acoustics - Giant Wind Chimes

I am building large wind chimes out of ALUMINUM TUBES with a D2 at 73.41 hertz as the lowest and two other higher frequencies of A2 at 110 hertz and E3 at 164.8 hertz. I know how to find each length for each frequency respectively, but I need to know how to find what the optimal diameter would be for each frequency. I understand that as the desired frequency goes lower, the diameter needs to increase in order to get more surface area so that the fundamental remains louder than the partials. But I do not know at what rate the diameter should increase by for each change in frequency respectively. In particular as I said I am making a D2 at 73.41 and I need to know what diameter I need. I was thinking either a 5 or 6 inch diameter. But I would like to know why. And it needs to be strongly heard from at least 10 feet away without hearing the annoying partials that are produced from metal materials. Anyways, I would greatly appreciate any formulas as well as answers that directly relate with finding the required diameter. Thank you!