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Early I spent much time and effort to try to coordinate the different versions of the Easter Island moon calendar with the glyphs. This was in principle my result:

Ohiro Oata -
Kokore tahi Kokore rua Kokore toru Kokore ha Kokore rima Kokore ono
Maharu Ohua - Otua
Maśre Ina-ira Rakau Omotohi
Kokore tahi Kokore rua Kokore toru Kokore ha Kokore rima
Tapume Matua Orongo
Orongo Tane Mauri-nui Mauri-kero Omutu Tireo
- -

From my present point of view I would like to move Ohiro and Oata to the end of the structure, because the pair of marama glyphs at the end are signs for nights but not those at the beginning.

The moon calendars which I used were basically recorded as follows by Métraux and by Englert:

Englert Métraux
Ohiro (Oari?)
(O)ari
Kokore tahi
Kokore rua
Kokore toru
Kokore ha
Kokore rima
Kokore ono
Kokore tahi
Kokore rua
Kokore toru
Kokore ha
Kokore rima
Kokore ono
Maharu
Ohua
Otua
Maharu
(O)hua
Atua / Otua
Maśre
Ina-ira
Rakau
Omotohi
Maśre
Ina-ira
Rakau
Motohi
Kokore tahi
Kokore rua
Kokore toru
Kokore ha
Kokore rima
Kokore tahi
Kokore rua
Kokore toru
Kokore hį
Kokore rima
Tapume
Matua
Orongo
Tapume
Matua
(O)Rongo
Orongo taane
Maśri-nui
Maśri-kero
Omutu
Tireo (Tueo?)
(O)Rongo Ta(a)ne
Mauri-nui
Mauri-kero
(O)Mutu
Tireo
Hiro
(O)ata
 
Oata

The number of moon crescents of different kinds can be summarized as follows:

26
2

26 is also the number of Moon nights if we exclude those at the beginning and end of the calendars:

6 3 4 5 3 5
13 13