Bell A carillon, which is a musical instrument consisting of at least 23 cast bronze cup-shaped bells, is tuned so that the bells can be played serially to produce a melody, or sounded together to play a chord. A traditional carillon is played by striking a baton keyboard with the fists, and by pressing the keys of a pedal keyboard with the feet. The keys mechanically activate levers and wires that connect to metal clappers that strike the inside of the bells, allowing the performer to vary the intensity of the note according to the force applied to the key. In
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