It's not arithmetically possible to have different frequencies on two branches and still have even intervals on the trunk section - but this is a common enough situation, and you have to compromise to smooth it out.
I seem to remember a time some years ago when there were 3 trains every 10 minutes on the Piccadilly off-peak, with 2 going to the airport branch and one to Rayners Lane / Uxbridge. If my memory is right (though it might not be!) the trunk section ran something like Airport - 3-min gap - Uxbridge - 3-min gap - Airport - 4-min gap, and repeating. So the trunk had 3, 3, 4 gaps (not too uneven), and the more frequent branch had 4 and 6 gaps alternating (again not too uneven).
If the existing published TfL Rail timetable to Paddington is to be believed the gaps between arrival times of TfL services is quite variable anyway. Here are the gaps in minutes of Tfl services arriving at Paddington between 8am and 10am:
10, 6, 9, 4, 4, 8, 6, 9, 3, 4, 9, 5, 9, 3, 12, 5, 11, 2
The next two hours is a bit more amenable to fitting in with a 3 minute 10tph service.
12, 15, 3, 12, 15, 3, 12, 15, 3, 12, 15, 4
Of course, the current published timetable is running only 4 tph to Heathrow. I imagine there will be 6 tph soon enough as T4 is opening again.
(I have used the published timetable on the TfL web site for this which only goes down to the nearest minute)