I know the subject of banjo head tension has been beat to death over the years. Maybe my observation has been witnessed in the past, but I was not able to find a thread about what I am seeing.
First is a reference to an archived thread on this subject:banjohangout.org/archive/343194
Second: I have never been able to hear a note by tap tuning a head.
I have a 1998 Stelling banjo with the original head ( I believe). The banjo has really good all around tone with the Drum Dial reading 92 uniformly and with a quarter's worth of clearance under a 10" straightedge. The strings are mediums and the bridge is a Stelling 11/16".
I have an RB-250 with a new Remo head. I am still tweaking the head on this banjo to get the best tone. The Drum Dial is reading 90 uniformly with only a dime's worth of clearance under a 10" straightedge. The strings are mediums and the bridge is a 5/8" Snuffy Smith.
The new head has less bridge deflection at 90 than an old head has at 92. So is bridge deflection measurement of any use on a new head?
My thoughts are that age of a head plays into the coin under the straightedge results. It appears to me a new head will deflect less at the bridge than the deflection of an old head. I would think a Drum Dial may not be a direct correlation to a specific tap tune note, but perhaps the Drum Dial is a consistent reference over the life of a banjo head.
In the end I will set up the new head where is sounds best to me and use the Drum Dial as a reference for keeping the head set where I like. I am interested in hearing what I am missing in my observations.
I have often thought that the size of the bridge's feet and the down pressure of the tailpiece will affect the coin method. I like the method and use it along with the drum dial to evaluate tension, but like you, continue to question what I see sometimes.
I failed to take tailpiece down pressure into account. The banjo with the new head has the tailpiece set level. The banjo with the old head has the tailpiece set where it is angled up a little towards the bridge.
The only reason why an old head would sag would be because it has stretched over time. That stretching would cause a decrease in tension. In other words, age shouldn't mean a thing.
I suspect that the Stelling head was made somewhat differently, perhaps with an older mylar formulation, and that's the main reason for the differences between it and the new head.
Also, it's not just the tailpiece angle that affects the down pressure; there's the length of the tailpiece, too. Bridge height also has an effect, and differences in scale length figure into the string tension, which is also a part (although a very minor part) of the down force equation. There can also be differences in the neck angle causing some down pressure differences.
I think you are wise to go by what sounds best, and just keep a record of what's best on each banjo by checking tyhe final readings with your drum dial.
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