Certain tempos in the triplet column do not appear in the duplet or quadruplet columns: 56, 64, 112, 128. This theoretical distinction excludes these tempos for pieces in 2/4, 3/4, 4/4, or 2/2 with prevailing triplets, for the dotted quarter note of pieces in 3/8, 6/8, 9/8, and 12/8, as well as the dotted eighth note of pieces in 3/16, 6/16, 9/16, 12/16, 18/16, and 24/16. Conversely, the tempos in the duplet and quadruplet columns that do not appear in the triplet column—54, 63, 108, 126—must be excluded for pieces with prevailing triplets. Thus, a piece in 4/4 with prevailing sixteenth-note motion may have one of the tempos q = 54, 63, 108, 126 but not q = 56, 64, 112, 128, whereas a piece in 6/8 with prevailing eighth- or sixteenth-note motion may have one of the tempos dq = 56, 64, 112, 128 but not dq = 54, 63, 108, 126. Should quadruplets and triplets prevail equally (like in some of Bach’s allemandes), then the faster tempo (triplet) shall overrule the slower tempo (quadruplet). Should quadruplets clearly be dominant and triplets function as occasional embellishments, then the quadruplet tempo shall overrule the triplet tempo; conversely, the opposite also holds true.
Furthermore, prime numbers greater than 7 and all multiples thereof also do not appear—more specifically, 11, 13, 17, 19, 22 (11 x 2), 23, 26 (13 x 2), 29, 31, 33, 34 (17 x 2), 37, 38 (19 x 2), 41, 43, 46 (23 x 2), 47 . . . etc. That 5 and integers divisible by 5 do not appear corroborates the preliminary conclusion that the threshold tempo “x” must be an integer divisible by 5.
