I pretty uncertain that I understand your question, though here is my approach anyways.
I prepared Minutes table in different datasource. Created in excel and just copied and pasted.
But needed to add specific "Date"
Modify original data into specific date's time with the "Minutes" scale.
/// just assume your time is on "1/2/2016".
Blend Master and original Data.
Then you can get below table.
hour_Minutes_9.3.twbx 69.2 KB
Thank you, this is a good choice
Happy to hear that. Hope it works.