Carillon batons are almost never played with the fingers as one does a piano, though this is sometimes used as a special carillon playing technique. The keys activate levers and wires that connect directly to the bells' clappers; thus, as with a piano, the carillonneur can vary the intensity of the note according to the force applied to the key. In addition to the manual keys, the heavier bells are also played with a pedal keyboard. These notes can either be played with the hands or the feet. The world's first international carillon school, the Royal Carillon School "Jef Denyn", is
Partition of a set "coarser" than "α"—if every element of "α" is a subset of some element of "ρ". Informally, this means that "α" is a further fragmentation of "ρ". In that case, it is written that "α" ≤ "ρ". This "finer-than" relation on the set of partitions of "X" is a partial order (so the notation "≤" is appropriate). Each set of elements has a least upper bound and a greatest lower bound, so that it forms a lattice, and more specifically (for partitions of a finite set) it is a geometric lattice. The "partition lattice" of a 4-element set has 15 elements