Archbishop Cranmer’s 30-day cycle of Psalms applies to each month of the year, but it works out differently according to what month you’re dealing with. Several months have 31 days, and his appointment was to repeat the 30th day’s Psalms on the 31st day. February has 28 or 29 days, though, so presumably that means you don’t quite finish the psalter that month, right?
Right, the 1662 Prayer Book (and all thereafter) state that you get to the 28th or 29th day, and leave it at that.
However… this seems to be a simplification of a slightly different approach that came before. I picked up a facsimile edition of the 1611 “King James” Bible some years ago, and it has a number of Prayer Book rubrics in it, including the table of daily lessons throughout the year and the order of the Psalms. I expect these reflect the then-current 1559 (Elizabethan) Prayer Book’s order.
Check out what it says about February (and I’ll update the spelling for you)…
And because January and March have one day above the said number, and February, which is placed between them both, hath only 28 days; February shall borrow of either of the months (of January and March) one day : and so the Psalter which shall be read in February, must begin at the last day of January, and end the first day of March.
In other words, once you finish the 30-day cycle in January, start the cycle at the beginning on the 31st (today!) and carry it through to March 1st. That means you’ll be a day off between the Psalter and the calendar date throughout February and March, but on the upside you’ll get through all the Psalms three times without repetition or omission in the first three months of the year!
The fact that the Prayer Books after this point don’t include this rubric indicate to me that this proved too complicated in actual practice, and so the powers that be gave up on it and simplified it when the next Prayer Book was produced (in 1662).
The latest draft of the 2019 Prayer Book doesn’t look as flexible about the Psalms as its predecessors, but the fact that it authorizes two different Psalm cycles plus allows the option of further shortening and simplification indicates that our liturgists care more that we pray the Psalms regularly and in an orderly fashion than about total conformity to one system. Therefore, consider yourself well within your rights to give “old-school February” a try, if you want! Start with day 1 today, finish with day 30 on March 1st, and carry on through March a “day off” from the norm until we all meet back together with day 1 on April 1st.
At the end of the day, it doesn’t matter a ton which system you use, as long as you do use one. It’s just nice to know (and sometimes try out) the ways of our forebears.