Carillon defines a carillon as "A musical instrument composed of tuned bronze bells which are played from a baton keyboard. Only those carillons having at least 23 bells may be taken into consideration." The Guild of Carillonneurs in North America (GCNA) defines a carillon as "a musical instrument consisting of at least two octaves of carillon bells arranged in chromatic series and played from a keyboard permitting control of expression through variation of touch. A carillon bell is a cast bronze cup-shaped bell whose partial tones are in such harmonious relationship to each other as to permit many such bells to
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