Actually, October was the eighth month in the Roman calendar. And the surrounding months are named for their number in the order – SEPTember (7th), OCTober (8th), NOVember (9th), DECember (10th).
Roman Calendars are absolutely bonkers.
Months 7, 8, 9, and 10 are named for their number, but month 1 is named for the god Janus, who was associated with time and doorways. March is named for Mars etc.
HOWEVER, this is just the start of the crazy. Roman January had no fixed length. It was just "January" until it was springtime. THEN it was March.
However, the Roman's had some festivals that took place in January and this is where Febuary originates. It wasn't it's own month, it was a "sub-month" of January incorporating some important religious festivals.
So in the republican period of Rome, it would be January, then February for a bit, then freaking January again then March.
This was part of why Augustus was able to convince people it was fine to take days from February so August would have 31 days. Romans already thought of February as not really a thing.
Now, December was the last month and month 10, and yes the republican Calendar had 10 months. However, a calendar for the earth with 10 months is basically crap. A Lunar/Solar calendar will have 13 months, and solar calendars will have 12 months, and even the ancients could do solar calendars well enough to get the length of a year to ~360 days.
However, the fact that the length of the year is 365 and change pissed the Romans off. So they stuck with their calendar that was 9 months of 30 days and then January was "the rest of winter till spring".
However, even by cheating with January, the Romans experienced some of the worst seasonal drift of all ancient peoples. Although some if this was political as the plebeian tribunes and the the priests of Janus got to decide when the new year began (oh yeah, Roman need year was March 1). So if you were a consul or a bunch of senators and you needed somebodies term to be up, and you could find some flowers sticking up through the snow, well then it must be March now. Time to strip last years consul of his power and appoint a new one!
Anyway, the calendar situation was so abysmal that when new calendars were proposed to fix some of this stuff people cheered! Actually, the sources say that lots of people faught prevent any change arguing that the calendar came from the gods. However, the administrators loved it and adoption was rapid.
However the Julian calendar still has seasonal drift. Hence the Gregorian reforms.
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