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What is the difference between Temporary Hardness and Permanent Hardness of Water for Aquarium

Hardness is dependent on the total amount of minerals such as calcium carbonate and magnesium sulphate dissolved in the water.

KH is the term used to describe temporary hardness. KH comes from Karbon Hardness (Karbon is German for, well, carbon).  This is the amount of dissolved Carbonate and bicarbonate anions.  Temporary hardness can be softened by boiling. 

GH stands for General Hardness.  General Hardness refers to the amount of calcium and magnesium cations.  Temporary Hardness is also known as Carbonate Hardness.  This is also referred to as the buffering capacity of the water.

Buffering capacity refers to the ability of the water to resist changes in pH.  It is not possible to adjust the pH without adjusting the Carbonate Hardness of the water.
Most tropical fish species tend to tolerate common values of hardness.  For exotic species such as discus, check your hardness before purchasing the fish.