def durations_to_nonreduced_fractions(
durations: typing.List,
) -> typing.List[mathtools.NonreducedFraction]:
"""
Changes ``durations`` to nonreduced fractions sharing least common
denominator.
.. container:: example
Changes durations to nonreduced fractions:
>>> durations = [abjad.Duration(2, 4), 3, (5, 16)]
>>> result = abjad.Duration.durations_to_nonreduced_fractions(durations)
>>> for x in result:
... x
...
NonreducedFraction(8, 16)
NonreducedFraction(48, 16)
NonreducedFraction(5, 16)
"""
durations_ = [Duration(_) for _ in durations]
denominators = [_.denominator for _ in durations_]
lcd = mathtools.least_common_multiple(*denominators)
nonreduced_fractions = [
mathtools.NonreducedFraction(_).with_denominator(lcd)
for _ in durations_
]
return nonreduced_fractions
def durations_to_nonreduced_fractions(
durations: typing.List,
) -> typing.List[mathtools.NonreducedFraction]:
"""
Changes ``durations`` to nonreduced fractions sharing least common
denominator.
.. container:: example
Changes durations to nonreduced fractions:
>>> durations = [abjad.Duration(2, 4), 3, (5, 16)]
>>> result = abjad.Duration.durations_to_nonreduced_fractions(durations)
>>> for x in result:
... x
...
NonreducedFraction(8, 16)
NonreducedFraction(48, 16)
NonreducedFraction(5, 16)
"""
durations_ = [Duration(_) for _ in durations]
denominators = [_.denominator for _ in durations_]
lcd = mathtools.least_common_multiple(*denominators)
nonreduced_fractions = [
mathtools.NonreducedFraction(_).with_denominator(lcd)
for _ in durations_
]
return nonreduced_fractions
def _make_tied_leaf(
class_,
duration,
increase_monotonic=None,
forbidden_duration=None,
multiplier=None,
pitches=None,
tag=None,
tie_parts=True,
repeat_ties=False,
):
from abjad.spanners import tie as abjad_tie
duration = Duration(duration)
if forbidden_duration is not None:
assert forbidden_duration.is_assignable
assert forbidden_duration.numerator == 1
# find preferred numerator of written durations if necessary
if forbidden_duration is not None and forbidden_duration <= duration:
denominators = [
2 * forbidden_duration.denominator,
duration.denominator,
]
denominator = mathtools.least_common_multiple(*denominators)
forbidden_duration = NonreducedFraction(forbidden_duration)
forbidden_duration = forbidden_duration.with_denominator(
denominator
)
duration = NonreducedFraction(duration)
duration = duration.with_denominator(denominator)
forbidden_numerator = forbidden_duration.numerator
assert forbidden_numerator % 2 == 0
preferred_numerator = forbidden_numerator / 2
# make written duration numerators
numerators = []
parts = mathtools.partition_integer_into_canonic_parts(
duration.numerator
)
if forbidden_duration is not None and forbidden_duration <= duration:
for part in parts:
if forbidden_numerator <= part:
better_parts = LeafMaker._partition_less_than_double(
part, preferred_numerator
)
numerators.extend(better_parts)
else:
numerators.append(part)
else:
numerators = parts
# reverse numerators if necessary
if increase_monotonic:
numerators = list(reversed(numerators))
# make one leaf per written duration
result = []
for numerator in numerators:
written_duration = Duration(numerator, duration.denominator)
if pitches is not None:
arguments = (pitches, written_duration)
else:
arguments = (written_duration,)
result.append(class_(*arguments, multiplier=multiplier, tag=tag))
result = Selection(result)
# tie if required
if tie_parts and 1 < len(result):
if not issubclass(class_, (Rest, Skip)):
abjad_tie(result, repeat=repeat_ties)
return result
def _make_tied_leaf(
class_,
duration,
increase_monotonic=None,
forbidden_duration=None,
multiplier=None,
pitches=None,
tag=None,
tie_parts=True,
repeat_ties=False,
):
from abjad.spanners import tie as abjad_tie
duration = Duration(duration)
if forbidden_duration is not None:
assert forbidden_duration.is_assignable
assert forbidden_duration.numerator == 1
# find preferred numerator of written durations if necessary
if (forbidden_duration is not None and forbidden_duration <= duration):
denominators = [
2 * forbidden_duration.denominator,
duration.denominator,
]
denominator = mathtools.least_common_multiple(*denominators)
forbidden_duration = NonreducedFraction(forbidden_duration)
forbidden_duration = forbidden_duration.with_denominator(
denominator)
duration = NonreducedFraction(duration)
duration = duration.with_denominator(denominator)
forbidden_numerator = forbidden_duration.numerator
assert forbidden_numerator % 2 == 0
preferred_numerator = forbidden_numerator / 2
# make written duration numerators
numerators = []
parts = mathtools.partition_integer_into_canonic_parts(
duration.numerator)
if (forbidden_duration is not None and forbidden_duration <= duration):
for part in parts:
if forbidden_numerator <= part:
better_parts = LeafMaker._partition_less_than_double(
part,
preferred_numerator,
)
numerators.extend(better_parts)
else:
numerators.append(part)
else:
numerators = parts
# reverse numerators if necessary
if increase_monotonic:
numerators = list(reversed(numerators))
# make one leaf per written duration
result = []
for numerator in numerators:
written_duration = Duration(
numerator,
duration.denominator,
)
if pitches is not None:
arguments = (pitches, written_duration)
else:
arguments = (written_duration, )
result.append(class_(*arguments, multiplier=multiplier, tag=tag))
result = Selection(result)
# tie if required
if tie_parts and 1 < len(result):
if not issubclass(class_, (Rest, Skip)):
abjad_tie(result, repeat=repeat_ties)
return result