September 1st is not only the first day of the month, it is the beginning of the ecclesiastical year, that is the “New Year” for our ecclesia, which is called “the beginning of the indictus”.
S. Eustratiadis writes the following about Indictus: “The Latin word indictio means definition, in which the emperors of the Romans were paid the taxes by a 10-year period. During the ecclesiastical tradition, the beginning of indictus determined Augustus Caesar, when he ordered the general census of the inhabitants of the Roman state and the collection of taxes, during the first of the month of September. From M. Konstantinos (313) became officially the use of the Indictus as a date, and since then ecclesia celebrates on 1 September as the beginning of the ecclesiastical year.
The Indictus was therefore a more general way of measuring time per 15 years. Later, Indictus means the year and the beginning of the year and the beginning od Indictus the New Year’s Day.
After 462 ad, for practical reasons and for the first of the year to coincide with the first of the month, the ecclesiastical New Year was transferred on September 1st.
The New Year’s Day of January 1st is Roman catholic in origin and came to the Orthodox east in the later years.