Generic time range word
Periodic : Happening or appearing at regular intervals
appears to fit well- as in a periodic allowance.
For your counter example, Interval may work- as in an interval counter.
If an event occurs at fixed intervals, it is regular, as in ‘I have a regular income.’ You can also use the adverbial form as in ‘My income is paid regularly.’
(On a matter of terminology, daily and monthly are not idioms, because their meaning can be deduced solely from a knowledge of what the words mean.)