Assignability — Abjad v1.1.1 documentation

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# Assignability

Western notation admits rational values like 1/4 readily. But values like 1/5 notate only without recourse to tuplet brackets or special time signatures.

We can capture the instinct that quarter notes appear more frequently, in western notation, than fifth notes, by an appeal to assignability. Abjad identifies those rational values that can assign to notes, rests, chords and skips directly as assignable.

Which rational values meet the conditions of assignability?

Rational values n/d are assignable when, and only when, n is of the form k * (2 ** u - j) and d is of the form 2 ** v , with integers u, v ≥ 0 , with integer k > 0 , and with integer j ∈ {0, 1} .

Note

Abjad relies on these conditions of assignability to determine which rational values can initialize notes, rests, chords and skips, and which can’t.

This explains why initializing `Note(0, (1, 4))` works where `Note(0, (1, 5))` doesn’t.

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