Even in equal temperament a G minor chord sounds different than a D minor chord because they fall on different ranges of the instruments and the human auditory system. If you try transposing a piece in G minor to D minor, you'll notice a clear difference. You could either go up a 5th or down a 4th. If you choose to go up a 5th, things will sound quite a bit brighter. Conversely, going down a 4th could very well cause the piece to sound muddier, depending on the orchestration. At any rate, the other forms of tuning have other effects, of course, and are worthwhile to explore.