All you need for this is three sheets of wet-or-dry sandpaper (#320, #400, and #600 grit), and a magnifier (40x preferred; comes with a little LED light) that sells for around $5.00. Sand the stock-end of the reed, first with the #320, then #400, then #600, to obtain a smooth finish (lubricate the sandpaper with a little water), then examine the end-surface with the magnifier. You will see cross-sections of the "vascular bundles," appearing as dark rings. Quoting a web article by Marilyn Veselak, "Each vascular bundle consists of a ring of fiber cells surrounding the xylem and phloem. The vascular bundles are what the woodwind musician refers to as the 'fiber' or 'grain' of the reed."
According to Montague, citing two other studies, as well as his own experience, the rings should be complete; if the cane has any incomplete rings at all, it is "not optimal for use." He notes that he examined three boxes of Vandoren V12 clarinet reeds, one each of #2.5, #3.5, and #5+. He found that the average percentage of discontinuous rings was 17.4%, 10.9%, and 3.9% respectively. This might suggest that stiffer cane is better cane. I'm not so sure that this is as simple as it sounds; I have not had much luck taking down hard reeds to the medium strength that I like on my tenor setup.
Below are some photos looking through the magnifier, of three different tenor saxophone reeds: a Prestini #5, a Vandoren Java #3, and a La Voz medium soft.
Prestini #5 tenor |
Vandoren Java #3 tenor |
La Voz medium soft tenor |
The Vandoren Java seems to have a somewhat more even distribution of rings, with evenly-distributed smaller rings towards the bark of the reed. I do think that Vandoren reeds are generally higher-quality than Prestini or La Voz (that is to say, they usually seem to work better for me). I could guess that the apparent structure is a factor.
I've looked at a sampling of brands, strengths, and cuts; as you might expect, the cheaper reeds seem to be made from cane with less regular structure, and more discontinuous rings. I have a few Rico reeds from an old box I got from a music store that was going out of business, that seemed to be marked as dating from 1969. The structure was similar to the Prestini reed pictured above. A more recent Rico reed looked very much the same.
I don't really have enough information yet to say definitively which visual qualities make for better reeds. Some day, if I ever have the time, I'd like to make a more detailed study, and assemble a gallery of photos - many brands, many strengths, and noting whether each reed played well or not - then see if any conclusions can be drawn. Or maybe some reader would like to take on that project. It would cost you about $8.00 for a magnifier and three sheets of sandpaper. If you do, please let me know how it turns out.