Carillon be sounded together in varied chords with harmonious and concordant effect." The GCNA defines a "traditional carillon" as one played from a carillon mechanical (not electrified) baton keyboard, and a "non-traditional carillon" as a musical instrument with bells, but played by automated mechanical or electro-mechanical means, or from an electrical or electronic keyboard. Since each note is produced by an individual bell, a carillon's musical range is determined by the number of bells it has. Different names are assigned to instruments based on the number of bells they comprise: The Riverside Carillon in New York City has the largest tuned
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