I just put "John Hartford D-Strings" on my 12" banjo. The head is tuned to 89 on the drum dial. Is there a head tension that would work better with tunings in D, D modal, and "Double-G".
I've wondered the same, namely should head tension be different for different keys/tunings?
G# and A pitch have been recommended on BHO by different posters for standard G. So, by extrapolation, a head tuning similar (but not identical) to the 5th string for your D tuning might be a place to start. I have experienced wolf harmonics when the head is tuned to the same pitch as one of the open strings (probably why G# is recommended instead of G).
I don't know how to convert head pitch to drum dial tension, sorry.
If you get any of the wolf notes Brooks mentioned then go a little tighter/looser on the head tension.
If you're happy with the sound/tone you're getting you'll get pretty much the same performance regardless of what tuning you use.
Don't overthink it - you only need to please your ears, you don't have to impress oscilloscopes
Bart, I find my Stelling can handle different tunings/keys w/o head tension change, just as you said.
Another of my banjos has problems, so I'm experimenting with head tension. Banjo used to sound nice, but last few months, not so fine, even with new strings. Trying different changes Keeps me off the street :-)
'Clawhammer, Savarez Users' 14 min
'Gold Tuner' 46 min
'Victor Furtado' 1 hr