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Jean Christian Petitfils in his historical survey on Jesus' live states that this feast is more likely to be the Rosh ha-Shanah, the Jewish new year, which took place on 1st and 2nd of Tishiri (begining of automn 31). Unfortunatly he does not elaborate on that.
Cf. Jean Christian Petitfils, JΓ©sus, Fayard, Paris, 2011, p 219.