Western notation readily admits rational values like 1/4. But values like 1/5 notate only with tuplet brackets or special time signatures. Abjad formalizes the difference between rationals like 1/4 and 1/5 in the definition of rational assignability.
Rational values n/d are assignable when and only when numerator n is of the form k(2**u-j) and denominator d is of the form 2**v. In this definition u and v must be nonnegative integers, k must be a positive integer, and j must be either 0 or 1.
Abjad initializes notes, rests and chords with assignable durations only.