I hope this doesnt confuse the situation, but the OP is infusing alcohol with that butter machine (way cool btw, never seen one) I just might buy one today just to play with, (thanks OP)
So I have to make the assumption that he is using the tincture internally as a dosing method. Or whatever, but he doesn't seem to be doing any further extraction on the product, the use of the word tincture sort of implies this. Correct me if I am wrong. So here's the deal if thats the case, also assuming you would store the tincture in a cool dark place. maybe even the refrigerator. So you have three variables here, temperature pressure and the purity of the solution. As others have already demonstrated the water content of the solution will alter its saturation point, as would anything else that may be dissolved in the water alcohol solution. Atmospheric pressure I think would also affect solubility, lets assume sea level and room temp.... I looked for solubility tables for cannabinoids but came up zippo.
However,
The alcohol will as a matter of physics hold more oils in solution at warmer temperatures. So what happens if you store it at a different cooler temperature? I would think that the oils would precipitate out of the solution. But only if you reached saturation at that warmer temperature. As you lower the temperature the saturation point changes and the solution has to precipitate oils. I recall doing a similar experiment with salt water in grade nine science. perhaps you could do that exact experiment. Start with fresh alcohol and just keep infusing and storing until you see oils in the bottom. Then measure your dry herb total weight. (and hopefully you would post back the results)