Sept means 7,
Octo means 8, and
Dece means 10.
Yes that's what I was getting at.
Also Julius Caesar had 31 days in July so Augustus changed August from 30 to 31 days.
Full moon occurs on average every 29.530589 days so if if you want a calendar that follows the moon you have alternately 29 and 30 days in a month with a correction as needed. That gives 12.37 months in a year so you need an extra month about every 3 years or so if you want to have 29 or 30 days in a month.
It gets messy.
See for Moon phases.
http://www.lunarrepublic.com/info/phases.shtml