Table 3b

Final matrix of ideal tempos and tempo relationships expressed in the form of “ax/b” where “a” and “b” represent integers and “x” represents a constant, namely, the subdivision-consolidation threshold expressed in beats per minute. This matrix possesses the unique characteristic of consisting of values in which all denominators are divisible by five. Assuming the subdivision-consolidation threshold to be 40 beats per minute, all possible ideal tempos (shown in Table 3a) are derived by assigning this value (x = 40) to the fractions here. This table best exemplifies the concept of “tempo relativity,” in that substituting another value for “x” (like 41 instead of 40) would generate a matrix of completely different tempos, although the mathematical relationships between the tempos would remain unaltered. To put it simply, universally perfect or ideal tempos all have one common denominator, which is the subdivision-consolidation threshold of “x” beats per minute, and can all be expressed as fractions “ax/b”. The progression in this matrix can continue infinitely.