Time Machine Keeps Weekly Backups.
If you want to keep backups that are more regular than weekly, but less regularly than hourly then it's probably best to use a different solution. Time Machine doesn't have these settings (apparently not even in hidden settings).
Time machine keeps weekly backups as space permits. It also stores daily backups for the past month, and hourly backups for the past 24 hours.
Pros and Cons (case examples)
In the case that you create a file one day and then delete it about two days later, more than a month passes before you want to recover the file, and the weekly backup that is kept for that time period is not between the time the file was created and the time it was deleted, then a daily backup will keep the file and a weekly backup will not. This is the specific scenario where another backup solution will be desirable. However if you create a file one hour, delete it two hours later, and less than a day has passed, then Time Machine would have the file backed up, but a daily backup is unlikely to have it backed up.
I suspect that you'll find doing hourly backups with rsync will be more intensive for your computer than Time Machine's hourly backups.