 327 on side a.

JUNE 7 (*78) 8 9 10 (161) 11 12
Ga3-19 (78) Ga3-20 Ga3-21 Ga3-22 Ga3-23 Ga3-24
The Knot (Ukdah) Rishu A.-13 (Head of the Lion) VATHORZ PRIOR = υ Carinae (147.9)
Star-25 / ANA-HEU-HEU-PO-5 (Pillar where debates were held) Al Tarf-7 A Hydrae (144.1)

VEGA (α Lyrae)

UKDAH = ι Hydrae (145.4), κ Hydrae (145.5), SUBRA = ο Leonis (145.8) ψ Leonis (146.4), RAS ELASET AUSTRALIS = ε Leonis (146.6)
ALPHARD = α Hydrae (142.3), ω Leonis (142.6), τ¹ Hydrae (142.7)   ψ Velorum (143.3), ALTERF = λ Leonis, τ² Hydrae (143.4), ξ Leonis (143.5)
August 10 11 12 13 14 (*146) 15 (227)
°August 6 7 8 (220) 9 10 11 (*143)
'July 14 15 16 17 (*118) 18 19 (200)
SIRIUS "July 1 2 3 (*104) 4 5 (186)
NAKSHATRA DATES:
DECEMBER 7 8 9 10 11 (345) 12 (*266)
BUNDA (Foundation) / KAKKAB NAMMAΧ (Star of Mighty Destiny) θ Piscis Austrini (330.1), λ Oct. (330.7)
Al Sa'd al Su'ud-22 / Emptiness-11 no star listed (326) CASTRA = ε Capricorni (327.2), BUNDA = ξ Aquarii (327.5)

SIRIUS (α Canis Majoris)

Mahar sha hi-na Shahū-26 (Western One in the Tail of the Goat) Arkat sha hi-na Shahū-27 (Eastern One in the Tail of the Goat)
TSIN = 36 Capricorni (325.2), ALPHIRK = β Cephei (325.7), SADALSUD = β Aquarii, ξ Gruis (325.9) NASHIRA = γ Capricorni (328.0), ν Oct. (328.3),  AZELFAFAGE = π¹ Cygni, κ Capricorni (328.7) ENIF (the Nose) = ε Pegasi, ERAKIS = μ Cephei (329.2), 46 Capricorni, JIH (the Sun) = κ Pegasi (329.3), ι Piscis Austrini (329.4), λ Capricorni (329.6), ν Cephei (329.7), DENEB ALGIEDI =  δ Capricorni (329.8)
February 9 (40) 10 11 (407) 12 13 (*329) All Hearts' Day
°February 5 6 7 8 (*324) 9 (40) 10
'January 13 (378) 14 15 (*300) 16 17 18 (383)
"December 30 31 (*285) "January 1 2 3 (368) 4

How could this be possible? There is no mystery, because I had assumed the C text was beginning at 0h:

March 21 22 (81) 23 322
no glyph
Ca1-1 Ca1-2
koia ki te hoea
Al Fargh al Thāni-25

0h (365.25)

Caph, SIRRAH (0.5), ε Phoenicis (0.8)
Uttara Bhādrapadā-27 / Wall-14

ALGENIB PEGASI (1.8)

χ Pegasi (2.1), θ Andromedae (2.7)
NAKSHATRA DATES:
September 20 21 Equinox (265)
Alchita, Ma Wei (183.1), Minkar (183.7), ρ Centauri (183.9) Pálida (184.6), Megrez (184.9) Hasta-13 / Chariot-28

GIENAH (185.1), ε Muscae (185.2), ζ Crucis (185.4), Zaniah (185.9)

February 9 (40) 10 11 12 (408)
Ca12-9 Ca12-10 (326) Ca12-11 Ca12-12
oho te vae ki hukiga o te ra kua oho ra kua ere te tagata - te hetu
Al Sa'd al Su'ud-22 / Emptiness-11

Tsin (325.2), Alphirk (325.7), SADALSUD (325.9)

no star listed (326) Castra (327.2), Bunda (327.5)

Sirius

Nashira (328.0), Azelfafage, κ Capricorni (328.7)
NAKSHATRA DATES:
August 10 (222) 11 12 13
Star-25

ANA-HEU-HEU-PO

ALPHARD (142.3), ω Leonis (142.6), τ¹ Hydrae (142.7)
Al Tarf-7

ψ Velorum (143.3), ALTERF, τ² Hydrae (143.4), ξ Leonis (143.5)

A Hydrae (144.1)

Vega

Ukdah (145.4), κ Hydrae (145.5), Subra (145.8)

My method of arranging heliacal stars from 0h (at the time of rongorongo) in parallel with the glyphs on side a of the C text will automatically lead to the corresponding nakshatra stars also being arranged in parallel with the glyphs. This leads to a dilemma - are the glyphs illustrations of the heliacal or of the nakshatra side of the sky?

I guess the 5-flame Suns could have referred to an old system with a calendar based primarly on the stars rather than on the yearly path of the Sun (which evidently measured not 10 but 12 months). The 5-flame Suns are attatched with strings rather than with broad bands to the preceding elements. Looking at the nakshatra side we will find the knot (Ukdah) stars. And this place was at the End (Al Tarf) rather than at a Foundation (Bunda).

... When it was evident that the years lay ready to burst into life, everyone took hold of them, so that once more would start forth - once again - another (period of) fifty-two years. Then (the two cycles) might proceed to reach one hundred and four years. It was called 'One Age' when twice they had made the round, when twice the times of binding the years had come together. 

Behold what was done when the years were bound - when was reached the time when they were to draw the new fire, when now its count was accomplished. First they put out fires everywhere in the country round. And the statues, hewn in either wood or stone, kept in each man's home and regarded as gods, were all cast into the water. Also (were) these (cast away) - the pestles and the (three) hearth stones (upon which the cooking pots rested); and everywhere there was much sweeping - there was sweeping very clear. Rubbish was thrown out; none lay in any of the houses ...

Thus:

325 55
Ca12-10 (326) Ca12-11 Ca12-12 *Ca14-21 (384)
February 10 (41) 11 (*327) 12 April 9 (464)
(*326) Bunda

SIRIUS

Nashira Adhil (*384)
Alterf (*143) VEGA Ukdah (*145) (*201)
August 11 12 (*144) 13 October 8 (281)

*384 (April 9) - *326 (February 10) = 58 = 2 * 29. April 9 (464) - 58 = 406  = 365 + 41 (February 10). At the time of rongorongo the heliacal stars at the Julian 3-25 for spring equinox were in day 84 (March 25) + 27 = 111 (April 21, *31):

 

Cb1-5
η Arietis (31.9)