A vibration analysis of a banjo head has been conducted to see if it supports current theories of preferred tuning of the head; 3rd string G, or G#, or other. A summary of the analysis is included in the attachment that includes pictures of the 1st 6 mode shapes (the deflected shape of the mylar head) and vibration frequency.

The results are in pretty good agreement that tunning the head to a G or G# is a pretty good bet.

Warning, the attachment is pretty "GEEK" oriented but it does have some good color pictures.Hope you enjoy it.

Martinezg -

Excellent job. If you'd like, I can try to publish this as an article on the Fretmentor website (credited to you of course).

Dave

Thanks for the compliment.
I like the idea of publishing the article but I would like to edit it before doing so.
In an effort to reduce the words and graphics to 110KB I really butchered the graphics and cut the narrative down.
I would like to dress it up a bit and I promise that it wont go over the top with technical stuff.

Great job Gonz!!!!

First of all very cool and great work. If I am interpreting this properly my comments are.

If the head is tuned to the G and the G string is examined I would expect exactly what you found since the modes (harmonics) are equal fractions of the fundamental tone. I would expect the harmonic series for G to cause the fractional response you so ably demonstrated. So you had a great graphic representation of the fractions. I think by the time you get to the 6th harmonic the response is so little that you essentially get very little response (mass vs energy).

However, banjos play more than the G string so it is quite a bit more complicated. The key to the head tuning is being able to get a good 4th string (D) and 3rd string (G). Since the D is the 5th of the G you would expect that if the head is tuned properly you should get some sympathetic response (since it is a harmonic of G)

The real question is "why G#???? I think that the head tuning has more to do with "opening up or closeing the sound" than the actual frequency. Too tight and the head does not vibrate appropriately to (as you illustrated). Too loose and it just doesn't repond very well at all. Physics alone will only get you so far. I think that head tuning has to do with the whole pot assembly.

But again, not to be picky really cool work. Nice job.

BTW - Am I being Geeky enough?

Definitely registered on the GEEK scale.
Without getting into the harmonics, and how it affects response and sound, I was surprised by how close the 4th strimg D fundamental freqency matches the 3rd mode of the head (when the head is tuned to a G). This very simple analysis would suggest that both the 3rd and 4th strings (which as you noted will have more energy than the others) will drive the head nicely when played open. It almosts suggests that somebody put a little thought into the design of the head, imagine that.

I did the analysis several months ago and have not had time to format it into something that could be posted. If I had more time I would like to go much further with it. Which brings me to my next desire which would be to to put some accelerometers on the head and actually measure response with the rest of the instrument contributing.

Thanks for the feedback