In one example of an embodiment of the invention, a method for producing an aggregate is disclosed comprising mixing sewage sludge from a waste water treatment facility with a non-coal combustion ash silicoaluminous waste material, agglomerating the mixture to form an agglomerate, and pyroprocessing the agglomerate to form an aggregate. The waste material may comprise municipal solid waste incinerator bottom ash, incinerator fly ash, incinerator filter dusts, cement kiln dusts, waste glass, blast furnace slag, kiln dusts, and/or granite sawing residues, for example. The method may further comprise milling the waste material prior to mixing. Preferably, the milling is wet milling. Pyroprocessing of the agglomerate may take place in a rotary kiln. The resulting aggregate may be a lightweight or a normal weight, sintered or vitrified aggregate. Aggregates and methods for making aggregates of high and low calcium silicoaluminous materials are also disclosed.