Dacite, tonalite, rhyolite and granite - how are they related?

Dacite, like rhyolite is a fine-grained, rapidly cooled, igneous extrusive rock produced by erupting tonalitic magma (or granitic in the case of rhyolite). The volcano of Diasen in Tottori prefecture in Japan is a dacitic volcano and it shows many of the typical minerals as phenocrysts within a fine grained matrix - black biotite mica, amphibole, calcic plagioclase feldspar and quartz. These minerals differ from those typical of granite - potassic orthoclase feldspar, white or black mica and quartz because tolanite has high calcium and low potassium, being part of the calc-alkaline igneous series, related to subducting oceanic crust. Interestingly, the oldest components of Lewisian Gneiss and other Archean basement rocks are very close to tonalite in composition, suggesting that something similar to subduction processes were occurring 3 billion years ago.