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 __call__(self, pitches, durations) -> Selection:
"""
Calls note-maker on ``pitches`` and ``durations``.
"""
from .Tuplet import Tuplet
if isinstance(pitches, str):
pitches = pitches.split()
if not isinstance(pitches, collections.abc.Iterable):
pitches = [pitches]
if isinstance(durations, (numbers.Number, tuple)):
durations = [durations]
nonreduced_fractions = Sequence(
[mathtools.NonreducedFraction(_) for _ in durations])
size = max(len(nonreduced_fractions), len(pitches))
nonreduced_fractions = nonreduced_fractions.repeat_to_length(size)
pitches = Sequence(pitches).repeat_to_length(size)
durations = Duration._group_by_implied_prolation(nonreduced_fractions)
result: typing.List[typing.Union[Note, Tuplet]] = []
for duration in durations:
# get factors in denominator of duration group duration not 1 or 2
factors = set(mathtools.factors(duration[0].denominator))
factors.discard(1)
factors.discard(2)
ps = pitches[0:len(duration)]
pitches = pitches[len(duration):]
if len(factors) == 0:
result.extend(
self._make_unprolated_notes(
ps,
duration,
increase_monotonic=self.increase_monotonic,
tag=self.tag,
))
else:
# compute prolation
denominator = duration[0].denominator
numerator = mathtools.greatest_power_of_two_less_equal(
denominator)
multiplier = Multiplier(numerator, denominator)
ratio = multiplier.reciprocal
duration = [ratio * Duration(d) for d in duration]
ns = self._make_unprolated_notes(
ps,
duration,
increase_monotonic=self.increase_monotonic,
tag=self.tag,
)
tuplet = Tuplet(multiplier, ns)
result.append(tuplet)
return Selection(result)
def _group_by_implied_prolation(durations):
durations = [
mathtools.NonreducedFraction(duration) for duration in durations
]
assert 0 < len(durations)
group = [durations[0]]
result = [group]
for d in durations[1:]:
d_f = set(mathtools.factors(d.denominator))
d_f.discard(2)
gd_f = set(mathtools.factors(group[0].denominator))
gd_f.discard(2)
if d_f == gd_f:
group.append(d)
else:
group = [d]
result.append(group)
return result
def with_denominator(self, denominator) -> mathtools.NonreducedFraction:
"""
Changes duration to nonreduced fraction with ``denominator``.
.. container:: example
Changes duration to nonreduced fraction:
>>> duration = abjad.Duration(1, 4)
>>> for denominator in (4, 8, 16, 32):
... print(duration.with_denominator(denominator))
...
1/4
2/8
4/16
8/32
"""
nonreduced_fraction = mathtools.NonreducedFraction(self)
return nonreduced_fraction.with_denominator(denominator)
def t_FRACTION(self, t):
r'([1-9]\d*/[1-9]\d*)'
parts = t.value.split('/')
t.value = mathtools.NonreducedFraction(int(parts[0]), int(parts[1]))
return t
for subdivision in division:
for _ in subdivision:
number_of_measures += 1
measures_per_stage.append(number_of_measures)
# make time signatures from resulting divisions
time_signatures = []
for division in divisions:
stage = []
for subdivision in division:
stage_division = []
for duration in subdivision:
if duration.denominator < 8:
multiplier = int(8 / duration.denominator)
duration = mathtools.NonreducedFraction(
duration.numerator * multiplier,
duration.denominator * multiplier
)
time_signature = abjad.TimeSignature(duration)
stage_division.append(time_signature)
stage.append(stage_division)
time_signatures.append(stage)
subsection_indices = [
[0, 3, 5, 9, 12,16, 20, 22, 25,27,30, 32],
[0, 4, 7, 11, 13, 16, 18, 22, 25, 27, 31, 35],
[0, 3, 5, 9, 13, 16, 20, 22, 26, 29, 32, 34, 38, 41, 45],
[0, 3, 5, 9, 13, 16, 20, 22, 25, 27],
[0, 3, 5, 9, 12, 14, 17, 20, 22, 26, 30],
]