New in version 2.0.
Yield all prolation rewrite pairs of prolated_duration in Cantor diagonalized order.
Ensure written duration never less than minimum_written_duration.
The different ways to notate a prolated duration of 1/8:
abjad> from abjad.tools import durationtools
abjad> pairs = durationtools.yield_all_prolation_rewrite_pairs_of_rational_in_cantor_diagonalized_order(Fraction(1, 8))
abjad> for pair in pairs: pair
...
(Fraction(1, 1), Fraction(1, 8))
(Fraction(2, 3), Fraction(3, 16))
(Fraction(4, 3), Fraction(3, 32))
(Fraction(4, 7), Fraction(7, 32))
(Fraction(8, 7), Fraction(7, 64))
(Fraction(8, 15), Fraction(15, 64))
(Fraction(16, 15), Fraction(15, 128))
(Fraction(16, 31), Fraction(31, 128))
The different ways to notate a prolated duration of 1/12.
abjad> pairs = durationtools.yield_all_prolation_rewrite_pairs_of_rational_in_cantor_diagonalized_order(Fraction(1, 12))
abjad> for pair in pairs: pair
...
(Fraction(2, 3), Fraction(1, 8))
(Fraction(4, 3), Fraction(1, 16))
(Fraction(8, 9), Fraction(3, 32))
(Fraction(16, 9), Fraction(3, 64))
(Fraction(16, 21), Fraction(7, 64))
(Fraction(32, 21), Fraction(7, 128))
(Fraction(32, 45), Fraction(15, 128))
The different ways to notate a prolated duration of 5/48.
abjad> pairs = durationtools.yield_all_prolation_rewrite_pairs_of_rational_in_cantor_diagonalized_order(Fraction(5, 48))
abjad> for pair in pairs: pair
...
(Fraction(5, 6), Fraction(1, 8))
(Fraction(5, 3), Fraction(1, 16))
(Fraction(5, 9), Fraction(3, 16))
(Fraction(10, 9), Fraction(3, 32))
(Fraction(20, 21), Fraction(7, 64))
(Fraction(40, 21), Fraction(7, 128))
(Fraction(8, 9), Fraction(15, 128))
Return generator of paired fractions.