Belmont Tower and Carillon 1850 to be used as a water tower for the Belmont Mansion and gardens. In 1864 during the Battle of Nashville union troops led by General T.J. Wood used the structure as a signal tower. When a carillon of twenty-three bronze bells was installed at Ward-Belmont College in 1928, it became the first carillon in Tennessee and one of the first twenty-five carillons in North America. The original carillon bells were exchanged for an electronic carillon in 1951, shortly after the property became Belmont College. In 1986, a second carillon of twenty-three bells was installed. A gift of nineteen more
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